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Absolute optical oscillator strengths for electronic excitations of noblae gas atoms and diatomic molecules Chan, Wing Fat 1992

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ABSOLUTE OPTICAL OSCILLATOR STRENGTHS FOR ELECTRONIC EXCITATIONS OF NOBLE GAS ATOMS AND DIATOMIC MOLECULES By Wing-Fat Chan B. Sc. (Chemistry) The Chinese University of Hong Kong, 1984 M. Phil. (Chemistry) The Chinese University of Hong Kong, 1986  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF CHEMISTRY  We accept this thesis as conforming to the required standard  Signature(s) removed to protect privacy  THE UNIVERSITY OF BRITISH COLUMBIA September 1992 © Wing-Fat Chan, 1992  In presenting this  thesis in  partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission.  Signature(s) removed to protect privacy Signature(s) removed to protect privacy  (Signature)  (2/88)  Abstract  A new high resolution dipole (e,e) method is described for the measurement of absolute optical oscillator strengths (cross sections) for electronic excitation of free atoms and molecules throughout the discrete region of the valence shell spectrum. The technique, utilizing the virtual photon field of a fast electron inelastically scattered at negligible momentum transfer, avoids many of the difficulties and errors associated with the various direct optical techniques which have traditionally been used for absolute optical oscillator strength measurements. In particular, the method is free of the bandwidth (line saturation) effects which can seriously limit the accuracy of photoabsorption cross section measurements for discrete transitions of narrow linewidth obtained using I=exp(n1o)). Since these perturbing “line /(I the Beer-Lambert law 0 saturation” effects are not widely appreciated and are only usually considered in the context of peak heights a detailed new analysis of this problem is presented considering the integrated cross section (oscillator strength) over the profile of each discrete peak. Using a low resolution dipole (e,e) spectrometer (—1 eV FWHM), absolute optical oscillator strengths for the photoabsorption of the five noble gases He, Ne, Ar, Kr and Xe have been measured up to 180, 250, 500, 380 and 398 eV respectively. The absolute scales for the measurements of helium and neon were obtained by TRK sum rule normalization and it was not necessary to make the difficult determinations of photon flux or target density required in conventional absolute cross section determinations. Single point continuum normalization to absolute optical data was employed for the  H  measurements of argon, krypton and xenon due to the closely space in the subshells of these targets which cause problems in the extrapolation procedures required for TRK sum—rule normalization. The newly developed high resolution dipole (e,e) method (0.048 eV FWHM) has then been used to obtain the absolute optical oscillator strengths for the valence discrete excitations of the above five noble gases with the absolute scale normalized to the low resolution dipole (e,e) measurements in the smooth ionization continuum region. The measured dipole oscillator strengths for helium excitation (1 1 S—n P , n=2-7) are in excellent quantitative agreement with the calculations reported by Schiff and Pekeris (Phys. Rev. 134, A368 (1964)) and by Fernley et al. (J. Phys. B 20, 6457 (1987)). High resolution absolute optical oscillator strengths are also reported for the autoionizing resonances, corresponding to the double excitation of  two  valence  electrons and/or single excitation of a inner valence electron, of the above five noble gases. High resolution absolute optical oscillator strengths (0.048 eV FWHM) for discrete and continuum transitions for the photoabsorption of five diatomic gases (H , 02, CO and NO) throughout the va1ence shell 2 , N 2 region are reported. The absolute scales were obtained by normalization in the smooth continuum to TRK sum rule normalized data determined using the low resolution dipole (e,e) spectrometer. Absolute optical oscillator strengths for the vibronic transitions of the Lyman and Werner bands of hydrogen, the b’fl and b”Z valence excited states, the c’H, c?lu+ and 1 o f l Rydberg states and the e’H and e”D states of nitrogen, the A 11, 1 11), 2 X  1  1 and 1 B E f l states of carbon monoxide, and the y (A — 2  11—X 2 (B f l), ô H fl—X 2 (C ) and  E  — 2 (D f l) X systems of nitric oxide,  In  were determined. Absolute intensities for the Schumann—Runge continuum region and for the discrete bands below the first ionization potential of oxygen are also reported. The variation of the electronic transition moment with internuclear distance was studied for the Lyman 1 and Werner bands of hydrogen and for the vibronic bands of the X  _  1 transition of carbon monoxide. The dipole strengths of the Lyman A 1 1 and Werner bands of hydrogen at the equilibrium internuclear distance (0.74 lÀ) are also reported. The present results are compared with previously published experimental data and theoretical calculations. The results for molecular hydrogen are in excellent agreement with high level theory (Allison and Dalgarno, At. Data 1, 289 (1970)).  iv  Table of Contents  Abstract  il  Table of Contents  v  List of Tables  Ix  List of Figures  xiv  Acknowledgements 1  General Introduction  1  2  Measurement of Absolute Optical Oscillator Strengths by Photoabsorption and Electron Impact Methods  6  2.1 Photoabsorption Cross Section Measurements via the Beer—Lambert Law  6  2.2 Optical Methods for Determining Absolute Optical Oscillator Strengths for Discrete Transitions 2.3 “Line Saturation” Effects in Beer—Lambert Law Photoabsorption for Discrete Transitions 2.4 Electron Impact Methods 2.4.1 Theoretical Background for Fast Electron Impact Techniques 2.4.2 Experimental Approach 3  4  Experimental Methods 3.1 The Low Resolution Dipole (e,e) Spectrometer 3.2 The High Resolution Dipole (e,e) Spectrometer 3.3 Experimental Considerations and Procedures  9 15 29 30 33 38 38 42 47  3.4 Energy Calibration  52  3.5 Sample Handling and Background Subtraction  53  Absolute Optical Oscillator Strengths for the Electronic Excitation of Helium 4.1 Introduction  55 55  4.2 Results and Discussion  56  V  4.2.1 Low Resolution Optical Oscillator Strengths Measurements for Helium 4.2.2 High Resolution Optical Oscillator Strengths Measurements for Helium S—’n (n=2—7) P 4.2.2.1 The Discrete Transition of 1 4.2.2.2 The Autoionizing Excited State Resonances 4.3 Conclusions 5  56 63 63 72 74  Absolute Optical Oscillator Strengths for the Electronic Excitation of Neon  76  5.1 Introduction 5.2 Results and Discussion  76 84  5.2.1 Low Resolution Measurements of the Photoabsorption Oscillator Strengths for Neon up to 250 eV 5.2.2 High Resolution Measurements of the  84  Photoabsorption Oscillator Strengths for the Discrete Transitions of Neon Below the 2p Ionization Threshold 5.2.3 High Resolution Photoabsorption Oscillator Strengths for Neon in the 40—5 5 eV Region of the Autoionizing Excited State Resonances  6  92  104  5.4 Conclusion  107  Absolute Optical Oscillator Strengths for the Electronic Excitation of Argon, Krypton and Xenon  109 109  6.1 Introduction 6.2 Results and Discussion  118  6.2.1 Low Resolution Measurements of the Photoabs orption Oscillator Strengths for Argon, Krypton and Xenon 6.2.1.1 Low Resolution Measurements for Argon 6.2.1.2 Low Resolution Measurements for Krypton 6.2.1.3 Low Resolution Measurements for Xenon  vi  118 118 133 141  6.2.2 High Resolution Measurements of the Photoabsorption Oscillator Strengths for the Discrete Transitions Below the mp Ionization Thresholds for Argon (m=3), Krypton (m=4) and Xenon (m=5)  152  6.2.3 High Resolution Measurements of the Photoabsorption Oscillator Strengths in the Autolonizing Resonance Regions due to Excitation of the Inner Valence s Electrons 6.4 Conclusions 7  Absolute Optical Oscillator Strengths (11—20 eV) and Transition Moments for the Lyman and Werner Bands of Molecular Hydrogen 7.1 Introduction 72 Results and Discussion  182  184 184  7.2.1 Absolute Oscillator Strengths 7.2.2 The Variation of Transition Moment with the Internuclear Distance for the Lyman and Werner Bands  8  176  192 192  205  7.3 Conclusions  212  Absolute Optical Oscillator Strengths for the Discrete and Continuum Photoabsorption of Molecular Nitrogen (11—200eV)  213  8.i Introduction  213  8.2 Results and Discussion  221  8.2.1 Low Resolution Absolute Photoabsorption Oscillator Strength Measurements for Molecular Nitrogen (11—200eV)  221  8.2.2 High Resolution Absolute Photoabsorption Oscillator Strength Measurements for Molecular Nitrogen (12—22 eV) 8.3 Conclusions  vii  227 245  9  Absolute Optical Oscillator Strengths for the Photoabsorption of Molecular Oxygen (S-30 eV) 9.1 Introduction 9.2 Results and Discussion 9.3 Conclusions  10  12  248 252 267  Absolute Optical Oscillator Strengths for the Discrete and Continuum Photoabsorption of Carbon Monoxide (7— 200 eV) and Transition Moments for the Xl+-*Alfl System  269  10.1 Introduction  269  10.2 Results and Discussion 10.2.1 Low Resolution Absolute Photoabsorption Oscillator Strength Measurements for Carbon  275  Monoxide (7—200 eV) 10.2.2 High Resolution Absolute Photoabsorption Oscillator Strength measurements for carbon monoxide (12—22 eV)  276  10.2.3 The Variation of Transition moment with Internuclear Distance for the Vibronic Bands of the 1 — X f 1 A Transition 10.3 Conclusions 11  248  Absolute Optical Oscillator Strengths for the Photoabsorption of Nitric Oxide (5—30 eV) 11.1 Introduction  281  297 300  302 302  11.2 Results and Discussion 11.3 Conclusions  307  Concluding Remarks  325  323  References  327  viii  List of Tables  Page  Table 2. 1  Methods of obtaining optical oscillator strengths for discrete electronic transitions at high resolution  11  3.1  Sources and stated minimum purity of samples  54  4. 1  Absolute differential optical oscillator strengths for helium obtained using the low resolution (1 eV FWHM) dipole (e,e) 58  spectrometer (24.6—180 eV) 4.2  Theoretical and experimental determinations of the absolute , n=2 to 7) (1’S—n P optical oscillator strengths for the 1 68  transitions in helium 5. 1  Absolute differential optical oscillator strengths for neon obtained using the low resolution (1 eV FWHM) dipole (e,e) 87  spectrometer (2 1.6—250 eV) 5.2  Theoretical and experimental deteminations of the absolute optical oscillator strengths for the 2s discrete transitions of neon p — 6 p 2 P 2 ( 3/,1/)3s 25 2s  5.3  95  Theoretical and experimental deteminations of the absolute optical oscillator strengths for discrete transitions of neon 97  (19.5—20.9eV) 5.4  Theoretical and experimental deteminations of the absolute optical oscillator strengths for discrete transitions of neon 99  (20.9—21.2eV)  ix  6. 1  Absolute differential optical oscillator strengths for the photoabsorption of argon above the first ionization potential obtained using the low resolution (1 eV FWHM) dipole (e,e) 122  spectrometer (16—500 eV) 6.2  Absolute differential optical oscillator strengths for the photoabsorption of krytpon above the first ionization potential obtained using the low resolution (1 eV FWHM) dipole (e,e) 136  spectrometer (14.7—380 eV) 6.3  Absolute differential optical oscillator strengths for the photoabsorption of xenon above the first ionization potential obtained using the low resolution (1 eV FWHM) dipole (e,e) 145  spectrometer (13.5—398 eV) 6.4  Theoretical and experimental deteminations of the absolute optical oscillator strengths for the ( 2, 5 —’3s p 6 p 3 32 2 3s 31 )4s discrete transitions of argon P 2 11  6.5  159  Theoretical and experimental deteminations of the absolute optical oscillator strengths for discrete transitions of argon. (a) in the energy region 13.80—14.85 eV (b) in the energy 161  region 14.85—15.30eV 6.6  Theoretical and experimental deteminations of the absolute optical oscillator strengths for the 4s discrete transitions of krypton p 3/2,1/)5s 5 4s — 6 4 P 2 (  6.7  163  Theoretical and experimental deteminations of the absolute optical oscillator strengths for discrete transitions of krypton. (a) in the energy region 1 1.90—13.05 eV, (b) in the energy 165  region 13.05—13.50 eV  x  6.8  Theoretical and experimental deteminations of the absolute optical oscillator strengths for the ( P32,i /2)6s discrete transitions of xenon 5 —’5s p 6 p 5 52 2 5s  6.9  167  Theoretical and experimental deteminations of the absolute optical oscillator strengths for discrete transitions of xenon. (a) in the energy region 9.80—11.45 eV (b) in the energy 169  region 11.45—11.80eV 7. 1  Absolute osci1lator strengths for the vibronic transitions of the Lyman band of molecular hydrogen  7.2  Absolute oscillator strengths for the vibronic transitions of the Werner band of molecular hydrogen  7.3  203  Dipole strengths De(ro) for the Lyman and Werner bands of 211  molecular hydrogen 8. 1  197  Total integrated absolute oscillator strengths for the Lyman and Werner bands of molecular hydrogen  7.4  196  Absolute differential optical oscillator strengths for the photoabsorption of molecular nitrogen obtained using the low resolution (1 eV FWHM) dipole (e,e) spectrometer (11—200 224  eV) 8.2  Absolute optical oscillator strengths for discrete transitions from the ground state of molecular nitrogen in the energy 233  region 12.50—14.68 eV 8.3  Absolute optical oscillator strengths for transitions to the vibronic bands of the valence b’fl state from the ground state 237  of molecular nitrogen  xi  8.4  Absolute optical oscillator strengths for transitions to the vibronic bands of the valence  bhlZ+  state from the ground  state of molecular nitrogen 8.5  238  Absolute optical oscillator strengths for transitions to the vibronic bands of the lowest member of the Rydberg state from the ground state of molecular nitrogen  8.6  239  Absolute optical oscillator strengths for transitions to the vibronic bands of the lowest member of the Rydberg c’H state from the ground state of molecular nitrogen  8.7  240  Absolute optical oscillator strengths for transitions to the vibronic bands of the lowest member of the Rydberg 1 fl o state from the ground state of molecular nitrogen  8.8  241  Total absolute optical oscillator strengths for transitions to the b’II and  valence states, and the lowest members of the  fl, c’ 1 c 1 and o fl Rydberg states from the ground state of 1  244  molecular nitrogen 8.9  Integrated absolute optical oscillator strengths in selected regions over the energy range 14.92—16.9 1 eV for excitation of molecular nitrogen  9. 1  245  Absolute optical oscillator strengths for the photoabsorption of molecular oxygen in the energy region 9.75—11.89 eV  9.2  260  Integrated absolute optical oscillator strengths for the photoabsorption of molecular oxygen over intervals in the energy region 12.07—18.29 eV  xii  264  10. 1  Absolute differential optical oscillator strengths for the photoabsorption of carbon monoxide obtained using the low resolution (1 eV FWHM) dipole (e,e) spectrometer (7—200 eV)  10.2  278  Absolute optical oscillator strengths for the vibronic bands of the 1 —’A X f l transition of carbon monoxide  10.3  Absolute total optical oscillator strengths for the 1 —’A X f l transition of carbon monoxide  10.4  288  Absolute optical oscillator strengths for the vibronic bands from the X 1 ground state to the  C1+ and E fl excited 1  electronic states of carbon monoxide 10.5  285  290  Integrated absolute optical oscillator strengths for the photoabsorption of carbon monoxide over energy intervals in the region 12.13—16.98eV  11. 1  295  Absolute optical oscillator strengths for discrete transitions of nitric oxide in the energy region 5.48—7.44 eV  11.2  Absolute optical osciilator strengths for the vibonic bands of the y 2 fl—’A transition in nitric oxide (X )  11.3  fl—B (X H 2 ) transition in nitric oxide  317  Absolute optical osciilator strengths for the vibonic bands of the  11.6  316  Absolute optical osciilator strengths for the vibonic bands of the ô (X2H_C2fl) transition in nitric oxide  11.5  314  Absolute optical osciilator strengths for the vibonic bands of the  11.4  313  fl—’D transition in nitric oxide (X ) 2  318  Integrated absolute optical oscillator strengths over the energy region 7.52—9.43 eV in the photoabsorption of nitric oxide  322  xiii  List of Figures  Page  Figure 2. 1  Comparison of the absolute valence shell photoabsorption oscillator strength spectra of molecular nitrogen obtained by photoabsorption and dipole (e,e) experiments in the energy 18  region 12.4—13.2 eV 2.2  Diagrammatic representation of the “line saturation” effect occuring in Beer—Lambert law photoabsorption experiments  2.3  ...  21  Variation of integrated peak intensity (NxA ) with column 4 number for different ratios of (incident bandwidth 25  (AE))/(natural absorption line-width (AL)) 2.4  Variation of the observed integrated cross-section with 26  column number for different AE/AL ratios 2.5  Variation of the observed integrated cross-section with column number at AE/AL= 10 for peaks with true integrated cross-section  27  3.1  Schematic of the dipole (e,e+ion) spectrometer  40  3.2  Schematic of the high resolution dipole (e,e) spectrometer  3.3  Flow-chart showing the data recording and processing  ....  43  procedures used in determining the absolute dipole oscillator strengths for the discrete electronic excitation transitions 50  , n=2-7) of helium S—’n 1 (l P 4. 1  Absolute dipole oscillator strengths for helium measured by the low resolution dipole (e,e) spectrometer from 20—180 eV 57  (FWHM=l eV)  xiv  4.2  Absolute dipole oscillator strengths for helium measured by the high resolution electron energy loss spectrometer from 66  20—30 eV (FWHM=0.048 eV) 4.3  Absolute dipole oscillator strengths for helium In the autoionizing resonance regions measured by the high resolution electron energy loss spectrometer. (a) in the energy region 58—66 eV, (b) in the energy region 69—72 eV  5. 1  73  Absolute oscillator strengths for the photoabsorption of neon measured by the low resolution dipole (e,e) spectrometer (FWHM=leV). (a) 15.7—250 eV, (b) Expanded view of the 20— 85  60 eV energy region 5.2  Absolute oscillator strengths for the photoabsorption of neon measured by the high resolution dipole (e,e) spectrometer (FWHM=0.048 eV). (a) 16—26 eV, (b) 19.5—22 eV  5.3  93  Absolute oscillator strengths for the photoabsorption of neon in the autoionizing resonance region 40—55 eV (FWHM=0.098 106  eV) 6. 1  Absolute oscillator strengths for the photoabsorption of argon in the energy region 10—60 eV  6.2  Absolute oscillator strengths for the photoabsorption of argon in the energy region 40—240 eV  6.3  121  Absolute oscillator strengths for the photoabsorption of krypton in the energy region 5—60 eV  6.5  120  Absolute oscillator strengths for the photoabsorption of argon in the energy region 220—500 eV  6.4  119  134  Absolute oscillator strengths for the photoabsorption of krypton in the energy region 50—400 eV  xv  135  6.6  Absolute oscillator strengths for the photoabsorption of xenon In the energy region 5—60 eV  6.7  Absolute oscillator strengths for the photoabsorption of xenon in the energy region 40—200 eV  6.8  143  Absolute oscillator strengths for the photoabsorption of xenon in the energy region 160—400 eV  6.9  142  144  Absolute oscillator strengths for the photoabsorption of argon obtained using the high resolution dipole (e,e) spectrometer (FWHM=0.048 eV). (a) in the energy region 11—18 eV, (b) Expanded view of the 13.5—16.5 eV energy region  6. 10  153  Absolute oscillator strengths for the photoabsorption of krypton obtained using the high resolution dipole (e,e) spectrometer (FWHM=0.048 eV) in the energy region 9—16 154  eV 6. 11  Absolute oscillator strengths for the photoabsorption of krypton obtained using the high resolution dipole (e,e) spectrometer (FWHM=O.048 eV). (a) Expanded view of the 12.2—13.6 eV energy region, (b) Expanded view of the 13.5— 155  15.0 eV energy region 6. 12  Absolute oscillator strengths for the photoabsorption of xenon obtained using the high resolution dipole (e,e) spectrometer (FWHM=0.048 eV) in the energy region 8—15 eV  6. 13  156  Absolute oscillator strengths for the photoabsorption of xenon obtained using the high resolution dipole (e,e) spectrometer (FWHM=0.048 eV). (a) Expanded view of the 11—12 eV energy region, (b) Expanded view of the 12—13.7 eV energy 157  region  xvi  6. 14  Absolute oscillator strengths for the photoabsorption of argon in the autoionizing resonance region 25—30 eV  6. 15  Absolute oscillator strengths for the photoabsorption of krypton in the autolonizing resonance region 23—28.5 eV  6.16  180  Absolute oscillator strengths for the photoabsorption of krypton in the autoionizing resonance region 20—24 eV  7. 1  178  181  Absolute oscillator strengths for the photoabsorption of molecular hydrogen in the energy region 11—20 eV measured by the high resolution dipole (e,e) spectrometer (FWHM=0.048 eV)  7.2  193  Absolute oscillator strengths for the photoabsorption of molecular hydrogen in the energy region 11—14 eV  7.3  194  The absolute optical oscillator strengths for individual vibronic transitions as a function of the vibrational quantum number v’ for the Lyman band  7.4  199  The absolute optical oscillator strengths for individual vibronic transitions as a function of the vibrational quantum number v’ for the Werner band  7.5  200  The electronic transition moment Re(rvo)I in atomic units (a.u.) as a function of the internuclear distance rv’o in Angstroms  7.6  (A)  for the Lyman band  207  The electronic transition moment IRe(rv’o)I in atomic units (a.u.) as a function of the internuclear distance rv’o in Angstroms  (A)  for the Werner band  xvii  208  8. 1  Absolute oscillator strengths for the photoabsorption of molecular nitrogen measured using the low resolution (FWHM=l eV ) dipole (e,e) spectrometer. (a) in the energy region 10—50 eV, (b) in the energy region 50—200 eV  8.2  222  Absolute oscillator strengths for the photoabsorptlon of molecular nitrogen in the energy region 12—22 eV measured using the high resolution dipole (e,e) spectrometer (FWHM=0.048 eV)  8.3  228  Expanded view of figure 8.2 for the photoabsorption of molecular nitrogen in the energy region 12.4—13.4 eV  8.4  Expanded view of figure 8.2 for the photoabsorption of molecular nitrogen in the energy region 13.2—15.0 eV  8.5  230  Expanded view of figure 8.2 for the photoabsorption of molecular nitrogen in the energy region 15—19 eV  9. 1  229  231  Absolute oscillator strengths for the photoabsorption of molecular oxygen in the energy region 5—30 eV measured using the high resolution dipole (e,e) spectrometer (FWHM=0.048 eV)  9.2  253  Absolute oscillator strengths for the photoabsorption of molecular oxygen. Expanded view of figure 9.1 in the energy region 6.5—10 eV, showing the Schumann—Runge continuum region  9.3  255  Absolute oscillator strengths for the photoabsorption of molecular oxygen. (a) The energy region 9.5—15 eV, (b) The energy region 14—25 eV  259  xviii  10. 1  Absolute oscillator strengths for the photoabsorption of carbon monoxide measured using the low resolution (FWHM= 1 eV) dipole (e,e) spectrometer. (a) in the energy region 5—50 eV, (b) in the energy region 50—200 eV  10.2  277  Absolute oscillator strengths for the photoabsorption of carbon monoxide in the energy region 7—21 eV measured using the high resolution dipole (e,e) spectrometer (FWHM=0.048 eV)  10.3  282  Absolute oscillator strengths for the photoabsorption of carbon monoxide in the energy region 7.5—10.5 eV at 0.048 eV 284  FWHM 10.4  Absolute oscillator strengths for the photoabsorption of carbon monoxide in the energy region 10.5—12 eV at 0.048 eV 289  FWHM 10.5  Absolute oscillator strengths for the photoabsorption of carbon monoxide in the energy region 12—20 eV at 0.048 eV FWHM  10.6  294  The electronic transition moment IRe(rvo)I in atomic units (a.u.) as a function of the internuclear distance rv’o in Angstroms  (A)  for the vibronic bands of the X1+  —b  fl 1 A 299  transition 11. 1  Absolute oscillator strengths for the photoabsorption of nitric oxide in the energy region 5—30 eV measured using the high resolution dipole (e,e) spectrometer (FWHM=0.048 eV)  308  11.2  Expanded view of figure 11.1 in the energy region 5—8.2 eV  309  11.3  Expanded view of figure 11.1. (a) in the energy region 8—10 eV, (b) in the energy region 10—13 eV  11.4  310  Expanded view of figure 11.1. (a) in the energy region 13—16 eV, (b) in the energy region 16—22 eV  xix  311  Acknowledgements  I would like to express my sincere thanks to my research supervisor, Dr. C. E. Brion for his Interest, assistance and encouragement throughout the course of my study. It has been a pleasure to work with him and with other members in his research group. Special thanks are due to Dr. G. Cooper for a lot of help in my research work and for his helpful comments and suggestions on the writing of my thesis. Thanks are due to Dr. K. H. Sze for introducing me to the high resolution spectrometer and to Dr. W. Zhang and G. R. Burton for many helpful discussions. I would like to thank Professor M. J. Seaton for sending me his calculated data for helium and Professor J. A. R. Samson for sending me his measured data for argon, krypton and xenon. Helpful comments and discussions concerning the present work with Professor M. J. Seaton, Professor J. A. R. Samson, Dr. W. L. Wiese and Dr. M. Inokuti are also ackn owleciged. I would like to thank the staff of the mechanical and electronic workshops for their assistance in maintenance the spectrometers, in particular B. Greene and E. Gomm. Thanks are also due to D. Jones and M. Hatton (Electronic workshop) for the design and construction of the fast data buffer. Financial support in the form of a University of British Co1umbia Graduate Fellowship is gratefully acknowledged. The research work has been supported by operating grants from the Canadian National Networks of Centres of Excellence Programme (Centres of Excellence in Molecular  xx  and Interfacial Dynamics) and from the Natural Sciences and Engineering Research Council of Canada. Finally, I wish to thank to my parents and Josanna for their patience and encouragement. This thesis is dedicated to them.  xxi  1 Chapter 1  Introduction  Absolute optical oscillator strength (cross section) information is of importance because of the need to know electronic transition probabilities for both valence and Inner shell excitation and ionization processes In many areas of application including plasmas, fusion research, lithography, aeronomy, astrophysics, space chemistry and physics, laser development, radiation biology, dosimetry, health physics and radiation protection. Such information is also a crucial requirement for the development and evaluation of quantum mechanical theoretical methods and for the modelling procedures used for various phenomena involving electronic transitions induced by energetic radiation [1]. However, most spectroscopic studies to date for discrete electronic excitation processes have emphasized the determination of transition energies rather than oscillator strengths, since the former quantities are generally relatively easier to obtain both experimentally and theoretically. In contrast only rather limited information is available for the corresponding absolute optical oscillator strengths (or equivalent quantities reflecting transition probability such as cross section, lifetime, linewidth, extinction coefficient, A value etc.) for atoms. In the case of discrete electronic transitions for molecules such quantities are extremely sparse, while for core (inner shell) processes the available data are even more limited. In particular oscillator strengths are in very short supply for transition energies beyond 10 eV where most valence shell electronic excitation and ionization processes occur. This situation is  2 partly due to the well known inherent difficulties of quantitative work in the vacuum UV and soft X-ray regions of the electromagnetic spectrum (i.e. beyond the L1F cut-off). These and other limitations provide considerable challenges in both photoabs orption and photoemission studies. The situation a1so reflects the limitations and application restrictions involved in other types of optical methods such as lifetime, line profile, self absorption and level crossing techniques. Furthermore, the commonly employed direct photoabsorption methods using the Beer— Lambert law transmission measurements are subject to so—called “line saturation” (bandwidth) effects, which can lead to large errors in the derived absolute optical oscillator strengths for discrete transitions. These spurious effects become more severe for transitions with narrow linewidth and high cross section. In such cases the measured oscillator strengths are too small. Detailed discussions of Beer—Lambert law photoabsorption and the associated “line saturation” effects are given in chapter 2 section 3. From a theoretical standpoint, calcu1ation offers an alternative approach to experimental oscillator strength determination. However, theoretical ca1culations of oscillator strengths involve computational methods that require extremely sophisticated correlated wavefunctions and reasonable accuracy is at present only feasible for the simplest atoms such as hydrogen [21 and helium [3-9]. Electron energy loss spectroscopy (EELS), utilizing the virtual photon fie1d induced in a target by fast electrons at negligible momentum transfer, provides an alternative and versatile means of measuring optical oscillator strengths for electronic transitions in atoms and molecules in both the discrete and continuum regions. Under such experimental  3 conditions the electron energy loss spectra are governed by dipole selection rules, and for this reason EELS based methods for optical oscillator strength determination are often referred to as dipole electron impact experiments. The theoretical groundwork showing the quantitative relationship between photoabsorption measurements and electron scattering experiments was laid earlier, in 1930, by Bethe [10], by using the First Born approximation. The Bethe—Born theory has been further discussed by Inokuti [11] and Kim [121 and its application in experimental studies has been reviewed by Lassettre and Skerbele [131 and Brion and Hamnett [14]. Since 1960, there has been growing interest in electron scattering experiments partly due to recognition of the importance of phenomena involving electron—atom and electron— molecule interactions, and partly due to advances in high—vacuum technology, low energy electron optics, and detection techniques such as fast pulse counting using channel electron multipliers (channeltrons). Electron energy loss experiments have been applied to the measurements of absolute optical oscillator strength for discrete transitions following the pioneering work of Lassettre et al. [15—18] and of Geiger [19,20]. In other work Van der Wiel and co—workers 12 1—23] developed a variety of “photon simulation” experiments using high Impact energy, small angle electron scattering techniques to determine absolute differential optical oscillator strengths in the continuum region. In recent years, the techniques used by Van der Wiel and his co—workers [21—23] have been modified and further developed here at the University of British Columbia where a variety of low resolution dipole electron impact methods have now provided absolute differential optical oscillator strengths for a wide range of valence—shell [24—27] and inner—shell  [28,291 photoabsorption and photoionization processes . A review and compilation of photoabsorption and photolonizati on data obtained by direct optical and dipole electron impact methods for small molecules In the continuum region has recently been published by Gallagher et al. [301. In other work, a high impact energy, zero—degree scattering angle, high resolution EELS spectrometer [311 was built in this laboratory for the study of valence—shell [32—341 and inner—shell [32,34,351 electronic excitation spectra of a variety of molecules. In the present work, the operation of this EELS spectrometer [311 has now been modified to provide a new high resolution dipole (e,e) meth od for the determination of optical oscillator strength for discrete photoabs orption processes in free atoms and molecules. This new method is free of the spurious “line saturation” effects that complicate the measurem ent of absolute optical oscillator strengths (cross sections) in Beer—La mbert law photoabsorption experiments for discrete transitions. The meth od is applicable to all transitions throughout the discrete valence shell region of the valence shell spectrum at high energy resolution (0.04 8 eV FWHM). The Bethe— Born conversion factor for the high resolution dipole (e,e) spectrometer, developed here in the University of British Colu mbia has been determined by calibration against a previously deve loped low resolution dipole (e,e) spectrometer. The absolute scales of the present oscillator strength data were obtained from Thomas—Reic he—Kuhn (TRK) sum—rule normalization of the B ethe—B orn transformed elect ron—energy—loss spectra and as such do not involve the difficult determinations of photon (or electron) flux or target density required in phot oabsorption and other types of electron scattering experiments.  4  5 In chapter 2 of this thesis the photoabsorption and electron Impact methods are compared, together with a consideration of other techniques for optical oscillator strength determination. The presently used electron impact based dipole (e,e) methods are discussed In chapter 3. Absolute optical oscillator strengths for photoabsorption In the discrete and continuum regions for five noble gases (helium [36,371. neon [38] and argon, krypton and xenon [39]) and five diatomic gases (hydrogen [40], nitrogen [41], oxygen [42], carbon monoxide [43] and nitric oxide [44]) are presented from chapters 4 through 11. The variations of electronic transition moment with the internuclear distance for the Lyman and Werner bands of molecular hydrogen and for the l bands of carbon monoxide are also discussed In chapters 7 and —’A 1 X f 10 respectively. The present results are compared with previously reported experimental and theoretical data from the literature.  6 Chapter 2  Measurement of Absolute Optical Oscillator Strengths by Photoabsorption and Electron Impact Methods  2.1 Photoabsorption Cross Section measurements via the Beer— Lambert Law In photoabsorption experiments, quantitative cross section measurements are governed by the Beer—Lambert law. Consider first the reduction in the photon intensity when a light flux I passes through a distance dl containing a sample target of number density ri. The loss of intensity dl of the incident photon beam is proportional to the distance travelled dl, the number density ri. of the target, and the photoabsorption cross section of the target a(E). The relationship can be written as  dI=—IoE)nd1  (2.1)  where the photoabsorption cross section o(E) is related to the probability that a photon of energy E will be absorbed in passing through the target and has the dimension of area. Integrating equation 2.1 over the path length 1, we obtain xp(-oE)n1) I=I e 0 1 exp  (—  o(E) N)  (2.2)  Equation 2.2 is the familiar Beer—Lambert law [30,45] where 1 and I are the incident and transmitted light intensities, respectively.  The  7 quantity N is equal to ni and is sometimes referred to as the column number. The Beer—Lambert photoabsorption method can in principle be readily applied to the complete electronic spectrum of a given atomic and molecular target in both the discrete and continuum regions. Furthermore, the measurement procedure would at first seem to be quite straight forward. Extensive measurements using this technique have been made for atoms and molecules in the continuum region. Reviews and compilations of such cross section (oscillator strength) data can be found in references [30,45—48]. However, in the discrete excitation region, only limited cross section information is available from use of the Beer—Lambert law photoabsorption methods, and most of the measurements performed are for molecules. This situation arises because of the large errors which can occur in Beer—Lambert law cross section measurements for discrete transitions due to “line saturation” (i.e. bandwidth) effects. These spurious effects are particularly severe for discrete transitions with narrow natural linewidths and high cross sections. A comparison of different optical methods for determining absolute oscillator strengths in the discrete excitation region is given in section 2.2, while the perturbing “line saturation” effects in Beer— Lambert law photoabsorption are discussed in detail in section 2.3. A dimensionless quantity, namely the optical oscillator strength, i(E), is also often used in optical absorption spectroscopy. The oscillator strength is related [49] to the integrated photoabsorption cross section c for a discrete transition through the equation (in atomic units):t  All equations are in atomic units.  2it  8  2  (2.3)  In quantum mechanics, f°(E) is defined [14] as: N  o  f(E)  =  )I 0 2EI(WIrIW  2  (2.4)  S  r gives the coordinates of the N where E is the excitation energy, 5 electron species, and W and W are the initial and excited state wavefunctions respectively. At sufficiently high photon energies, ionization occurs and transitions occur from the bound initial state to a continuum final state. Instead of using the integrated photoabsorption cross section, a, and the optical oscillator strength, 1°, equation 2.3 can be rewritten as [50]  o(E)  =  2i12 df°(E) c dE  (2.5)  where a(E) is the photoabsorption cross section as defined earlier and df°(E)/dE is the differential optical oscillator strength with the dimension of (energy)’. If the energy E is expressed in electron volts (eV) and a(E) is in megabarns (1 megabarn  aGE) [Mbarns]  =  109.75  10-18 cm ), we have 2  df°(E)  [eV’]  (2.6)  9 Equation 2.6 may be used for the interconversion of cross section and differential oscillator strength data. The optical oscillator strengths f(E) In the discrete region and df(E)/dE in the continuum region have an important property that is useful for establishing the absolute intensity scale in the presently developed dipole (e,e) method (see chapter 3). It has been shown that for an N electron species [50,51],  f°(E)  +  f  df°(E) dE  =  N  (2.7)  This simply means that the total integrated optical oscillator strength (i.e. summing over all discrete transitions and integrating over all continuum states) is equal to the total number of electrons. Equation 2.7 is the famous Thomas-Reiche-Kuhn (TRK) sum-rule which In general holds for any atomic and molecular system. Generally, a valence shell partial sum rule is applied and in this case spectral area (i.e. the total oscillator strength) is normalized to the number of valence shell electrons plus a small correction for the Pauli excluded transitions from the core orbitals to the already occupied ground state valence orbitals [52,53].  2.2 OptIcal Methods for Determining Absolute Optical Oscillator Strengths for Discrete Transitions A variety of different optically based methods have traditionally been used for the determination of most of the optical oscillator strength  10 data available for discrete electronic transitions in the literature. Only a limited amount of data is available for atoms and much of this is to be found in the important compilations published by Wiese and co workers 154]. Very little information is available for molecules. The oscillator strength data base is extremely limited because such measurements are difficult to perform and also because most available methods suffer from a variety of often serious difficulties and/or limitations which severely restrict their range of application. Wiese and co—workers [54] have discussed various aspects of the optical methods used for atoms and provide useful conversion formulae relating the various quantities produced by the different types of measurements. The most commonly used optical measurement techniques include (a) Photoabsorption via the Beer—Lambert law [55], (b) Lifetime measurements by level crossing techniques (including the Hanle effect) [56,57], (c) Lifetime measurements by beam foil methods [58], (d) Emission profile measurements from plasmas [59] and beams [60], (e) Resonance broadening emission profiles [611, (1) Self absorption [62—64], (g) Total absorption [65] and (h) Optical phase—matching [66]. The strengths and weaknesses of these methods with regard to their widespread general application to atomic and molecular electronic excitation spectra are summarised in Table 2.1. Also shown in table 2.1 are corresponding considerations for theory as well as for electron impact based oscillator strength methods [67—7 1], including the present work, as discussed in section 2.4 below. Methods (b)—(h) have all been used but only in selected favourable cases involving relatively intense atomic transitions. However such approaches are generally complex and various limitations make them unsuitable for widespread application  [58]  (ii) Beam foil  (1-lanle effect) [56,571  (i) Level crossing  Blending of unresolved spectral lines.  excIted state atomic and ionic levels  Cascades from other states.  background pressure.  Slight dependence of line width on  Molecular energy states must be known.  Branching ratios must be known.  Extrapolation to zero column number.  Useful for mean lifetimes of  Good for strong resonances  No bandwidth problem  Lifetime Methods  [56—581  use of logarithmic relation to obtain  Wide spectral range  1551  Not generally suitable  favourable circumstances  resonant nature of discrete excitation and  Very high resolution  Photoabsorption  Stray light, order overlapping.  Limited suitability under  Molecular Studies  Suitability for General  Bandwidth effect (line saturation) due to the  Difficulties and Problem Areas  11=expfrt lop) 0 Simple relation, l  Advantages  Beer-Lambert Law.  ERef.]  Method  resolution  Methods of obtaining optical oscillator strengths for discrete electronic transitions at high  Table 2.1  not generally suitable  Relies on calculated electron collision cross  [62-64)  Self absorption  not generally suitable  Re-emission from atoms excited by absorption of resonance photons.  Difficult and  Possible departure from Doppler profile.  different excitation to upper levels.  [611  No bandwidth problem  not generally suitable  Different Doppler width corresponding to  Resonance broadening  emission profile  section.  Difficult and  not generally suitable  Uncertainties in calculated Stark width.  Time variations in Doppler width.  Difficult and  Molecular Studies  Suitability for General  Only good for optically thick emission.  Difficulties and Problem Areas  Difficult and  No bandwidth problem  No bandwidth problem  No bandwidth problem  Advantages  Extrapolation to zero pressure.  [60]  Beam emission profile  159]  profile  Plasma emission  LRef.1  Method  Table 2.1 (continued)  Absolute scale requires external procedures.  [67—701  application  Tedious procedure for each transition. Electron optical effects and lens ratios.  0 at fixed 0) (Vary E  [711  Absolute scale requires external procedures.  Difficult for general  Electron scattering  0 is problematical. K = Extrapolation to 2  No bandwidth problem  Tedious procedure for each transition.  =0 is problematical. 2 Extrapolation to K  (Vary 9 at fixed E ) 0  Electron scattering  wavelength must be known.  Difficult but possible  not generally sutiable  collision effects.  [66)  No bandwidth problem  Difficult and  Transition peak must not be perturbed by  Optical phase-matching No bandwidth problem  Refractive index of buffer gas at particular  not generally sutiable  Total absorption the absence of collision broadening.  Molecular Studies  Suitability for General  [65)  Difficulties and Problem Areas  Difficult and  No bandwidth problem  Advantages  Only good for optically thick absorption in  (Ref.1  Method  Table 2.1 (continued)  (continued)  on extrapolation. Resolution limited to AE  measurements required. Direct measurement over wide  methods.  Infinite energy resolution,  13-91  data for comparison.  Lack of sufficiently accurate experimental  wavefunction accuracy and calculation  No instrumental effects.  calculation  Extension to large systems limited by  Very accurate for small atoms.  Quantum mechanical  Good accuracy.  spectral range.  since B(E) in low energy region is dependent  No pressure or incident flux  Lthis work)  0.01eV FWHM.  Absolute scale via TRK sum rule. Accuracy of Bethe Born conversion factor  HR Dipole (e,e)  Stray electrons.  Difficulties and Problem Areas  No bandwidth problem  Advantages  Electron scattering  (Ref.1  Method  Table 2.1  accuracy.  Very difficult to obtain good  experiments.  overcome with very careful  Most difficulties can be  spectral range.  Readily applicable over wide  Molecular Studies  Suitability for General  15 across the complete valence shell spectral range for atomic and in particular molecular targets. Although in principle Beer—Lambert law photoabsorption measurements would seem to offer a straightforward means for routine measurement of absolute optical oscillator strengths for atomic and molecular transitions over a wide spectral range, application of the method may often result in large errors In the measured cross section. Since the limitations of this method are not widely appreciated, the special case of the Beer—Lambert law photoabsorption method will now be discussed in detail.  2.3 “Line Saturation” Effects in Beer—Lambert Law Photoabsorption for Discrete Transitions Photoabsorption via the Beer—Lambert law (method (a) in table 2.1) can in principle be applied readily to the complete valence shell spectrum of atoms and molecules, and the measurement procedure would seem to be quite straightforward in principle. While the method works well for continuum processes, very few accurate determinations of absolute oscillator strengths for discrete electronic transitions have actually been made using the Beer—Lambert law. This is because very serious problems can arise when Beer—Lambert law discrete photoabsorption spectra are used for absolute intensity (oscillator strength) determinations [721 rather than just for indicating the energy levels. These problems, which are not always widely appreciated or well understood, arise from the finite energy resolution of any real optical monochromator and the resonant nature of discrete photoabsorption. In particular, it should be noted that equation 2.2 is only strictly valid for  16 the unphysical situation of zero bandwidth (i.e. infinite energy resolution) as discussed in references [11,37,46,73,74]. DiffIculties arise because a logarithmic transform is required (equation 2.2) in order to obtain the absolute cross—section a(E) from the percentage transmission (l/1) obtained from the experimental measurements. As a result of this logarithmic transform the measured cross section at the characteristic energy will correspond to a weighted average observed cross section (which is often much less than the true cross section a(E)) in situations where the bandwidth (BW=AE) Is a significant fraction of, or greater than, the natural linewidth (LW=AL) for a transition [46,73,74]. This limitation and the fact that measured peak cross—sections are often a function of the instrument as much as of the target, has been reviewed in some detail by Hudson [46] and commented on by others [11,75]. The situation is potentially particularly serious for intense narrow lines in the discrete region because of the Bohr frequency condition and the fact that the line profile varies rapidly within the BW unless the latter is very much narrower than the natural LW. Hudson [46] has also discussed the so— called “apparent pressure” effect and shown how the bandwidth effects can be minimised (but never entirely eliminated) by the tedious procedure of extrapolating peak intensities measured at a series of pressures, for each separate transition, to zero column number N. However, even with such procedures, as Hudson [46] correctly points out, I approaches 10 as this optically thin limit is approached and thus the greatest weight is placed on the least accurate data! The net result is that accurate optical oscillator strengths often cannot be obtained from Beer—Lambert law photoabsorption measurements for very sharp, intense lines (for example compare references [55,76—80]). These problems are  17 likely to be particularly severe in the vacuum UV and soft X—ray regions of the spectrum where low light fluxes, even from monochromated synchrotron sources, often require the use of wide monochromator exit slits. These bandwidth effects will occur when the monochromator is placed between the continuum light source and the sample cell. This arrangement is the usual situation on synchrotron beam lines (i) because of the ultra high vacuum requirements in the storage ring and the monochromator and (ii) because the monochromator is usually an integral part of the beam line facility feeding different possible experimental arrangements. However, these spurious bandwidth effects would also influence the measured cross sections in the same way if the sample cell was placed between the source and monochromator as occurs in many laboratory—based spectrometer arrangements. Despite the well documented and serious deficiencies which can complicate the determination of absolute optical oscillator strengths for discrete transitions using the l3eer—Lambert Law, it is still sometimes used and it can then often result in spurious results which are not always apparently realised by the experimenters. A particularly drastic example of such “line saturation’ BW effects occurs in the vacuum UV absorption 2 [801 illustrated in figure 2.1. The vacuum UV spectrum spectrum of N as reported by Gurtler et al. [80] on an absolute scale (figure 2.1(a)) has high enough resolution to show evidence of rotational effects. This optical absorption spectrum [80] is compared with a high impact energy, negligible momentum transfer, high resolution (zE0.O17 eV) electron energy loss spectrum placed on an absolute scale [37,4 1] in figure 2.1(b) over the same energy region. Clearly there are large differences in relative intensity between the two spectra in the 12.6—13.0 eV range, and  400  (a) Photoabsorption 3.  2I  1•  I?  0-  k L.JL L —F  13.2  13.0  12.8  300  II I  i IIII  2•  18  •100 C.) 0 Cl)  0  -—-—  12.6  0  12.4  0  C.)  8  (b) Dipole (e,e) spectroscopy -800 4 p 0  6  600  I  4  j  =  0.017 eV  .1  2  0  0 =2500eV E  —‘/  “b  I  13.2  200  __%__‘  —  400  0  I  13.0  12.8  12.6  12.4  Photon energy (eV) Figure 2.1: Comparison of the absolute valence shell photoabsorption oscillator strength spectra of molecular nitrogen obtained by Beer—Lambert law photoabsorption and dipole (e,e) experiments in the energy region 12.4—13.2 eV. (a) Beer—Lambert law absolute photoabsorption spectrum adapted from figure 1 of reference [80]  —  the dashed lines have been drawn to show the  positions of the maximum cross—sections of the peaks according to the values given in the text of reference [80]. (b) Dipole (e,e) spectrum [37,41] the electron energy loss spectrum was placed on an absolute optical oscillator strength scale by referencing to the high resolution oscillator strength spectrum reported in the present work (see chapter 8).  —  19 particularly in the 12.9—13.0 eV region. These differences reflect serious “line saturation” effects in the optical work In the 12.9—13.0 eV region due to the finite bandwidth of the incident radiation and the extremely narrow natural linewidth of these intense transitions. As can be seen from figure 2.1 these factors have dramatic effects on the derived optical oscillator strengths (cross sections). Clearly not only the peak heights but also the peak areas (and thus the apparent oscillator strengths) are drastically reduced in the optical spectrum. In contrast the corresponding absolute optical oscillator strength spectrum obtained via Electron Energy Loss Spectroscopy (EELS) in figure 2.1(b) (see section 2.4 following) shows the correct relative intensities (band areas) even though it is at lower energy resolution than the optical work. This large 2 was pointed out earlier intensity effect in the electronic spectrum of N in electron impact studies by Lassettre [81] and also by Geiger [82]. Subsequently, extrapolation of very carefully controlled optical measurements [78,79], made as a function of column number N, was found to give results much more consistent with the intensities derived from the EELS measurements [81.821. It is important to note that the earlier treatment of “line saturation” effects by Hudson [46] only emphasized the effects of finite BW on the peak heights of sharp spectral lines (i.e. the cross section at the peak maximum) and how such effects may, hopefully, be minimised by extrapolation to zero column number. As Hudson [46] has shown, a 40% error still exists in a peak height cross section for the situation where LW=BW, even at N=0! However it should be remembered that an accurately measured oscillator strength for a discrete transition should involve an integral over the whole profile of the spectral line and should  20 not just be assessed from the peak height. The peak area in a photoabsorption experiment is also severely Influenced by the BW effects, which results in a significant reduction in both peak height and peak area, as can be seen in figure 2.1. This clearly leads to an Integrated optical oscillator strength for the transition which is significantly in error unless the BW is very narrow compared with the narrowest features in the spectrum  —  regardless of whether or not such features are resolved!  Such errors are therefore likely to be particularly serious for molecular spectra because of the vibrational and rotational fine structure  —  as can  be seen in figure 2.1. Since in general different lines in the same spectrum have different natural LW, the cross section perturbations are different for every transition (see again figure 2.1(a) and (b)). Thus the complete spectroscopy (i.e. all line widths and line shapes) must already be known if any meaningful understanding of photoabsorption cross sections for spectral lines is to be obtained from Beer—Lambert law measurements. If such information was available then of course the oscillator strengths wou1d already be known from the linewidths! Clearly then, one can never be sure that the correct oscillator strength has been obtained in a Beer—Lambert law photoabsorption experiment unless either the information is already available in some form from other sources, or unless the absolute integrated spectral intensities can be shown to be effectively independent of the BW as well as the column number N. Given the above considerations it is necessary to extend the peak height analysis of Hudson [46] to consider the effects of bandwidth on the integrated cross section over the spectral line profile (i.e. peak area) in a discrete photoabsorption experiment. For example, consider (figure 2.2)  21  Gaussian  absorption  peak  % absorption of 1 (E) 0  a(E)  o(E)  =  [n  \ 7  E  E  convoluted with triangular bandwidth áE  % absorption of 1 (AE,E) 0  ap(tE,E) oE,E)  (]2+2)W2 JA2\  =  Ln  A  (i..E,E) 0 I  I(iE,E)  \ /  F  £  E  A 2 = 1 A  4 3 A  Figure 2.2: Diagrammatic representation of the “line saturation” effects occuring in photoabsorption experiments when the Beer-Lambert law is used to determine the Integrated cross-section of a discrete transition.  22 the effects of convoluting an assumed Gaussian shaped absorption peak of natural linewidth iL with a triangular monochromator bandwidth AE. In this case, equation 2.2 can be rewritten as  I(AE,E)  =  (2.8)  (tE,E) exp (—(o(AE,E)N) 0 I  The area A 1 (see figure 2.2  —  left hand side) of the unconvoluted  Gaussian absorption peak depends linearly on the percentage absorption (E) at the peak maximum for a given zL. The area of the 0 {(I—I)/I} of 1 Gaussian peak is, of course, unchanged by convolution with the bandwidth AE regardless of AE/iL. That is, considering the % absorption pPi1{  I  I  J  or  I (E)  —  (AE,E) 0 1  1(E)  (E) 0 1 ) 1 (A  —  I(AE,E) dE  dE=  (2.9)  ) 2 (A  However, in order to calculate the photoabsorption cross section a(E), a logarithmic transformation (see equation 2.2) of 1/I is needed. The logarithmic transform together with the resonant nature of discrete excitation by photons is the root cause of the “line saturation” bandwidth effects and the resulting spurious experimental cross sections which often occur in absolute photoabsorption measurements using Beer’s law. In the case of the logarithmic conversion we have for the cross sectional areas before and after convolution (figure 2.2  —  right hand side)  3 A  dE  =  =  I J  23  Pk  E) 1 ( 0 I  dE  (2.10)  1(E)  Pk  4 A  =  fo1zEE) dE =  In  dE  (2.11)  4 unless AE is equal to zero, 3 is always greater than A It is found that A which is only true of course for the hypothetical case of Infinitely narrow bandwidth. In more detail mathematically, area Ai is convoluted by 2 is also a A If area A 2 = 1 A 2 such that . bandwidth AE to yield an area A Gaussian distribution with full width at half maximum (FWHM) +t\E then under this circumstance, (tL 2 / 1 approximately equal to ) A 1 IS) (where S is a scale factor in order that we may vary the area = 2 = 1 A ( under the Gaussian peak). After integration of equations 2.10 and 2.11, we obtain  1  Cnl  (2.12)  A3=N-  1  CO  A = 4  n-i [n=1(AL2+AE2)  (2.13)  where  U =  2I1n2  24  3 Is always greater Comparing each term for equation 2.12 and 2.13, A :A.. A = 4 unless AE is zero, and only in this case does 3 than A In figure 2.3, the variation of observed peak area (NxA4) with column number N for a given transition is shown for different AE/AL ratios. It shows that the area becomes smaller as the ratio AE/AL is increased for the same column number. Figure 2.4 shows the variation of integrated cross section for a given transition obtained by use of the Beer—Lambert law with column number for different values of LE/AL. The true integrated cross section (100Mb eV) is only attained at N=0 or where AE=0 (i.e. infinite resolution). Figure 2.5 ((a)—(e)) shows the variation of observed integrated cross section with column number at AE/AL=10, calculated for a series of transitions of different true cross section (given at zero column number). Note that for each cross section the behaviour is different even for a fixed AL. Since in general different lines will have different natural linewidths AL, it can be seen that the effects and therefore the interpretation of photoabsorption experiments  can be very complex indeed. These effects are known as the “line saturation” or “apparent pressure’ effects occurring in photoabsorption experiments [46]. With a very narrow natural linewidth (i.e. large AE/AL) and a high cross section the problem is obviously more severe, in order to attempt to obtain a result closer to the correct cross section, the only experimental approach is the tedious procedure of performing the measurements for each transition in the spectrum at a series of pressures and extrapolating to zero column number as shown in figures 2.4 and 2.5.  25  V  V  V I  V I-.  U C.,  0 0  1  2  4  3  Column number  5  6  ) 2 ( x lOlócm-  ) with column number for 4 Figure 2.3: Variation of integrated peak intensity (NxA different ratios of (incident bandwidth (AE))/(natural absorption line-width (AL)), calculated using equations 2.12 and 2.13.  26  V  0 4-  U V U) U) U)  0 I  U 4) I  V C  a)  V I  a) V U)  0  0  1  2  4  3  Column number  (  5  6  x lOlócm) 2  Figure 2.4: Variation of the observed integrated cross-section with column number for different AE/zL ratios, calculated using equations 2.12 and 2.13. The true integrated cross-section is taken to be 100Mb eV.  27  1o0 .  .  80  C)  0 I C)  V I  V  40 V  V b.  20  V I-.  C) .0  o  0 0.00  0.05  Column number  0.10  0.15  ) 2 cm 18 ( x 10  Figure 2.5: Variation of the observed integrated cross-section wIth column number at AE/zL=1O for peaks with true integrated cross-section of(a) 100, (b) 50, (c) 30, (d) 20 and (e) 10Mb eV. The curves were calculated using equations 2.12 and 2.13.  28 Such procedures have been used by Lawrence [781 and Carter [79]. In figure 2.5 we can see that for peaks with the same AE/AL va1ue, the higher the true cross section, the greater the error in the optically measured cross section at a given column number. Thus It can be seen that for very narrow peaks of very high cross section, extrapolation to extremely low pressure would be required to obtain the correct cross section experimentally. However, in an actual experiment, the error In measuring I (tE,E)/I(E,E) increases with decrease In pressure. As 0 Hudson [46] has pointed out, extrapolation procedures put the mOst emphasis on the least accurate data and hence the extrapolated value Is likely to be inaccurate. These extrapolation procedures only minimise the BW effect and the resulting cross sections may in some cases still be subject to large errors. In such situations direct photoabsorption measurements are meaningless and for example, Yoshino et al. [55] have stated that the (12,0) transition of 18j is too narrow to be measured using the Beer—Lambert law photoabsorption method. in summary then, the above model calculations Indicate that it Is often extremely difficult to obtain highly accurate optical oscillator strengths for discrete transitions in optical photoabsorption experiments based on the Beer—Lambert law, especially for very sharp peaks with high cross section. As such, absolute photoabsorption cross sections obtained for discrete transitions using the Beer—Lambert law must always be viewed with some caution because of the possibility of significant systematic errors due to finite bandwidth effects which in general will be different for every transition. Therefore, widespread application of Beer— Lambert law photoabsorption methods to the study of discrete atomic and molecular spectra is not practical if accurate cross—sections are desired.  29 In the following discussion alternative methods of determining optical oscillator strengths are described which do not suffer from these spurious bandwidth effects.  2.4 Electron Impact Methods An alternative and entirely independent approach to optical oscillator strength determination, free of spurious bandwidth effects, is provided by exploiting the virtual photon field induced in a target by fast electrons. This can be achieved by means of fast electron impact electron energy loss techniques at vanishingly small momentum transfer. The theoretical relation between high energy electron scattering and optical excitation has long been understood [10]. The resonant process of absorption of a photon of energy E  hv(E)+M—’M  (2.14)  may be compared with the non—resonant process of electron Impact excitation  ) 0 e(E  + M  —  M  —E) 0 + e(E  (2.15)  Clearly the electron energy loss (E) is analogous to the photon energy E. The Intensity of scattered electrons resulting from the excitation process is measured rather than a percentage absorption. The non—resonant nature of the electron impact excitation process together with avoidance of the logarithmic Beer—Lambert law in determining oscillator strength  30 (cross section) means that the “line saturation” bandwidth problem which often complicates discrete photoabsorption experiments is eliminated In the EELS method [111.  2.4.1 Theoretical Background for Fast Electron Impact Techniques The process involving the collision between a fast electron and a target atom or molecule can be considered as a sudden but small perturbation of the target by the incident electron. The sudden transfer of energy and momentum to the target electrons due to the perturbation results in excitations within the target molecule [11]. Under these conditions the perturbation is due to an induced electric field, sharply pulsed in time and therefore corresponding broad in the frequency domain. This provides a “virtual photon field” or dipole excitation of constant flux in the spectral region of interest. A key quantity in the electron impact method for determining optical oscillator strengths is the momentum transfer (K) in the collision. A momentum transfer dependent, generalised oscillator strength f(K,E), describing the transition probability, can be defined as [10,11,141  f(K,E)  =  (2.16)  where the quantities have the same physical meanings as in equation 2.4. It can be seen that equations 2.4 and 2.16 are very similar in form. It will be shown later that equation 2.4 is a limiting case of equation 2.16. In the continuum region, f{K,E) is replaced by dUK,E)/dE, the  31 differential generalised oscillator strength, which will be used throughout the following discussion. In fact, even for discrete transitions the quantity measured at a given energy in an actual experiment is also df(K,E)/dE, and integration over the discrete peak area gives fK,E). The quantity dfK,E)/dE is related [11] to the differential inelastic electron e(K,E)/dEdQ# (which is proportional to the d a impact cross—section 2 inelastically scattered current) by the equation  df(KE) dE  =  !-K2 dOe(E) 2 k dEdQ  (2.17)  , k are the incident and scattered 0 where E is the energy loss and k momenta respectively. The various momenta are related to the polar scattering angle 0 by the cosine rule  2 K  =  k  +  k  —  cos0 2k k 0  (2.18)  k K=k — 0  and  (2.19)  According to the Bethe—Born theory [10], equation 2.16 can be expanded 2 if 1K is small in terms of a power series in K  df(KE)  =  df°(E) + AK 2  +  4 + BK  ...  (2.20)  #d ue(K,E)/dEdQ as a function of energy loss E is the electron energy loss spectrum at 2 momentum transfer K involving scattering into a solid angle element dQ.  32  where  A  =  , B (s—2E ) 3 E 1  =  2E 2 — 5 E 1 2E ) 4 (+ 8  (2.21)  Nm  and  m =  1 (q:J  (2.22)  where df(E IdE is the differential optical oscillator strength and  Em  Is  the mt order multipole matrix element with m= 1 for electric dipole and m=2 for electric quadrupole, etc.. AsIKI— 0, the so—called OPTICAL LIMIT, which corresponds to zero momentum transfer, can be obtained from equation 2.20 [11]  df(K,E) dE  -  df°(E) dE  (2.23)  Under such conditions of negligible momentum transfer dipole selection rules apply and equation 2.17 can be rewritten as  df°(E) dE  =  øe(E) 2 -L.K2 d 2 k  dEdQ  =  B(E)  e(E) d G 2 dEdQ  (2.24)  The quantity B(E) is called the Bethe—Born factor and it can be seen that  it depends on kinematic (i.e. instrumental) factors alone. B(E) relates the electron impact differential cross—section at negligible momentum transfer to the differential optical oscillator strength. In an actual experiment the factor B(E) must also take into account the finite  33 acceptance angle of the spectrometer about the mean scattering angle of 00.  This will be considered in the following section.  2.4.2 Experimental Approach It is clear from equations 2.17—2.24 that electron impact measurements made under appropriate conditions may be used to make absolute optical oscillator strength measurements if appropriate absolute normalisation procedures can be established. The momentum transfer K, which depends on the impact energy E , the energy loss E and the 0 mean scattering angle 0, can be obtained for a particular experimental condition by substituting k =2E and — 2 0 0 = 2 k 2(E E) into equation 2.18 [14].  2 K  =  0 + 0 2E 2(E — E)  -/2(E 0 2/2E — E) cosO  —  (2.25)  Equation 2.25 can be rearranged to become  2 K  =  0 (2 2E  —  E —  2 cosO)  (2.26)  From equation 2.26, it can be seen that if we require 2 K — ’O, 0 E/E and 0 should be made as small as possible. Under these conditions, we can 2 into a binomial series and neglect the contribution of / 1 ) 0 expand (1—E/E the higher terms for small E/E . In addition, cosO can be made equal to 0 (1_02/2) for small 0. Equation 2.26 can then be simplified to  K  2 =  0 (x 2E  2 +  0  2  (2.27)  )  . By 0 where x is a dimensionless quantity and Is equal to E/2E substituting equation 2.27 into equation 2.24 and integrating over the finite half angle of acceptance 00 of the detector, the Bethe—Born conversion factor B(E) can be derived for a particular spectrometer geometry to be [14,83]  B(E)  =  EEk 00 t  k,  in  1  +  (2.28)  Two general approaches have been used for optical oscillator strength determination by electron impact: (a) An indirect EELS method, pioneered in the 1960’s by E. Lassettre and co—workers [67—70]. involves measurement of the relative intensity for a given transition as a function of scattering angle (i.e. of , see equation 2.25) at a fixed intermediate impact energy 2 K (typically —500 eV). This results in a relative generalized oscillator strength curve (see equations 2.17—2.23) which can be extrapolated O to give an estimate of the relative optical oscillator strength K = to 2 for the transition. The extrapolation procedure is tedious since a series of measurements is required for each transition. In addition the procedure can often be problematical due to unusual behaviour of the functional form of fIK) at low K [67] and also due to the fact that  2 was often still quite large [67— the minimum experimental value of K  35 701 so that a lengthy extrapolation was required. The minimum 2 was further limited [67—701 by the fact that the attainable value of K spectrometer could not be operated at 0=00 due to interference from the incident primary electron beam in the electron energy loss analyzer. The relative value of the oscillator strength was usually made absolute by reference to concurrent measurements of the relative elastic scattering Intensity which was in turn normalized on a published value of the calculated or experimental absolute elastic scattering cross section. A variation of this extrapolation approach used by Ross et a!. to study alkali metals [71], involved scanning the impact energy at fixed scattering angle for each transition. However such an approach is even more difficult for general application to quantitative work because of electron optical effects on the scattered electron intensities and as a result its use has been extremely limited. (b) A more direct and versatile approach which avoids the need for the undesirable extrapolation procedures is to choose the experimental ’O) is effectively K — conditions so that the OPTICAL LIMIT (i.e. 2 satisfied directly [2 1—23]. This can be achieved by measuring at high 0 (typically 3000 eV for valence shell processes) and impact energy E designing the electron analyzer and associated electron optics so that a mean scattering angle of 00 can be used [83—871. This typically < 10-2 a.u.. 2 results in K  Under such conditions equation 2.24 is  satisfied to better than 1% accuracy and an entire EELS spectrum covering both the discrete and continuum regions can be scanned directly under dipole (optical) conditions. To obtain a relative optica1 oscillator strength spectrum it suffices merely to transform the  36 relative electron impact differential cross section (at K —0) by the 2 known Bethe—Born factor B(E) for the spectrometer. B(E) must take into account the effects caused by the finite acceptance angles of the electron energy loss analyzer (i.e. a spread of K , see equation 2.28). 2 The relative optical oscillator strength spectrum obtained in this way has the correct relative intensity distribution because of the “flat” nature of the virtual photon field [14,88] associated with inelastically scattered fast electrons at 2 K — O [10]. This means that no determination of beam flux is required. The relative spectrum can be made absolute by using a known theoretical [85] or experimental [87] value of the photoabsorption cross section at a single photon energy, usually in the photoionization continuum. However, an independent and accurate means of obtaining an absolute scale, frequently used in this laboratory (for some examples see references [24—27,30]), is to obtain the Bethe—Born transformed valence shell EELS spectrum (i.e. oe(E)/dEdQ 2 d  —  see equations 2.24 and 2.28) out to high energy loss.  The proportion of valence shell oscillator strength from the limit of the data to E=cc is estimated by extrapolation of a curve fitted to the higher energy measurements. The total area of the spectrum is then normalised to the number of valence shell electrons. This overall procedure makes use of the valence shell Thomas—Reiche—Kuhn (TRK) sum rule (see equation 2.7). The TRK sum rule normalisation of a Bethe—Born converted EELS spectrum produces an accurate absolute scale without the need for measurements of beam flux and target density which are required in conventional absolute cross section determinations.  37 In summary, the selection of experimental conditions corresponding directly to the optical limit, together with TRK sum rule normalisatlon, provides an extremely direct and versatile approach which Is the basis of the dipole (e,e), (e,2e) and (e,e+lon) techniques for measuring absolute optical oscillator strengths. These three methods provide quantitative simulations of tunable energy photoabsorptlon, photoelectron spectros copy and photolonization mass spectros copy respectively [14,30,881. The three dipole electron scattering techniques have been used extensively in recent years for total and partial optical oscillator strength measurements [30] for photoabsorption and photoionization in the continuum at modest energy resolution (1 eV FWI-IM) for a wide variety of valence shell and inner shell processes (see references [24—30] for some recent examples). The modest energy resolution results from using an unmonochromated incident electron beam of thermal width. At such a low energy resolution the sharp peaks in the valence shell excitation spectra of atoms and molecules are largely unresolved [24—27] but the spectral envelope nevertheless encloses the correct integrated discrete oscillator strength, regardless of the bandwidth, since electron impact excitation (equation 2.15) is non— resonant [11,14,88]. In the high resolution dipole (e,e) method (0.048 eV FWHM) developed in the present work a detailed absolute differential optical oscillator strength spectrum is obtained throughout the valence shell discrete region, free of “line saturation” effects.  38 Chapter 3  Experimental Methods  The complementary performance characteristics of two different zero degree, high—impact—energy electron—energy—loss spectrometers (or dipole (e,e) spectrometers), one with low resolution and a known Bethe— Born conversion factor, the other with high energy resolution, have been used to obtain the results reported in this thesis. Absolute optical oscillator strengths for the discrete and continuum photoabsorption of five noble gases and five diatomic gases have been obtained. The combined techniques establish a general method suitable for routine application to measurements of absolute optical oscillator strengths for electronic excitation (i.e. photoabsorption) of atoms and molecules at high resolution over a wide spectral range.  3.1 The Low Resolution Dipole (e,e) Spectrometer The present low resolution dipole (e,e) spectrometer is the non— coincident forward scattering portion of a dipole (e,e÷ion) spectrometer that has been extensively used in this laboratory in recent years to obtain highly accurate photoabsorption and photoionization continuum total and partial oscillator strengths for a large number of molecular targets [24— 301. This dipole (e,e+ion) spectrometer was originally built at the FOM institute in Amsterdam [2 1—23,85—87], but was moved to the University of British Columbia in 1980 where the spectrometer has been further modified [89,901. Details of the construction and operation of this  39 spectrometer can be found in references [21—23,85—87,89,90]. A schematic diagram of the dipole (e,e+ion) spectrometer is shown in figure 3.1. Briefly, a black and white television electron gun with an indirectly heated oxide cathode (Philips 6AW59) at —4 kV potential with respect to ground is employed to produce a narrow (-1 mm diameter) beam of fast electrons. The electron beam is collided with the target molecules in a collision chamber which is at potential of +4 kV. Thus, the kinetic energy of the incident electrons is 8 keV in the interaction region containing the target molecules. The inelastically scattered electrons are 4 steradians about the zero degree collected in a small cone of 1.4x10 mean scattering angle, defined by an angular selection aperture. After passing through Einzel lenses and a decelerating lens, the electrons are energy—analyzed by a hemispherical electron analyzer and finally are detected by a channel electron multiplier (Mullard B4 1 9AL) used in the pulse counting mode. The resolution of this electron energy loss spectrometer is  -  1 eV FWHM. The time—of—flight mass spectrometer,  consisting of extraction plates, ion lenses and an ion multiplier, capable of detecting the positive ions produced in the collision chamber is arranged at 90 degrees to the incident electron beam but this arrangement (dipole (e,e+ion) spectroscopy) was not used in the present work. Helmholtz coils and high permeability mumetal are employed to shield the scattering regions from external magnetic fields. The use of turbo molecular pumps provides a clean vacuum environment suitable for quantitative electron spectroscopy. Recently, some modifications have been made to this dipole (e,e+ion) spectrometer [27,291. A differential pumping chamber pumped by a Seiko—Seiki (STP300) magnetic levitation  40  ELECTRON GUN  (e,e +ion) SPECTROMETER  COLLISION CHAMBER GAS INEr  ANGULAR SELECTION EINZEL LENSES  TIME OF FLIGHT MASS SPECTROMETER AND ION LENSES  DECELERATING LENS  PRiMARY BEAM DUMP ELECTRON ANALYSER  Figure 3.1: Schematic of the dipole (e,e+ion) spectrometer In the present work, this instrument has been used only in the dipole (e,e) mode (i.e. the forward electron energy loss spectrometer has been employ ed without the time—of—flight spectrometer).  41 turbo—molecular pump, was added to the existing spectrometer between the electron gun vacuum chamber and the collision chamber In order to effectively isolate the electron gun from the sample gas such that the oxide cathode of the electron gun will have a longer life. In addition, the extra differential pumping chamber also stabilizes the electron beam and only slight retuning of the beam Is necessary when the sample Is introduced into the system. The modifications above involved adding a further set of quadrupole electrostatic deflectors and a new electron beam monitoring aperture (—1 mm diameter). The electron gun was moved back from the target region by -7 cm. A vacuum isolation valve was also added between the electron gun and the differential pumping chamber and with this device in place maintenance work can be performed on either the gun chamber or the main system without letting the whole system up to atmospheric pressure. 8 keV and half—angle of 0 The experimental conditions (E 6.7xlO radians) of this low resolution dipole (e,e) O = acceptance 0 spectrometer satisfy the small momentum transfer (K) condition when the energy loss E  500 eV according to the Bethe—Born theory (see  chapter 2). The electron energy loss spectrum is then converted to a , E and 0 relative optical spectrum from the known scattering geometry (E O) of the spectrometer using the equation 2.28. The absolute differential oscillator strength scale for the relative optical spectrum can then be established by using the (partial) TRK sum—rule or by normalizing at a single point in the smooth continuum to published optical data. The latter procedure has only been used when the sum—rule normalization procedures are not tractable because of closely spaced inner shells  42 adjacent to the valence shell (see results for argon, krypton and xenon, chapter 6).  3.2 The High Resolution Dipole (e,e) Spectrometer All the high resolution spectra reported in this thesis were measured using the high resolution dipole (e,e) spectrometer which was built earlier by Daviel, Brion and Hitchcock [31] to record EELS spectra. The design and construction of this spectrometer.have been described In detail in reference [31]. Figure 3.2 shows a schematic diagram of the high resolution dipole (e,e) spectrometer. The following features of the spectrometer provide improved performance in terms of resolution, sensitivity and stability, compared with older designs: (a) Differential pumping of the four vacuum chambers including the electron gun, the monochromator, the collision region and the analyzer, alleviates the problems of surface contamination, retuning and frequent cleaning of the system. This arrangement ensures long term stability as well as high sensitivity and good resolution of the spectrometer. The vacuum isolation of the electron gun also enhances the study of thermally unstable compounds. (b) Advanced electron optics were designed [31] to improve the beam currents and also minimize the effects of scattering of the incident beam from s1it edges and the surfaces of the analyzers into the detector. The large background originating from the primary electron beam is strongly suppressed and operation at zero—degree mean scattering angle is possible with minimial background effects.  43  MONOCHROMATOR  TURBO PUMP 360 L/S  ANALYSER  SCALE  o  I  10  20cm  TURBO PUMP 360 L/S  TURBO PUMP 450 L/S  Figure 3.2: Schematic of the high resolution dipole (e,e) spectrometer Legend: A anode C cathode CC collision chamber T tube L/S liter per second  G grid  1 P  F focusing lens  Qi  V valve  1 L  HV high voltage D decoupling transformer  —  —  —  8 apertures P  Q deflectors 7 L  GAS  lenses gas inlet  44  0 (c) Large hemispherical electron energy analyzers (mean radius R 19 cm  =  =  7.5 in) are employed. As a result, high transmission and  high resolution at relatively high pass energy can be attained. The high pass energy in turn permits the required high impact energy while retaining reasonable lens voltage ratios. Briefly, a thoriated tungsten filament, spot welded onto an externally adjustable mount and located just in front of the grid of an oscilloscope electron gun body (Cliftronics CE5AH), is heated by a direct current to produce thermal electrons. Except for the grounded first and third elements of the focussing Elnzel lens F, the filament cathode (C), grid (0), anode (A) and the second element of the focussing lens F are all floated on top of—3 kV in the present design. A two element lens (Li) Is used to retard the 3 keV electron beam (—1 mm diameter) to the required pass energy of the monochromator before being energy—selected by a hemispherical electron energy analyzer. A virtual slit generated by the accelerating (voltage ratio 1:20) lens (L2) is located at the monochromator exit. The monochromated beam is further accelerated ) and then focussed onto the entrance of the reaction 3 (x5) by lens (L chamber. After passing through the Einzel lens (L4), the electron beam collides with the sample molecules in the collision chamber which Is at ground potential. The kinetic energy of the incident electrons Is 3 keV in the collision region. The electron beam then passes through a zoom, 6 and energy—add, lens (L5). The design of the analyzer entrance lenses (L 2 and L3) and a ) is similar to that of the monochromator exit lenses (L 7 L virtual slit is employed. In the present work, the pass energy of the  45 analyzer was always set to be equal to that of the monochromator. The inelastically scattered electrons are energy analyzed before being detected by the channel electron multiplier (Mullard B4 1 9AL) which Is mounted just behind the analyzer exit aperture. Hydrogen—annealed mumetal enclosures located outside the vacuum housing provide magnetic shielding in various regions of the spectrometer. Seiko—Seiki (STP 300 and 400) magnetic levitation turbo molecular pumps have been used to establish a clean vacuum environment. The spectrometer is tuned up by using the primary (unscattered) electron beam which is directed to the cone of the channeltron with ) and the 7 energy analyzer deflection voltages, lens voltages (Li to L ciuadrupole deflectors (Q1 to  Q).  The quadrupole deflectors each consist  of two pairs of electrostatic plates in the x and y directions. ) to monitor the 8 Electrometers are connected to the apertures (Pi to P collimation and direction of the electron beam, while a floated vibrating reed electrometer (Cary, model 401) is used to measure the small currents on the cone of the channeltron. In the present work, the lens voltages (Li to L ) were recorded after the initial tuning of the 7 spectrometer for a given resolution (which is set by pass energy of the energy analyzers). The same lens voltages were then used for subsequent measurements performed at the same energy resolution. This procedure was used in order to ensure the same half—angle of acceptance 00 of the analyzer/detection system (which may be changed by different lens voltages) at a given resolution. To obtain an energy loss spectrum, a voltage corresponding to the energy loss of the inelastically scattered electrons is added to the lens L5 and to the complete analyzer and detection system. The inelastically scattered electrons thus regain their  46 energy loss and are transmitted to the detector. At the same time, the primary (incident) electron beam gains the same energy and is strongly defocused by the advanced electron optics at the input of the analyzer. This results in a strong suppression of the primary, unscattered, beam and permits operation at zero degree scattering angle. High gain pre amplifier and amplifier/discriminator units (PRA models 1762 and 1763 respectively) are employed to process the signals coming from the channeltron. The signals are collected using a Nicolet 1073 signal averager operated in a multichannel scaling mode. The data are then transmitted to the PDP 11/23 computer which is also used to control the scanning voltages on L5 and the analyzer of the spectrometer as well as the channel advance of the signal averager. The energy resolution AE (FWHM) of the spectrometer depends on the selected pass energies E for both the monochromator (Em) and analyzer (Ea). The theoretical resolution (neglecting angular effects) for a hemispherical analyzer is given [9 ii by zEw ---—-  (3.1)  where w is the slitwidth and r is the mean radius. For the combining monochromator and analyzer the individual resolution functions must be added quadrature. The observed halfwidth of the monochromated and analyzed primary beam at a pass energy of 10 eV is 0.036 eV in excellent agreement with equation 3.1. Under these conditions the halfwidth of the inelastically scattered beam originating in the collision chamber, is somewhat larger (0.048 eV FWHM) due to the additional angular spread.  47  3.3 ExperImental Considerations and Procedures The high resolution dipole (e,e) spectrometer had been used extensively in recent years for the measurement of high resolution valence shell [32—341, and inner she1l [32,34,35] excitation spectra. However, prior to the present work no attempt had been made to quantitative measurements of absolute oscillator strengths because the Bethe—Born factor of the spectrometer was not known. In order to obtain absolute optical oscillator strengths from the high resolution EELS spectra, an absolute scale must be established, and in addition the energy dependent Bethe—Born conversion factor for this high resolution spectrometer (BHR) must be determined. The conversion factor is in practice more complex than that given by the single expression in equation 2.24 because it must account for integration over the finite spectrometer acceptance angles about 0=00 (see equation 2.28). A sufficiently exact knowledge of the effective acceptance angles would require a very accurate and detailed understanding of the complex electron optical functions of the lenses in all regions of the high resolution dipole (e,e) spectrometer as a function of energy loss. Furthermore, this detailed information would be required for each analyser/monochromator pass energy combination selected to provide a given energy resolution. Such detailed information is difficult to obtain with sufficient precision by model calculations for the complex electron optics in this type of instrument. A better and more feasible approach [37] is to calibrate the intensity response of the high resolution instrument and obtain an  48 empirically determined, relative, Bethe—Born factor by referencing the high resolution EELS signal to the known optical cross section in the smooth photolonization continuum spectral region of a suitable gas. This could be achieved by taking the ratio of the high resolution EELS intensity to that of an independently measured absolute photoabsorption cross section, as a function of energy loss (photon energy). An obvious choice for this calibration Is helium gas. Recommended experimental va1ues of absolute photoabsorption cross section for the helium continuum have been tabulated by Marr and West [47] from a consideration of a large number of published optical experiments. We have, however, chosen an alternative and entirely independent approach, in which the high sensitivity low resolution (—1 eV FWHM) dipole (e,e) spectrometer (described In section 3.1), with no monochromator, simpler optics and collision geometry. and a well characterised Bethe— Born factor (BLR) [24—30], has been used to obtain a new wide range measurement of the helium discrete and continuum absolute photoabsorption oscillator strengths, entirely independent of any optical measurement. It has been found [14,30] that TRK sum rule normalization of Bethe—Born converted EELS spectra obtained on this low resolution dipole (e,e) spectrometer provides a highly accurate absolute photoabsorption oscillator strength scale, without the need for any measurement of beam flux or target density. Helium is a particularly suitable choice for the calibration measurements since it Is has only a single (1 s ) shell and thus no shell separation or corrections for Pauli 2 excluded transitions are required for the TRK sum rule procedure, in contrast to the situation for more complex targets.  49 The absolute photoabsorption oscillator strengths obtained on the low resolution dipole (e,e) spectrometer may then be used to generate the relative Bethe—Bom factor for the high resolution instrument by taking the ratio of the signals In the smooth continuum region above the first ionization energy of helium, as described above. The relative Bethe— Born factor for the high resolution spectrometer can then be obtained at lower energies by extrapolation of a suitable function (see chapter 4) fitted to the measured factor in the region above 25 eV. Finally, the Bethe—Born converted high resolution EELS spectrum of helium was placed on an absolute scale by single point normalization in the continuum (at 30 eV) to the absolute optical oscillator strength determined using the low resolution dipole (e,e) instrument. Employing these procedures, both the Bethe—Born calibration and the measurement of absolute optical oscillator strengths is achieved entirely independently of any optical techniques. Furthermore, exploitation of the TRK sum rule avoids the difficulties and limitations of conventional methods of absolute scale determination. The resulting absolute measurements can thus be independently compared with published values of measured and calculated optical oscillator strengths for helium. The sequence of measurements and procedures used in the present work are summarised by the flow chart shown in figure 3.3. Similar procedures have been performed using the measurements for neon [38], and the values obtained for BHR are in excellent agreement with those using helium. The average of the two determinations provides further statistical precision, and this average value has been used In the high resolution absolute oscillator strength work performed with the high resolution dipole (e,e) spectrometer. The averaged BHR also  50  Figure 3.3: Flow-chart showing the data recording and processing procedures used in  determining the absolute dipole oscillator strengths for the discrete P, n=2—7) of helium. 1 electronic excitation transitions (1 ‘S—n  51 provides increased reliability when the curve above 25 eV is fitted and extrapolated down to equivalent photon energies as low as 5 eV. The high resolution electron energy loss spectra of the three heavier noble gases (Ar, Kr and Xe) and five diatomic gases (H2, N , 02, CO and NO) 2 have been converted to relative oscillator strength spectra using the Bi-ij factor obtained as described above. The absolute scales were then obtained by normalizing in the smooth continuum to the data determined using the low resolution dipole (e,e) spectrometer. Low resolution dipole (e,e) measurements have been made in the present work for the argon, krypton and xenon. However, the TRK partial valence shell sum rule normalization procedures used to establish the absolute scales for helium and neon could not be used for the heavier noble gases since the successive atomic inner subshell energy separations are relatively small and thus a good fit to the valence shell tail is not possible. In these circumstances the extrapolation procedures used to estimate the amount of valence shell oscillator strength above a certain energy become unreliable. Therefore, the alternative procedure of single point normalization to a previously published photoabsorption measurement has been used to establish the abso1ute scale for argon, krypton and xenon. For the five diatomic gases, low resolution dipole (e,e) oscillator strength measurements have been previously reported [86,87,92,93]. The TRK sum rule normalization procedures were used to establish the absolute scale for the measurements of hydrogen [86], oxygen [921 and nitric oxide [93]. In contrast, single point normalization procedures were used for the earlier reported measurements for nitrogen and carbon monoxide [871 since the data were only obtained up to 70 eV energy and hence sufficiently accurate extrapolation procedures could not be carried  52 out. Therefore in the present work, new wide ranging low resolution dipole (e,e) measurements of nitrogen and carbon monoxide have been performed up to an equivalent photon energy of 200 eV. The TRK partial valence shell sum rule has now been employed In order to establish the absolute oscillator strength scale for these new measurements for nitrogen and carbon monoxide. Thus, the presently determined absolute optical oscillator strength data for all five diatomic gases at both high and low resolution are completely independent of any directly obtained optical data. For quantitative measurements it is essential to ensure that saturated count rates are obtained in the channeltron detectors of both spectrometers over the full dynamic range of the signals. In order to avoid dead—time errors it was also necessary to use a fast data buffer between the output of the high resolution spectrometer and the PDP 11/23 computer. Since for the high resolution instrument no fast MCA compatible with the PDP 11/23 computer was available, a specially adapted Nicolet 1073 signal averager was used as the data buffer in the present work. Maximum count rates were restricted to a maximum of 20000 per second in order to ensure linearity over the full dynamic range of the spectra.  3.4 Energy Calibration The absolute energy scale of the electron energy loss spectrum of helium measured using the high resolution dipole (e,e) spectrometer was obtained by referencing to the 1 2 S —’2 1 P transition of helium at 21.218 eV. For the other gases, the absolute scale was established in separate  53 experiments by simultaneous admission of helium and referencing the sample spectrum to the 21S21P transition of helium at 21.2 18 eV [54]. In practice, the calibration corrections were found to be O.015 eV. The energy scale for the low resolution dipole (e,e) measurements was obtained by referencing the energy position of a prominent spectral feature to the corresponding peak in the high resolution electron energy loss spectrum.  3.S Sample Handling and Background Subtraction The sample gases studied in the present work were obtained commercially. Their sources and stated minimum purities are summarized in table 3.1. No impurities were apparent in the high resolution electron energy loss spectra. Appropriate gas regulators were used to establish a steady gas flowrate and sample introduction to the spectrometers was achieved using Granville—Phillips series 203 stainless steel leak valves. Ambient gas pressures were adjusted to be in the range 0.5—2.0 x1O torr and 0.1—1.0 x1O torr for the high resolution and low resolution spectrometers, respectively, by using the Granville—Phillips leak valves. It is important to maintain single collision conditions and no evidence for double scattering was found In the energy loss spectrum under the selected conditions. Contributions to the electron energy loss spectra from background gases remaining at the base pressures (2x10— 7 torr) of the turbo molecular pumped spectrometers and/or non—spectral electrons were removed by subtracting the signals obtained when the sample pressures were quartered. Such procedures were used because complete remova1  54 of the sample gas was found to influence slightly the tuning of the energy loss spectrometers.  Table 3.1: Sources and stated minimum purity of samples  Sample  Source  Stated minimum purity_(%)  He  Linde  99.995  Ne  Matheson  99.99  Ar  Linde  99.998  Kr  Linde  99.995  Xe  Matheson  99.995  2 H  Linde  2 N  Medigas  99.0  2  Medigas  99.0  cO  Matheson  99.5  NO  Linde  98.5  99.95  55 Chapter 4  Absolute Optical Oscillator Strengths for the Electronic Excitation of Helium  4.1 Introduction The availability of very accurate quantum mechanical calculations, together with the fact that helium has only a K shell and thus a total oscillator strength of exactly 2, with no corrections needed for Pauli excluded transitions [52,53], makes the dipole excitation of ground state helium an ideal test case for the high resolution dipole (e,e) method. In addition further consistency checks can be made involving oscillator strength sums in appropriate regions of the discrete and continuum spectrum. In the present work, test measurements, involving a comp1etely independent determination of the absolute optical oscillator S—’n series (n=2—7) for helium, are compared with P strengths for the 1 1 previously published experimental data for n=2 and 3 obtained using a range of optical [56—64] and electron impact [19,68,84] methods. The measured results n=2—7 are also compared for with high level quantum mechanical calculations employing correlated wavefunctions [3—9,54]. The present measurements represent the first absolute experimental results for n=4—7 and very few previous measurements for n=3 have been reported. Measurements of the absolute continuum photoabsorption oscillator strengths up to 180 eV photon energy, including the Fano profile resonance regions of double excitations around 60 eV and 70 eV, were also obtained and are compared with existing direct optical  56 measurements [94—97] and calculations [9,98—100]. The results for helium are used to establish the viability of the high reso1ution dipole (e,e) method for general application to measurements of absolute optical oscillator strengths in the discrete valence shell spectral regions of electronic excitation for atoms and molecules.  4.2 Results and Discussion 4.2.1 Low Resolution Optical Oscillator Strength Measurements for Helium Using the low resolution dipole (e,e) spectrometer, electron energy loss measurements were performed in the energy ranges 20—25.5, 25.5— 50, 50—110 and 110—180 eV at intervals of 0.1, 0.5, 1, and 2 eV respectively. The energy resolution was  1 eV FWHM. Absolute optical  oscillator strengths for helium were obtained by Bethe—Born conversion (using BLR, see figure 3.3) and TRK sum rule normalization (to a value of two) of the electron energy loss data as described above. The portion of the relative oscillator strength from 180 eV to infinity was first estimated by extrapolation of a least squares fit to the measured data In the 72—180 eV region using a function of the form AE-B (E=energy and A and B are best fit parameters). The fit gives B=2.5583 and the fraction of the total oscillator strength above 180 eV was estimated to be 4.65%. The helium 1 1S_2 1 P transition (21.218 eV) was used for calibration of the energy scale of the spectrum and is the only discrete structure resolved at the resolution of this spectrometer. The measured data is recorded in table 4.1 and illustrated in figure 4.1 (solid circles). Also shown on figure 4.1  57  1 ft  • X 3 67  > Z’P  •.0  ‘i  :  •.1  0  04 •••6  0.3  0  20  ..,  300  320  to  0  tao  t€o  C.) V U) U) Cl)  0.•  I’ II II  ‘-4  H ej  .4  *  4 II I,  —‘  ,0  a ...a  20  a)  30  ‘-4  C.)  U)  •  I  0  .4-’  LR Dipole (e,e) this work Marr and West [47) Fernley et al. [9)  0  a  10f  (sp,22+)Ip.  C-) C,)  0 •  •  h.  C-)  ô .À. ,  a  .4-’  0  0 10  •  •4 •*. •  •  I  20  30  40  50  60  70  80  90  100  Photon energy (CV)  Figure 4.1: Absolute dipole oscillator strengths for helium measured by the low resolution dipole (e,e) spectrometer from 20—180 eV (F’WHM=1 eV). Solid circles are this work, open triangles are photoabsorption data of Marr and West [471, solid line is theory, Fernley et al. [91.  58 Table 4.1 Absolute differential optical oscillator strengths for helium obtained using the low resolution (1  cv  FWHM) dipole (e,e) spectrometer (24.6—  180 CV)  Energy  Oscillator  Energy  Oscillator  Energy  Oscillator  (eV)  Strength  (eV)  Strength  (eV)  Strength eV2 (10 ) 1  eV 2 (10) 1  eV’) 2 (10  24.6  7.05  29.5  5.12  38.0  3.21  24.7  6.96  30.0  4.98  38.5  3.11  24.8  6.85  30.5  4.92  39.0  2.97  24.9  6.76  31.0  4.65  39.5  2.89  25.0  6.62  31.5  4.57  40.0  2.90  25.1  6.71  32.0  4.45  40.5  2.76  25.2  6.66  32.5  4.34  41.0  2.73  25.3  6.58  33.0  4.26  41.5  2.63  25.4  6.58  33.5  4.07  42.0  2.54  25.5  6.55  34.0  3.95  42.5  2.56  26.0  6.37  34.5  3.87  43.0  2.46  26.5  6.08  35.0  3.81  43.5  2.42  27.0  5.94  35.5  3.63  44.0  2.33  27.5  5.81  36.0  3.55  44.5  2.26  28.0  5.61  36.5  3.49  45.0  2.25  28.5  5.45  37.0  3.40  45.5  2.23  29.0  5.33  37.5  3.32  46.0  2.14  59 Table 4.1 (continued)  Energy  Oscillator  Energy  Oscillator  Energy  Oscillator  (eV)  Strength  (eV)  Strength  (eV)  Strength  eV2 (10) 1  eV 2 (10 ) 1  eV 2 (10 ) 1  46.5  2.04  63.0  1.14  83.0  0.598  47.0  1.97  64.0  1.11  84.0  0.569  47.5  2.00  65.0  1.08  85.0  0.557  48.0  1.92  66.0  1.05  86.0  0.540  48.5  1.90  67.0  1.01  87.0  0.529  49.0  1.89  68.0  0.968  88.0  0.508  49.5  1.75  69.0  0.926  89.0  0.491  50.0  1.77  70.0  0.912  90.0  0.475  51.0  1.68  71.0  0.869  91.0  0.464  52.0  1.63  72.0  0.850  92.0  0.448  53.0  1.56  73.0  0.822  93.0  0.429  54.0  1.52  74.0  0.785  94.0  0.421  55.0  1.48  75.0  0.757  95.0  0.412  56.0  1.43  76.0  0.735  96.0  0.397  57.0  1.40  77.0  0.708  97.0  0.388  58.0  1.37  78.0  0.698  98.0  0.393  59.0  1.43  79.0  0.669  99.0  0.370  60.0  1.61  80.0  0.652  100.0  0.360  61.0  1.18  81.0  0.632  101.0  0.341  62.0  1.11  82.0  0.612  102.0  0.350  60 Table 4.1 (continued)  Energy  Oscillator  Energy  Oscillator  Energy  Oscillator  (eV)  Strength  (eV)  Strength  (eV)  Strength  eV 2 (1O ) 1  eV2 (10) 1  eV2 (1O ) 1  103.0  0.335  136.0  0.168  178.0  0.0856  104.0  0.326  138.0  0.162  180.0  0.0824  105.0  0.321  140.0  0.155  106.0  0.302  142.0  0.147  107.0  0.314  144.0  0.144  108.0  0.310  146.0  0.138  109.0  0.288  148.0  0.136  110.0  0.284  150.0  0.130  112.0  0.273  152.0  0.125  114.0  0.262  154.0  0.123  116.0  0.250  156.0  0.118  118.0  0.240  158.0  0.112  120.0  0.232  160.0  0.109  122.0  0.219  162.0  0.106  124.0  0.211  164.0  0.106  126.0  0.204  168.0  0.0998  128.0  0.194  170.0  0.0980  130.0  0.187  172.0  0.0932  132.0  0.181  174.0  0.0916  134.0  0.173  176.0  0.0893  o (Mb)  =  1.0975 x 102-eV1  61 are “recommended values” of the absolute photoabsorption (photolonization) oscillator strengths of helium (open triangles) reported in the compilation by Marr and West [471. The values compiled In reference [47] were obtained by Marr and West as follows: Various optical measurements of the photoionization cross sections of helium In different energy ranges have been reported by different groups using optical methods [45,101,1021. West and Marr [103] have also themselves measured the photoionizatlon of helium in the 340—40A (35—3 10 eV) range using synchrotron radiation. There are some slight discrepancies between the different data sets in some energy ranges. A critical evaluation of the various cross section measurements was carried out [103] by giving a weight to the various data sets according to criteria such as the scatter of data points, performance and quality of the monochromator used  .. . .  etc. Then all the data was combined and the  “best values” were obtained by fitting polynomials to the weighed data points. The resulting absolute photoionization cross section data for helium and also for other noble gases in the vacuum UV and soft x—ray regions were then tabulated [471. It can be seen from figure 4. 1 that the presently reported Bethe Born converted, TRK sum rule normalised, low resolution dipole (e,e) results are generally in good quantitative agreement with the absolute photoabsorption data recommended by Marr and West [47], from a consideration of a range of published results. It should be noted that the dipole (e,e) and direct photoabsorption techniques are physically different and also that the associated methods of obtaining the absolute scales are completely different. The good agreement therefore provides convincing proof of the validity of the Bethe—Born theory and the  62 quantitative equivalence of the dipole (e,e) and photoabsorption (photolonization) methods at least in the continuum region. In the region near 60 eV the dipole (e,e) data show evidence of the well known double excitation resonances of helium whereas the Marr and West data [47] were obtained by fitting a smooth curve through the resonance region. Notwithstanding the excellent overall quantitative agreement some small differences in shape are apparent. In particular, the Marr and West data [47] are slightly below and slightly above the present data in the 30—40 eV and 80—180 eV regions respectively. Also shown on figure 4.1 are the very accurate photoionlzation (equivalent to photoabsorption for helium) oscillator strength (cross section) calculations for helium recently reported by Fernley et aL. [9] (solid line). The calculated data [9] have been shifted up in energy by 0.280 eV as the first ionization energy of helium calculated by Fernley et al. [9] is 0.280 eV lower than the accurately known spectroscopic value (24.59 eV). It can be seen that the oscillator strength calculations [91 are in excellent agreement with the present dipole (e,e) measurements. Similar calculations were reported earlier by Cooper [104] and by Bell and Kingston [105]. The presently obtained low resolution dipole (e,e) measurements (table 4.1, figure 4.1) have been used to obtain the Bethe—Born conversion factor (BHR) for the high resolution spectrometer and for normalization of the high resolution spectrum of helium (at 30 eV). The high resolution oscillator strength results are presented in the following section.  63 4.2.2 High Resolution Optical Oscillator Strength Measurements for Helium S—’n (n=2 to 7) 1 4.2.2.1 The Discrete Transitions P Using the high resolution electron energy loss spectrometer. electron energy loss spectra of helium were obtained at an Impact energy of 3000 eV in the energy loss range 20—60 eV at a resolution of 0.048 eV FWHM and in the range 20—100 eV at resolutions of 0.072, 0.098, 0.155 and 0.270 eV FWHM. The data have been processed using the procedures outlined in section 3.3. The intensity of the high resolution electron spectrum at each energy loss in the smooth continuum region above 25 eV was divided by the absolute optical oscillator strengths measured by the LR dipole (e,e) spectrometer (see section 4.2.1, table 4.1 and figure 4.1). This quotient provided a relative Bethe--Born conversion factor (BHR, see figure 3.3) for the high resolution instrument in the energy range above 25 eV. In order to extend this Bethe—Born factor to the excitation region below 25 eV, the quotient has been fitted to a suitable function (which effectively represents the Bethe—Born correction factor for the HR spectrometer) over the energy range 28-60 eV, which can then be extrapo1ated to lower energy. This fitting and the extrapolation must be done very carefully if correct experimental dipole oscillator strengths are to be obtained in the discrete excitation region down to 21 eV for helium and to even lower energies (5 eV) for other atoms and molecules. In particular the effects of finite angular resolution about the forward scattering direction must be properly accounted for in the Bethe—Born conversion factor if it is to be accurate over the long  64 extrapolation down to 5 eV. Therefore the effects of angular resolution must be accounted for in some way in the fitting function [14]. In the real situation of finite acceptance angles, the Bethe—Born conversion factor has been derived as shown in equation 2.28. At sufficiently high impact energy and k —k, equations 2.24 and 2.28 can be combined to 0 give  —  d O 2 e(E)/ /dEdQ  A —  a  1  ALA  /  0  2 —  1  I  +  00 (4.1)  —  df(E)/ /dE  x  where F(E) is equal to 1 /B(E) and a is a constant. Thus we might expect a function of the form of the right hand side of equation 4.1 to fit the ratio of the high resolution electron energy loss spectrum to the absolute optical oscillator strength. While the use of equation 4.1 gave a quite reasonable fit, in practice a further improved fit to the ratio F(E) in the continuum (28—60 eV) was obtained by adding an energy dependent term to the constant a on the right hand side of equation 4.1 to give  F(E)  =  d e 2 (E)/ /dEdQ dfo(E)/  2 =  a + cE  E  in  1 +  (4.2)  /dE  In this equation a and c are constants. (F(E) is equal to 1 /Bj  —  see figure 3.3). Values of a, c and 00 were determined from a least squares best fit. The value of the half angle 0 was found to be approximately 0.17 degrees. At each resolution a function of this form  65 fitted the data very well over the range 28—’60 eV and was extrapolated to lower energies in order to convert d cTe(E)/dEdQ for the discrete 2 transitions in helium to a relative optical oscillator strength scale. The effectiveness of the extrapolation method employed has been examined by comparing the shapes of the photoabsorption oscillator strength curves down to 5 eV for a range of molecules (02 [42], NO [441 and also 0, CO 2 N 2 and H 0 [1061), obtained using the high resolution dipole (e,e) 2 method, with those obtained earlier using the low resolution dipole (e,e) method [30]. The oscillator strength distributions of the high and low resolution dipole (e,e) spectra are consistent for each molecule for energies down to 5 eV when the differences in energy resolution are considered. Further confirmation of the accuracy of the high resolution Bethe—Born conversion factor at low energies is provided by the very good agreement between the high resolution dipole (e,e) and photoabsorption measurements for 02 [421 and NO [441. It should be noted that the exact form of BHJ changes for the different resolution settings of the spectrometer. These Bi-m factors will be used for future oscillator strength measurements of other atoms and molecules. The high resolution energy loss spectra of helium were multiplied by the appropriate BHR function in order to obtain relative optical oscillator strength spectra which were then normalised in the continuum region at 30 eV using the absolute data of table 4.1, as determined using the low resolution spectrometer. A typical result at an energy resolution of 0.048 eV FWHM is shown in figure 4.2, which is the first reported absolute optical oscillator strength spectrum of helium covering the range n=2—7 of the optically allowed discrete transitions (1 1 S—n P ) preceding the first ionization threshold. Over the near threshold  66  -4  •> a.) 0 .— C.) V 11) U)  ‘Sto a)  U)  1  0  ‘-4  U)  C.)  I  0  0  C.)  ‘-4  0  U)  0  I  C)  C  20  22  24  26  28  30  Photon energy (eV)  Figure 4.2: Absolute dipole oscillator strengths for helium measured by the high resolution electron energy loss spectrometer from 20—30 eV (FWHM=0.048 eV). Solid line above the ionization edge on X8 spectrum is photoabsorption data from Marr and West [47] and Fernley et al.  19].  67 continuum region (24.6—30 eV) there is excellent quantitative agreement (see Insert to figure 4.2) between the present work and the photoabsorption measurements compiled by Man and West [47] and also the continuum calculations reported by Fernley et al. [91 (the data of references [9,47] are both represented by the same solid line). P series are resolved. A very small peak 1 Transitions up to n=7 for the n barely visible at 20.6 eV represents a contribution from the dipole forbidden 1 l5_.2 is transition due to the finite (but very small) momentum transfer of the dipole (e,e) experiment. This non—dipole P peak. 1 contribution is less than 0.5 percent of the 2 Integration of the peak areas in each spectrum, such as that in figure 4.2, provides a measure of the absolute oscillator strengths for S—’n’P series. An analysis of the each discrete transition in the 1 spectra obtained at a series of different energy resolutions results in the values shown in table 4.2. The uncertainties quoted represent the scatter in the measurements made at different resolutions. The absolute uncertainty is estimated to be —5%. Other than the relative values for n=3 and 4 reported by Jongh and Eck [62], previously reported work (see table 4.2) has been confined to absolute values for n=2 and a few measurements [19,57,64,85] for n=3. The present data which extend to n=7 represent the first measured values above n=3. Various other calculated and measured values for the helium 1  series are shown  in table 4.2. Immediately it can be seen that the present high resolution dipole (e,e) measurements are in excellent agreement across the range of n values with the calculations for helium reported by Schiff and Pekeris [4], Fernley et al. [9] and others [3,5—8,54] (see table 4.2). The earlier electron impact measurements of Lassettre et al. [68] for n=2 and of  0.00593 0.00848 0.0 153  0.0299 0.0302  0.0734 0.0734 0.00734 0.0746  0.276 0.2762 0.02762 0.270  Dalgarno and Parklnson(1966) [61  Wiese, Smith and Glennon(1966) [541  Schiff and Pekeris( 1964) 141  Dalgarno and Stewart(1960) [31  0.0 153  0.00878  0.0054 0.0086 0.015 1  0.02959  0.07294  0.27562  Green etal.(1966) [51  0.0304  0.00525 0.00846 0.01484  0.0303  0.0732  0.2760  Welss(1967) [71  0.0 15  0.030  0.073  0.2762  0.005469  7’P  Schiff, Pekeris and Accad(1971) [81  0.008734  P 1 6  0.03028  0.0 1524  p 1 5  0.07434  p 1 4  0.2811  31p  S to Oscillator Strength for Transition from 1 1  Fernley, Taylor and Seaton(1987) [91  A. Theory:  2’P  —’nlP, n= 2 to 7) transitions in heliumt (1 S 1  Theoretical and experimental determinations of the absolute optical oscillator strengths for the  Table 4.2  0.424  Threshold  Ionization  Total to  C)  (0.003)  (0.008) 0.262 (0.018) 0.276  (Self absorption)  Westerveld and Eck( 1977)1631  (Self absorption)  Backxetal.(1975) [851  0.076  0.276  Jongh and Eck(1971) [621  0.269 (0.01) 0.27 (0.01)  Lassettre et al.(1970) [681  (Electron impact)  Martinson and Bickel(1969) [581  (Lifetime: Beam foil)  (0.004)  (0.005)  (0.007)  (Lifetime: Level-crossing)  (Self absorption)#  0.073  0.275  Burger and Lurio(1971) 1571  (Electron impact)*  (0.002)  0.029  0.071  0.273  Tsurubuchl et aL(1989) [641  0.073  (0.0003)  (0.0007)  (0.0007)  Present work (HR dipole (e,e)) (0.007)  P 1 5  0.0152  P 1 4  0.0303  P 1 3  0.0741  P 1 2  (0.006) (0.0003)  (0.0005)  0.421  0.431  Threshold  0.00587  P 1 7  Ionization  Total to  0.00892  P 1 6  S to Oscillator Strength for Transition from 1 1  0.280  B. Experiment  Table 4.2 (continued)  0) CD  (0.011) 0.26 (0.07) 0.28 (0.02)  (Lifetime: Hanle effect)  LlnckeandGriem(l.966)(59J  (Plasmas emission profile)  Korolyov and Odintsov(1964) 1601  (Beam emission profile)  (0.03) 0.312 (0.04)  (Resonance broadening emission profile)  Gelger(1963) 1191  (Electron impact)  (0.006)  0.0898  P 1 3 P 1 5  Relative measurements normaltzed to the theoretical value for n=2 reported by Schiff and Pekeris (1964) 141.  # Relative measurements normalized to the theoretical value for n=2 reported by Weiss (1967) [7).  *  P 1 4 6’P  Oscillator Strength for Transition from 1 1 to  + Estimated uncertainties In experimental measurements are shown in brackets.  0.37  Kuhn and Vaughan(1964) 1611  (0.012)  0.26  0.273  P 1 2  Fry and Wllliams(1969) 156)  B. Experiment : (continued)  Table 4.2 (continued)  P 1 7  Threshold  Ionization  Total to  C  71 Backx et al. [85] for n=3 respectively, are reasonably consistent with the present more comprehensive work. The slightly lower value obtained for n=2 by Lassettre et al. [68] may reflect the difficulties of extrapolation to O (see section 1.4). The electron impact data for n=2 and 3 reported K = 2 by Geiger [19] show large departures from the present data and also from the calculations [3—9,54]. This could partly be due to the normalization procedure used by Geiger [191, which was based on elastic scattering values, but as Lassettre [681 has pointed out the ratio of the values for n=2 and 3 reported by Geiger shows a significant departure from the ratio of the calculated oscillator strength values [3—9,54]. The various optical measurements are in almost all cases restricted to n=2 [56,58—61,63] and in general are reasonably consistent with the present measurements and with theory [3—9,541. The Hanle effect measurement for n=2 reported by Fry and Williams [56] and the level crossing lifetime measurements reported for n=2 and 3 by Burger and Lurio [57] would seem to be the most accurate optical determinations. To the best of our knowledge, no Beer—Lambert law photoabsorption measurements have been reported for the helium discrete transitions, probably due to the bandwidth! un ewidth difficulties or “line—saturation” effects discussed in section 2.3. Such effects would be particu1arly difficult to avoid for the intense and extremely narrow lines in the helium resonance series. The self—absorption method used by Jongh and Eck [62], Westerveld and Eck 163] and Tsurubuchi et al. [64] is not subject to “line saturation” effects but unfortunately like most other optical methods it is restricted in its application to the lower n values. A further interesting check on the presently reported data is the integrated oscillator strength for the discrete region up to the first ionization threshold. The value of 0.431  72 obtained in the present work is in good agreement with earlier estimates of 0.424 [6], 0.421 [85] and 0.427 [851.  4.2.2.2 The Autoionizing Excited State Resonances The energies and profiles of the well—known autoionizing doubly excited state resonances of helium in the 5 9—72 eV energy region have been previously studied in some detail both experimentally [94—97,107] and theoretically [98—100,108]. In the present work, this region containing the autoionizing resonances was remeasured using the HR dipole (e,e) spectrometer at medium resolution. By dividing the HR electron energy loss spectrum at each energy loss in the smooth regions of the continuum by the absolute optical oscillator strength measured by the LR dipole (e,e) spectrometer (see section 4.2.1, table 4.1 and figure 4.1) values of BHR in the energy region of the autolonizing resonances were obtained. A fitted curve through these points permitted interpolated values of BHR to be obtained in a continuous form throughout the resonance region. The Bethe—Born converted relative optical oscillator strength spectrum was norma1ised in the smooth continuum region at 75 eV using the absolute photoabsorption oscillator strength data from table 4.1, as determined by the LR dipole (e,e) spectrometer. The present results for the absolute optical oscillator strengths throughout the region of the autoionizing doubly excited state resonances below the He(2s) and He(3s) thresholds are shown in figures 4.3(a) and (b) respectively. In figure 4.3(a) the absolute oscillator strengths for the autoionizing resonances below the He(2s) threshold calculated by Fernley et at. [9]  73 fl:2  0.05  [Hel  5  0.04 3  0.03  >  4  (sp,2n+)lpo 45  [  3  0.02  2 0  0.01  -‘  1  0 00  66  64  6  C,)  C.) V Cl) Cl) ci, 0  C  0  C  0.015  I-I  C.)  (b)  Cl)  15  [He  C  0 Ci) 0 0  C.)  0 (Sp,33+) P 1 ° (sp,34+) P 1  0.010  1.0  0.5  0.005 69  70  71  72  Photon energy (eV)  Figure 4.3: Absolute dipole oscillator strengths for helium in the autolonizing resonance regions measured by the high resolution electron energy loss spectrometer. (a) in the energy region 58—66 eV; solid circles are this work, solid line is data from Fernley et al. 19] (convoluted with the present experimental bandwidth of 0.115 eV), (b) in the energy region 69—72 eV; solid circles are this work, solid triangles are data of Kossmann et al. 197], open squares are data of Lindle et al. [96], solid line Is theory. Gersbachber et al. [99].  74 (solid line) have been convoluted with a Gaussian of 0.115 eV FWHM, which was used to represent the experimental energy resolution. The energy scale of the data calculated by Fernley et al. [9] has been shifted by +0.280 eV to give a correct energy scale, It can be seen that there is generally excellent agreement in both the shapes and magnitudes of the resonances between the convoluted calculations of Fernley et al. [9] (solid line) and the present experimental work (dots) except for the minimum of the (sp,22÷) IPO state. Slight differences in the energies of the maxima of the resonances are also observed. The energies of the maxima of the (sp,2n+) ipo resonances for n=2 to 5 have been determined In the present work to be 60.150, 63.655, 64.465 and 64.820 eV respectively. These values are in good agreement with previous experimental determinations [94,95,97,98,100]. ° were also 1 The autoionizing resonances (sp,33+) and (sp,34+) P observed in the present work. In figure 4.3(b), the present data (dots) is compared with other experimental results by Lindle et al. [96] (open squares) and by Kossmann et al. [97] (solid triangles) both of whom normalised their results at 68.9 eV using the Marr and West tabulated data [47]. The solid line on figure 4.3(b) represents theoretical values calculated by Gersbacher et al. [991.  4.3 Conclusions The present high resolution dipole (e,e) measurements of optical S—n’P, oscillator strengths for the discrete excitation transitions (1 1 n=2—7), the autoionizing doubly excited state resonances and also the photoionization continuum have considerably extended the range of  75 measured absolute oscillator strength data for the photoabsorption of helium. The presently reported results are all in excellent quantitative agreement with state of the art quantum mechanical calculations carried out using correlated wavefunctions [4—9] and are consistent with most optical and other measurements for those few transitions where previous experimental data were available. These findings confirm the validity of the Bethe—Born approximation and the suitability of the high resolution dipole (e,e) method using TRK sum rule normalization for general application to the measurement of optical oscillator strengths for discrete electronic excitations and ionization in atoms and molecules. The dipole (e,e) method therefore provides a versatile and accurate means of oscillator strength measurement across the entire valence shell region at high resolution and does not suffer from the problems of “line saturation” (bandwidth) effects that can complicate Beer—Lambert law photoabsorption studies for discrete transitions.  76 Chapter 5  Absolute Optical Oscillator Strengths for the Electronic Excitation of Neon  5.1 Introduction Absolute optical oscillator strengths for discrete and continuum electronic excitation of neon are important quantities in areas such as radiation physics, plasma physics and astrophysics. For instance, Auer and Mihalas [1091 have used Ne I oscillator strength data to re—evaluate the abundances of neon in the B stars. Recently there has also been strong interest in the energy levels and oscillator strengths of neon—like systems because of their application in the development of soft X—ray lasers [110]. Discrete oscillator strengths also provide a sensitive test for atomic structure calculations, since the simple LS and  j—j coupling  schemes are not strictly applicable for neon and some sort of intermediate coupling scheme must be used instead [111]. In contrast to the situation for helium, the photoionization cross section maximum of neon is not at threshold, showing a significant departure from hydrogenic behavior due to more prominent electron correlations. Cooper [104] has calculated the oscillator strength distribution for the outer atomic subshefl of neon by assuming an electron moving in an effective central potential similar to the Hartree—Fock potential. McGuire [112], approximating the Herman—Skiliman central field with a series of straight lines, has computed the photoionization cross section of neon with the continuum orbitals calculated from the approximate potential. Kennedy  77 and Manson [1131, utilizing Hartree—Fock wave functions with complete exchange, Luke [1141. employing a multi—configuration close coupling method for the wavefunctions, Burke and Taylor [1151, using the R— matrix theory, and Amus’ya et al. [116] applying the RPAE (random—phase approximate with exchange) method have also calculated photolonization cross sections for neon. Relativistic random—phase approximation (RRPA) calculations carried out by Johnson and Cheng [1171 showed that relativistic effects are small in neon and gave results in good agreement with the non—relativistic RPAE results of Amu&ya et al. [116]. Parpia et al. [118] have also reported the photoionization cross sections of the outer shells of neon using the re1ativistic time—dependent local—density approximation (RTDLDA) method, which is closely related to the RRPA method of Johnson and Cheng [1171. Although the calculated values are much improved with the inclusion of electron correlation, some discrepancies (>15%) still exist between the experimental [21,23,45,47,102,103,119—123]andtheoretical[104—118] photoionization cross sections in certain energy ranges. Experimental total photoabsorption and photolonization measurements for neon in the continuum performed using the Beer— Lambert law [45,47,102,103,119—1221 show good agreement with each other in terms of the shape (i.e. relative cross section). However, the various reported values of the absolute cross sections in the continuum show substantial differences (—10%), probably due to difficulties In obtaining sufficiently precise measurements of the sample target density in a ‘windowless’ far UV system. In addition, inadequately accounted for contributions from stray light and/or higher order radiation will affect measured cross sections. Lee and Weissler [119], and Ederer and  78 Tomboulian [120] have measured the photoabsorption cross section of neon using discharge lamp line sources in the energy ranges 15.5—54, and 20—155 eV respectively. Lee and Weissler [119] recorded the absorption photometrically in a grazing incidence vacuum spectrograph. Ederer and Tomboulian [120] have made measurements combining the conventional photographic recording method with a Geiger—Muller counter for selected wavelengths. Samson [45,121,122] has designed an extremely effective double ion chamber technique which is capable of measuring very accurate photoionization cross sections using either line or continuum sources. Using this apparatus Samson [45,121,122] has reported measurements for neon in the range 21.6—310 eV. Saxon [1241 reviewed the limited neon photoabsorption data available in 1973 and provided a sum rule analysis which suggested that the measured cross sections were reasonably accurate. Wuilleumier and Krause [125] derived 2p, 2s and is subshell partial photoionization cross sections by combining photoelectron branching ratio studies using x—ray line sources with existing total photoabsorption measurements. In addition contributions from multiple ionization were estimated [125]. With the advance of synchrotron radiation (SR), an intense and continuous light source became available for measuring the photoionization cross sections of atoms and molecules up to high energies. However with SR sources very careful work is required to correct for the effects of contributions from stray light and higher order radiation on absolute cross section measurements [126—1281. Watson [102] obtained photoionization cross sections for neon in the 60—230 eV photon energy range. West and Marr [103] not only used synchrotron radiation to make absolute absorption measurements for neon over the range 36—310 eV, but also gave a critical  79 evaluation of existing published cross section data and obtained recommended weighted—average values [47] throughout the vacuum ultraviolet and X—ray region. Electron impact based techniques [21,23,1231 have also been employed to obtain photoionization cross sections of neon. By approximating the generalized oscillator strength (f(K,E) where K=momentum transfer and E=energy) as the optical oscillator strength U(E)) using an impact energy 500—1000 eV and collecting the inelastically scattered electrons at small angles, Kuyatt and Simpson [123] converted the electron energy loss spectrum of neon (up to 100 eV energy loss) to a relative photoabsorption cross section curve. Using high electron impact energy (10 keV) and the calculated scattering geometry of the beam to obtain the relative Bethe—Born factor, electron energy loss results at small momentum transfer have been converted to relative photoionization cross sections for neon by Van der Wiel [21]. Van der Wiel and Wiebes [23] have also studied multiple photoionization of neon using the same method. The relative optical oscillator strength data obtained by the electron impact methods described above were normalized using a literature value of the absolute photoabsorption cross section at a single energy. Apart from the difficulty of measuring an accurate sample density, Beer—Lambert law photoabsorption measurements for the discrete excitation region of neon may also be subject to serious errors due to so— called “line—saturation” (i.e. bandwidth) effects [36,37,46,72] (see chapter 2) since the neon valence shell (2p) electronic transitions have extremely narrow natural line—widths [65, 129—137]. These effects are most significant when the cross section is large and where the bandwidth of the incident radiation is greater than the natural line—widths of the  80 spectral lines being measured. In such situations the oscillator strengths (cross sections) may be much smaller (by as much as an order of magnitude) than the true values unless careful measurements are made as a function of pressure [3 7,46]. Detailed discussions and quantitative assessments of “line saturation” effects have been given in refs. 137,461. Other experimental methods for optical oscillator strength determination which avoid the “line saturation” problems include profile analysis [129,1381, self absorption [62,139,140], total absorption [65], and life time measurements [130—137], as well as the completely independent approach afforded by electron impact based methods using electron energy loss spectroscopy [20,36,37,141,1421. These various optical and electron impact methods have been used in earlier reported work to obtain absolute optical oscillator strengths for neon in the discrete region, but the measurements have been mainly restricted to the 16.67 1 eV (f ) and 16.848 eV (f 1 ) resonance lines corresponding to the 2 5 (2s — 6 2 P 2 ( 3/2,/2)3s) p transitions. Korolev et al. [1291 measured ’2s the transition probability of the f 2 line from the natural broadening profile, while Lewis [138] studied the pressure broadening profile and gave the oscillator strengths for both the f 1 and f 2 resonance lines. The relative self—absorption method was used by Jongh and Eck [62] to measure the oscillator strength of the f 2 resonance line using the calculated oscillator strength of the helium 11S_,21P line as a reference. Westerveld et al. [1391 and Tsurubuchi et al. [140] used the absolute self— absorption method to determine the oscillator strengths of the f 1 and f 2 resonance lines. Aleksandrov et al. [65] employed the total—absorption method to obtain oscillator strengths for various lines in the 20—8Onm (15.5—62 eV) range. Radiative lifetimes for some of the resonance  81 transitions of neon have been determined using: a) a pulsed electron source for excitation and studying the resulting photon decay curve [130,1311; b) the beam foil method [132, 1331; c) the level—crossing technique [134]; d) the phenomena of hidden alignment [1351; e) relaxation upon polarized laser irradiation in a magnetic field [136,137]. Knowing the branching ratios for the resonance lines, the obtained lifetimes can then be converted to the optical oscillator strengths for the respective transitions. In electron impact based studies, Geiger [20] obtained the sum of the absolute photoabsorption oscillator strengths for the f 1 and f 2 resonance lines at low resolution by measuring both the electron elastic scattering cross section and the small—angle inelastic scattering cross section at very high impact energy (25 keV) and normalising on known absolute values of the elastic scattering cross section. Later, Geiger [141] obtained the ratio 1 /f of the oscillator 2 (f ) strengths of the resonance lines using a high resolution electron energy loss spectrometer, and by combining the values obtained from the low resolution spectrometer with this ratio he obtained values for the individual oscillator strengths for the two resonance lines. The electron impact method has also been employed by Natali et al. [142] to measure discrete optical oscillator strengths of neon. The unpublished results of Natalietal. [142] are quoted in refs. [139,143]. A variety of discrete oscillator strength calculations have been reported for neon. Cooper [104], employing a one electron central potential model, Kelly [144], using the Slater approximation to the Hartree—Fock method, and Amus’ya et al. [145], applying the RPAE method, have calculated the oscillator strengths for the transitions from the ground state of neon to the )ns 2 2s 3 P 2 ( 5 1 , 12 p and nd states. Other  82 calculations of the oscillator strengths for individual transitions from the ground state to various 2 2 2s P ( 5 ) ns 3/ p and nd states, and also to 2 2s P 2 ( 5 1/2)ns’ p and nd’ states, have likewise been reported, but In most cases these are only for the transitions to the 5 2 2s P 2 ( 3/2)3s p (fi) and 2 2s P 2 ( 5 1/2)3s’ p (f ) states. The oscillator strengths of the f 2 1 and f 2 resonance lines were calculated by Gold and Knox [1461 using the Hartree Fock equation based on experimental energies and dipole matrix elements computed from theoretical atomic wavefunctions. Gruzdev [111], using the techniques of intermediate coupling and values of the transition integral obtained from the Coulomb approximation, has reported the oscillator strengths for the f 1 and f 2 resonance lines. Aymar et al. [1471 calculated Ne I transition probabilities and lifetimes with the introduction of an effective operator for the angular part of the wavefunctions and a parametrized central potential for the radial part of the wavefunctions. Gruzdev and Loginov [148] carried out a calculation of the radiative lifetimes of several levels of neon with a many—configuration approximation using Hartree—Fock self—consistent field wavefunctions. Albat and Gruen [149] have reported the excitation cross section of the lowest resonance level of neon using a Cl calculation based on the orthogonal set of orbitals obtained from a ground state Hartree—Fock calculation. The time dependent Hartree—Fock equations were also employed by Stewart [150,151] to study the excitation energies and bound—bound oscillator strengths for atoms isoelectronic with neon over a wide range of energies. Aleksandrov et al. [65] not only reported measurements for the discrete oscillator strengths of neon by the total— absorption method, but have also calculated oscillator strengths for the same discrete lines of neon based on an intermediate—coupling scheme  83 with the electrostatic, spin—orbit, and effective Interactions Included in the energy matrices. An examination of the various experimental [62,65,129—1401 and theoretical [104,111,144—151] studies reveals a considerable spread in oscillator strength values for a given transition, even in the case of the Intense f 1 and f 2 resonance lines of neon. Recently, we have reported a new, highly accurate, electron Impact method [36,37] (see chapters 2—4) for obtaining absolute photoabsorption oscillator strengths for discrete excitation processes over a wide spectral range at high resolution. In chapter 4, helium was used to check the accuracy of the new high resolution method [37]. Excellent agreement S—’n (n=2—7) P was found between experiment and theory for the He 1 series as well as in the photoionization continuum and doubly excited state resonance regions [36,371. The new high resolution dipole (e,e) method is now applied to the electronic transitions for neon. In this chapter, we also report measurements of the absolute photoabsorption continuum oscillator strengths up to 250 eV. The absolute scale has been obtained by TRK sum rule normalization and is thus completely independent of any direct optical measurement. The absolute (photoabsorption) oscillator strengths for the dipole—allowed electronic transitions of neon from the 2p 6 subshell to lower members of the 2p 2 2.s n 5 s and 5 2d 2 2s n p ) 312 manifolds have been obtained from P 2 ( 1 , high resolution dipole (e,e) spectra of neon normalised on the low resolution results in the smooth continuum region. The present measurements are compared with other published experimental and theoretical data. Absolute optical oscillator strengths have also been obtained in the energy range 43—55 eV in the region of the Beutler—Fano autoionization resonance profiles arising from processes involving single  84 excitation of a valence 2s electron as well as processes due to double excitation of 2p electrons.  5.2 Results and Discussions 5.2.1 Low Resolution Measurements of the Photoabsorption Oscillator Strengths for Neon up to 250 eV A relative photoabsorption spectrum of neon was obtained by Bethe—Born conversion of an electron energy loss spectrum measured with the low resolution dipole (e,e) spectrometer from 15.7 to 250 eV. This was then least squares fitted to the function AE—B over the energy range 120—250 eV, and extrapolation of the formula gave the relative photoabsorption oscillator strength for the valence shell from 250 eV to infinity. The fit gave B= 1.959 and the fraction of the total valence shell oscillator strength above 250 eV was estimated to be 17.6%. The total area was then TRK sum rule normalized to a value of 8.34, corresponding to the number of valence electrons of neon (eight) plus a small correction (0.34) for Pauli excluded transitions [52,53]. Figure 5.1(a) shows the resulting absolute optical differential oscillator strengths for the photoabsorption of neon below 250 eV. Also shown in figure 5.1(a) are previously reported theoretical and experimental data from the literature [23,45,102,103,112,113,116,118,121,152]. Figure 5.1(b) is an expanded view (on an offset vertical scale) of the spectrum in the energy region 20—60 eV, where in addition to previous experimental data [23,45,47, 103, 121,152], theoretical oscillator strengths from refs. [112— 116,118] are also shown for comparison. Numerical values of the  18  85  (a)  [Ne]  16  18 16  14 0 A  12  I  *  10 8  Present work LR dipole (e,e) West & Marr [47,103] Samson [45,121) Van der Wiel & Wiebes [23] Watson [102] Henke ct a!. [152] Amusya et a!. [116] Kennedy & Manson [113] McGuire [112) Porpic et a!. [118]  14 12 10 8  cv 0  6 6 4  4  C.)  2  2 0  0 C) I  C  50  0  200  250  C)  0  (b)  .-  C.)  100  10  —  0  INel  9 C  0  C  C.)  0  C  8  8 7  . •  o  6  * x C  5 .  — — -  — —  x  0D  Present work LR dipole (ce) West & Mcrr [47,103] Samson [45121] Van der Wiel & Wiebes [23) Henke et al. [152] Burke & Taylor [115] Luke [114] Amusya et a!. [106] Kennedy & Monson [113) McGuire [112] Parplo et a!. [118]  7 ••  A  6  5  4 20  25  30  35  40  45  50  55  60  Photon energy (eV)  Figure 5.1: Absolute oscillator strengths for the photoabsorption of neon measured by the low resolution dipole (e,e) spectrometer (FWHM=1 eV). (a) 15.7—250 eV compared with other experimental [23,45,47,102,103,121,152] and theoretical [112,113,116,118] data. (b) Expanded view of the 20—60 eV energy region compared with other experimental [23,45,47,103,121,152] and theoretical [112—116,118] values. Note offset vertical scale.  86 absolute photoabsorption oscillator strengths for neon obtained In the present work from 21.6 to 250 eV are summarised in table 5.1. From figures 5.1(a) and (b), it can be seen that the presently reported Bethe—Born converted, TRK sum rule normalized results obtained from the low resolution spectrometer are generally in quite good quantitative agreement with the measurements of Samson [45,121], the compilation data of Henke et al. [152] and the earlier electron impact based measurements by Van der Wiel and Wiebes [23]. The data of Samson [45,121] and Henke et al. [152] are slightly higher than the present work in the energy region 60—150 eV, while the results reported by Van der Wiel and Wiebes [23] are lower at energies above 180 eV. The photoionization oscillator strengths for neon measured by Watson [102] In the energy range 60—230 eV are larger than all other reported experimental data below -200 eV but are in better agreement at higher energies. West and Marr [103] measured photoionization cross sections for neon in the energy range 36—3 10 eV using synchrotron radiation and gave a critical evaluation of several published cross section data (including the data of Samson [45,121] and Watson [102]) which they used to obtain “best weighted—average” values [47] throughout the vacuum ultraviolet and X—ray spectra1 regions. However the West and Marr measured and compiled values [47,103] are significantly higher than the present data and than the other experimental data from Samson [45,121], Henke et al. [152], and Van der Wiel and Wiebes [231 in the energy range 35—200 eV. The calculated photoionization cross sections for neon generally show great differences in absolute values between calculations using the dipole—length and dipole—velocity forms. The dipole—length data have  87 Table 51 Absolute differential optical oscillator strengths for neon obtained using the low resolution (1 eV FWHM) dipole (e,e) spectrometer (2 1.6—250  cv)  •  Energy  Oscillator  Energy  Oscillator  Energy  Oscillator  (eV)  Strength  (eV)  Strength  (eV)  Strength  1 e 2 (10) V-  1 e 2 (10) V-  1 e 2 (10 ) V-  21.6  5.75  23.3  6.52  25.0  7.22  21.7  5.88  23.4  6.73  25.5  7.42  21.8  5.82  23.5  6.69  26.0  7.46  21.9  5.86  23.6  6.77  26.5  7.58  22.0  5.98  23.7  6.80  27.0  7.67  22.1  6.00  23.8  6.82  27.5  7.76  22.2  6.05  23.9  6.74  28.0  7.69  22.3  6.10  24.0  6.97  28.5  7.95  22.4  6.15  24.1  7.02  29.0  7.99  22.5  6.22  24.2  7.05  29.5  7.98  22.6  6.25  24.3  7.07  30.0  8.09  22.7  6.35  24.4  7.07  30.5  8.03  22.8  6.40  24.5  7.11  31.0  8.05  22.9  6.47  24.6  ‘7.13  31.5  8.13  23.0  6.60  24.7  7.14  32.0  8.08  23.1  6.55  24.8  7.18  32.5  8.08  23.2  6.55  24.9  7.14  33.0  8.06  88 Table 5.1 (continued)  Energy  Oscillator  Energy  Oscillator  Energy  Oscillator  (eV)  Strength  (eV)  Strength  (eV)  Strength  eV2 (10) 1  eV 2 (10 ) 1  eV-’) 2 (10  33.5  8.10  43.5  7.32  57.0  6.17  34.0  8.00  44.0  7.29  58.0  6.08  34.5  8.14  44.5  7.27  59.0  5.99  35.0  8.08  45.0  7.45  60.0  5.86  35.5  7.96  45.5  7.32  61.0  5.83  36.0  7.88  46.0  7.06  62.0  5.71  36.5  7.83  46.5  7.01  63.0  5.69  37.0  7.90  47.0  6.96  64.0  5.59  37.5  7.92  47.5  7.04  65.0  5.43  38.0  7.86  48.0  6.91  66.0  5.35  38.5  7.80  48.5  6.91  67.0  5.31  39.0  7.73  49.0  6.89  68.0  5.24  39.5  7.76  49.5  6.78  69.0  5.13  40.0  7.72  50.0  6.75  70.0  5.03  40.5  7.62  51.0  6.70  71.0  4.99  41.0  7.52  52.0  6.59  72.0  4.93  41.5  7.50  53.0  6.49  73.0  4.88  42.0  7.42  54.0  6.37  74.0  4.78  42.5  7.39  55.0  6.29  75.0  4.73  43.0  7.35  56.0  6.30  76.0  4.59.  89 Table 5.1 (continued)  Energy  Oscillator  Energy  Oscillator  Energy  Oscillator  (eV)  Strength  (eV)  Strength  (eV)  Strength  eV 2 (10 ) 1  eV 2 (1O ) 1  eV’) 2 (1O  77.0  4.52  97.0  3.37  117.0  2.39  78.0  4.48  98.0  3.25  118.0  2.36  79.0  4.41  99.0  3.22  119.0  2.46  80.0  4.33  100.0  3.19  120.0  2.36  81.0  4.28  101.0  3.18  122.0  2.28  82.0  4.22  102.0  3.09  124.0  2.23  83.0  4.16  103.0  3.10  126.0  2.17  84.0  4.07  104.0  2.99  128.0  2.09  85.0  4.06  105.0  2.94  130.0  2.02  86.0  3.92  106.0  2.84  132.0  1.99  87.0  3.89  107.0  2.83  134.0  1.93  88.0  3.84  108.0  2.90  136.0  1.88  89.0  3.78  109.0  2.81  138.0  1.82  90.0  3.72  110.0  2.71  140.0  1.77  91.0  3.65  111.0  2.67  142.0  1.73  92.0  3.59  112.0  2.63  144.0  1.69  93.0  3.60  113.0  2.59  146.0  1.62  94.0  3.51  114.0  2.67  148.0  1.58  95.0  3.44  115.0  2.58  150.0  1.57  96.0  3.46  116.0  2.55  152.0  1.52  90 Table 5.1 (continued) Energy  Oscillator  Energy  Oscillator  Energy  Oscillator  (eV)  Strength  (eV)  Strength  (eV)  Strength  eV 2 0) (11  eV 2 O ) (11  eV 2 O ) (11  154.0  1.46  194.0  0.915  234.0  0.649  156.0  1.44  196.0  0.887  236.0  0.635  158.0  1.39  198.0  0.906  238.0  0.614  160.0  1.38  200.0  0.857  240.0  0.596  162.0  1.32  202.0  0.848  242.0  0.612  164.0  1.31  204.0  0.826  244.0  0.595  166.0  1.29  206.0  0.823  246.0  0.607  168.0  1.25  208.0  0.786  248.0  0.581  170.0  1.21  210.0  0.792  250.0  0.572  172.0  1.16  212.0  0.791  174.0  1.14  214.0  0.771  176.0  1.13  216.0  0.736  178.0  1.11  218.0  0.740  180.0  1.08  220.0  0.724  182.0  1.06  222.0  0.700  184.0  1.00  224.0  0.703  186.0  1.00  226.0  0.706  188.0  0.981  228.0  0.678  190.0  0.971  230.0  0.684  192.0  0.929  232.0  0.649  o(Mb)  =  1.0975x 102eVl  91 better agreement with the experimental values than the dipole—velocity data. The dipole—length data of McGuire [112], obtained using the H artree—Fock—Slater approach with the Herman—Skiliman central field, show good agreement with the present experimental values from the 2p ionization threshold to 35 eV, but are significantly higher in the region 35—210 eV. Kennedy and Manson [113], employing Hartree—Fock functions with complete exchange, have also reported calculations of the photoionization cross sections of neon from the 2p ionization threshold up to 400 eV. Their dipole—length data [113] give lower results below the 2s threshold and become much higher at higher energies when compared with the present experimental values. Both the McGuire [1121 and Kennedy and Manson [113] data show a lower calculated 2s threshold energy than other theoretical [115] and experimental [153,154] work. The dipole—length data calculated using a Hartree—Fock core as reported by Luke [114] (see figure 5. 1(b)) are considerably higher than all other reported experimental and theoretical data. The R—matrix theory dipole— length results of Burke and Taylor [115] show good agreement with the experimental values at the 2p ionization threshold but agreement becomes worse at higher energies, although below the 2s ionization threshold there is less than 10% difference with the experimental values (note offset intensity scale in figure 5.1(b)). Amus’ya et al. [1161, using the RPAE method, report very close agreement between the dipole— length and dipole—velocity results. However the RPAE calculation [116] shows a shift of several electron—volts from experiment in the photoionization cross section maximum and also the energy of the 2s ionization threshold for neon. The predicted oscillator strengths [116] are also considerably larger than experiment in the energy region 40—100  92 eV. Since the values calculated by Johnson and Cheng [117] using the RRPA method show good agreement with those calculated by Amus’ya et al. [116] using the non—relativistic RPAE method, only values from Amus’ya et al. [116] are shown on figure 5.1. Except in the region near the maximum, the values calculated by Parpia et al. [118] using the RTDLDA method show better agreement with experiment than the other theoretical data [112—117].  5.2.2 High Resolution Measurements of the Photoabsorption Oscillator Strengths for the Discrete Transitions of Neon Below the 2p Ionization Threshold High resolution electron energy loss spectra of neon at resolutions of 0.048, 0.072 and 0.098 eV FWHM in the energy range 16—26 eV were multiplied by the appropriate BHR functions for the high resolution dipole (e,e) spectrometer (see section 3.3) to obtain relative optical oscillator strength spectra which were then normalized in the smooth continuum region at 25 eV using the absolute data of table 5.1, as determined in the present work with the low resolution spectrometer. Figure 5.2(a) shows the typical absolute differential optical oscillator strength spectrum of neon over the range 16—26 eV at an energy resolution of 0.048 eV FWHM. Figure 5.2(b) is an expanded view of the spectrum In the energy region 19.5—22 eV showing the dipole—allowed electronic transitions from the )ns and p 3/2,l/2 2 2s P 2 ( p configuration of neon to members of the 5 6 2 2 2s nd manifolds. Very small peaks, barely visible at 18.96 and 20.38 eV, represent contributions from the dipole forbidden )3p and 4p transitions respectively. These non— s ’2s p 3/2,1/2 5 2 — 6 2 P 2 (  93 4 400  3. 300  2  200  > 100 0  .5  C.)  IC  U) U) U)  C  0  C.)  C  ::  40.4  o  0  0.3  D.2 20  0.1  10  0.0  0 20.5  21.0  Photon energy (eV)  Figure 5.2: Absolute oscillator strengths for the photoabsorption of neon measured by the high resolution dipole (e,e) spectrometer (FWHM=O.048 eV). Assignments are from reference [1551. (a) 16—26 eV. (b) 19.5—22 eV with deconvoluted peaks shown as dashed lines.  94 dipole transitions which occur because of the finite but very small 0.Ola.u.) of the dipole (e,e) experiment, are all (K < momentum transfer 2 2 peak. The positions and assignments less than 0.3 percent of the f [155] of the various members of the nl and nl’ series are indicated on figure 5.2. Above 19 eV the peaks have been deconvoluted as indicated (figure 5.2(b)) to obtain the separate oscillator strengths for the various transitions. Since the peak energies of the nd[ 1/21 and nd[3/2] states 12 limit are very close, especially at 2 3 which converge to the same P higher n values, the two transitions have been treated as single peak in the deconvolution. For peaks in the experimental spectrum which can be completely 2 resonance lines (I.e. the 3s, 35’ lines, figure 1 and f resolved such as the f 5.2(a)), integration of the peak areas provides a direct measure of the absolute optical oscillator strengths for the individual discrete electronic transitions. For the higher energy peaks which cannot be completely resolved, absolute oscillator strengths have been obtained from the deconvoluted peak areas as shown in figure 5.2(b). The accuracy of the presently developed method is confirmed by the consistency of the oscillator strengths determined for given transitions at the three different resolutions. The results obtained from the analysis of the spectrum at the highest resolution (0.048 eV FWHM) are given in tables 5.2, 5.3 and 5.4. The uncertainties are estimated to be —5% for the lower energy resolved transitions and lO% for those such as 6s, 6s’, 5d and 5d’ at higher energies due to additional errors involved in deconvoluting the peaks. Also shown in tables 5.2, 5.3 and 5.4 are the absolute oscillator strength values for several discrete electronic  95 Table 5.2 Theoretical and experimental determinations of the absolute optical (2P3,2,l,2)3S discrete 5 oscillator strengths for the 2S22p6*2s22p  transitions of neon  Oscifiator strength for transition from p where m= 5 2s — 6 2 2 m ’2s 312 P 2 [ ]3s__(i’)  I  112 P [ ) 2 ]3s’__(f  A. Theory: Amus’ya(1990)[145]  0.163*  Kelly (1964) [144]  0.188*  Cooper (1962) [1041  0.163*  Aleksandrovetal.(1983)[65]  0.0106  0.141 0.159  Stewart (1975) [1501 Albat and Gruen (1974) [149]  0.0113  0.149  Gruzdev and Loginov (1973) [1481  0.0106  0.139  (a) dipole length  0.0121  0.16 1  (b) dipole velcity  0.0100  0.130  0.035  0.160  (a)wavefunction  0.011  0.110  (b) semi-empirical  0.0 12  0.12 1  0.01 18  0.159  (0.0006)  (0.008)  0.0122  0.123  (0.0006)  (0.006)  Ayrnaretal. (1970) [147]  Gruzdev (1967) [111] Gold and Knox (1959) [1461  B. Experiment: Present work (HR dipole(e,e))  Tsurubuchiet al.(1990)[140] (Absolute self-absorption) Aleksandrovetal. (1983) [651 (Total absorption)  0.012  0.144  (0.003)  (0.024)  96 Table 5.2 (continued)  Oscillator strength for transition from p 2 2s — 6 2 ..2s  312 P 2 [ ]3s  m where m= 5 112 P 2 [ ]3s’  ) 1 (f  B: Experiment: (continued)  Westerveldetal. (1979)1139] (Absolute self-absorption) Bhaskar and Luiro (1976) [134] (Lifetime: Hanle effect) Knystautas  and  Drouin (1974)  [1321  (Lifetime: Beam foil)  Irwinetal.  (1973)  0.0109  0.147  (0.0008)  (0.0 12)  0.0122  0.148  (0.0009)  (0.0 14)  0.0078  0.161  (0.0008)  (0.011)  [1331  0.158  (0.006)  (Lifetime: Beam foil)  0.158  0.012  Natalietal.(1973)[142] (Electron impact)  0.134  Jongh and Eck (1971) [62]  (0.01 0)  (Relative self-absorption) Kazantsev and Chaika (1971)  [1351  (Lifetime: Hidden alignment) Geiger(1970)[20,l4ll (Electron impact) Lawrence and Liszt (1969) [130] (Lifetime: Delay coincidence) Lewis(l967)[138] (Pressure broadening profile) Korolevetal.  0.0138 (0.0008) 0.009  0.131  (0.002)  (0.026)  0.0078  0.130  (0.0004)  (0.0 13)  0.012  0.168  (0.002)  (0.002) 0.160  (1964)1129]  (Natural broadening profile)  —  tEstimated uncertainties in experimental measurements are shown in brackets. *Total oscillator strength (fj+f ). 2  (0.0 14)  ) 2 (f  0.0238  0.0260  (0.002) (0.0036) (0.0017) (0.0031) (0.0029) (0.0046) (0.006)  (0.0035)  (Totalabsorptlon)  (0  0.005 0.0147 0.0049 0.0083 0.0082 0.0222 0.0185  0.0145  Aleksandrovetal. (1983) [65j  Present work (HR dipole (e,e))  (0.00033) (0.00032) (0.00023) (0.00047) (0.00022)  0.00439  0.0041  (0.0009)  0.00944  0.0091  (0.0008)  0.0046 1  0.0037  0.0032  0.0046  0.0043  (0.0006)  0.00637  0.0058  0.0060  0.00665  0.0081  0.0064  0.0 186  0.0156  0.0164  0.0176  0.0160  0.0 165  0.0121  0.0124  0.0 129  B: Experiment:  (1) IC and HFS  Klose (1969) [1581  (11) IC and CF  (1) IC and HFS  Klose (1969) (1311  Gruzdev and Loginov (1973) [1481#  Stewart(1975)[150)  Aleksandrovetal. (1983) [651  0.020 0.009  0.037  0.026  ’ 12 )4d 1 P 2 (  Cooper (1962) 1104]  12 )4d 3 P 2 (  0.025  1/2)5s’ ( P 2  0.008  I  0.036  12 )5 3 P 2 (  0.029  ’ 72 )3d 1 P 2 (  Kelly (1964) 11441*  I  0.021  12 )3d 3 P 2 (  0.028  1/2)4s’ ( P 2  Amusya(1990)f145]*  A: Theory:  3 12 P 2 ( )4s  ’2s where m is s p p°— 5 2 2 2 2 Oscillator strength from m  tor strengths for Theoretical and experimental determinations of the absolute optical oscilla 1 discrete transitions of neon (19.5—20.9 eV)  Table 5.3  @Recalculated by Westerveld et at. 1139] using branching ratios reported In refs. 11481, (156), and 1157)  reported in refs. 11561 and 1157) #Llfetlme data converted by Westerveld et a!. 1139) to oscillator strengths using transition probabllties  summed oscillator strength as indicated  f Estimated uncertainties In experimental measurements are shown in brackets  (0.00023) (0.0020)  (0.0010) (0.0010)  (0.0025)  (0.0010)  (Lifetime: Laser IrradIation)  (0.0010)  0.0062 0.0068  0.0178  0.0134  0.00598  0.0048  (0.0010)  (0.0010)  (0.0022)  (0.0020)  (0.0010)  0.0164  (0.0010)  0.0057 0.0064  0.0042  (0.0003)  0.0040  0.0043  0.0217  0.006  0.0130  0.006  0.0086  0.016  Decomps and Dumont (1968)E1361  (2)@  (Lifetime: Delay coincidence) (1)  Lawrence and Liszt (1969) [130]  (Lifetime: Delay coincIdence)  Klose (1970) [131]  (Electron impact)  0.013  (0.0030)  (Lifetime: Laser irradiation)  Natalletal. (1973)[142]  0.0153  Ducloy (1973—74)11371  (0.0003)  (0.0005)  (0.0005)  (0.00 12)  (0.0010)  (Absolute self-absorption)  12 )5s’ 1 P 2 (  0.0042  12 )5s 3 P 2 (  0.0061  12 )3d 1 P 2 (  0.0064  0.017  12 )3d 3 P 2 (  0.0153  1/2)4s ( P 2  0.0128  12 )4s 3 P 2 (  0.0085  12 )4d 3 P 2 (  p 2s where m Is 5 2s — 6 2 2 Oscillator strength from m  Westerveldetal.(1979)[139]  B: Experiment: (continued)  Table 5.3 (continued)  0.0043  CD  12 )4d’ 1 P 2 (  0.0031  0.004  Cooper (1962) 11041*  (0.015)  (0.00023) (0.00054)  (0.000 16) 0.003 (0.00 1)  (0.00030) 0.0045 (0.0019)  Aleksandrov et al. (1983) [65]  (Total absorption)  *summed oscillator strength as indicated  tEstimated uncertainties in experimental measurements are shown in brackets  (Electron_Impact)  Natall et al.(1973) [142]  0.277  0.292  Present work (HR dipole (e,e))  0.00229  0.0024  0.00543  0.0050  0.011  Ionization  0.00 156  0.0018  j )5d’ 112 P 2 (  0.018  12 )5d 3 P 2 (  0.00330  B: Experiment:  Aleksandrov et al. (1983) [651  0.003  i2s’ ( P 2  Kelly (1964)11441*  A: Theory:  f  to  where m is 12 s 3 P 2 (  Total  p ’.2s 5 2s — 6 2 2 Oscillator strength from m  Theoretical and experimental determinations of the absolute optical oscillator strengths for discrete transitions of neon (20.9—2 1.2 eV)+  Table 5.4  CD CD  100 transitions of neon reported in various other experimental [20,62,65,129—142] and theoretical [65, 104,144—1501 studies. It can be seen (table 5.2) that there is very little variation In the oscillator strength values for the f 1 resonance line calculated by different theoretical approaches (0.010—0.012) and these results [65,111,146— 1491 correspond closely with the presently reported experimental value 2 resonance line there is substantial variation (0.0118). However, for the f in the calculated oscillator strengths (0.110 to 0.16 1). The dipole— length result reported by Aymar et al. [147], the result of Gruzdev [111] and the calculation by Stewart [150] all show good agreement with the presently reported experimental value (0.159) for f . Other theoretical 2 calculations [65, 146—149] for the f 2 resonance line give lower oscillator strengths. Cooper [104], Kelly [1441 and Amus’ya [145] have reported calculated summed (nl +nl’) oscillator strengths for transitions from 2p to several 5 2 2s 6 2 2s P 2 ( 3/2.1/2)ns p or nd states. For the 2p—’(3s+3s’) transitions (table 5.2), the summed absolute optical oscillator strengths (i.e. 2 +f calculated by Cooper [104] and Amusya [145] are slightly lower 1 f ) while the value of Kelly [144] is slightly higher than the presently reported summed result (0.171). For the higher energy transitions (tables 5.3 and 5.4) such as 2p—4.(4s+4s), all three calculations [104,144,145] give good agreement with the present work, while for the p—(Ss+S&) and 2p—(6s+6s’) transitions the data of Cooper [104] and 2 Kelly [144] are slightly lower. For the 2p—’(3d+3d’), 2p—(4d÷4d’) and 2p—’(5d+5d’) transitions the Cooper [104] and Kelly [1441 data are significantly higher while the Amus’ya [145] data for the 2p—(3d+3d’) transitions are slightly lower when compared with the present experimental results. The calculated f 2 value reported by Gruzdev [111]  101 using intermediate coupling techniques Is consistent with the presently reported value while the f 1 value Is much higher than all the other values quoted in table 5.2. The calculated data reported by Aleksandrov et at. [651 using an intermediate—coupling scheme are more comprehensive and comparison with the presently reported experimental data is possible for individual transitions up to the 6s, 6&, 5d and 5d’ states as shown in tables 5.2, 5.3 and 5.4. Immediately It can be seen that the calculated data of Aleksandrov et at. [65] are in good agreement with the presently reported values except for the f 1 and f 2 values for which their data are slightly lower. Gruzdev and Loginov [148] have calculated the radiative lifetimes of several transitions of neon using an intermediate type coupling and the Hartree—Fock self—consistent field method. Westerveld et at. [139] have converted the lifetime data of Gruzdev and Loginov [148] to oscillator strength values using transition probabilities reported by Gruzdev and Loginov in refs [156,157] and these values show good agreement with the present work for oscillator strength values of the 4s, 4s’, 5s and 5s’ lines, while their value for the 3d’ line is slightly higher. Stewart [1501, using fully—coupled time dependent Hartree—Fock equations, has reported calculated oscillator strength values for the 4s’ and 3d lines which are considerably higher than the present experimental results. Klose [131], using intermediate coupling and a Hartree—Fock—Slater calculation (IC—HFS), and intermediate coupling and the central field approximation (IC—CF), has reported two oscillator strength values for the 5s’ line but both values are considerably lower than the presently reported experimental values. In a second paper, Kiose [158] reported an oscillator strength for the 4s’ line from an IC—  102 HFS calculation which is slightly lower than the present experimental result. Turning now to a consideration of the various experimental results, it can be seen from tables 5.2, 5.3 and 5.4 that the presently reported data are In very good agreement over the whole discrete region with the earlier electron impact based results of Natali et al. [142]. The latter unpublished results [142] have been quoted in references [139] and [143]. The high resolution data reported by Aleksandrov et al. [65], using the total absorption method, have rather large uncertainties and 2 resonance lines 1 and f agreement with the present data is good for the f but generally poorer for the higher transitions. The measured absolute oscillator strengths [651 for the discrete transitions at higher energy are significantly higher than those determined in the present work (see tables 5.3 and 5.4). The self—absorption method was used by three groups [62,139, 1401 and the reported values range from 0.123 to 0.147 2 resonance line. All these for the absolute oscillator strength of the f values are lower than the present value of 0.159. Agreement between different groups using the self—absorption method is generally better for 1 resonance line where the value of Tsurubuchl et al. [140] is the f consistent with the present work, and that obtained by Westerveld et al. [139] is slightly lower but still within the quoted uncertainty. Westerveld et al. [1391 have also measured oscillator strengths for the transitions p and 5s states, and also to 2)4s 2 2s / 3 P 2 ( from the ground state to the 5 , 5s’ and 3d’ states. Their results [1391 for these p 12 )4s’ 2 2s 1 P 2 ( the 5 transitions all show very good agreement with the present work. Lifetime measurements using various experimental procedures [130—137] show good agreement for the absolute oscillator strength of  103 2 resonance line with the present data, with the exception of ref. the f 1 resonance line the result of [130] which is —20% lower. For the f Kazantsev and Chaika [135] is somewhat higher and the values reported by Knystautas and Drouin [132], and by Lawrence and Liszt [130] are much lower than most other reported values which are in close agreement with the present work. In the case of discrete transitions at high energy (table 5.3), the Lawrence and Liszt [130] values are slightly lower than the present work except for the transitions to the p states. Westerveld et al. [1391 2)3d’ 5 2 2s / 1 P 2 p and ( 12 )3d 2 2s 3 P 2 ( 5 have re—evaluated the lifetime data of Lawrence and Liszt [130] using the transition probabilities calculated by Gruzdev and Loginov [148,156.157] and it is note—worthy that the re—evaluated oscillator strength values are in all cases in better agreement with the present work. The absolute oscillator strength for the 5s’ line determined by Kiose [131] using a delayed coincidence method is slightly lower than the present value while that determined by Decomps and Dumont [136] is -33% higher. For the 4s’ line, the values of Decomps and Dumont [136] and Ducloy [1371 are both consistent with the presently reported experimental measurement. With the use of a high resolution electron impact spectrometer, /f resonance lines 2 f Geiger [141] measured the intensity ratio of the 1 giving a value consistent with the ratio derived from the present data. However, the total absolute optical oscillator strength sum for the two resonance lines obtained [141] in Geiger’s earlier work [20], which was normalized on the elastic electron scattering cross section, is about 20% lower than the presently reported value. The absolute oscillator strengths 2 by 2 by Lewis [138] and for f 1 and f obtained from line profile analysis for f  104 Korolev et al. [1291 are in good agreement (see table 5.2) with the present work. Finally, the total discrete oscillator strength sum up to 112 P P3/ and 2 21.6 16 eV, which Is the middle point between the 2 ionization thresholds of neon, has been determined in the present work to be 0.292 compared with estimates of 0.277 reported by Natali et al. [142] and 0.4 reported by West and Marr [103]. The latter value would seem to be too high.  5.2.3 High Resolution Photoabsorption Oscillator Strengths for Neon in the 40-55 eV Region of the Autoionizing Excited State Resonances The spectroscopy (i.e. the energy levels) of the autoionizing excited state resonances of neon involving excitation of a 2s electron and also double excitation of 2p electrons, has been studied in some detail experimentally [65,154,159]. However, prior to the present quantitative work no detailed high resolution absolute intensity measurements have been reported for neon in this region. Similar absolute intensity measurements in the double excitation region for helium in excellent agreement with theory [9] have recently been reported from this laboratory for helium [37] (see section 4.2.2.2). In the present study, the electron energy loss spectrum in the 40—55 eV energy region of neon was measured with the use of the high resolution dipole (e,e) spectrometer at a resolution of 0.098 eV FWHM. This was then converted to a relative optical oscillator strength spectrum by multipling with the BHR function (see section 3.3). Normalization was performed in the smooth continuum region at 55 eV using the absolute optical oscillator strength  105 data given in table 5.1, as determined by the low resolution dipole (e,e) spectrometer. The present high resolution absolute dipole oscillator strengths (solid circles) are shown in figure 5.3. The few photoabsorption (absolute) data points earlier reported by Samson [45,1211 In this region are seen from figure 5.3 (open circles) to be reasonably consistent with the present high resolution dipole (e,e) results. As shown in figure 5.3, the energies (± 0.005 eV) of the maxima of the transitions corresponding to excitation of the 2s electrons to np subshells with n=3 to 6, and the double excitation transition of 2p electrons to the 3s3p configuration of neon have been determined in the present work to be 45.550, 47.127, 47.677 and 47.975, and 44.999 eV respectively. These energies are in good agreement with the high resolution experimental studies reported by Codling et al. [154] and by Aleksandrov et al. [651, as well as with the multi—configuration close coupling calculations of Luke [1141. For peaks observed at higher energies in the present work, the assignments and energy positions of the excited state resonances shown in figure 5.3 are taken from the photoabsorption data reported by Codling et al. [154]. A small peak (X) at 43.735 eV has not been reported in previous photoabsorption measurements [65,154,159], but it should be noted that the published spectra in all of these measurements did not extend below 44 eV. However, a threshold electron impact study by Brion and Olsen [1601 and a lower electron impact energy (400 eV) study of the ionization continuum of neon by Simpson et al. [161] also detected a peak at —43.7 eV and it was suggested that this was probably due to excitation to the s state which had earlier been reported [162] to be at 43.65 eV. 2s2p 3 6  106  0.11  12 F  >  12 p )np 2 2s — 1 S 2 ( 6 42s2p  0.10  I1%eI  I  I  I  456  0  —  I  to ‘.4  3  I  Cl)  0  .-  56  D)3s( 1 ( D 2 )np  9 0 ‘-4 C.)  3 P 3d(P3p P,3d 0.07  8 0  I-  I,  tI  —  0  lII  4  X  0.08  ‘-4  0  4  3  0.09  .)  1 1  )ns p 2s — 6 2 2 ( 4 P ’D)3p( 42s  0.06  0  12 p )np 2 —2s P 3 ( 4 3 P 2 )3s( 12 p 2 2s P 3 ( 4 1 P 2 )np )3s( 3  005  7  6  I  Cl)  p 2 P 3 3 D 3d  2 S 1 3s( 3p P53p 2 3 D 3d S S)3p2P3S  6  56  )ns p 2 2 —2s P 3 ( 4 P )3p(  0.04  5 I  40  ‘-4  0  45  55  Photon energy (cv)  Figure 5.3: Absolute oscillator strengths for the photoabsorption of neon in the autoionizing resonance region 40—55 eV (FWHM=0.098 eV) measured by the high resolution dipole (e,e) spectrometer. Solid circles are this work and open circles are photoabsorption data reported by Samson [45,121]. Assignments are from reference [154]. Note offset vertical scale.  0 0  107 However, it seems unlikely that the forma1ly dipole forbidden transition 2 2 2s — 3 6 ’2s2p p s would be so prominent at the very low momentum transfer (K =0.014 a.u.) corresponding to the present experimental 2 conditions of high impact energy (3 keV) and zero degree mean scattering angle. This peak at 43.735 eV is also too high in energy to be due to any double scattering processes involving below edge outer valence processes.  5.3 Conclusions The present absolute oscillator strength data for neon, unlike the optical measurements, are subject to the stringent constraints of the TRK sum rule and are considered to be of high accuracy. Optical oscillator strengths for the discrete transitions involving valence 2p electrons and also for the photoionization continuum up to 250 eV have been measured for neon. The presently reported results were compared with theory and also with earlier reported experimental data, all of which are less comprehensive than the present work. The accuracy of the earlier unpublished electron impact data of Natali et al. [142] at lower impact energy (i.e. large momentum transfer) in the discrete region is confirmed. Unlike the situation for helium, theoretical calculations for the absolute oscillator strengths of neon in both the discrete and continuum regions show a wide spread of values. The present data provide a critical test for these quantum mechanical calculations throughout the spectrum and especially for the valence 2p discrete electronic excitations such as the f 1 and f 2 resonance lines. The first high resolution absolute optical oscillator strengths have been obtained  108 for the autolonizing excited state and doubly excited state resonance region (40—55 eV) involving 2s excitation and double excitation, and It Is hoped that these measurements will stimulate calculation In this region.  109 Chapter 6  Absolute Optical Oscillator Strengths for the Electronic Excitation of Argon, Krypton and Xenon  6.1 Introduction Similar to the situation for neon [104,112,113,115—118,163] (see chapter 5), the photoionization cross section maxima of argon and krypton [112,113,115—118,163,1641 are shifted to energies above the ionization threshold, showing significant departure from the hydrogenic model. While this departure is not so obvious for xenon [113,116— 118,1631 it does nevertheless show significant non— hydrogenic behaviour. In addition minima (sometimes called Cooper minima) have been observed in the photoionization cross sections of argon, krypton and xenon[104,112,113,115—118,163—165]. Instead ofusinga pure Coulomb nuclear potential, Cooper [104], employing a more realistic potential similar to the Hartree—Fock potential for the outer subshell of each atom, and also both Manson and Cooper [165] and McGuire [1121, starting with Herman-Skiliman central potentials, have been able to theoretically reproduce the maxima above the threshold and also the existence of the minima in the photoionization cross sections starting from one—electron approximations. However the above calculations give narrower peaks shifted in energy relative to the experimental cross sections, with the cross sections at the peak maxima two or three times higher than the experimental values. The 4d shell in xenon is an example where significant discrepancies between experimental and  110 theoretical results have been observed. It has been found that electron correlation is important in many cases [113, 115—118,163,164,166]. Starace [164] has computed the photoionizatlon cross sections of argon and xenon starting from a local Herman—Skillman central field and including final—state correlation. Amus’ya et al. [116], employing the random—phase approximation with exchange (RPAE), Kennedy and Manson [113], using Hartree—Fock functions with exchange, Burke and Taylor [115], applying the R—matrix theory, and Zangwill and Soven [163], using density—functional theory, have also calculated the photoionization cross sections of the noble gas atoms. The relativistic random—phase approximation (RRPA) [117] and the relativistic time—dependent local— density approximation (RTDLDA) [118], two methods which are closely related, have also been applied to calculation of the photoionization cross sections of the outer shells of argon, krypton and xenon. Recently, Rozsnyai [166] has reported the photoionization cross sections of the 3p and 3d electrons in krypton and the 4d electrons in xenon based on a self—consistent Dirac—Slater model including the effect of the hole in the ionized shell. With the inclusion of electron correlation, the calculated photoionization cross sections [115—118,163] are generally in better agreement with experiment, however some discrepancies (>20%) still remain between the experimental and theoretical values in certain energy ranges. Experimentally, ph otoabs orption and photoionization cross section measurements in the ionization continuum regions of argon, krypton and xenon have been widely performed using Beer—Lambert law photoabsorption and the double ion chamber methods [45,47,48,102,103,167—179]. Line—emitting light sources [45,167,169—  111 172,175,178,179] have most commonly been used. The Hopfleld continuum [168,173], generated by a repetitive, condensed discharge through helium, provides a useful continuum source In the energy region 11.3—21.4 eV. With the advance of synchrotron radiation an Intense and continuous light source has become avaflable for measuring the photoionization cross sections of atoms and molecules up to high energies [47,48,102,103,174,176,177]. However, contributions from stray light and higher order radiation have to be carefully assessed and the measurements appropriately corrected if synchrotron radiation is to be used as the light source for accurate absolute cross section measurements [126—128]. Photographic plates [167,1721, Geiger counters [172] (used at high energy), photomultiplier tubes [47,48,103,168,171,174] and channel electron multipliers [102,176,1771 have been employed as detectors. Ionization chambers of different geometries have been constructed [45,173,176,178,179] and photoionization cross sections of the sample gases have been obtained from the length of the ion collector plates, the sample target density and the current flowing from the collector plates. These Beer—Lambert law measurements give good agreement for the individual noble gases In terms of the shapes of the continua. However the absolute values of the photoabsorption cross sections in the continua typically show substantial differences (—10%), especially at higher energies, due to difficulties in obtaining precise measurements of the sample target density in a ‘windowless’ far UV system and also due to contributions from stray light and/or higher order radiation. By using the dipole excitation associated with inelastic scattering of electron beams of high impact energy (10 keV) and small scattering angle, the single and multiple photoionization  112 of argon [221, krypton and xenon [1801 has been studied using electron/ion coincidence techniques. Relative optical oscillator strengths were obtained [22,1801 by Bethe—Born conversion of electron scattering data and absolute scales were established by normalizing at a single energy to previously published [451 abso1ute photoabsorption cross sections. For the excitation of the heavier noble gas atoms in the discrete region, several theoretical oscillator strength calculations have been reported. Cooper [1041, employing a one electron central potential model, and Amus’ya [145], applying the RPAE method, have calculated oscillator strengths for the transitions from the ground states to the p and nd states where n>m and m is 3, 4 and 5 for 3/2,l,2)ns 5 m ms P 2 ( argon, krypton and xenon respectively. Calculations of the oscillator strengths for the separate transitions from the ground state to the p and nd’ states 1,2)ns’ m ms P 2 ( p and nd states, and the 5 3/2)ns 5 m ms P 2 ( have also been reported [111, 147,151,181—189], but mostly these p 1)s 3,2)(m+ m ms P 2 ( calculations only give oscillator strengths for the 5 and 5 p 1)s’ states [111,147,181—183,151,186—1891. 2)(m+ m ms , 1 P 2 ( Theoretical discrete oscillator strength values have been reported by Knox [181] for argon, and Dow and Knox [182] for krypton and xenon. The first [1811 set of data is based solely on solving the Hartree—Fock equations while the second [182] is based on experimental energies with the dipole matrix elements computed from the Hartree—Fock wavefunctions.  Gruzdev [ill] has reported the oscillator strengths of  resonance lines in the spectra of Ar I, Kr I and Xe I atoms using the technique of intermediate coupling with the transition integral obtained from the Coulomb approximation. Kim et al. [1831, using Hartree—Fock  113 wavefunctions without freezing of the core orbitals, have calculated the generalized oscillator strengths of the Xe I resonance lines, which in the optical limit gave optical oscillator strengths for these transitions. Aymar et al. [147] calculated Ar I, Kr I and Xe I transition probabilities and lifetimes using a least—squares fit procedure on energy levels for the angular part of the wavefunctions and a parametrized central potential for the radial part of the wavefunctions. Lee and Lu [184], who have determined three sets of parameters: eigen—quantum defects, transformation matrices and excitation dipole moments by fitting to experimental data, have reported a semi—empirical calculation of discrete oscillator strengths for argon. Later, Lee [185] calculated the same parameters by solving the many—electron Schrodinger equation for an atom within a limited spherical volume. The radiative lifetimes of the levels of Ar I [186] and Kr 1 [1871 have been calculated by Gruzdev and Loginov using an intermediate coupling scheme with radial integrals obtained from Hartree—Fock functions. Albat et al. [188], carrying out Born and four—state “close coupling” calculations, have reported oscillator strengths for the low lying argon levels while Stewart [1511, using simplified time—dependent Hartree—Fock calculations, has reported the oscillator strength for the (3p 6 5 S—’3p 1 4 s 1 P) transition of argon. Aymar and Coulombe [189] have computed the transition probabilities and lifetimes for Kr I and Xe I spectra using a central field model which takes into account intermediate coupling and configuration mixing. Since the valence shell electronic transitions of noble gas atoms have extremely narrow natural line—widths, absolute oscillator strength measurements for the discrete regions of the argon, krypton and xenon photoabsorption spectra via the Beer—Lambert law are not viable since  114 significant errors may arise due to so—called “line—saturation” (i.e. bandwidth) effects. Detailed discussions of “line—saturation” effects and their Implications for absolute photoabsorptlon oscillator strength (cross section) measurements have been given in refs. [36,37,46,72] (see chapter 2). Several alternative experimental methods for determining discrete optical oscillator strengths which avoid “line—saturation” problems have been reported. However, in most cases these methods are somewhat complex and also are often severely restricted in their range of application so that only a very few transitions can be studied for a given target [37]. In the cases of argon, krypton and xenon, other techniques which have been used include the self—absorption method [62,64,139,140], the total (optical) absorption method [190—192], the linear absorption method [193], refraction index determination [194], lifetime measurements [195—202], pressure—broadening profile analysis [138,203—206], phase—matching techniques [66,2071, study of the electron excitation function [208] and electron Impact methods [20,141,209—216]. The relative self—absorption method has been used by Jongh and Eck [62], while the absolute self—absorption method has been used by Westerveld et al. [1391 and Tsurubuchi et al. [64,140]. Oscillator strengths for the resonance lines of krypton and xenon have been determined by Wilkinson [190.191], and Griffin and Hutcherson [192] using the total (optical) absorption method. Chashchina and Shreider [1931 used the method of linear absorption and reported oscillator strengths for the resonance lines of krypton, while in a further paper they reported the oscillator strength for one resonance line (8.434 eV) of xenon by determining the refractive index of xenon using the spectral line—shift method [194]. The radiative lifetimes of the resonance  115 transitions of the noble gases have been determined using: a) the beam— foil method [199]; b) the zero—fIeld level—crossing technique (Hanle effect) [195]; (c) study of the photon decay curve using a pulsed electron excitation source [196—198,200] or pulsed light source [2011; (d) electron—photon delayed coincidence techniques [202]. By studying the pressure—broadening profiles of the noble gas resonance lines, several groups [138,203—2061 have reported their oscillator strengths. With the development of lasers, a phase—matching technique involving focused beams for optical wave—mixing became possible and oscillator strengths for the resonance lines In the noble gases have been determined using these techniques by Kramer et al. [207] for xenon and by Ferrell et al. [66] for krypton and xenon. By analyzing the electron excitation function, McConkey and Donaldson [2081 have reported optical oscillator strengths for the resonance lines of argon. Electron impact based methods have also been employed for measuring the discrete optical oscillator strengths of argon, krypton and xenon. By using very high Impact energy (25—32 keV) and very small scattering angle (-.-1x10- rad), Geiger [20,141,210,212,213] obtained optical oscillator strengths for the resonance lines of the noble gases by converting electron energy loss spectra to relative optical spectra and normalizing on the elastic differential cross section. In other electron impact work Li et al. [2141 for argon, Takayanagi et al. [215] for krypton, and Delage and Carette [2111 and also Suzuki et al. [216] for xenon, have reported optical oscillator strengths for resonance lines in the heavier noble gases by extrapolating the generalized oscillator strengths of lines, measured at different scattering angles and at low electron impact energy, to zero momentum transfer. Delage and Carette [211] normalized their data on  116 one of the transition peaks of xenon that was measured by Geiger [2101, while Lietal. [214], Takayanagietal. [2151 andSuzukietal. [2161 normalized their data on the elastic scattering cross section. The unpublished electron Impact work of Natali et aL. [1421 for the optical oscillator strengths of the noble gases has been quoted In references [139,212,1431. Consideration of the various experimental and theoretical oscillator strength values published to date for argon, krypton and xenon shows that there is a large body of existing information for the continuum regions. In contrast there is relative little information available in the valence shell discrete region. For the discrete spectra of argon, krypton and xenon only the transitions to the 5 m ms P 2 ( 3/2)(m+ p 1)s and m ms , 1 P 2 ( 5 2)(m+ p 1)s’ states, where m is 3, 4 and 5 respectively, have been studied in any detail and even for these considerable variations in oscillator strength values have been reported. In the case of argon the optical oscillator strength data available in 1975 was reviewed by Eggarter [217] for both the discrete and continuum regions up to 3202 eV. On the basis of the information available Eggarter [217] listed recommended optical oscillator strength values for argon. In chapters 4 and 5, we have reported detailed and comprehensive measurements for helium [37] and neon [38] respectively. These results were obtained using a recently developed highly accurate high resolution electron impact based method for obtaining absolute optical oscillator strengths for the discrete, continuum and autoionizing resonance regions in atoms and molecules. This method [37,38] is not subject to the “line saturation” effects which can cause serious errors in Beer—Lambert law photoabsorption experiments when the bandwidth is comparable to or  117 larger than the natural linewidth. The method involves combining measurements obtained using a high resolution (0.048 eV FWHM) dipole (e,e) spectrometer in conjunction with a lower resolution (—1 eV FWHM) dipole (e,e) instrument. The absolute oscillator strength scales for helium and neon were obtained by TRK sum rule normalization and were thus completely independent of any direct optical measurement. The same general method is now applied to provide independent and wide— ranging measurements of the absolute photoabsorption oscillator strengths for the discrete, continuum and autoionizing resonance regions of argon, krypton and xenon. However, in practice the TRK sum rule normalization procedures which were employed for helium [37] and neon [38] are difficult to apply for the heavier noble gases due to difficulties in carrying out the necessary lengthy valence shell extrapolations. These difficulties arise because of the smaller energy separations between the different subshells of the argon, krypton and xenon atoms compared with the relatively simple electronic configurations of helium and neon. The absolute scales of the presently reported data have therefore been obtained by normalizing on recently reported high precision photoabsorption oscillator strengths measured at helium and neon resonance line photon energies by Samson and Yin [178]. In this chapter, we now report measurements of (i) absolute photoabsorption continuum oscillator strengths for argon, krypton and xenon up to 500, 380 and 398 eV respectively, (ii) absolute photoabsorption oscillator strengths for the discrete dipole allowed electronic transitions from the 6 subshells to 1evels of the lower members of the n mp 5 m 2 ms p and s 5 m 2 ms n d p ) 112 P 2 ( 2 1 3 , manifolds where n>m and m is 3, 4 and 5 for argon, krypton and xenon respectively, and (iii) absolute photoabsorption  118 oscillator strengths in the regions of the Beutler—Fano autoionization resonance profiles involving excitation of the inner valence ms electrons. The results are compared with previously published experimental and theoretical data in regions where such data are available.  6.2 Results and Discussion 6.2.1 Low Resolution Measurements of the Photoabsorption Oscillator Strengths for Argon, Krypton and Xenon Relative photoabsorption spectra of argon, krypton and xenon were obtained by Bethe—Born conversion of electron energy loss spectra measured with the low resolution dipole (e,e) spectrometer (see chapter 3) from 10—500 eV, 8—380 eV and 7—398 eV for argon, krypton and xenon respectively. The relative spectra were normalized at 21.2 18 eV for argon and krypton and at 16.848 eV for xenon using the recently published photoionization data of Samson and Yin [178]. The uncertainties of the present low resolution dipole (e,e) work are estimated to be -5%. The results for argon, krypton and xenon are presented in the following separate sections.  6.2.1.1 Low Resolution Measurements for Argon Figures 6.1—6.3 show the presently measured absolute optical oscillator strengths for the photoabsorption of argon. The corresponding numerical values in the energy region 16—500 eV are summarized in table 6.1. Of the three noble gases (argon, krypton and xenon) studied in the present work, the photoionization cross sections of argon have been  40  119  (a) Experimental measurements  IA1  3s1  30  0  Present work (E = 1 eV FWHM) West & Morr [47,103] Sornson [45]  * A  Henke et ci. Von der Wiel  • ‘  30  [152]  & Wiebes [22] Corison et ci. [176] Modden et ci. [218) Rustgi [171)  x 0 •  20  40  20  > C  10  10 0  x.  C.)  S  U) •cy •*• •  0 10  V  1.4  I  I  40  50  I  20  30  r  Cl)  U)  0  60  ‘.4  C)  U)  0  ‘.4  0 —  (b) Comparison with theory  60  0  C) Cl)  0  IAiJ  60  50  C.)  •  .-  — —  0  ‘.4  40  —  3s’  3p  —  —  ..-+  0  1  :  3D  —  +  a  40 30  • :  20  20 \  10 •  0  50  Present work (Expt.) Storoce [164] Burke end Tcyior [115] Amu&yc et ci. [116] Kennedy end Mcnson [113] McGuire [112] Zcngwiii & Soven [163] Johnson & Cheng [117] Porpia et ci. [fl8]  \  1•  10  s•.•  .-.-  : 10  0 20  30  40  50  60  Photon energy (eV)  Figure 6.1: Absolute oscillator strengths for the photoabsorption of argon in the energy  region 10-60 eV. (a) comparison with other experimental data [22,45,47,103,152,171,176,218]. The discrete region below 16 eV is shown at high resolution in figure 6.9. The resonances In the region 26—29.2 eV preceding the 3s’ edge are shown at high resolution in figure 6.14. (b) comparison with theory [112,113,115—118,163,164].  120  2.5  -4  >  2.5  V  •  C  *  2.0  —I  *  A o -  S  — —  1 .5  G  Present work (E = 1 eV FWHM) West & Mcrr [47,103] Henke et ci. [152] Lukirskii end Zimkinc [169) Van der Wie? & Wiebes [221 Samson et ci. [179) Amusyc et ci. [116] Kennedy & Manson [113] McGuire [112]  •‘)f  0 —  L.LI  C.)  U) U)  1.5  U)  o  3C-)  V  1  I.  ci)  1 .0  C  0  1.0k  0 /  = .0  Cl) C  0.5  0.5  0.0  0.0  0 4  40  8b  120  160  200  240  Photon energy (eV)  Figure 6.2: Absolute oscillator strengths for the photoabsorption of argon in the energy region 40—240 eV compared with other experimental [22.47.103,152,169,1791 and theoretical [112,113,116] data.  121  -S  >  6  1 2p  c;IV  0  • *  *  I’  5  A —  S  o  rI  6 5 Cl) U)  4 A  I.  a) U)  —  Present work (E = 1 eV FWHM) West & Marr [47,103] Henke et ol. [1521 Lukirski and Zimkno [169] Von der Wiel & Wiebes [22) Amusyo et al. [116] Kennedy & Monson [113] McGuire [112]  3  A  A A  .t-  1 2s  0  C)  3 4 C  I  2 C) U) 0  *  ‘I  C.?  0 220  0 1.4  r  1-4  U)  260  I  I  300  340  380  420  460  500  Photon energy (eV)  Figure 6.3: Absolute oscillator strengths for the photoabsorption of argon In the energy region 220—500 eV compared with other experimental [22,47,103,152,169] and theoretlcal[112,113,1161 data.  :i 1  122 Table 6.1 Absolute differential optical oscillator strengths for the photoabsorption of argon above the first ionization potential obtained using the low resolution (1 eV FWHM) dipole (e,e) spectrometer (16— 500 cv)  Energy  Oscillator  Energy  Oscillator  Energy  Oscillator  (eV)  Strength  (eV)  Strength  (eV)  Strength V1 e 2 (10 )  V1 e 2 (10)  V-l) (10 e 2  16.0  27.74  17.7  31.05  19.4  32.02  16.1  27.96  17.8  31.09  19.5  32.19  16.2  28.16  17.9  30.86  19.6  32.35  16.3  28.48  18.0  30.87  19.7  32.52  16.4  28.55  18.1  31.33  19.8  32.71  16.5  28.94  18.2  31.15  19.9  32.23  16.6  28.95  18.3  31.57  20.0  32.49  16.7  29.25  18.4  31.67  20.1  32.51  16.8  29.25  18.5  31.81  20.2  32.36  16.9  29.52  18.6  31.61  20.3  32.38  17.0  29.71  18.7  31.73  20.4  32.71  17.1  29.99  18.8  31.78  20.5  32.40  17.2  29.97  18.9  32.19  20.6  32.58  17.3  30.30  19.0  32.03  20.7  32.91  17.4  30.25  19.1  32.02  20.8  32.94  17.5  30.39  19.2  32.51  20.9  32.57  17.6  30.73  19.3  32.41  21.0  32.75  123 Table 6.1 (continued)  Energy  Oscillator  Energy  Oscillator  Energy  Oscillator  (eV)  Strength  (eV)  Strength  (eV)  Strength V 1 e 2 (10 )  V1 e 2 (l0)  V1 e 2 (1O)  21.1  32.62  28.5  24.50  38.5  4.38  21.2k  33.00  29.0  23.37  39.0  3.84  21.3  32.72  29.5  22.24  39.5  3.51  21.4  32.89  30.0  19.84  40.0  3.03  21.5  33.09  30.5  18.66  41.0  2.48  21.6  33.16  31.0  17.85  42.0  1.970  21.7  32.80  31.5  17.08  43.0  1.521  21.8  32.86  32.0  16.25  44.0  1.312  22.5  32.90  32.5  15.19  45.0  1.141  23.0  32.36  33.0  13.81  46.0  0.991  23.5  32.16  33.5  12.69  47.0  0.956  24.0  31.66  34.0  11.73  48.0  0.905  24.5  31.49  34.5  10.50  49.0  0.906  25.0  31.24  35.0  9.89  50.0  0.883  25.5  31.08  35.5  9.02  51.0  0.909  26.0  30.63  36.0  8.28  52.0  0.923  26.5  29.02  36.5  7.20  53.0  0.946  27.0  25.76  37.0  6.34  54.0  0.977  27.5  26.06  37.5  5.71  55.0  1.009  28.0  25.71  38.0  5.04  56.0  1.036  124 Table 6.1 (continued)  Energy  Oscillator  Energy  Oscillator  Energy  Oscillator  (eV)  Strength  (eV)  Strength  (eV)  Strength  eV-l) 2 (10-  eV2 (10 ) 1  eV’) 2 (10  57.0  1.059  77.0  1.373  97.0  1.278  58.0  1.078  78.0  1.374  98.0  1.244  59.0  1.094  79.0  1.376  99.0  1.248  60.0  1.110  80.0  1.366  100.0  1.241  61.0  1.146  81.0  1.371  102.0  1.236  62.0  1.175  82.0  1.371  104.0  1.219  63.0  1.196  83.0  1.359  106.0  1.182  64.0  1.223  84.0  1.363  108.0  1.171  65.0  1.245  85.0  1.353  110.0  1.154  66.0  1.259  86.0  1.341  112.0  1.139  67.0  1.278  87.0  1.340  114.0  1.112  68.0  1.290  88.0  1.338  116.0  1.101  69.0  1.314  89.0  1.337  118.0  1.081  70.0  1.316  90.0  1.322  120.0  1.074  71.0  1.325  91.0  1.312  122.0  1.043  72.0  1.341  92.0  1.310  124.0  1.035  73.0  1.347  93.0  1.304  126.0  1.011  74.0  1.348  94.0  1.288  128.0  0.999  75.0  1.364  95.0  1.288  130.0  0.975  76.0  1.365  96.0  1.288  132.0  0.963  125 Table 6.1 (continued)  Energy  Oscillator  Energy  Oscillator  Energy  Oscillator  (eV)  Strength  (eV)  Strength  (eV)  Strength V 1 e 2 (10)  V1 e 2 (10)  V1 e 2 (10)  134.0  0.936  174.0  0.665  214.0  0.495  136.0  0.920  176.0  0.654  216.0  0.487  138.0  0.910  178.0  0.658  218.0  0.480  140.0  0.895  180.0  0.636  220.0  0.484  142.0  0.879  182.0  0.609  222.0  0.459  144.0  0.857  184.0  0.614  224.0  0.455  146.0  0.851  186.0  0.593  226.0  0.470  148.0  0.829  188.0  0.606  228.0  0.446  150.0  0.816  190.0  0.579  230.0  0.436  152.0  0.793  192.0  0.566  232.0  0.439  154.0  0.789  194.0  0.569  234.0  0.457  156.0  0.784  196.0  0.552  236.0  0.425  158.0  0.762  198.0  0.550  238.0  0.408  160.0  0.737  200.0  0.548  240.0  0.405  162.0  0.740  202.0  0.530  240.5  0.412  164.0  0.726  204.0  0.538  241.0  0.404  166.0  0.696  206.0  0.521  241.5  0.402  168.0  0.701  208.0  0.514  242.0  0.409  170.0  0.687  210.0  0.506  242.5  0.406  172.0  0.689  212.0  0.485  243.0  0.416  126 Table 6.1 (continued)  Energy  Oscillator  Energy  Oscillator  Energy  Oscillator  (eV)  Strength  (eV)  Strength  (eV)  Strength V 1 e 2 (1O )  V 1 e 2 (1O)  V1 e 2 (1O )  243.5  0.439  253.5  3.93  263.5  3.35  244.0  0.578  254.0  3.90  264.0  3.36  244.5  0.849  254.5  3.89  264.5  3.34  245.0  0.774  255.0  3.81  265.0  3.36  245.5  0.593  255.5  3.78  265.5  3.34  246.0  0.609  256.0  3.76  266.0  3.34  246.5  1.049  256.5  3.69  266.5  3.35  247.0  1.615  257.0  3.65  267.0  3.35  247.5  1.838  257.5  3.63  267.5  3.36  248.0  2.00  258.0  3.58  268.0  3.34  248.5  2.30  258.5  3.57  268.5  3.33  249.0  2.69  259.0  3.55  269.0  3.27  249.5  3.13  259.5  3.48  269.5  3.22  250.0  3.42  260.0  3.49  270.0  3.19  250.5  3.59  260.5  3.43  270.5  3.14  251.0  3.77  261.0  3.40  271.0  3.08  251.5  3.86  261.5  3.44  271.5  3.07  252.0  3.94  262.0  3.39  272.0  3.07  252.5  3.94  262.5.  3.38  272.5  3.04  253.0  3.97  263.0  3.36  273.0  3.03  127 Table 6.1 (continued)  Energy  Oscillator  Energy  Oscillator  Energy  Oscillator  (eV)  Strength  (eV)  Strength  (eV)  Strength eV-l) 2 (1O-  eV2 (1O) 1  eV2 (1O) 1  273.5  3.02  287.0  2.83  307.0  2.67  274.0  3.02  288.0  2.83  308.0  2.64  274.5  3.01  289.0  2.83  309.0  2.62  275.0  2.99  290.0  2.81  310.0  2.63  275.5  2.96  291.0  2.79  311.0  2.63  276.0  2.97  292.0  2.79  312.0  2.62  276.5  2.96  293.0  2.77  313.0  2.62  277.0  2.96  294.0  2.76  314.0  2.63  277.5  2.91  295.0  2.74  315.0  2.59  278.0  2.92  296.0  2.76  316.0  2.57  278.5  2.91  297.0  2.75  317.0  2.59  279.0  2.90  298.0  2.74  318.0  2.59  279.5  2.92  299.0  2.71  319.0  2.57  280.0  2.89  300.0  2.71  320.0  2.59  281.0  2.88  301.0  2.73  321.0  2.59  282.0  2.87  302.0  2.70  322.0  2.60  283.0  2.85  303.0  2.67  323.0  2.66  284.0  2.87  304.0  2.67  324.0  2.70  285.0  2.84  305.0  2.67  325.0  2.74  286.0  2.85  306.0  2.66  326.0  2.74  128 Table 6.1 (continued)  Energy  Oscillator  Energy  Oscillator  Energy  Oscillator  (eV)  Strength  (eV)  Strength  (eV)  Strength  eV-l) 2 (10-  eV2 (10) 1  eV2 (10) 1  327.0  2.70  347.0  2.44  384.0  2.11  328.0  2.74  348.0  2.41  386.0  2.06  329.0  2.69  349.0  2.46  388.0  2.03  330.0  2.69  350.0  2.44  390.0  2.07  331.0  2.65  352.0  2.40  392.0  2.03  332.0  2.61  354.0  2.38  394.0  2.01  333.0  2.64  356.0  2.35  396.0  1.971  334.0  2.62  358.0  2.31  398.0  2.01  335.0  2.61  360.0  2.28  400.0  1.983  336.0  2.58  362.0  2.30  402.0  1.898  337.0  2.56  364.0  2.27  404.0  1.931  338.0  2.52  366.0  2.27  406.0  1.917  339.0  2.54  368.0  2.21  408.0  1.869  340.0  2.54  370.0  2.22  410.0  1.891  341.0  2.52  372.0  2.22  412.0  1.875  342.0  2.52  374.0  2.18  414.0  1.854  343.0  2.48  376.0  2.17  416.0  1.839  344.0  2.50  378.0  2.14  418.0  1.820  345.0  2.43  380.0  2.14  420.0  1.778  346.0  2.47  382.0  2.11  422.0  1.827  129 Table 6.1 (continued)  Energy  Oscillator  Energy  Oscillator  Energy  Oscillator  (eV)  Strength  (eV)  Strength  (eV)  Strength  t  V 1 e 2 (10 )  V1 e 2 (10)  V 1 e 2 (10 )  424.0  1.784  458.0  1.597  492.0  1.374  426.0  1.769  460.0  1.587  494.0  1.411  428.0  1.805  462.0  1.605  496.0  1.400  430.0  1.743  464.0  1.578  498.0  1.364  732.0  1.724  466.0  1.528  500.0  1.346  434.0  1.686  468.0  1.532  436.0  1.728  470.0  1.507  438.0  1.751  472.0  1.532  440.0  1.677  474.0  1.501  442.0  1.675  476.0  1.523  444.0  1.655  478.0  1.453  446.0  1.637  480.0  1.471  448.0  1.601  482.0  1.482  450.0  1.604  484.0  1.436  452.0  1.606  486.0  1.454  454.0  1.635  488.0  1.452  456.0  1.608  490.0  —  normalized to ref. [1781 at 21.218 eV o(Mb)  =  l.0975x 102-eV1  1.437  130 previously studied in the greatest detail. Figures 6.1(a) and 6.1(b) show the presently measured absolute optical oscillator strengths for the valence shell photoabsorption of argon in the energy region 10—60 eV along with previously reported experimental [22,45,47,103,152,171,176,218,152] and theoretical[112—118,163,164] data, respectively. In figure 6.1(a), the higher resolution data from Samson [45] and Carlson et al. [176] in the 26—29 eV autoiOnizlng region have been omitted to permit clearer comparison with the present low resolution data. The data reported by Samson [45] and Carlson et al. [176] in the continuum autoionization regions will be compared with the present data obtained from the high resolution dipole (e,e) spectrometer in section 3.3 below. West and Marr [103] have made absolute photoabsorption measurements for argon over the range 36—310 eV and have given a critical evaluation of existing published cross section data to obtain recommended (weighted—average) values throughout the vacuum ultraviolet and x—ray regions. These values [47,103] did not take Into account previously published data in the autoionizlng region (26—29 eV) and simply reported interpolated smooth cross sections throughout the autoionizing region. From figure 6.1(a) it can be seen that all the experimental data including the present low resolution results show a similar shape for the continuum and are In generally good quantitative agreement. The data from Madden et al. [218] are slightly higher than other experimental values in the vicinity of 25 eV. In contrast to the experimental data, the theoretical values for argon show substantial differences in terms of both the shape and the absolute values of the cross sections when compared with the present results (see figure 6.1(b)). The one—electron calculation by McGuire [112] gives much  131 higher cross sections just above the 3p threshold and the cross sections drop very quickly to a very low value before reaching the Cooper minimum at —50 eV. Even with the inclusion of electron corre1ation, the calculations reported by Starace [164] and by Kennedy and Manson [1131 still show large discrepancies with the present and other measured values. Since relativistic effects in argon are small, the RPAE calculation of Amusya et al. [1161 and the relativistic RPAE of Johnson and Cheng [117] agree very closely with each other. However, these calculations [116,117] are considerably higher than the present and other experimental values below 30 eV and are somewhat lower in the energy region 30—50 eV. The values reported by Parpia et al. [1181 using the RTDLDA method give excellent agreement with the presently reported experimental values above 25 eV, but in common with most of the other theoretical work there still exist some discrepancies with the experimental data in the energy region between the 3p threshold and the cross section maximum. Figure 6.2 shows the presently measured absolute photoabsorption oscillator strengths for argon from 40 to 240 eV just below the inner shell 2p excitations of argon. Other previously reported experimental and theoretical data that are available in this energy region are also shown for comparison. The present data are in generally good agreement with the compilation data reported by Henke et al. [152] and West and Marr [47,103]. The photoabsorption data of Lukirskii and Zimkina [169] and the earlier electron impact data of Van der Wiel and Wiebes [22] give lower values at energies above 120 eV. The values measured recently by Samson et al. [179] using a double ionization chamber in the energy region 40—120 eV are slightly lower than the present work. In  132 theoretical work, the one—electron calculation of McGuire [112], which shows very high cross sections just above the 3p threshold (figure 6.1(b)) gives very good agreement with the present results from an energy just above the Cooper minimum to 240 eV (figure 6.2). The RPAE calculations reported by Amus’ya et aL. [116] show a similar shape in the continuum to the present measurements, but the theoretical values are slightly lower from 40 to 150 eV and become increasingly lower above 150 eV. The photoionization cross sections calculated by Kennedy and Manson [113] show large discrepancies with the present and all other experimental data and furthermore the predicted position of the Cooper minimum is  -  15 eV too high in energy.  Figure 6.3 shows the presently measured absolute photoabsorption oscillator strengths for argon in the energy region from 220 to 500 eV where excitation and ionization of the argon 2s and 2p electrons take place on top of the valence shell continuum. The limited previously published experimental and theoretical data in this energy region are also shown in figure 6.3 for comparison. Unlike the situation below 240 eV, the agreement between the available experimenta1 data is poor in this energy region. It can be seen in figure 6.3 that the data reported by Lukirskii and Zimkina [169] and the compilation data of Henke et al. [1521 are —10—25% lower than the present results. The data of West and Marr [47, 103], which are slightly higher than the presently reported values in the energy region 250—290 eV, are lower by more than 30% at energies above 320 eV. The theoretical calculations reported by Kennedy and Manson [1131, which show considerable discrepancies with the experimental data below 240 eV, exhibit very good agreement with the presently measured values in the energy region 270—500 eV, while the  133 calculations ofAmu&yaetal. [116] and of McGuire [112] are (—40—15%) lower than the present results in this energy region.  6.2.1.2 Low Resolution Measurements for Krypton Figures 6.4 and 6.5 show the presently measured absolute optical oscillator strengths for the photoabsorption of krypton. Table 6.2 summarizes the numerical absolute oscillator strength values in the energy region 14.7—380 eV. In figures 6.4(a) and 6.4(b), the presently measured valence shell photoabsorption oscillator strengths for krypton in the energy region 5—60 eV are compared with the previously reported experimental and theoretical values, respectively. The earlier reported photoionization data of Samson [451 are slightly lower than the present work in the energy region from the 4p threshold to 30 eV. The weighted—average values reported in the West and Marr compilation [47,1031, which included the data from Samson [45], show similar behavior to the original Samson data [45]. In contrast, the most recent data reported by Samson et al. [179] show excellent agreement with the presently reported values. As shown in figure 6.4(b), the situation for the theoretical cross sections of krypton when compared with the experimental data is similar to that for argon (in figure 6.1(b)). Even though agreement between theoretical and experimental values is better at higher energies, difficulties still remain in describing the behavior of the photoionization cross sections just above the 4p threshold and in the region around the cross section maximum. Ionization from the 3d sub—shell of krypton takes places at —90 eV. The ejection of the d—electrons is delayed due to the angular momentum  ‘34  —  >  .0  C 0 C.) C)  U)  U) U) C.) U) I  0  C.) U)  10  20  30  40  50  C  1-4  C.)  70  0  -4  (b) Comparison with theory 60  IIr1  4s  70  0 C.)  0  60  60  I  50 —  40  —  O +  o  3D  Present work (Expt.) Amuyso et ci. [116] Kennedy & Monson [113] McGure [112) Zongwiii & Soven [163) Johnson & Cheng Eli?] Porpia et ci. [118]  50 •40 •30  20  20  10  •10 0 1  .  0  -S --  1’O  20  30  40  50  60  Photon energy (eV)  Figure 6.4: Absolute oscillator strengths for the photoabsorption of krypton in the energy region 5-60 eV. (a) comparison with other experimental data [45,47,103,152,1801. The discrete region below 15 eV is shown at high resolution in figure 6.10. The resonances in the region 24.5—27.5 eV preceding the 4s edge are shown at high resolution in figure 6.15. (b) comparison with theory 1112,113,116—118,163].  0 0  135  7  ,-  0  6  1 3p  1 3d  Kr!  1 3s  H -  I  5  ‘•  --  4  XAA > A  V Cl)  *  3  X  *  A  A  *  AX AX  0 • .—  2  A  •7  A  C)  *  Cl)  \  0  1-1/  <  •  *  * C)  -  — —  O x  0 50  100  150  Present work (E = 1 eV FWHM) West & Marr [47,103] El—Sherbini & Van der Wiel [180] Lukirskii et at. [170] Land & Watson [177] Henke et at. [152] Amuy’so et ci. [116] Kennedy & Manson [113] McGuire C 112] Rozsnyio [1 661  200  250  300  4 X AX  *  350  400  Photon energy (eV)  Figure 6.5: Absolute oscillator strengths for the photoabsorption of krypton in the energy region 50—400 eV compared with other experimental [47,103,152,170,177,180]andtheoretjcal[112,113,116,166]data.  136 Table 6.2 Absolute differential optical oscillator strengths for the photoabsorption of krypton above the first ionization potential obtained using the low resolution (1 cv FWHM) dipole (e,e) spectrometer (14.7— 380 eV)  Energy  Oscillator  Energy  Oscillator  Energy  Oscillator  (eV)  Strength  (eV)  Strength  (eV)  Strength  eV 2 (10) 1  eV 2 (10) 1  eV 2 (10 ) 1  14.7  40.22  16.4  41.41  18.1  39.82  14.8  40.16  16.5  41.81  18.2  39.96  14.9  40.56  16.6  41.04  18.3  39.55  15.0  40.42  16.7  41.46  18.4  39.65  15.1  40.64  16.8  41.62  18.5  39.58  15.2  40.50  16.9  41.76  18.6  40.00  15.3  41.25  17.0  40.77  18.7  39.64  15.4  41.13  17.1  41.02  18.8  39.35  15.5  41.41  17.2  41.63  18.9  38.59  15.6  41.46  17.3  41.53  19.0  38.40  15.7  41.49  17.4  40.70  19.1  38.53  15.8  41.22  17.5  40.67  19.2  38.83  15.9  41.28  17.6  40.65  19.3  37.98  16.0  41.20  17.7  41.07  19.4  38.41  16.1  41.73  17.8  40.70  19.5  38.32  16.2  40.78  17.9  40.26  19.6  38.38  16.3  41.57  18.0  40.70  19.7  37.57  137 Table 6.2 (continued)  Energy  Oscillator  Energy  Oscillator  Energy  Oscillator  (eV)  Strength  (eV)  Strength  (eV)  Strength V 1 e 2 (1O )  V 1 e 2 (1O )  V1 e 2 (10)  19.8  37.76  25.0  25.81  35.0  9.30  19.9  37.85  25.5  25.57  35.5  8.33  20.0  37.46  26.0  24.22  36.0  7.77  20.1  36.80  26.5  23.37  36.5  7.39  20.2  36.79  27.0  22.99  37.0  6.92  20.3  37.33  27.5  21.14  37.5  6.28  20.4  36.98  28.0  20.38  38.0  5.85  20.5  35.65  28.5  19.85  38.5  5.65  20.6  35.42  29.0  17.92  39.0  5.15  20.7  35.39  29.5  17.04  39.5  4.81  20.8  35.09  30.0  16.08  40.0  4.47  20.9  35.03  30.5  15.47  41.0  4.10  34.90  31.0  14.96  42.0  3.66  21.5  35.15  31.5  14.01  43.0  3.12  22.0  33.57  32.0  12.69  44.0  2.74  22.5  32.49  32.5  12.30  45.0  2.49  23.0  31.38  33.0  11.58  46.0  2.17  23.5  30.79  33.5  10.78  47.0  1.983  24.0  29.62  34.0  10.20  48.0  1.787  24.5  28.12  34.5  9.69  49.0  1.675  138 Table 6.2 (continued)  Energy  Oscillator  Energy  Oscillator  Energy  Oscillator  (eV)  Strength  (eV)  Strength  (eV)  Strength  eV 2 (10 ) 1  eV 2 (10 ) 1  eV’) 2 (10  50.0  1.475  70.0  0.551  110.0  1.566  51.0  1.319  72.0  0.527  112.0  1.684  52.0  1.220  74.0  0.528  114.0  1.797  53.0  1.135  76.0  0.505  116.0  1.878  54.0  1.057  78.0  0.499  118.0  2.00  55.0  1.014  80.0  0.494  120.0  2.14  56.0  0.880  82.0  0.497  122.0  2.27  57.0  0.862  84.0  0.494  124.0  2.38  58.0  0.818  86.0  0.489  126.0  2.52  59.0  0.788  88.0  0.508  128.0  2.67  60.0  0.737  90.0  0.565  130.0  2.78  61.0  0.722  92.0  1.064  132.0  2.89  62.0  0.679  94.0  1.088  134.0  3.01  63.0  0.657  96.0  1.138  136.0  3.17  64.0  0.667  98.0  1.170  138.0  3.26  65.0  0.599  100.0  1.171  140.0  3.33  66.0  0.645  102.0  1.199  142.0  3.47  67.0  0.605  104.0  1.252  144.0  3.53  68.0  0.582  106.0  1.327  146.0  3.62  69.0  0.553  108.0  1.444  148.0  3.70  139 Table 6.2 (continued)  Energy  Oscillator  Energy  Oscillator  Energy  Oscillator  (CV)  Strength  (eV)  Strength  (eV)  Strength V’) (1O e 2  V 1 e 2 (1O )  V 1 e 2 (1O )  150.0  3.75  190.0  4.40  230.0  4.55  152.0  3.84  192.0  4.33  232.0  4.57  154.0  3.91  194.0  4.32  234.0  4.46  156.0  3.94  196.0  4.41  236.0  4.46  158.0  4.02  198.0  4.36  238.0  4.49  160.0  4.01  200.0  4.31  240.0  4.46  162.0  4.05  202.0  4.32  242.0  4.40  164.0  4.14  204.0  4.32  244.0  4.37  166.0  4.18  206.0  4.30  246.0  4.36  168.0  4.12  208.0  4.34  248.0  4.34  170.0  4.19  210.0  4.41  250.0  4.32  172.0  4.25  212.0  4.43  252.0  4.28  174.0  4.35  214.0  4.50  254.0  4.29  176.0  4.27  216.0  4.54  256.0  4.26  178.0  4.25  218.0  4.59  258.0  4.25  180.0  4.32  220.0  4.61  260.0  4.21  182.0  4.35  222.0  4.59  262.0  4.20  184.0  4.29  224.0  4.61  264.0  4.14  186.0  4.28  226.0  4.60  266.0  4.17  188.0  4.31  228.0  4.57  268.0  4.09  140 Table 6.2 (continued)  Energy  Oscillator  Energy  Oscillator  Energy  Oscillator  (eV)  Strength  (eV)  Strength  (eV)  Strength V 1 e 2 (10 )  V 1 e 2 (10)  V1 e 2 (10 )  270.0  4.07  308.0  3.79  346.0  3.21  272.0  4.11  310.0  3.75  348.0  3.24  274.0  4.04  312.0  3.73  350.0  3.25  276.0  4.05  314.0  3.68  352.0  3.34  278.0  4.01  316.0  3.68  354.0  3.21  280.0  4.03  318.0  3.67  356.0  3.15  282.0  3.96  320.0  3.63  358.0  3.25  284.0  3.97  322.0  3.56  360.0  3.16  286.0  3.91  324.0  3.54  362.0  3.14  288.0  3.98  326.0  3.58  364.0  3.17  290.0  3.92  328.0  3.54  366.0  3.09  292.0  3.98  330.0  3.48  368.0  3.02  294.0  3.95  332.0  3.48  370.0  3.00  296.0  3.94  334.0  3.41  372.0  2.97  298.0  3.92  336.0  3.40  374.0  2.97  300.0  3.88  338.0  3.43  376.0  3.02  302.0  3.86  340.0  3.41  378.0  2.93  304.0  3.90  342.0  3.33  380.0  2.91  306.0  3.83  344.0  3.34  normalized to ref. [178] at 21.218 eV a (Mb)  =  1.0975 x 102eV1  141 barrier which separates the inner well and outer well states. The photoionizatlon cross sections reach a maximum value at -180 eV which is —90 eV above threshold. Figure 6.5 shows the presently measured photoionization cross sections of krypton in the energy region 50—400 eV which includes not only the 3d ionization threshold but also the 3s (-290 eV) and 3p (-220 eV) thresholds as well. The optical data of West and Marr [47,103], Land and Watson [1771, and Henke et al. [152] show 10— 15% higher values than the present work around the 3d cross section maximum, while the values of Lukirskii et al. [1701 are lower by more than 25%. The electron impact data of El-Sherbini and Van der Wiel [180] agree very well with the present work. The one—electron calculation of McGuire [112] gives cross sections which are too high. In contrast all theoretical calculations which include electron correlation [113,116,166] adequately describe the behavior of the photoionization oscillator strength of the 3d—electrons. In particular the RPAE data of Amus’ya et al. [116] show extremely good agreement with the present data.  6.2.1.3 Low Resolution Measurements for Xenon Figures 6.6—6.8 show the presently measured absolute optical oscillator strengths for the photoabsorption of xenon and table 6.3 summarizes the corresponding absolute oscillator strength values in the energy region 13.5—398 eV. Figures 6.6(a) and 6.6(b) show the presently measured photoabsOrption oscillator strengths for xenon in the energy region 5—60 eV along with previously reported experimental and theoretical data respectively. It can be seen from figure 6.6(a) that the  80  142  (a) Experimental measurements 1 5s  1 5p  70  80 70  60 50  0 A  D  40  60  Present work (E = 1 eV FWHM) West & Morton [48) Samson [45] Et—Sherbini & Van der Wiel [ 180] Samson et ci. [179]  50 40  -,  30 C  30  20  .0  20  -t  0  10  10 0  0 10  V  1.4  U) 1-4  C.) Cl) 0 C.)  40  30  50  0  60  C.)  90  2 =  20  C.) V U) U) U)  80  0  (b) Comparison with theory 5s’  Ix  90 ‘.4  80  70  70 60 •  /  50  -  —  34.  —  —  +  40  Present Amt.syo Kennedy ZcngwHi  60  work (Expt.) et ci. [116] & Manson [113] & Soven [163]  50  Johnson & Cheng [117] Porpia et ci. [118]  4D  30  30  S.  20  20  •—  1D  10 ....  1’D  20  30  40  . ...  50  •  0  60  Photon energy (eV)  Figure 6.6: Absolute oscillator strengths for the photoabsorption of xenon In the energy region 5—60 eV. (a) comparison with other experimental data [45,48,179,,180]. The discrete region below 13.5 eV is shown at high resolution in figure 6.12. The resonances in the region 20.5—27.4 eV 1 edge are shown at high resolution in figure 6.16. (b) preceding the 5s compared with theory [113,116—118,1631.  0  U)  ,0  0 0  143  Ix  (a) Experimental measurements 30  A  •  * *  A  *  *  •  *  * *  ••  C *  •  20  Present work (E = 1 eV FWHM) West & Morton [48) El—Sherbini & Von der Wiel [180] Land & Watson [177) Ederer [172) Hansel et CI. [174] Samson et 01. [179] Lukirskii et ci. [170]  *  .I  •  20  *•  4d’  30  A  .  J.  c  10 C  10  4  C C.) V U)  A A  0 40  V  C  2b0  160  120  80  C.)  U) 1  0  Ixel  (b) Comparison with theory  C  — —  V U)  C  — —  — —  C.) 4-i  x  C  0  U)  Present work (Expt.) Staroce [164] Amuyso et ci. [116) Kennedy & Monson [113 Zongwiii & Soven [163] Porpio et cI. [118) Rozsnyia [1  30 C 0  1 4p  10  10  -x  x x  x  \  x  0  1 60  120  Photon energy  200  (cv)  F’Igure 6.7: Absolute oscillator strengths for the photoabsorption of xenon in the ener’ region 40—200 eV. (a) comparison with other experimental data [48,170,,172,174,179,,180,]. [113,116,118,163,164,166].  (b) comparison with theory  144  2.5  —  • C  A  2.0  U  * — —  Present work (E = 1 eV FWHM) West & Morton [ 48] EI—Sherbini & Von der WieI 1 180] Land & Watson [ 177] Lukirskii et al. 1 1 701 Kennedy & Manson [113]  2.5  Xci  0  2.0  A  1 .5 \  *_—  \ C  1.5  4s .  —  —  \  1 .0  ..‘ • •fl_..o••.•St  C.)  0 I  0  *  — ___  1 fl  A  A  A  •4-  A  0.5  U)  A A  L).J  A  —  0  C-)  0  U) r:1)  0  .—  C  C-) V U)  0  —  —  Cl)  +.  0.0  0.0 160  200  240  280  320  360  400  Photon energy (eV)  Figure 6.8: Absolute oscillator strengths for the photoabsorption of xenon In the energy region 160—400 eV compared with other experimental [48,17,0,177,180] and theoretical[1 13] data.  145 Table 6.3 Absolute differential optical oscillator strengths for the photoabsorption of xenon above the first ionization potential obtained using the low resolution (1 eV FWHM) dipole (e,e) spectrometer (13.5— 398 cv)  Energy  Oscillator  Energy  Oscillator  Energy  Oscillator  (eV)  Strength  (eV)  Strength  (eV)  Strength V 1 e 2 (10 )  V 1 e 2 (10 )  V’) (10 e 2  13.5  58.35  15.2  54.37  16.9  47.11  13.6  58.29  15.3  53.74  17.0  45.63  13.7  57.96  15.4  54.25  17.1  45.82  13.8  57.98  15.5  53.62  17.2  44.48  13.9  57.80  15.6  53.16  17.3  44.70  14.0  57.53  15.7  52.20  17.4  44.16  14.1  56.71  15.8  52.65  17.5  44.74  14.2  56.95  15.9  51.86  17.6  43.80  14.3  56.62  16.0  51.64  17.7  44.09  14.4  56.86  16.1  51.07  17.8  43.58  14.5  56.34  16.2  50.88  17.9  42.73  14.6  56.58  16.3  50.84  18.0  42.01  14.7  56.34  16.4  49.54  18.1  41.44  14.8  55.87  16.5  48.68  18.2  40.88  14.9  54.59  16.6  48.20  18.3  41.07  15.0  54.47  16.7  48.41  18.4  40.62  15.1  54.16  16.8k  47.44  18.5  40.43  146 Table 6.3 (continued)  Energy  Oscillator  Energy  Oscillator  Energy  Oscillator  (eV)  Strength  (eV)  Strength  (eV)  Strength  eV 2 (10 ) 1  eV 2 (1O ) 1  eV 2 (1O ) 1  18.6  40.28  24.0  19.62  34.0  4.02  18.7  39.55  24.5  18.13  34.5  3.69  18.8  38.70  25.0  16.17  35.0  3.28  18.9  38.84  25.5  15.22  36.0  3.11  19.0  37.61  26.0  14.78  37.0  2.77  19.1  37.49  26.5  13.20  38.0  2.49  19.2  37.00  27.0  12.39  39.0  2.23  19.3  36.96  27.5  11.39  40.0  2.05  19.4  36.19  28.0  9.59  41.0  1.944  19.5  35.28  28.5  8.97  42.0  1.789  19.6  34.60  29.0  8.27  43.0  1.696  19.7  33.83  29.5  7.72  44.0  1.664  20.0  33.04  30.0  7.17  45.0  1.578  20.5  31.21  30.5  6.54  46.0  1.493  21.0  27.93  31.0  6.12  47.0  1.407  21.5  26.88  31.5  5.80  48.0  1.398  22.0  24.88  32.0  5.28  49.0  1.341  22.5  24.01  32.5  4.95  50.0  1.314  23.0  22.08  33.0  4.48  51.0  1.243  23.5  20.84  33.5  4.26  52.0  1.219  147 Table 6.3 (continued)  Energy  Oscillator  Energy  Oscillator  Energy  Oscillator  (eV)  Strength  (eV)  Strength  (eV)  Strength  eV 2 (10 ) 1  eV 2 (10 ) 1  eV 2 (10 ) 1  53.0  1.203  86.0  14.25  126.0  8.90  54.0  1.201  88.0  15.91  128.0  8.15  55.0  1.160  90.0  17.80  130.0  6.94  56.0  1.153  92.0  18.96  132.0  6.73  57.0  1.178  94.0  20.30  134.0  5.36  58.0  1.145  96.0  21.19  136.0  4.55  59.0  1.137  98.0  21.83  138.0  4.19  60.0  1.148  100.0  22.33  140.0  3.41  62.0  1.124  102.0  22.05  142.0  3.03  64.0  1.177  104.0  21.67  144.0  2.82  66.0  1.900  106.0  21.41  146.0  2.43  68.0  2.33  108.0  20.40  148.0  2.41  70.0  2.71  110.0  19.37  150.0  2.11  72.0  3.36  112.0  18.23  152.0  1.838  74.0  4.36  114.0  17.39  154.0  1.702  76.0  5.66  116.0  16.45  156.0  1.554  78.0  7.38  118.0  13.91  158.0  1.454  80.0  8.92  120.00  12.66  160.0  1.366  82.0  10.29  122.0  11.96  162.0  1.297  84.0  11.99  124.0  10.29  164.0  1.241  148 Table 6.3 (continued)  Energy  Oscillator  Energy  Oscillator  Energy  Oscillator  (eV)  Strength  (eV)  Strength  (cv)  Strength  1 e 2 (10 ) V  1 e 2 (10 ) V  1 e 2 (10 ) V  166.0  1.189  206.0  0.974  246.0  1.277  168.0  1.130  208.0  0.983  248.0  1.265  170.0  1.111  210.0  1.037  250.0  1.284  172.0  1.056  212.0  1.072  254.0  1.305  174.0  1.031  214.0  10.90  258.0  1.319  176.0  0.999  216.0  1.092  262.0  1.315  178.0  1.015  218.0  1.159  266.0  1.315  180.0  0.986  220.0  1.114  270.0  1.323  182.0  0.983  222.0  1.154  274.0  1.342  184.0  0.982  224.0  1.151  278.0  1.341  186.0  0.977  226.0  1.181  282.0  1.365  188.0  0.977  228.0  1.190  286.0  1.339  190.0  0.972  230.0  1.188  290.0  1.347  192.0  0.960  232.0  1.197  294.0  1.350  194.0  0.981  234.0  1.194  298.0  1.363  196.0  0.984  236.0  1.235  302.0  1.337  198.0  0.979  238.0  1.258  306.0  1.356  200.0  0.990  240.0  1.248  310.0  1.340  202.0  0.969  242.0  1.263  314.0  1.338  204.0  0.995  244.0  1.267  318.0  1.321  149 Table 6.3 (continued)  Energy  Oscillator  Energy  Oscillator  Energy  Oscillator  (eV)  Strength  (eV)  Strength  (eV)  Strength  V 1 e 2 (1O )  V 1 e 2 (1O )  322.0  1.322  382.0  1.249  326.0  1.332  386.0  1.208  330.0  1.306  390.0  1.207  334.0  1.297  394.0  1.208  338.0  1.313  398.0  1.175  342.0  1.309  346.0  1.302  350.0  1.288  354.0  1.300  358.0  1.283  362.0  1.241  366.0  1.264  370.0  1.254  374.0  1.279  378.0  1.237  normalized to ref. [1781 at 16.848 eV a(Mb)  1.0975x 102-eV1  V 1 e 2 (1O )  150 present data are in excellent agreement with the recent work of Samson et al. [179] over the entire energy range shown. The data from the West and Morton compilation [48] are much higher than the present work just above the 5p threshold but are very close to the present data at 20 eV. The earlier reported Samson data [451 is slightly lower in the region 16— 30 eV. In theoretical work, the relativistic RPAE data of Johnson and Cheng [1171 show better agreement with the present work than do the non—relativistic RPAE data of Amus’ya et al. [116]. which give much higher cross sections just above the 5p threshold. The calculations reported by Zangwill and Soven [163] in the 15-25 eV region using density—functional theory show very good agreement with the present work. In contrast other theoretical calculations yield less satisfactory results particularly below 20 eV. Photoionization cross sections for the 4d—subshell of xenon have been studied extensively both experimentally and theoretically. Figures 6.7(a) and 6.7(b) show the presently measured photoabsorption oscillator strengths of xenon in the energy region 40—200 eV. It can be seen from figure 6.7(a) that the values obtained in the present work are slightly lower than other experimental data in the energy region around the 4d ionization cross section maximum. The data from Lukirskii et al. [170], Ederer [172] and El—Sherbini and Van der Wiel [180] give the highest oscillator strengths in this region. All one—electron calculations [112, 165] are in severe disagreement with experiment and are not shown in figure 6.7(b). This disagreement is not surprising in view of the many—electron effects which influence the 4d cross sections. The more complex calculations [113,116,118,163,164,166] which Include electron correlation achieve closer agreement with experimental values.  151 In figure 6.7(b) it can be seen that the theoretical calculations Including electron correlation give photolonization cross sections reasonably similar In shape to the present experimental work. However, the cross section maxima reported by Starace [1641, Kennedy and Manson [113] and Rozsnyai [166] are shifted to higher energy. The calculations reported by Zangwill and Soven [163] and Parpla et al. [118] show reasonable agreement with the present work, although the calculated values are slightly higher. Figure 6.8 shows the presently determined photoabsorption oscillator strengths for xenon in the energy region 160—398 eV. There are few previously reported data in this energy region. The data from the West and Morton compilation [48] are lower than the present values in the energy region 160—200 eV but show good agreement with the present work at higher energies. Similar to the results obtained from the data reported by Lukirskii and Zimkina [1691 for argon and by Lukirskii et al. [170] for krypton, the data reported by Lukirskii et al. [1701 for xenon are lower than the present values at energies higher than 160 eV. The earlier dipole electron impact data of El—Sherbini and Van der Wiel [180] show large statistical errors in this energy region, and are much lower than the present work above 200 eV. The calculation by Kennedy and Manson [1 13], also shown in figure 6.8, shows fair agreement with experiment above 200 eV.  152 6.2.2 High Resolution Measurements of the Photoabsorption Oscillator Strengths for the Discrete Transitions Below the mp Ionization Thresholds for Argon (m=3), Krypton (m=4) and Xenon (m=5) High resolution electron energy loss spectra at resolutions of 0.048, 0.072 and 0.098 eV FWHM in the energy range 11—22 eV for argon, 9—22 eV for krypton and 8—22 eV for xenon were multiplied by the appropriate Bethe—Born factors for the high resolution dipole (e,e) spectrometer (see refs. [37,38] and chapter 3) to obtain relative optical oscillator strength spectra which were then normalized In the smooth continuum regions at 21.218 eV for argon and krypton, and at 16.848 eV for xenon using the absolute data determined by Samson and Yin [178]. Figures 6.9—6. 13 show the resulting absolute differential optical oscillator strength spectra of argon, krypton and xenon at a resolution of 0.048 eV FWHM. The dipole—allowed electronic transitions from the 6 mp 2 ms configurations of argon, krypton and xenon with m=3, 4 and 5 respectively, to members of the 5 m ms P 2 ( 3/21/2)ns p and nd manifolds (where n>m) were observed. The positions and assignments [155] of the various members of the nl and ni series are indicated in the figures where the nd[1/2] and nd[3/2] states which converge to the same limit are labelled as nd and n respectively. For peaks in the experimental spectrum which are completely resolved such as the 4s and 4& resonance lines of argon, integration of the peak areas provides a direct measure of the absolute optical oscillator strengths for the respective individual discrete electronic transitions. For states at higher energies which cannot be completely resolved, absolute oscillator  153 700 600 500 400 300  0 IJL.)  C.)  0 0 ‘-4  C.)  ‘-I  0  I  0 I  0  VJ  0 0  2  0  Photon energy (eV)  Figure 6.9: Absolute oscillator strengths for the photoabsorption of argon obtained using the high resolution dipole (e,e) spectrometer (FWHM=O.048 eV). The assignments and energy positions are taken from reference [155]. (a) 11—18 eV. (b) Expanded view of the 13.5—16.5 eV energy region. The deconvoluted peaks are shown as dashed lines.  154  500  400  300 0 C.)  I!  0 200 0 0  12  Photon energy (eV)  Figure 6.10: Absolute oscillator strengths for the photoabsorption of krypton obtained  using the high resolution dipole (e.e) spectrometer (FWHM=0.048 eV) in the energy region 9—16 eV. The assignments and energy positions are taken from reference [155].  155  2 2  0  C  -.  .—  Q  1 .2  0 120  0  0 0  Q  0  ,  0.8 80  0.4  40  0.0 14.5  Photon energy (eV)  Figure 6.11: Absolute oscillator strengths for the photoabsorption of krypton obtained using the high resolution dipole (e,e) spectrometer (F’WHM=O.048 eV). The assignments and energy positions are taken from reference [155]. (a) Expanded view of the 12.2—13.6 eV energy region. The deconvoluted peaks are shown as dashed lines. (b) Expanded view of the 13.5-15.0 eV energy region.  156  8  6s  I I  5d  5d7s -  1111111111  2  Sd6dBs -  6s  5d7s  P 2 / 3 I II II  6d8s7d  I iXe1 I 1/2  800  0 C)  600c, 0 ‘-4  o  C)  4  4000  C.) 0  0  2  200 0  C.)  0  I  I  8  0  •  10  12  14  Photon energy (eV)  Figure 6.12: Absolute oscillator strengths for the photoabsorption of xenon obtained using the high resolution dipole (e,e) spectrometer (FWHM=0.048 eV) in the energy region 8—15 eV. The assignments and energy positions are taken from reference [1551.  157  500  400  300  200  ,  0 00 .— C.)  0  I C.)  0  .—  o  0  1.6 160  0  01.2 120  08  80  0.4  40  0.0  0  Photon energy (eV)  Figure 6.13: Absolute oscillator strengths for the photoabsorption of xenon obtained using the high resolution dipole (e,e) spectrometer (FWHM=O.048 eV). The assignments and energy positions are taken from reference [155]. (a) Expanded view of the 11—12 eV energy region. The deconvoluted peaks are shown as dashed lines. (b) Expanded view of the 12—13.7 eV energy region.  158 strengths have been obtained from fitted peak areas as shown in the figures, according to least squares fits of the experimental data. The same fitting procedures have been applied to the spectra obtained at the three different experimental resolutions. The consistency of the oscillator strength values obtained for given transitions at the different resolutions confirms the accuracy of the fitting procedures and the respective Bethe—Born factors determined as described in refs. [37,38] and chapter 3. Tables 6.4—6.9 summarize the optical oscillator strengths for the discrete transitions of the three noble gases obtained from the analyses of the spectra (figures 6.9—6.13) at the highest resolution (0.048 eV FWHM). The uncertainties are estimated to be -5% for resolved transitions and 1O% for unresolved peaks such as the 5s, 5s’, 3d and 3d’ excited states of argon due to the additional errors involved in deconvoluting the peaks. Other previously reported experimental and theoretical oscillator strengths for the discrete electronic transitions of the three noble gases are also shown in the tables for comparison. Figure 6.9(a) shows a typical absolute differential optical oscillator strength spectrum of argon obtained at a resolution of 0.048 eV FWHM over the energy range 11—18 eV. Figure 6.9(b) shows an expanded view of the spectrum in the 13.5—16.5 eV energy region including the fitted peaks corresponding to partially resolved or unresolved states. Since most of the previously reported experimental [62,138,139,141,197,199,202,205,206,208,209,214] and theoretical [111,147,151,181,186,1881 data are restricted mainly to the 4s (ai) and  Table 6.4  159  Theoretical and experimental determinations of the absolute optical oscillator strengths for the ( 5 3s — 6 3 P 2 3/2,1/2)4s ’3s p discrete transitions of argont  Oscillator strength for transition  Oscillator  3s — 6 3 2 m *.3s p where m is from 5  strength  ) 1 312 (a P 2 ( )4s  )4s’ (a , 1 P 2 ( ) 2  ratio  (11.614 eV)#  (11.828 eV)  (al/a2)  A. Theory: Amus’ya (1990) [1451  0.298  Cooper (1962) [104]  0.33  Stewart (1975) [151]  0.270  Albatetal. (1975) [188]  0.048  0.188  0.255  Gruzdev and Loginov(1975)[1861  0.06 1  0.231  0.264  Lee(1974)[185]  0.059  0.30  0.197  LeeandLu(1973)[184]  0.080  0.210  0.381  (a) dipole length  0.07 1  0.286  0.248  (b) dipole velocity  0.065  0.252  0.258  0.075  0.15  0.500  (a)wavefunction  0.052  0.170  0.306  (b) semi-empirical  0.049  0.200  0.245  0.0662  0.265  0.250  (0.0033)  (0.013)  Aymaretal. (1970)[147]  Gruzdev(1967)[111] Knox (1958) [181]  B. Experiment: Present work (HR dipole(e,e))  Tsurubuchietal. (1990) [140] (Absolute self-absorption) L,ietal. (1988) [143] (Electron impact)  0.057  0.213  (0.003)  (0.011)  0.058  0.222  (0.003)  Chornayetal. (1984) [202]  0.065  (Lifetime: electron-photon  (0.005)  0.268  0.261  (0.02)  coincidence) Westerveld et al. (1979) [139] (Absolute self-absorption) Geiger (1978) [213] (Electron_impact)  0.063 (0.005) 0.066  0.240  0.263  (0.02) 0.255  0.259  Table 6.4 (continued)  160 Oscillator strength for transition  Oscillator  from m 5 3s 6 3 2 .3s p where m is  strength  312 (ai) P 2 ( )4s (11.614 eV)  112 P 2 ( )4s  ) 2 (a  ratio  (11.828 eV)  (al/a2)  0.051  0.210  0.243  (0.00 7)  (0.030)  0.067  0.267  0.251  0.076  0.283  0.269  (0.008)  (0.024)  B: Experiment: (continued)  Valleeetal. (1976) [206] (Pressure broadening profile) Kuyatt (1975) [219] (Electron impact) Copley and Camm (1974) [205] (Pressure broadening profile)  Irwinetal. (1973) [199] (Lifetime: beam foil)  Natalietal. (1973) [142]  0.083  0.35  (0.027)  (0.130)  0.070  0.278  0.237  0.252  (Electron impact) McConkey and Donaldson (1973) 1208] (Electron excitation function)  0.096 (0.02)  Jongh and Eck (1971) [62]  0.22  (Relative self-absorption) Geiger (1970) [141] (Electron impact) Lawrence (1968) [198] (Lifetime: Delay coincidence) Morack and Fairchild (1967) [197] (Lifetime: delayed coincidence) Lewis (1967) [138] (Pressure broadening profile) Chamberlainetal. (1965) [209]  (0.02) 0.047  0.186  (0.009)  (0.037)  0.059  0.228  (0.003)  (0.02 1)  0.259  0.024 (0.003) 0.063  0.278  (0.004)  (0.002)  0.049  0.181  (Electron_impact)  + Estimated uncertainties in the experimental measurements are shown in parentheses. Summed oscillator strength 2 +a 1 (a ) .  0.253  0.227  0.271  0.014  0.0031  0.11  0.025  0.053  0.034  0.0011  Lee and Lu (1973)1184)  142]  (0.0 15) (0.003) (0.006)  (0.002)  (Lifetime: delayed  @ Values obtained by reanalyzing the lifetime data of Lawrence (1968)1198 I.  The transition energies were obtained from ref. 11551.  312 limit. P rid and n refer to the ndl 1/21 and nd)3/21 states respectively which converge to the same 2  Estimated uncertainties in the experimental measurements are shown in parentheses.  coincidence)  0.107  0.0106  0.013  0.0119  0.093  0.093  0.028  0.0268  Lawrence (1968) (1981  (Lifetime data from ref. 1198))  Wieseetal. (1969) ]54  (Electron impact)  Natalletal. (1973)  (Electron impact) 0.110  0.004  0.0094  0.097  0.0108  0.108  0.032  <0.0025  Geiger (1978) 12131  0.0124  (0.007)  (0.0008)  (0.006)  (0.002)  (0.00007)  (Absolute se1fabsorpt1on)  0.092  0.086  0.0106  0.079  0.025  0.00089  Westerveldetal. (1979) 11391  0.028  (0.0014) (0.0002)  (0.011)  (0.0013)  (0.0091)  (0.0026)  (0.0001)  0.0010  0.0144 0.0019  0.106  0.0126  0.09 14  0.0264  Present work (HR dipole (e,e))  0.0013  B: Experiment:  0.023  0.0026  0.128  0.039  0.045  0.045  0.0016  (14.848 eV)  (14.711 eV)  (14.304 eV)  (14.255 eV)  (14.153 eV)  (14.090 eV)  t (13.864 eV)  Lee (1974) 11851  A: Theory:  12 )6s 3 P 2 (  12 )4d 3 P 2 (  12 )3d 1 P 2 (  1/2)5s ( P 2  3. ( ) i 3 P 2  3/2)Ss ( P 2  ..3s p where m Is 5 3s — 6 3 2 Oscillator strength from m )3d 312 (2p  argon in the energy region 13.80—14.85 eV  Theoretical and experimental determinations of the absolute optical oscillator strengths for discrete transitions of  Table 6.5(a)  The transition energies were obtained from ref. 11551.  nd and nd refer to the ndl 1/21 and ndl3/2} states respectively which converge to the same 213,2 limit.  0.827  0.0032  0.0224  0.015  0.048  0.0234  (0.0043) (0.0043)  (0.0004)  (0.0022)  (0.0021)  (0.0048)  0.0139  0.859 0.0426  0.0041  0.022 1  0.0209  0.013  Estimated uncertainties In the experimental measurements are shown in parentheses.  (Electron_impact)  Natalietal. (1973) 11421  Present work (HR dipole (e.e))  0.032  (15.190 eV)  (15.186 eV)  (15.118 eV)  0.82  to Ionization  5. ( ) i 3 P 2  )7 312 (2p  12 )5d 3 P 2 (  Total  0.0484  0.039  LeeandLu(1973)11841  B: Experiment:  0.036  (15.022 eV)  (15.004 eV)  t (14.859 eV)  Lee (1974) 11851  A: Theory:  12 )6s’ 1 P 2 (  12 )4d 1 P 2 (  312)4d.. ( P 2  p where 111 is ..3s 5 3s — 6 3 2 Oscillator strength from m  t argon in the energy region 14.85—15.30 eV  Theoretical and experimental determinations of the absolute optical oscillator strengths for discrete transitions of  Table 6.5(b)  163 Table 6.6 Theoretical and experimental determinations of the absolute optical oscillator strengths for the ( 5 4s — 6 4 2 .4s p2 3 /2.1 /2)5 S discrete transitions of kryptont P  Oscillator strength for transition  Oscillator  from m 5 4s — 6 4 2 4s where m is p  strength  ) 1 312 (b P 2 ( )5s  )5s’ / 1 P 2 (  (10.033 eV)#  ) 2 (b  (10.644 eV)  ratio  1b 1 (b ) 2  A. Theory: Amusya (1990) [145]  0.353  Cooper (1962) [1041  0.405  Aymar and Coulombe (1978) [189] (a) dipole length  0.176  0.177  0.99  (b)dipolevelcity  0.193  0.172  1.12  Geiger (1977) [2121  0.250  0.143  1.748  Gruzdev and Loginov (1975) [1871  0.190  0.177  1.073  (a) dipole length  0.2 15  0.2 15  1.000  (b) dipole velcity  0.185  0.164  1.128  0.20  0.20  1.000  (a)wavefunction  0.138  0.136  1.015  (b) semi-empirical  0.152  0.153  0.993  0.214  0.193  1.109  (0.011)  (0.010)  0.155  0.139  (0.01 1)  (0.010)  0.143  0.127  (0.015)  (0.0 15)  Aymaretal. (1970) [147]  Gruzdev(1967)[llll Dow and Knox (1966) [1821  B. Experiment: Present work (HR dipole(e.e))  Tsurubuchiet al. (1990) [1401 (Absolute self-absorption) Takayanagietal.(1990)[2151 (Electron impact)  1.115  1.126  164 Table 6.6 (continued)  Oscillator strength for transition  Oscillator  from 5 4s — 6 4 2 m ’4s p where m is  strength  ) 1 P3/2)5s (b 2 (  ) 2 P1/2)5s’ (b 2 (  ratio  (10.033 eV)  (10.644 eV)  ) 2 (biIb  B: Experiment: (continued) Ferrelletal. (1987)166]  0.180  (Phase-matching) Matthiasetal. (1977) [2011 (Lifetime: resonance fluoresonance) Geiger (1977) [2121  (0.027) 0.208  0.197  1.056  (0.006)  (0.006)  0.195  0.173  1.127  0.212  0.191  1.110  (Electron impact) Natalietal.(1973)[142] (Electron impact) Jongh and Eck (1971) [621  0.142  (Relative self absorption) Geiger(1970)[141] (Electron impact) Griffin and Hutchson (1969) [1921 (Total absorption) Chashchina and Shrieder (1967) [193]  (0.015) 0.173  0.173  (0.035)  (0.035)  0.187  0.193  (0.006)  (0.009)  0.21  0.21  (Linear absorption)  (0.05)  (0.05)  Lewis (1967) [138]  0.204  0.184  (0.02)  (0.02)  0.159  0.135  (Pressure broadening profile) Wilkinson(1965)[190] (Total absorption) Turner (1965) 1196]  0.166  (Lifetime:_resonance_imprisonment)  Estimated uncertainties In the experimental measurements are shown in parentheses. The transition energies were obtained from ref. 11551. Summed oscillator strength (b 2 +b 1 ) .  1.000  0.969  1.000  1.109  1.178  *  0.0044  0.0817  0.152  The transition energies were obtained from ref. [155].  312 limit. P nd and n refer to the nd] 1/21 and nd[3/21 states respectively which converge to the same 2  0.0138  0.0420  0.0056  0.015 0.0439 0.014 0.142  0.0649  0.0055  (0.0011)  (0.0082)  (0.0003)  (0.0044)  0.154  (0.0014)  0.0105  0.0065  (13.037eV)  12 )6s’ 1 P 2 (  (0.015)  0.0438  (13.005eV)  12 )4d’ 1 P 2 (  0.0435  0.0114  (12.870eV)  12 )5d 3 P 2 (  0.0140  0.108  0.0824  0.0973  (12.385eV)  12 )6s 3 P 2 (  0.0053  0.0144  (12.355eV)  P3,12)4d 2 (  Estimated uncertainties in the experimental measurements are shown in parentheses.  (Electron_impact)  Natalietal..(1973)1142]  (Electron Impact)  Geiger(1977) 1212]  Present work (HR dipole (e,e))  B: Experiment:  Geiger(1977)[2121  A: Theory:  (12.037eV)#  4d* (2p ) 2 / 3  p 4s where m is 5 4s — 6 4 2 Oscillator strength from m  discrete transitions of krypton in the energy region 11.90—13.05 eVt  Theoretical and experimental determinations of the absolute optical oscillator strengths for  Table 6.7(a)  0)  0.119  0.048  0.0024  0.0042  The transition energies were obtained from ref. [1551.  312 limit. P nd and n refer to the nd[ 1/21 and nd[3 / 21 states respectively which converge to the same 2 tm  0.0295  0.054  0.0290  (0.0020)  (0.0044)  (0.0002)  (0.011)  (0.0061) 0.187  0.0203  0.0163  (13.437 eV)  0.0439  0.0307  (13.423 eV)  12 )8s 3 P 2 (  0.0015  0.0025  (13.350 eV)  P3/2)6d. 2 (  0.113  0.0436  (13.114 eV)  12 )6d 3 P 2 (  0.0610  0.0960  (13.099 eV)#  12 )7s 3 P 2 (  Esthnated uncertainties in the experimental measurements are shown In parentheses.  (Electron_impact)  Nataliet al. (1973) [142J  (Electron impact)  Geiger(1977)12121  Present work (HR dipole (e,e))  B: Experiment:  Geiger (1977) (2121  A: Theory:  .  )5* 312 (2p  ’4s p where m is 5 4s — 6 4 2 Oscillator strength from m  discrete transitions of krypton in the energy region 13.OS—13.50 eV  1.10  (0.056)  1.126  ionization  to  Total  Theoretical and experimental determinations of the absolute optical oscillator strengths for  Table 6.7(b)  C)  —  167 Table 6.8 Theoretical and experimental determinations of the absolute optical oscillator strengths for 3 /2.1 / 2)6S discrete transitions of xenon P p(2 the 2 5 5s — 6 5 ’5s  Oscillator strength for transition  Oscillator  p where m is from m 5 5s — 6 5 2 ’5s  strength  )6s (cj) / 3 P 2 (  ) 2 112 (c P 2 ( )6s’  ratio  (8.437 eV)#  (9.570 eV)  /c 1 (c ) 2  A. Theory: 0.403  Amus’ya (1990) [145] Aymar and Coulombe (1978) [1891 (a) dipole length  0.282  0.306  0.922  (b) dipole velcity  0.294  0.270  1.089  0.28  0.365  0.767  (a) dipole length  0.273  0.235  1.162  (b) dipole velcity  0.176  0.118  1.492  Kimetal.(1968)[183]  0.212  0.189  1.122  Gruzdev(1967) 1111]  0.28  0.25  1.120  (a) wavefunction  0 194  0.147  1.320  (b) semi-empirical  0.190  0.170  1.118  0.273  0.186  1.468  (0.014)  (0.009)  0.222  0.158  (0.027)  (0.019)  Geiger (1977) [212] Aymaretal. (1970) [147]  Dow and Knox (1966) 1182]  B. Experiment: Present work (HR dipole(e.e))  Suzukietal.(1991)1216] (Electron impact) Ferrell et al. (1987) [66] (Phase-matching)  0.260 (0.05)  0.19 (0.04)  1.405  1.368  168 Table 6.8 (contInued)  Oscillator strength for transition  Oscillator  p where m Is 5 5s — 6 5 2 i.5s from m  strength  ) 1 312 (c P 2 ( )6s  112 (c2) P 2 ( )6s’  ratio  (8.437 eV)#  (9.570 eV)  (cj/c2)  0.263  0.229  1.148  (0.007)  (0.007)  B: Experiment: (continued)  Matthiasetal. (1977) [201] (Lifetime: resonance fluoresonce) Geiger (1977) [212]  0.26  0.19  1.368  0.183  0.169  1.083  0.272  0.189  1.439  0.213  0.180  1.183  (0.020)  (0.040)  (Electron impact) DelageandCarette(1976)[211] (Electron impact) Natalietal. (1973) [142] (Electron impact) Wieme and Mortier (1973) [200] (Lifetime: resonance imprisonment) Geiger (1970) [141]  0.26  0.19  1.368  (Electron impact) 0.194  Griffin and Hutchson (1969) [192]  (0.005)  (Total absorption) Lewis (1967) [138] (Pressure broadening profile) Wilkinson (1966) [191] (Total absorption) Anderson (1965) [1951 (Lifetime: level-crossing)  0.256  0.238  (0.008)  (0.0 15)  0.260  0.270  (0.020)  (0.020)  0.256  0.238  (0.008)  (0.015)  Estimated uncertainties In the experimental measurements are shown in parentheses. The transition energies were obtained from ref. 11551. Summed oscillator strength (cl+c2).  1.071  0.963  1.076  0.381  0.395@  0.09  0.110  The transition energies were obtained from ref. 11551.  0.002  0.0025  <0.00 1  0.0025  (10.979 eV)  3 )6d P 2 1 2  312 limit. P nd and n4 refer to the adi 1/21 and ndl3/21 states respectively which converge to the same 2  @TbJs value was normalized to the experlmentalvalue of Geiger(1977) 1212).  #  0.012  0.019  0.0968  Estimated uncertainties In the experimental measurements are shown In parentheses.  (Electron_impact)  Natalletal. (1973) [1421  (Electron impact)  DelageandCarette(1976)12111  (Electron Impact)  Geiger (1977) [212]  (Phase-matching)  Krameretal. (1984) (2071  0.395  (0.01)  (0.07)  (Phase-matchIng)  0.0095  0.088  0.370  Ferrelletal. (1987) [66]  0.098  (0.0043)  (0.019)  Present work (HR dipole (e,e)) (0.0005)  0.0769  0.0859  0.550  (10.593 eV)  0.379  0.0237  (10.401 eV)  (9.917 eV)#  3 )7s 1 P 2 ( 2  0.0105  B: Experiment:  GeIger (1977) [212]  A: Theory:  P312)5d. 2 (  0.082  0.123  0.021  0.032  0.0236  (0.0022)  (0.0084)  0.0862  0.0222  0.0126  (11.274 eV)  P3/2)8s 2 (  0.0835  0.0940  (11.163 eV)  Pl/2)6d. 2 (  p 5s where m Is Oscillator strength from m 5 5s — 6 5 2 3 )5d 1 P 2 ( 2  xenon In the energy region 9.80-11.45 eV+  0.021  0.027  0.0217  (0.0023)  0.0227  0.0190  (11.423 eV)  P3/2)7d 2 (  Theoretical and experimental determinations of the absolute optical oscillator strengths for discrete transitions of  Table 6.9(a)  CD.  0.001  0.006  0.004  0.0003  <0.001  0.0009  <0.001  0.0024  I  ®  This value Is quoted In ref. I143J.  The transition energies were obtained from ref. 11551.  12 limit. 2 3 nd and nhj refer to the ad) 1/2) and nd(3 /21 states respectively which converge to the same P  0.006  I  fo.ioo  0.015  1.640® 0.0204 0.123  0.0096  0.205  0.l86  (0.080) (0.0029) (0.0097)  (0.0009)  (0.019)  0.171  1.606 0.0288  0.0169  0.0967  0.123  0.0088  0.0155  0.19 1  0.206  ionization  (11.752 eV)  (11.740 eV)  (11.683 eV)  (11.607 eV)  0.251  (11.583 eV)  (11.495 eV)#  to  3/ lOs P 2 ( )  3/2)8 ( P 2  3/2)8d ( P 2  Total  1/2)Sd’ ( P 2  Estimated uncertainties In the experimental measurements are shown In parentheses.  (Electron impact)  Natalletal.(1973)[142]  (Electron Impact)  Delage and Carette (1976) (2111  (Electron impact)  Geiger (1977) [2121  Present work (HR dipole (e.e))  B: Experiment:  Geiger (1977) (2121  A: Theory:  3/2)95 ( P 2  p where m Is ’5s 5 5s — 6 5 2 Oscillator strength from m )7 12 (2p  xenon in the energy region 11.45-11.80 eV  of absolute optical oscillator strengths for discrete transitions Theoretical and experimental determinations of the  Table 6.9(b)  C  171 4& (a2) resonance lines#, the results for these two lines are presented separately in table 6.4. Immediately it can be seen that there are great variations in the oscillator strength values reported for the 4s and 4s’ lines in both experimental work and also in the theoretical calculations. However, experimental work gives a reasonably consistent result (-0.25) for the oscillator strength ratio (ai /a2) as shown In the fourth column of table 6.4. This suggests that systematic errors, such as uncertainties In measuring the target density or errors in normalizing the data, may be the cause of the large variations in the absolute values. The summed absolute optical oscillator strength (i.e. al+a2) calculated by Cooper [104], using a one—electron approximation, (value of Cooper) agrees very well with the sum of the presently measured values (0.33 1) while the value (0.298) reported by Amus’ya [1451 using the RPAE method is slightly lower. The calculated data reported by Aymar et al. [147] for ai and a, and the value reported by Stewart [151] for a are consistent with the present work. The calculations by Knox [181] and by Albat et al. [188] give very low values. Experimentally, the oscillator strength values reported by three groups [62,139,140] using the self—absorption method are all lower than the present values by 5—20%. Lifetime measurements performed by Irwin et al. [199] using the beam foil method show values for ai and a much higher than the present work, while the value of al reported by Morack and Fairchild [197], who used a delayed coincidence method, is much lower than all other experimental values. The values measured by Copley and Camm [205] and by Lewis [138] from analyses of  # The designations al,a2; b , b 1 ; and c1,c; are used for convenience in the present work 2 for the respective ns, ns’ resonance lines of argon, krypton and xenon, respectively.  172 the pressure broadening profiles are consistent with the present work. Several electron impact based experimental methods have been employed for deriving the absolute oscillator strengths for al and a. The values reported by Chamberlain et al. [2091, Geiger in his earlier work [141] and Li et al. [2141, are all lower than those measured In the present work. However the unpublished data of Natali et aL. [1421, the data of Kuyatt [219] which are quoted in the compilation of Eggarter [2171, and the later work of Geiger [213] which has been quoted in refs. [139,143], show quite good agreement with the presently measured values. In a compilation published by Wiese et al. [54] values of ai and a2 (not shown in table 6.4) were obtained from averaging the data reported by Lawrence [198] and Lewis [1381. A summary of the absolute optical oscillator strengths for the discrete transitions of argon at higher energies is given in tables 6.5(a) and 6.5(b). Two sets of theoretical results [184,185] have been published, but both show substantial differences with the presently reported and most other experimental data. The lifetime measurements of Lawrence [198], obtained using a pulsed electron source, show good agreement with the present values for the 5s, 3d, 5s’ and 3d’ transition lines. A reanalysis of the lifetime data of Lawrence [198] by Wiese et al. [54] gave absolute oscillator strength values for the above four transition lines which are also consistent with the present work. Similar to the situation for the 4s and 4s’ resonance lines, the self—absorption data for other lines at higher energies measured by Westerveld et al. [139] are lower than the present values. A more comprehensive data set was reported in the electron impact based work of Natali et al. [142], and the oscillator strength values for most of the more intense lines are  173 consistent with the present work. The total discrete osci1lator strength sum up to the 2 312 ionization threshold of argon has been determined In P the present work to be 0.859, a value which agrees within 5% with estimates of 0.82 calculated by Lee [1851 and 0.827 measured by Natali et al. [1421. In the earlier compilation reported by Eggarter [2171, the total discrete oscillator strength of argon was estimated to be 0.793 on the basis of the more limited data available at that time. Figure 6.10 shows the presently determined absolute differential optical oscillator strength spectrum for krypton over the energy range 9— 16 eV. Figures 6.11(a) and 6.11(b) show expanded views of the spectrum in the energy regions 12.2—13.6 eV and 13.5—15 eV, respectively. Since higher members of the ns’ and nd’ series which converge to the 2 112 Ionization threshold are above the 2 P 312 ionization P threshold, autoionizing resonance profiles are observed as shown in figure 6.11(b) due to the interaction between the discrete and continuum states. The absolute optical oscillator strengths for the individual discrete electronic transitions of krypton determined in the present work are summarized in tables 6.6 and 6.7. There are considerable variations between the various experimental and theoretical oscillator strength values for both the 5s (b ) and the 5s’ (b 1 ) resonance lines as 2 can be seen in table 6.6. However, on the basis of the oscillator strength ratio 2 1b the reported data can be divided into two groups. For one 1 (b ) group the ratio is close to 1 while for the other it is  —  1.1. The summed  absolute optical oscillator strength (i.e. 0.405 for 2 +b computed by 1 b ) Cooper [1041 is consistent with the present value (0.407). The values of 2 calculated by Dow and Knox [182] are too low compared with 1 and b b the present and most other experimental work. Similar to the situation  174 for argon the self—absorption data reported by Tsurubuchi et al. [1401 for 2 and Jongh and Eck [62] for b 2 are lower than the presently 1 and b b reported values. The experimental data of Ferrell et al. [661 obtained using the phase—matching method, that of Matthias et al. [2011, which was determined by measuring the lifetimes of the radiative fluorescence, the data of Natali et al. [142], who applied the electron Impact based method and the data of Lewis [138], which were obtained by studying the pressure broadening profiles, are all In good agreement with the presently reported oscillator strength values for b 1 and b 2 The absolute optical oscillator strength values for transitions at higher energies are shown in tables 6.7(a) and 6.7(b). The theoretical data available are limited to the semi—empirical calculations reported by Geiger [2121. Only the value for the 4d’ resonance line computed by Geiger [2121 agrees with the present results. Previously published data obtained by application of electron impact based methods [142,212] together with the present dipole (e,e) work provide the only available optical oscillator strength data for the discrete transitions of krypton at higher energies. Generally quite good agreement for the absolute optical oscillator strength values is observed among the different electron impact methods for most of the transition lines. The total discrete oscillator strength up to the 2 312 ionization threshold is determined to be 1.126 in the P present work compared with an estimate of 1.10 reported by Natali et al. [1421. Figure 6.12 shows the high resolution absolute differential oscillator strength spectrum of xenon obtained in the present work over the energy region 8—15 eV. Figures 6.13(a) and 6.13(b) show expanded views of the spectrum in the energy regions 11—12 eV and 12—13.7 eV  175 respectively. Broad autoionizing resonance profiles of higher members of the ns’ and nd’ series above the 2 312 limit are observed as can be seen in P figure 6.13(b). Tables 6.8 and 6.9 summarize all the discrete absolute optical oscillator strengths values for xenon determined in the present work along with various previously reported theoretica1 and experimental data. It can be seen from table 6.8 that there are large variations In the oscillator strengths reported for the 6s (ci) and 6s (c2) resonance lines. The oscillator strength ratio of ci/c2 also shows considerable variation from 0.767—1.492 for theory and 0.963—1.468 for experiment. Some theoretical data show agreement of either ci [111,147,189,212] or c2 [183] with the present work. However, no single set of theoretical data are consistent with the present work for both the ci and c2 values. Experimentally, the phase—matching data of Ferrell et al. [66], and the electron impact data of Geiger [141,2 121 and Natali et al. [142] show good agreement with the presently reported ci and c2 values. The recently reported data of Suzuki et al. [216] are --20% lower than the present values. Similar discrepancies were observed in the cases of the 2 transitions of krypton ai and a2 transitions of argon and the bi and b between the present work and absolute oscillator strengths reported by the same group [214,2151 (see above). The absolute data for the discrete transitions at higher energies are shown in tables 6.9(a) and 6.9(b). The phase—matching data of Ferrell et al. [66] show excellent agreement for the 5j and 7s lines with the present values while the earlier phase— matching value reported by Kramer et al. [207] for the 7s line is slightly higher. Other more comprehensive data for the discrete transitions of xenon at higher energies have all been measured by electron impact based methods [142,211,212]. It can be seen that the oscillator  176 strengths determined in the present work are in excellent agreement over the whole energy range with the data reported by Natall et al. [142], except for the lOs line. This discrepancy may be caused by errors In deconvoluting the peak. The data of Geiger [2121 are consistent with the present work for most of the transitions, while the data of Delage and Carette [2111, which have been normalized on the 5d line from the data of Geiger [212], show considerable variations compared with the presently reported values. Finally, the total oscillator strength sum up to the 2 312 ionization threshold of xenon was determined to be 1.606 in P the present work, which is in good agreement with the estimate of 1.640 reported by Geiger [212].  6.2.3 High Resolution Measurements of the Photoabsorption Oscillator Strengths in the Autoionizing Resonance Regions due to Excitation of the Inner Valence s Electrons The profiles and relative cross sections of the autoionizing excited state resonances of argon, krypton and xenon involving the excitation of an inner valence ms electron have been previously studied in some detail experimentally [45,176,218,220—226]. Although double excitation processes have also been reported in these energy regions [218,221— 223], these transitions are extremely weak and they are not specifically identified in the present work. Absolute intensity measurements [45,176,220,226] have also been reported. In the present study Bethe— Born converted electron energy loss spectra of the three noble gases were obtained in these regions with the use of the high resolution dipole (e,e) spectrometer at a resolution of 0.048 eV FWI-IM. The resulting  177 relative optical oscillator strength spectra were then normalized In the respective smooth continua at 21.218 eV for argon and krypton, and at 16.848 eV for xenon using the absolute data determined by Samson and Yin [178]. Figure 6.14 shows the resulting absolute optical oscillator strength spectrum of argon in the energy region 25—30 eV. The absolute data reported by Carison et al. [176] (crosses) using synchrotron radiation and Samson [45,220] (open circles) employing a double Ionization chamber are also shown in figure 6.14. Only the assignments for the transitions involving excitation of a 3s electron to an np states are shown. The energy positions of the resonances as indicated in the manifold on figure 6.14 are taken from the high resolution photoabsorption data reported by Madden et al. [218]. The data of Carison et al. [176] show a slight shift in energy scale with respect to the present work, which may be due to errors in digitizing the data from the small figure in the original paper. The absolute data reported by Samson [45,220] and Carison et al. [176] are in good agreement with the present work in the energy region 25—26 eV. However, the Samson data are higher than the present work above 29 eV while the data of Carison et al. [176] are lower. It seems likely that “line saturation” effects, which have been discussed in detail in refs. [36,37,46,72] are observed in the direct optical data reported by Samson [45,220] for the 3s—’np transitions. Since the widths of the 3s—’np transition peaks became much narrower as n increases, “line saturation” effects are expected to be more severe for the peaks at higher n values. it can be seen from figure 6.14 that for the relatively broad 3s—’4p transition, the data of Samson [45,220] show a lower minimum than the present data, which is consistent with the higher experimental  178  0 I  0.5  0.4  3s 2 3p 61 S 0  5  4  0.3-  :  0.1  6  Afl J  C  .  .4-i  C)  7 89  30 ‘  U) Cl) Cl)  oI  C) I  0  0.2  IAn  -z 62 )np 112 S 3sp IIIII I  —4  I  ‘  50  :  •‘:  xx  ,  C  ,,  ..  Present work Carison et al. [ 176) Samson [45,220]  -  o  0  0.025  26  27  28  29  30  Photon energy (eV)  Figure 6.14: Absolute oscillator strengths for the photoabsorption of argon in the autoionizing resonance region 25—30 eV. The solid circles represent the present work (FWHM=0.048 eV), the open circles and crosses represent the photoabsorption data reported by Samson 145,220] and Carison et al. [176], respectively. The assignments and energy positions are taken from reference [218].  179 resolution of Samson [45,2201. However, for the narrower 3s—’5p transition, the present work (which cannot show “line saturation” effects) gives a lower minimum than the Samson data [45,220]. This observation strongly suggests the presence of “line—saturation” effects at larger n due to the finite bandwidth of the optical experiments [45,220]. The same phenomenon is observed for the transitions to the higher np states. Figure 6.15 shows the presently determined high resolution absolute optical oscillator strength spectrum of krypton in the energy region 23—28.5 eV along with the reported absolute data of Samson [45,2201. The assignments and energy positions for the 4s—’np transitions are taken from Codling and Madden [221,223]. There are two 6 4 2 p ‘So J= 1 components for the transition 4s  —  51/2)np, where 2 ( 6 4s4p  one Rydberg series is labelled as n and the other one is labelled as shown in figure 6.15. Only fl=. and  .fj for  ,  as  the latter series are  unambiguously assigned [221—223]. The ‘line—saturation” effects that are observed in the optical data reported by Samson [45,220] for argon are also seen in the corresponding direct optical data for krypton. The effect is especially severe for the 4s—’7p transition. Samson [45,220] and other workers, using direct optical methods [22 1—223,2261, have reported a peak  (Q)  at 24.735 eV which was not observed In the present work.  The presently determined high resolution absolute optical oscillator strength spectrum of xenon in the energy region 20—24 eV is shown In figure 6.16. The figure also shows the photoionization cross sections for xenon in this energy range reported by Samson [451, which are significantly lower than those determined in the present work. The assignments and energy positions for the 5s—’np transitions are taken from the data reported by Codling and Madden [221,223]. Only one  180  0.5  KrI  a.)  ‘-r  0.4 4p 1 2 4s 6 0 S  a.)  50  Q3  66  5 5  •4Q  III I 8910  I  H  s. .  0  112 S 2 ( 6 4s4p )np  —  7  1/2  30  0  0 0 0 C)  7  ‘-4  0  0.2  •  = —  CL)  0 0  C.)  o 0  I  0.1  °  C.)  &  I Present work Samson [45,2201  10  oI.  0  0  0.0  I  23  24  25  I  •  26  27  28  Photon energy (eV)  Figure 6.15: Absolute oscillator strengths for the photoabsorption of krypton In the autoionizing resonance region 23—28.5 eV. The solid circles represent the present work (FWHM=0.048 eV), the open circles represent the photoabsorption data reported by Samson [45,220]. The assignments and energy positions are taken from references [221,223].  181  0.5  Xci 0.4  2  5s 5p •  0.3  0 S  4 Av.  •4 0•  0  0..  —— .  62  ( I  8  7  6 “.  5s5p  —  I  %%%9.  0  61  np S ) 2 / 1  III I  9 10  1/2 .•V.  ..  300  ..  I-I  C)  I  0 0  0  0  0  0.2  0  0.1  0  o  0  20  0  1  Present work Samson []I  .101  0  0.0  20  21  22  23  2’4  Photon energy (eV)  Figure 6.16: Absolute oscillator strengths for the photoabsorption of krypton in the autoionizirig resonance region 20—24 eV. The solid circles represent the present work (FWHM=0.048 eV), the open circles represent the photoabsorption data reported by Samson [45]. The assignments and energy positions are taken from references [221,223].  182 Rydberg series of the two J= 1 components of the 5s—’np transitions 12 Ionization threshold has been assigned [221— 2 1 converging to the S 2231.  6.3 Conclusions Comprehensive absolute differential optical oscillator strength data for argon, krypton and xenon in both the discrete and continuum regions have been reported, including measurements at high resolution. The present work represents the completion of the measurements for the noble gas series using the high resolution dipole (e,e) method recently developed for measuring absolute optical oscillator strengths for a wide range of transitions in atoms and molecules. The TRK sum—rule normalization method which was used for helium and neon could not be used for argon. krypton and xenon due to the smaller energy separations between the different subshells of the atoms. Therefore, single point normalization on very accurate photoabsorption measurements has been used. The presently reported results are compared with theory and also other earlier reported experimental data. In the continuum regions the various experimental values generally show reasonable agreement at low energy while there are certain variations at high energy. With the inclusion of more electron correlations and more sophisticated calculations, the theoretical data are in better agreement with experimenta1 values. In the discrete region a wide spread of values is 1 and seen for the resonance line oscillator strengths al arid a2 of argon, b 2 of krypton and c and c2 of xenon in both experiment and theory. For b discrete transitions at higher energies there is a shortage of theoretical  183 data. Electron impact based methods have thus far provided most of the absolute optical oscillator strength data for the valence shell discrete spectra. Generally, the present measurements are in quite good agreement with the earlier unpublished electron impact based data of Natali et al. [1421 which were obtained at lower impact energy. Absolute optical oscillator strengths for the autoionizing excited state regions involving mainly the inner valence s—electrons of the three noble gases have also been obtained. The previously published photoionization data of Samson [45,220] in this energy range show evidence of substantial “line saturation effects.  184 Chapter 7  Absolute Optical Oscillator Strengths (11—20 eV) and Transition Moments for the Lyman and Werner Bands of Molecular Hydrogen  7.1 Introduction An accurate knowledge of absolute transition probabilities for electronic excitation is essential for a quantitative understanding of the interaction of energetic radiation with matter. Very few accurate absolute optical oscillator strength (cross section) measurements have been reported for molecular photoabsorption processes at high resolution particularly in the discrete excitation region, below the first ionization potential. Even in the case of the simplest molecule, molecular hydrogen, such information is quite limited for discrete transitions. Absolute oscillator strength measurements require extremely precise and carefully controlled techniques and in particular direct optical methods using the Beer—Lambert law can be subject to serious quantitative errors. However a much larger body of absolute oscillator strength information exists for the photolonization continuum since experimental methods in these energy regions are generally more straightforward in their application [301. In terms of theoretical work there are few calculations of absolute oscillator strengths. Such calculations are limited by the lack of a sufficiently accurate knowledge of molecular wavefunctions and also by the shortage of precise absolute experimental data for the evaluation and testing of the theoretical methods. Both of these concerns are  185 addressed by recent advances made in electron impact based spectroscopies. Firstly, electron momentum spectroscopy [227] has provided detailed measurements of electron momentum distributions which have led to the evaluation and design of new molecular wavefunctions of unprecedented accuracy (for example see refs. [228— 2311). The growing availability of Improved molecular wavefunctions should lead to greater accuracy in calculated oscillator strengths. Secondly, high resolution dipole (e,e) spectroscopy [37—391 has been demonstrated to provide a versatile experimental method for the accurate determination of optical oscillator strengths for atomic and molecular discrete photoabsorption processes over broad ranges of excitation energy (see chapters 4—6 and refs. [27,36—39]). Hydrogen is an important constituent of the solar and planetary atmospheres and therefore a quantitative understanding of the interaction of molecular hydrogen with energetic radiation Is of great Interest in astrophysics, astronomy and space sciences [232,233]. For example, the absolute oscillator strength for photoabsorption Is an essential quantity in the determination of molecular abundances from interstellar molecular absorption lines [2321. Furthermore, absolute optical oscillator strengths can be used to provide an absolute scale for relative measurements of electron impact cross sections. For Instance, the theoretica1 absolute optical oscillator strengths for hydrogen reported by Allison and Dalgarno [234] were employed by De Heer and Carriere [235] to normalize their measured relative emission cross sections for molecular hydrogen, while Shemansky et al. [236] established absolute cross sections for the Lyman and Werner bands from absolute oscillator strengths derived from the lifetime measurements of Schmoranzer et al.  186 [2371 and the relative transition probabilities calculated by Allison and Dalgarno [2341. The photoabsorption of molecular hydrogen below the first ionization potential is dominated by the Lyman and Werner bands. However, only a very few rather incomplete experimental studies of their absolute oscillator strengths for excitation from the ground state have been reported in the literature. Furthermore, the available oscillator strength measurements show some discrepancies with each other and with theory, although the energy levels of these bands are well known [238]. Molecular hydrogen is the simplest neutral molecule and it is thus of fundamental interest since quantum mechanical calculations are possible with greater accuracy than for other molecular systems. The Lyman and Werner bands, which correspond to the transitions from the ground X  a, B 2 state to the p  and 2pr, C ‘H states respectively,  have been the subject of several theoretical Investigations. Mulliken and Rieke [239], employing the LCAO.-MO method, have reported ca1culated oscillator strengths for the Lyman and Werner bands using the dipole length operator. Shull [240] repeated the same computation using the dipole velocity operator. A theoretical investigation of the oscillator strengths of the Lyman band was carried out by Ehrenson and Phillipson [241] with several Improved ground state wavefunctions using dipole length, velocity and acceleration operators. By solving a one—electron Schrodinger equation, Peek and Lassettre [242] constructed a correlation diagram for hydrogen for several states and reported the oscillator strength values corresponding to the Lyman and the sum of the Lyman and Werner bands. Miller and Krauss [243] approximated the Hartree—Fock orbitals by a linear combination of Gaussian—type atomic  187 orbitals and calculated the inelastic electron scattering differential cross sections and oscillator strengths of the Lyman, Werner and several other bands in hydrogen. The theoretical Franck—Condon factors for the hydrogen Lyman band system have been computed by Geiger and Tops chowsky [244] employing the Wentzel—Kramers—Brillouin (WKB) approximation, by Nicholls [2451 using the Morse potential function, and by Halmann and Laulicht [246] and Spindler [247,248] based on Rydberg— Klein—Rees (RKR) potential functions. From a consideration of previously published experimental electron energy loss data [244,249,250] and lifetime measurements [251], it has been suggested [252] that the electronic transition moment for the Lyman band varies considerably with internuclear separation (r). Using the wavefunctions of Matsen and Browne [253] and Browne and Matsen [254], Browne [252] has computed the electronic transition moment as a function of r for the Lyman band, while Rothenberg and Davidson [255], employing the highly accurate wavefunctions of Kolos and Wolniewicz [256], have also reported the variation of electronic transition moment with r for several transitions of molecular hydrogen. In an earlier paper Dalgarno and Allison [257] reported calculations of the vibronic band oscillator strengths for the Lyman system. These calculations used the potentials developed by Kolos and Wolniewicz [256,258] in conjunction with the asymptotic formulae of Kolos [2591 and Chan and Dalgamo [2601. Dalgamo and Allison [257] also adopted transition moments reported by Schiff and Pekeris [4] at r=0, by Rothenberg and Davidson [2551 at r= 1 .4a 0 and r=2.0a , and by Browne 0 [2521 at large values of r. Using the more accurate transition moments reported by Wolniewicz [2611 for both the Lyman and Werner systems, Allison and Dalgamo [262] later repeated calculations similar to those  188 reported earlier by Dalgarno and Allison [2571. More comprehensive calculated data, Including the transition probabilities for the Lyman and Werner bands, were further reported by Allison and Daigarno [234]. The dependence of electronic transition moment on Internuclear distance was investigated at large r values experimentally by Schmoranzer [263] for the Lyman band and by Schmoranzer and Geiger [2641 for the Werner band based on measurements of the optical emission intensity from electron impact excited hydrogen molecules. These results are In good agreement with the theoretical predictions by Wolniewicz [261]. Dressier and Woiniewicz [265] have recomputed the transition moments for the Lyman and Werner bands using the most accurate wavefunctions available after 1969 and the results are in excellent agreement with the earlier work of Wolniewicz [2611. In other work Arrighini et al. [266] computed the inelastic scattering of fast electrons from the ground state of hydrogen and reported the total integrated absolute dipole oscillator strengths for the Lyman and Werner bands and also for some other higher Rydberg states within the random—phase approximation (RPA) and Tamm—Dancoff approximation (TDA). The transition probabilities for the individual bands of the transitions from the ground state X  to the  higher lying 3pa, B’ 1 and 3pit, D ‘flu states were also calculated by Glass—Maujean [267]. In 1975 Gerhart [2681 reviewed the existing optical oscillator strength and photoabsorption data for molecular hydrogen and recommended some revisions on the basis of sum rule considerations. Much less information on discrete optical oscillator strengths for molecular hydrogen is available from experiment due to the difficulties of conducting absolute optical cross section determinations. For example,  189 direct Beer—Lambert law photoabsorption experiments have apparently not been used for absolute optical oscillator strength measurements for molecular hydrogen because, even at high experimenta1 resolution (narrow incident band—width), the extremely narrow natural line—widths of the transitions can result in severe “line—saturation” effects as discussed for example in refs. [37,46] (see chapter 2). Experimentally the discrete valence transitions of hydrogen have been studied quite extensively by photo—emission [269—271] and also by photoabsorptlon and photoionization [272—278] methods. However, the optical photoabsorption and photoionization studies have been mostly limited to determinations of the energy positions of the discrete transitions rather than of the absolute optical oscillator strengths (i.e. transition probabilities), presumably because of the possibility of “line—saturation” effects. In an attempt to allow for such effects photoabsorption measurements with a ‘curve of growth analysis”, which relates the measured equivalent width to the line oscillator strength, have been employed by Haddad et al. [2791 and by Hesser et al. [280,281] to measure the oscillator strengths for a few vibrational levels of the Lyman band. The same approach has been used by Fabian and Lewis [282] to measure the oscillator strengths of the Lyman and Werner bands below 13.8 eV. In the same way Lewis [283] has measured the oscillator strengths of the Lyman and Werner bands for the higher vibrational levels above 13.8 eV and also the B’—X and the D—X bands. In other photoabsorption experiments Glass—Maujean, Breton and Guyon [284— 286] attempted to take into account the effects of the bandwidth of the monochromator on the measured linewidths of the discrete transitions by using Doppler profiles and they reported the photoabsorption  190 probabilities for several discrete transition peaks. However the results are restricted to very high vibrational levels of the Lyman and Werner bands close to the dissociation limit. Integrated (total) absolute oscillator strengths for the Lyman and Werner bands have also been reported by Hesser [251] using the phase—shift technique to measure the radiative lifetimes of hydrogen. Electron impact based methods have been previously applied to the study of the discrete transitions of molecular hydrogen [244,249,250,288—291]. Lassettre and Jones [2881 obtained absolute optical oscillator strengths in the continuum region of hydrogen by extrapolating the generalized oscillator strengths, determined at a range of different scattering angles, to zero momentum transfer. Direct, forward scattering, electro.n impact studies of hydrogen at very high impact energy and with very high resolution (0.007—0.040 eV FWHM) have been reported in the discrete region by Geiger [249], Geiger and Topschowsky [2441 and Geiger and Schmoranzer [2501. These relative intensity measurements [244,249,250] were subsequently placed on an absolute scale using calculated and measured elastic cross sections [2491. By measuring the elastic and inelastic differential cross sections at different scattering angles with a resolution of —1 eV FWHM, Geiger [2491 has also reported the sum of the total integrated oscillator strengths for the Lyman and Werner bands. These integrated values [249] were then used for normalization of the high resolution electron energy loss spectra [244,249,250]. However it should be noted that the elastic relative differential cross sections measured by Geiger [2491 were normalized on theoretical values. In addition the relative intensities produced by the Wien filter type of EELS spectrometer used by Geiger and co—workers  191 [244,249,250] have, in some cases, proved to be significantly in error (see for example the discussion in ref. [37] and chapter 4 for helium, where results including those of Geiger et al., are compared). Such discrepancies may be due to intensity perturbations caused by fringe magnetic fields from the Wien filters. In this regard the three sets of electron impact data reported by Geiger et al. for hydrogen [244,249,250] show differences In the (relative) Intensities determined for the Lyman and for the Werner bands. These results [244,249,250] are also in serious disagreement with some of the optical work [251,279,281,282] and also, in the case of the Werner bands, with theory [234,262]. The HR dipole (e,e) method [37,38] (described in this thesis in chapter 3) is particularly useful for studying discrete electronic transitions over a wide (photon) energy range and therefore, In view of the existing discrepancies and uncertainties outlined above, it has been used in the present work to make an independent absolute determination of the optical oscillator strengths for the Lyman and Werner band (discrete) transitions and also in the ionization continuum in the electronic spectrum of molecular hydrogen. The absolute scale was obtained by normalizing to earlier reported absolute optical oscillator strengths in the continuum region, as determined using a low resolution (LR) dipole (e,e) spectrometer and TRK sum rule considerations [86]. These LR dipole (e,e) measurements in the continuum [86] are in excellent agreement with direct photoabsorption results [292] obtained with the double ion chamber method.  192 7.2 Results and Discussion 7.2.1 Absolute Oscillator Strengths Figure 7.1 shows the absolute differential optical oscillator strength (photoabsorption) spectrum of molecular hydrogen in the (photon) energy region 11—20 eV obtained in the present work at a resolution of 0.048 eV FWHM. The entire spectrum has been placed on an absolute scale by normalization at 18 eV to the previously reported absolute photoabsorption data of hydrogen obtained by Backx et al. [86] using low resolution dipole (e,e) spectroscopy. It can be seen from figure 7.1 that both the shape and magnitude of the present oscillator strength distribution in the ionization continuum are highly consistent with the earlier reported low resolution dipole (e,e) work of Backx et al. [86] and also with the direct photoabsorption measurements reported by Samson and Haddad [292] over the continuum region shown (see also ref. [30]). Furthermore, in the discrete region the present high resolution and earlier low resolution [861 dipole (e,e) measurements are mutually consistent when the large difference in energy resolution (i.e. 0.048 eV FWI-IM and 1 eV FWHM respectively) is taken into account. Figure 7.2 which shows an expanded view of figure 7.1 in the 11— 14 eV energy region comprising mainly the absolute differential optical oscillator strength spectrum for the Lyman and Werner bands in more detail. The Lyman and Werner bands are the two strongest electronic transitions of molecular hydrogen and correspond to transitions from the 1+ and 2pit, C 1 fl states respectively. X 1 g ground state to the 2po, B  The positions of the vibrational levels shown in figures 7.1 and 7.2 are  193  1 .5  I_.irrcn  IIIIIIIIIIIIIIIII’IIII I I I I I I II  150  l Werner C l 1  1.0 ‘4  o  J . 4  100  Present work (HR Dipole (e,e)) Backx et al. [86] (LR Dipole (e,e)) Samson & Haddad [ 292] (Ph. Abs.)  0 ‘4 0  ‘4  0  = — 0  0 0  0  0.  50  E X 2 H  0 0  0  0.0 17  19  Photon energy (eV)  Figure 7.1: Absolute oscillator strengths for the photoabsorption of molecular  hydrogen in the energy region 11—20 eV measured by the high resolution dipole (e,e) spectrometer (FWHM=0.048 eV). The assignments are taken from references [270,272—274].  ‘4  0  I  194  I 1.5  I 1  B E  +  I  I  I  4  6  I  I  I  8  Lyman v’=O  I  I— I I I  10  12  14  I  I  I  1  2  3  I I  16  18  20  22  I  I  I  4  5  6  7  150  1 .0  V’=O  Cl)  Cl)  inr  1  •  0 V  Werner C fl 1  1H21  to V  I 2  v=0  Cl) Cl) 0 $-  0  B  0  0  0.5  50j  0  0.0 11  12  13  14  Photon energy (eV)  Figure 7.2: Absolute oscillator strengths for the photoabsorptlon of molecular hydrogen in the energy region 11—14 eV. The assignments are taken from references [270,272,273]. Deconvoluted peaks are shown as dashed lines and the solid line represents the total fit to the experimental data.  195 taken from the earlier reported optical spectroscopic data of Dieke [270] for v’=0—17 of the Lyman band and for v=0—4 of the Werner band, and from the photoabsorption data of Namioka [272,273] for  v’=  18—22 of the  Lyman band, for v’=5,6 of the Werner band and for v’=O, 1 of the B’ band. It can clearly be seen that the shapes of the vibronic peaks (v’=O— 6) of the Lyman band are slightly asymmetric due to rotational fine structure as observed in the very high resolution electron energy loss spectra reported by Geiger and Topschowsky [2441 and by Geiger and Schmoranzer [250]. In the present work, integration of the peak area corresponding to a particular discrete vibronic transition will give directly the absolute optical oscillator strength for that transition. Since all the peaks are expected to be asymmetric because of rotational broadening, asymmetric peak profiles were used to fit the spectrum in figure 7.2. The fitted peaks also incorporate the Instrumental energy resolution (0.048 eV FWHM). The resulting deconvoluted peaks and total fitted spectrum are shown as the dashed and solid lines respectively In figure 7.2. The present absolute optical oscillator strength values obtained by deconvoluting the (asymmetric) peak areas for individual vibronic transitions of the Lyman and Werner bands are summarized in tables 7.1 and 7.2 respectively. Previously reported experimental oscillator strength values [250,279,281,282] and the more accurate calculated data of Allison and Dalgarno [234,262], which included the dependence of electronic transition moment on internuclear distance r are also shown for comparison. For the three sets of electron impact data reported by Geiger and co—workers [244,249,250], the absolute scales of the data were obtained by normalizing to the sum of the total integrated oscillator strength of the Lyman and Werner bands [244] as  196 Table 7.1 Absolute oscillator strengths for the ‘vibronic transitions of the Lyman band of molecular hydrogen  Absolute optical oscillator strengths for transitions from  Excited state  *  v’=0 of X 1 2g to v of B Dipole (e,e) experiments  ‘+  (Lyman band)  Direct optical measurements  Theory  vibrational  Present  Geiger and  Fabian and  Hesser et a!.  Haddad et a!.  Allison and  level (v’)  work  Schmoranzer  Lewis  12811  12791  Dalgarno  12501  12821  0  0.00154  1  0.00575  2  1234.2621  0.00175  0.0019  0.001689  0.00545  0.00519  0.013  0.005790  0.0114  0.00994  0.0115  0.024  0.01156  3  0.0177  0.0165  0.0176  0.037  0.01755  4  0.0228  0.0210  0.0245  5  0.0263  0.0238  0,0258  6  0.0276  0.0264  0.02704  7  0.0276  0.0267  0.02673  8  0.0254  0.0232  0.02523  9  0.0236  0.0222  0.02298  10  0.0200  0.0203  0.02035  11  0.0174  0.0181  0.01764  12  0.0153  0.0155  0.01504  13  0.0122  0.0128  14  (0.0101)*  0.0104  15  0.00794  16  0.03  0.02250 0.02571  0.0114  0.012  0.00825  0.0101  0.0073  0.008730  0.00687  0.00703  0.00787  0.005  0.007185  17  0.00531  0.00612  0.00575  0.0042  0.005891  18  0.00468  0.00552  19  0.00384  0.00425  20  (0.00308)  0.00329  21  0.00267  0.002632  22  0.00209  0.002 154  Interpolated values.  0.01266 0.01055  0.004820 0.00344  0.0023  0.003939 0.0032 19  0.0348 0.0592 0.0555  0.0437 0.0337 0.0210  0.0454  0.0718 0.0695 0.0544#  0.0387 0.0255 0.0165  0  1  2  3  4  5  6  0.017  0.0224  0.0317  0.0442  0.0642  0.0592  # The contribution from the overlying v’=14 component of the Lyman band has been subtracted.  0.0153  [250]  Schmoranzer  work  (v’) [282]  Fabian and Lewis  Geiger and  Present  level  Direct optical measurement  Dipole (e,e) experiments  v=0 of X 1 t of C 1 I] (Werner band) g’ to v  vibrational  state  Excited  0.01700  0.02598  0.03874  0.05472  0.06982  0.07482  0.04760  [234,262]  Dalgamo  Allison and  Theory  Absolute optical oscillator strengths for transitions from  Absolute oscillator strengths for the vibronic transitions of the Werner band of molecular hydrogen  Table 7.2  CD  198 determined in separate low resolution experiments, which were In turn normalized on calculated elastic cross sections. Of these three experiments [244,249,2501 only the highest resolution data reported by Geiger and Schmoranzer [250] are shown in tables 7.1 and 7.2. It should be noted that the data of refs. [244] and [249] show much more scatter than those of ref. [2501. The uncertainties of the present results are estimated to be ±5% for fully resolved peaks, and ±7—15% for the partially resolved peaks because of the additional errors In the deconvolution procedures. Due to overlapping bands the values of v’= 14 and 20 for the Lyman band as shown in table 7.1 were obtained in the present work by interpolation. Also the value for v’=3 for the Werner band shown in table 7.2 was obtained by subtracting the contribution from the underlying v’= 14 component of the Lyman band. These peaks (i.e. for v’=14 and 20 of the Lyman band and v’=3 for the Werner band) were then generated using a computer program and are shown along with the directly fitted peaks as dashed lines in figure 7.2. A direct comparison of oscillator strength values as a function of vibrational quantum numbers, given by the different experimental studies [250,279,281,282] and the theoretical data reported by Allison and Dalgarno [234,2621, is shown in graphical form for the Lyman and Werner bands in figures 7.3 and 7.4 respectively. For the Lyman band it can be seen immediately from figure 7.3 that the presently obtained experimental absolute oscillator strength results are in excellent quantitative agreement with the theoretical work reported by Allison and Dalgarno [234,2621 over the entire range of vibrational quantum numbers shown. The calculated data reported by Allison and Dalgarno [234,262] are slightly lower at v’=5—7 and become slightly higher for v’=13—18 but  199  0.04 *  1H21 0.03  • a *  I Cd)  0  —  0.02  Lyman Bands  C) Cd)  0  C)  Present work Fabian & Lewis [ 282] Haddad et al. [279] Hesser et al. [ 281 ] Geiger & Schmoranzer [250] Allison & Dalgarno [ 234,262]  çBu+  *  0.01  c 4 C 0.00 02468  lb  12  14  16  18  2b  22  Vibrational quantum number (v’)  for individual vibronic transitions Figure 7.3: The absolute optical oscillator strengths Lyman band. as a function of the vibrational quantum number v’ for the  200  1H21  0.08 a  a)  Werner Bands  0.06 A  Eg 1 X  C,) I  *  Hu 1 C  0  —  0.04 A  C) Cl)  A C  0  • C)  C  0.02  0 0.00  a  Present work Fabian & Lewis [ 282] Geiger & Schmoranzer [ 250] Allison & Dalgarno [ 234,262]  4  Vibrational quantum number (v’)  vibronic transitions Figure 7.4: The absolute optical oscillator strengths for individual Werner band. as a function of the vibrational quantum number v’ for the  201 are still within the estimated experimental uncertainties of the present work.  The electron impact data of Geiger and Schmoranzer [2501 are  slightly lower than the present work for v’=2—5 and v’=8 but are In good agreement for higher v’ values. Apart from the electron impact based work of Geiger and Schmoranzer [250], three sets of data (see figure 7.3) obtained from photoabsorptlon measurements using a curve of growth analysis [279,281,282] provided the only other source of absolute vibronic oscillator strengths for the Lyman band prior to the present work. However, these three sets of optical data [279,281,282] only encompass a few of the vibrational levels and give rather inconsistent results (see figure 7.3). Of these studies only the work reported by Fabian and Lewis [2821 is in reasonable agreement with theory [234,262] as seen in figure 7.3. The Fabian and Lewis [282] data are also generally consistent with the presently reported values but the data are much less comprehensive than the present work which covers the entire range of the vibrational numbers from v=0 to 22. Haddad et al. [279] and Hesser et al. [2811 report only a few values mostly at low and high vibrational number respectively, and these show large discrepancies with the present data and with theory [234,2621. It has been suggested [2821 that the apparently high values observed by Haddad et al. [2791 above v’=O may be due to errors in the pressure measurements. Absolute optical oscillator strengths for the Werner band are shown in figure 7.4. It can be seen that the presently obtained experimental oscillator strength values are again in excellent agreement with the theoretical predictions by Allison and Dalgarno [234,262] except possibly for v’0 and 1 where the calculated values are slightly higher but nevertheless still well within the estimated uncertainties of the present  202 experiment. The only other absolute experimental data available for the Werner band of hydrogen prior to the present work are from the electron impact work of Geiger and Schmoranzer [250] and the optical work by Fabian and Lewis [282] respectively. However It can be seen from figure 7.4 that for v’=O to 5, both sets of data [250,282] are much lower than the present results and only for v’=6 are their values In reasonable agreement with the present work and with theory. The absolute oscillator strength value for the v’=O component of the B’ ç’ band at 13.702 eV (see figure 7.2) is estimated to be 0.00384 in the present work. The transition probability for this vibronic band has 8 sec been calculated by Glass—Maujean [267] to be 0.238x10 1 and this corresponds to an absolute oscillator strength of 0.00292 which is —25% lower than the present value of 0.00384. The total integrated absolute oscillator strengths for the Lyman and Werner bands are estimated in the present work to be 0.301 and 0.34 1 respectively. These estimates were obtained as follows: For the Lyman band the value was obtained from the summation of the absolute oscillator strength values for v’=0—22 as shown in table 7.1. The total absolute oscillator strength for the Werner band was obtained from the summation of the absolute oscillator strength values for v’=0—6 determined from the present experimental work (0.322), plus the sum for v’=7—13 as calculated [234,262] by Allison and Dalgarno (0.0 19) to give a total of 0.341. Table 7.3 summarizes the present results along with all the previously reported total absolute oscillator strengths for the Lyman and Werner bands. The present data are in good agreement with the theoretical estimates of Allison and Dalgarno [234,262] and also with those of Arrighini et al. [266] which were obtained using the TDA and  Table 7.3  203  Total integrated absolute oscillator strengths for the Lyman and Werner bands of molecular hydrogen  Total integrated absolute Reference  oscillator strengths Lyman band  Werner band  Theory: Arrighini et al. 12661 (i) TDA  0.3090  0.3615  (ii) RPA  0.2863  0.3451  Allison and Dalgarno 1234,2621  0.311  0.356  Browne 12521  0.28  Rothenberg and Davidson 12551 (1) dipole length  0.286  0.343  (ii) dipole velocity  0.287  0.380  Miller and Krauss 12431  0.2 79  0.330  Peek and Lassettre [242]  0.28  0.276  Ehrenson and Phillipson [2411  0.27  ShullI24O]  0.18  0.42  Mulliken and Rieke 12391  0.24  0.38  0.30 1  0.34 1  0.29  0.28  Experiment: Present work (dipole (e,e)) Geiger and Schmoranzer [2501 (electron impact) Hesser et al. [281]  0.29  (optical: curve of growth) Hesser [2511 (lifetimes)  0.51  0.71  204 RPA methods. Only three other sets of measurements have reported for the total integrated absolute oscillator strengths. The Integrated value reported in the electron impact work of Geiger and Schmoranzer [2501 is slightly lower than the present value while their value for the Werner band Is -20% lower. The total integrated value for the Lyman band as estimated by Hesser et al. [281], using the curve of growth analysis, Is also just slightly lower than the present work. However, values obtained from the lifetime data reported by Hesser [2511 are much higher than all the other reported experimental and theoretical values for both the Lyman and the Werner bands, which is likely caused by the variation of electronic transition moment with internuclear distance r, since the emission observed by Hesser [2511 occurs at large r. In the present work, the total integrated oscillator strength sum for all transitions below the first ionization potential (15.43 eV [274]) of hydrogen is estimated to be 0.836. Arrighini et al. [266] have reported oscillator strength values for the Lyman and Werner bands, and also l states. By adding up 1 several higher members of the Rydberg 1 u and f the oscillator strengths for all those states below the first ionization potential of hydrogen that were calculated by Arrighini et al. [266], values of 0.926 and 0.862 were obtained for the TDA and RPA computational methods respectively. The value reported using the RPA method Is consistent with the present result (0.836) while that reported using the TDA method is appreciably higher.  205 7.2.2 The Variation of Transition Moment with the Internuclear Distance for the Lyman and Werner Bands The vibronic band oscillator strengths (f’”) for the Lyman and Werner systems of molecular hydrogen can be written as [262];  2G  (E-E,,)  =  where  ‘vV”  (7.1)  )2  P’”  =  Pv’I1e(’)I  (7.2)  In these equations 0 is the statistical weighting factor which is equal to one for the Lyman bands and two for the Werner bands, E’—E’ is the transition energy in atomic units and PV’V’ is the band strength. The quantity Re(r) is the electronic transition moment which is a function of the internuclear distance r, and p’ and q,” are the vibrational eigenfunctions of the excited and ground states respectively. The dependence of the electronic transition moment on the internuclear distance for both the Lyman and the Werner bands can be obtained from the presently reported absolute vibronic oscillator strengths. Equation 7.2 can be rewritten as [250,2821  =  where  2 Re(rvtvi)  qTT  (7.3)  (7.4)  206 In equation 7.3, r’” is the internuclear distance at which the transition t takes place and qv’v’ is the Franck—Condon factor. Combining v”—’v equations 7.1 and 7.3, we obtain 2 =  Re(rvivi) q,v,  (75)  In the present work, the f’o values have been measured directly (see tables 7.1 and 7.2) for both the Lyman and the Werner bands so that if we take Franck—Condon factors (i.e. qv’o values) from the calculated data of Allison and Dalgarno [262],  ITe( rv’o) I may be derived. The  energies (E—E’) have been taken from the optical data of Dieke [270] and Namioka [272,273]. The rv’o values have been obtained by digitizing the data of Allison [293], which are shown in analog form as a private communication in the article by Fabian and Lewis [282]. The resulting values of  IRe( rv’o)I are plotted as a function of rv’o in figures 7.5 and 7.6  for the Lyman and Werner bands respectively. These figures therefore show the variation of electronic transition moment with internuclear distance in hydrogen for the Lyman and Werner bands. Previously reported experimental work [250,282] and theoretical calculations [243,252,255,26 1] are also shown for comparison. The data of Miller and Krauss [243] and Wolniewicz [261] were obtained by digitizing the data from the figures reported in their paper. It can seen from figure 7.5 that the presently determined variation of the electronic transition moment  IRe( rv’o) I with the internuclear distance rv’o is in generally good  agreement with the theoretical work of Wolniewicz [261], except at r’o—0.96A (v=0), where the present value is slightly lower. The  207  Vibrational quantum number (v’) -S  z  2018161412  10  9  1.5  H21  Lynian Bands  0  E 1 X  —  E 1 B  1.3  a.) D  0  E 0 .4J  *  0.9  *  Cl)  :  • D -  —  — —  *  *  0:6  0.7  Present work Geiger & Schmoranzer [250] Fabicn & Lewis [282] Wolniewicz [261] Miller & Krauss [243] Browne [252] Length Browne [252] Velocity  0.8  0.9  Internuclear distance rvo  Figure 7.5: The electronic transition moment  IRe(rj)I  (A)  in atomic units (a.u.) as a  function of the internuclear distance r,’O in Angstroms band.  1  (A) for the Lyman  208  Vibrational quantum number (v’) 2  .  0.9  0  Werner Bands  F  0  4  1  -  Xg  *  Hu 1 C  jr  -  -  0.8  [H21  *  0  E  0.7 *  0  9  9  .—  0.6 C  C.)  0 0 V  *  *  0.5 I  0.6  I  0.7  Present work Geiger & Schmoranzer [250] Fabian & Lewis [282] Wolniewicz [261 ] Miller & Krauss [243] Rothenberg & Davidson [255] Length Romenberg & Davidson [255] Velocity I  0.9  Internuclear distance rvo  Figure 7.6: The electronic transition moment  IRe(rv’o)I  I  •  0.8  (A)  in atomic units (a.u.) as a  function of the internuclear distance ro in Angstroms band.  1 .0  (A) for the Werner  209 calculated data reported by Miller and Krauss [243] are somewhat higher than the present work. The dipole length data reported by Browne [2521 are lower than the present results while their dipole velocity data are slightly higher. The electron impact work of Geiger and Schmoranzer [250] and the optical work of Fabian and Lewis [282] are also consistent with the present work but both sets of data exhibit more scatter. From a least—squares fit of a straight line to the present data, the dependence of electronic transition moment with internuclear distance in the range 0.63—0.96A for the Lyman band is found to be:  0 Re(rv=0.l42+ 1.l17r  (7.6)  In figure 7.6 the present results for the Werner band are also seen to be generally in rather good agreement with the theoretical values calculated by Miller and Krauss [243] and Wolniewicz [261]. The dipole length data calculated by Rothenberg and Davidson [2551 are also consistent with the present work while their reported dipole velocity data are slightly higher. The results derived from the electron impact work of Geiger and Schmoranzer [2501 are considerably lower than both the present work and theory [243,261]. Except for the value at r’o—0.66A, the data for the Werner band reported In the optical work of Fabian and Lewis [282] are also much lower than the presently reported values. A linear least—squares fit of the presently obtained data In the range 0.66—0.89A gives  Re(rvi&  0.456  +  0.378  0 r t  (7.7)  210 The dipole strengths De( r ) at equilibrium internuclear separation 0 0 have been investigated both experimentally [244,249,250,282] and r theoretically [239-243,252,255,261] by several groups. This quantity is defined as [250,282]:  De(ro)  =  G  2 IR1o)I  (7.8)  where 0 Is the statistical weighting factor as defined above. In the present work, the transition moment at the equilibrium internuclear distance r 0 for the Lyman and Werner bands can be calculated from equations 7.6 and 7.7 respectively by setting r’o=r = 0 0.741A. From equation 7.8 the dipole strengths are determined to be 0.94 for the Lyman band and 1.08 for the Werner band. Table 7.4 summarizes the present results and shows a comparison with other previously reported experimental [244,249,250,282] and theoretical data [239—243,252,255,26 1]. For the Lyman band the previously published experimental results [244,249,250] and the present work show good agreement with each other except for the value reported by Geiger [249] which is  -  10% lower. For the Werner band all the previously reported  experimental values [244,249,250,282] are lower than the present work. Of the theoretical studies only the values reported by Wolniewicz [261] and the calculated data of Rothenberg and Davidson [255] are In good agreement with the present values for both the Lyman and the Werner bands. The other calculated values show significant differences from the present results. Finally it should be noted that the dependence of the electronic transition moment on the internuclear distance and also the dipole  Table 7.4  211  Dipole strengths De(ro) for the Lyman and Werner bands of molecular hydrogen  Reference  Dipole strengths De( r ) in a.u. 0 Lyman band  Werner band  Theory: Wolniewicz [261]  0.96  1.10  Browne [252] (i) dipole length  0.78  (ii) dipole velocity  1.04  Rothenberg and Davidson [255] (i) dipole length  0.91  1.06  (ii) dipole velocity  0.92  1.18  Miller and Krauss 1243]  1.00  1.08  Peek and Lassettre 12421  0.97  0.81  Ehrenson and Phillipson 1241]  0.85  Skull 1240]  0.60  1.33  Milliken and Rieke [239]  0.77  1.21  0.94  1.08  0.96  0.92  0.98  0.89  0.95  0.92  0.84  1.03  Experiment: Present work (dipole (e,e)) Fabian and Lewis [2821 (optical: curve of growth) Geiger and Schmoranzer [250] (electron impact) Geiger and Topschowsky [244] (electron impact) Geiger 1249] (electron impact)  212 strength at the equilibrium internuclear distance determined in the present work for both the Lyman and Werner bands are consistent with the theoretical work by Rothenberg and Davidson [255], by Wolnlewicz [2611 and by Miller and Krauss [243]. It should be pointed out that some of these calculations [255,261] were used by Allison and Dalgarno [234,262] in their calculation of the absolute oscillator strengths for the Lyman and Werner bands.  7.3 Conclusions Absolute optical oscillator strengths for molecular hydrogen have been measured in the energy region 1 1—20 eV. The absolute scale was obtained by normalizing in the photoabsorption continuum region at 18 eV to the absolute value determined by Backx et al. [86] using low resolution dipole (e,e) spectroscopy and TRK sum rule normalization. Absolute optical oscillator strengths for the vibronic transitions of the Lyman and Werner bands have been determined. The presently reported experimental oscillator strength data are in very good agreement with the theoretical values reported by Allison and Dalgarno [234,262] for the Lyman and Werner bands. The optical data of Fabian and Lewis [2821 agree with the present results for the Lyman band but are more than 10% lower for the Werner band. The variations of the electronic transition moments of the Lyman and Werner bands of hydrogen with internuclear distance derived from the present measurements are found to be in very good agreement with theoretical calculations [243,255,261].  213 Chapter 8  Absolute Optical Oscillator Strengths for the Discrete and Continuum Photoabsorption of Molecular Nitrogen (11—200 eV)  8.1 Introduction Nitrogen is the most abundant molecule In the earth’s atmosphere and photoabsorption, photodissociation and photoionization processes resulting from its interaction with solar UV radiation play an Important role in the energy balance of the earth’s upper atmosphere. In addition the predissociation of electronically excited states of nitrogen is the principle process by which molecular nitrogen is dissociated in the atmosphere by solar radiation and by electron impact. Absolute optical oscillator strengths for nitrogen in the discrete valence region provide information on the excitation cross sections, and these together with emission cross section data can be used to determine the predissociation cross sections and emission yields [294—297] of electronically excited states of nitrogen. Transition energies and absolute optical oscillator strengths for excitation from the ground state of nitrogen to various Rydberg states have been calculated by a number of authors [298—303]. However, these calculations are at the level of electronic but not vibrational resolution. Duzy and Berry [298] based their calculation on a Hartree—Fock wavefunction for the ground state of nitrogen and excited state wavefunctions derived from an irredu cible—tensorial one—center representation of the effective potential of the nitrogen ion core.  214 Calculations have also been reported by Rescigno et al. [299] using the Stieltjes—Tchebycheff moment—theory technique and by Kosman and Wallace [300] using the multiple scattering model. Absolute optical oscillator strength calculations for the transitions from the ground state to the valence b’H and b’ ‘i states and some low—lying Rydberg states have been performed by Rose et al. [301] using the equation—of—motion method, by Hazi [3021 using the semi—classical impact—parameter method and by Bielschowsky et al. [3031 using extensive ab inltio calculations with highly correlated configuration interaction wavefunctions. Irregularities in the vibronic energy levels and intensity distributions associated with the b’H and b’  excited valence states have been  observed experimentally [304,305], which has been attributed to homogeneous configuration interaction of the b’fl and b’ the first two members of the c’H and  states with  Rydberg states, respectively.  By first fitting the eigenvalues of a vibronic interaction matrix to the observations, Stahel et al. [306] have reported vibronic energies, elgenvectors, B values and relative oscillator strengths for the b’fl and excited valence states and the c’H,  chl+  fl Rydberg 1 and o  states, based on a matrix optimization with direct solutions of coupled oscillator equations. The effects of configuration interaction on the nitrogen spectrum have been discussed in detail by Lefebvre—Brion and Field [307] and also by Carroll and Hagim [308]. The photoabsorption of molecular nitrogen in the valence discrete region has been the focus of many experimental studies and a large amount of spectroscopic data has been reported in the literature [76— 80,305,309—320]. Numerous studies using the Beer—Lambert law [76— 80,312,313,315,3161 have reported absolute optical oscillator strength  215 (cross section) values in the valence discrete region. However, very large differences in the relative peak intensities for the discrete transitions of nitrogen in the energy region 12.5—13.2 eV were observed between different Beer—Lambert law photoabsorption measurements [76— 80,313,316] and also with optical oscillator strength determinations based on a variety of electron energy loss experiments [11,37,81,82,304]. At first it was thought that the discrepancies were due to the failure of the Born approximation used to interpret the electron impact based experiments.  However, Lawrence et al. [78] subsequently remeasured  the absolute oscillator strengths for several discrete excitations of molecular nitrogen using Beer—Lambert law photoabsorption techniques in the same energy region at several different sample pressures, and found that the measured oscillator strengths showed large variations with sample pressure. Extrapolating to small values of the column number (i.e. low pressure), the resulting oscillator strength values [78] were found to be much more consistent with the relative intensities of the peaks obtained earlier by Lassettre et al. [81] and by Geiger et al. [82,304] from electron energy loss experiments. Following these observations the difficulties involved in using Beer—Lambert law photoabsorption for studies of discrete excitations were realised [11,46]. A detailed quantitative analysis and theoretical investigation of the bandwidth effects and associated errors in Beer—Lambert law photoabsorption has been given by Chan et al. [37] (see chapter 2). Chan et aL [37] also demonstrate that the bandwidth effects will be manifest in the peak areas as well as the peak heights in oscillator strength determinations for discrete transitions. These difficulties with the Beer— Lambert law, which can lead to very large errors in measured oscillator  216 strengths, are caused by the finite bandwidth of the optical spectrometer. Severe “line saturation” effects are likely to occur particularly when the measured discrete transition has a very narrow natural line—width and high cross section. In such cases the measured optical oscillator strengths are likely to be too small even when very careful Beer—Lambert law studies are made as a function of pressure. These difficulties could also be minimlsed in principle If extremely high optical resolution could be obtained [321], but it should be noted that this requires In practice that the spectrometer bandwidth be very much narrower than the natural linewidth of any spectral line being studied. Since electron Impact excitation is non—resonant, such “line saturation” or bandwidth effects cannot occur in optical oscillator strength determinations based on electron energy loss measurements [11 ,30,37]. In particular, the dipole (e,e) method is ideally suited for the accurate determination of photoabsorption oscillator strengths throughout the discrete and continuum spectral regions [37]. In contrast, the Beer—Lambert law optical absorption spectrum can exhibit a very variable relative intensity profile throughout the discrete region depending on the experimental resolution (bandwidth) since different electronic transitions in general have different natural line—widths. These spurious effects are particular well illustrated by a comparison of the optical oscillator strength spectra obtained by the electron energy loss [37] and Beer—Lambert law photoabsorption [80] methods for molecular nitrogen in the VUV region as shown in figure 2. 1 (see chapter 2). It can be seen that both the relative band strengths and the absolute intensities are dramatically different in the two spectra in the 12.4 to 13.0 eV region. The intensities are essentially correct in the electron energy loss spectrum in  217 figure 2. 1(b), whereas bandwidth/linewidth Interactions result In severe intensity perturbations In the synchrotron radiation Beer—Lambert law photoabsorptlon intensities of reference [80] shown In figure 2.1(a). It Is Instructive to note that It was In this specific spectral region that Lawrence et al. [78] made photoabsorption studies as a function of pressure [37,461 in an attempt to avoid the bandwidth effects. It can be seen from figure 3 of reference [78] that the relative intensities of the four transitions at 958 eV) and 972  A  A  (12.942 eV), 960  A (12.9 15  eV), 965  A (12.848  (12.756 eV) are drastically altered in different ways  (reflecting their different natural llnewidths and different true cross sections) as the column number (pressure) is reduced. At the lowest column number at which measurements were made [78], the derived oscillator strength order and relative magnitudes are consistent with the relative intensities in the electron energy loss based measurement shown in figure 2.1(b) of the present work. However, the errors bars in figure 3 of ref. [781 are necessarily very large at the lowest pressures at which oscillator strength measurements were made, and as a result the absolute magnitudes of the oscillator strengths are still significantly in error (see section 8.2.2 below of the present work). It Is clear that the errors are different for every transition because of the different natural linewidths. In addition, extrapolation of optical data to low pressure places the most emphasis on the least accurate data obtained at the lowest pressures. Therefore, as a result of finite bandwidth considerations, oscillator strength measurements obtained by Beer—Lambert law photoabsorption methods must, at best, be regarded with extreme caution since It Is clear that very large errors can occur in the measured oscillator strengths even where measurements are made as a function of pressure. Conversely, the  218 efficacy of Bethe—Born converted electron energy loss spectra, obtained directly using dipole (e,e) spectroscopy at negligible momentum transfer, as a means of obtaining accurate optical oscillator strengths in both the discrete [27,37,38—40] and continuum [30] regions has now been well established. The preceding perspectives concerning the accuracies of various types of absolute photoabsorption oscillator strength determination are important when considering the results of other studies using such information. For example, the extreme ultraviolet emission from nitrogen excited by electron impact has been studied by Zlpf and McLaughlin [2941 for the two excited valence states and several Rydberg states. Similar studies have also been made by Zipf and Gorman [295]  and by James et al. [297] for the b’fl state, and by Ajello et al. [296] for the ctlu+ and b’ 1 Rydberg states. In these studies the emission cross sections and the predissociation branching ratios for these states were reported. The excitation cross sections, which were used to obtain the predissociation branching ratios from the measured emission cross sections, were derived from previously published optical oscillator strengths [13,78,304]. Zipf and McLaughlin [294] and Zipf and Gorman [295] obtained optical oscillator strength va1ues from the re1ative electron scattering data of Geiger and Schroder [3041, with correction for the scattering geometry of the spectrometer and also taking into account the absolute generalized oscillator strength data of Lassettre and Skerbele [13]. James et al. [297] converted the excitation cross sections reported by Zipf and Gorman [2951 for the b’fl vibrational states at an Impact energy of 200 eV to those which would be obtained at an impact energy of 100 eV and normalized the data using the absolute optical oscillator  219 strength value for the (4,0) transition reported by Lawrence et al. [78]. Ajello et al. [296] obtained optical oscillator strengths for the c’ 1 and u+ states from their own experimental measurements using the b’ 1  relative flow technique and by applying the modified Born approximation formulation to the measured absolute emission cross sections. As indicated above, electron impact methods based on electron energy loss spectroscopy have also been applied to study the discrete electronic transitions of nitrogen [13,15,18,81,82,87,304,322—324]. Experimental conditions of low electron impact energy and variable scattering angle have been employed by several groups [13,15,18,322— 324]. In these studies generalized oscillator strengths as a function of momentum transfer (angle) for various discrete transitions were determined and optical oscillator strengths were obtained by extrapolating the generalized oscillator strengths to zero momentum transfer for each transition [13,18,324]. While Geiger and Sticke1 [82] and Geiger and Schroder [3041 obtained high—resolution dipole— dominated electron energy loss spectra of nitrogen in the valence discrete region by using very high incident impact energies (25—33 keV) and small scattering angles (1—4 xlO4 radians), no absolute oscillator strengths were derived. In other work Wight et aL. [871 reported absolute dipole oscillator strengths for the photoabsorption of nitrogen In the limited energy region 10—70 eV using low resolution dipole (e,e) spectroscopy with 8 keV impact energy and zero—degree mean scattering angle. However, the absolute scale was obtained by Wight et al. [87] by normalizing in the smooth continuum at 32 eV to the absolute photoabsorption data previously reported by Samson and Cairns [325]. In addition, the resolution of the spectrum reported by Wight et al. [87] was  220 limited to 0.5 eV FWHM and as a result absolute optical oscillator strengths for the Individually resolved discrete vibronic transitions of molecular nitrogen could not be determined. In summary, direct photoabsorption studies of the oscillator strengths for the discrete excitation of molecular nitrogen are clearly In error due to “line saturation’ effects, while earlier high resolution electron impact studies have provided only relative Intensities or In other cases Involve uncertainties due to the necessary extrapolations to zero momentum transfer. Definitive absolute photoabs orption oscillator strength measurements in the discrete region of nitrogen at high resolution should however be possible by electron energy loss measurements obtained directly at the optical limit, with the absolute scale established independently via TRK sum—rule considerations [30]. Therefore, in the present work, the high resolution dipole (e,e) method, as recently used to measure absolute optical oscillator strengths for discrete transitions over the entire spectral range for the noble gas atoms [37—39] (see chapters 4—6) and molecules [27,40] (see chapter 7), is now applied to the valence shell discrete transitions of molecular nitrogen. The excellent agreement obtained between experimental and theoretical optical oscillator strengths for “benchmark” targets such as helium [37] (see chapter 4) and molecular hydrogen [40] (see chapter 7) has confirmed the high accuracy of the high resolution dipole (e,e) method. In order to independently establish the absolute oscillator strength scale for molecular nitrogen, comprehensive new low resolution dipole (e,e) measurements have also been made in the energy range 10—200 eV and these data have been placed on an absolute scale by valence shell TRK sum rule normalization.  221  8.2 Results and Discussion The photoabsorptlon oscillator strengths and spectral assignments for molecular nitrogen are conveniently discussed with reference to the ground state molecular—orbital, independent particle, valence shell electronic configuration, which may be written as: ( 3ag) 4 2 ( 2a)2( l3rtU) 2 (2ag)  8.2.1 Low Resolution Absolute Photoabsorption Oscillator Strength Measurements for Molecular Nitrogen (11—200 eV) A relative valence shell oscillator strength spectrum was obtained by Bethe—Born conversion of the electron energy loss spectrum measured using the low resolution (—1 eV FWHM) dipole (e,e) spectrometer in the energy region 11—200 eV. The data were least—squares fitted to the function AE over the energy region 90—200 eV. The fit gave B=2.283 and on this basis the fraction of valence—shell oscillator strength above 200 eV was estimated to be 5.6%. The total area was then valence shell TRK sum—rule normalized to a value of 10.3, which includes the total number of valence electrons (10) plus a small estimated correction (0.3) for the Pauli—exciuded transitions from the core orbitals to the already occupied ground state valence orbitals [52,53]. Figures 8.1(a) and (b) show the resulting absolute optical oscillator strength spectra of nitrogen in the energy regions 10—50 and 5.0—200 eV respectively, compared with previously reported experimental data [87,175,292,326—329]. Numerical values of the absolute photoabsorption oscillator strengths for nitrogen  222  0.6  (a)  1 2 1N •  0.4  0  * +  60  Present work dipole (e,e) Wight et ci. [87] dipole (ee) Samson & Hoddod [292] Lee et ci. [326] Watson et ci. [327] Ph Abs Cole & Dexter [329] De Rellhoc & Domony [328]  40  °  0.2  20  £ 0 C)  a)  :a)  0  a  0.0  30  20  10  50  40  U) U)  0  U)  0.10 — —  A *  C) U)  o  0.08  (b)  10  j 2 JN  0 0  *  82  o  C)  • *  0.06  0 * +  *  0.04  Present work dipole (e,e) Wight et ci. [87] dipole (ce) Samson & Hoddod [292] Lee et ci. [326] Ph Abs Cole & Dexter [329] De Reilhac & Damany [328] Denne [175]  6  0  0.02  2 • at.. “M  0.00. 50  100  150  200  Photon energy (eV)  Figure 8.1: Absolute oscillator strengths for the photoabsorption of molecular nitrogen measured using the low resolution (FWHM=1 eV  ) dipole (e,e) spectrometer  comparison with previously reported experimental data [87,292,326—329] in the energy region 10—50 eV. (b) comparison with previously reported (a)  experimental data [87,175,292,326,328,329] In the energy region 50—200 eV.  223 obtained at low resolution in the present work from 11—200 eV are summarized in table 8. 1. It Is Important to note that In the discrete region the low resolution data In table 8.1 represent an Integral over the unresolved transitions. More detailed quantitative Information on the discrete region is available from the high resolution spectra (see section 8.2.2 below). Immediately It can be seen in figures 8.1(a) and 8.1(b) that the present results are in good agreement with the photoabsorption continuum data reported earlier by Samson and Haddad [292]. The data reported by Cole and Dexter [329] are slightly lower than the present work while those reported by Denne [1751 In the energy region 150—195 eV are —50% lower. The earlier electron impact based dipole (e,e) data reported by Wight et al. [87] are slightly lower than the present work In the energy region 18—35 eV but become higher In the energy region above 50 eV up to the limit of their measurements at 70 eV. However, it should also be pointed out that the relative data of Wight et al. [87] were normalized in the smooth continuum at 32 eV to the direct optical photoabsorption data reported much earlier by Samson and Cairns [325].. In contrast the present work is valence shell TRK sum—rule normalized and is thus independent of any other measurements. The presently obtained low resolution photoabsorption data has been used to establish an absolute scale for the high resolution measurements described in the following section.  224 Table 8.1 Absolute differential optical oscillator strengths for the photoabsorption of molecular nitrogen obtained using the low resolution (1 eV FWHM) dipole (e,e) spectrometer (11—200 eV)  Energy  Oscillator  Energy  Oscillator  Energy  Oscillator  (eV)  Strength  (eV)  Strength  (eV)  Strength  eV 2 0) (11  eV 2 0 ) ( 11  eV 2 0 ) (11  11.0  0.00  20.0  21.83  29.0  20.56  11.5  0.08  20.5  21.21  29.5  19.95  12.0  5.03  21.0  20.83  30.0  20.14  12.5  31.74  21.5  20.76  30.5  18.84  13.0  49.14  22.0  21.39  31.0  18.35  13.5  42.02  22.5  22.47  31.5  17.89  14.0  43.06  23.0  23.05  32.0  17.21  14.5  31.61  23.5  23.52  32.5  16.69  15.0  21.23  24.0  22.64  33.0  16.14  15.5  24.14  24.5  21.62  33.5  15.72  16.0  26.57  25.0  21.69  34.0  15.04  16.5  25.71  25.5  21.66  34.5  14.94  17.0  24.04  26.0  21.57  35.0  14.22  17.5  23.56  26.5  21.08  35.5  14.09  18.0  23.31  27.0  21.17  36.0  13.41  18.5  23.33  27.5  21.04  36.5  12.74  19.0  22.52  28.0  21.34  37.0  12.45  19.5  22.16  28.5  20.92  37.5  12.30  225 Table 8.1 (continued)  Energy  Oscillator  Energy  Oscillator  Energy  Oscillator  (eV)  Strength  (eV)  Strength  (eV)  Strength  eV 2 0 ) (1 1  eV 2 10) (1  eV 2 0 ) (1 1  38.0  12.27  49.0  9.08  70.0  4.06  38.5  11.76  50.0  8.81  71.0  3.94  39.0  11.26  51.0  8.68  72.0  3.83  39.5  11.09  52.0  8.41  73.0  3.75  40.0  10.78  53.0  8.03  74.0  3.62  40.5  10.85  54.0  7.71  75.0  3.47  41.0  10.55  55.0  7.47  76.0  3.35  41.5  10.37  56.0  7.14  77.0  3.33  42.0  10.15  57.0  6.82  78.0  3.18  42.5  10.16  58.0  6.53  79.0  3.06  43.0  10.02  59.0  6.37  80.0  3.06  43.5  9.85  60.0  6.00  81.0  3.00  44.0  9.81  61.0  5.78  82.0  2.90  44.5  9.79  62.0  5.52  83.0  2.79  45.0  9.69  63.0  5.31  84.0  2.70  45.5  9.68  64.0  5.11  85.0  2.58  46.0  9.51  65.0  4.89  86.0  2.55  46.5  9.27  66.0  4.60  87.0  2.52  47.0  9.37  67.0  4.49  88.0  2.44  47.5  9.31  68.0  4.34  89.0  2.39  48.0  9.22  69.0  4.22  90.0  2.32  226 Table 8.1 (continued)  Energy  Oscillator  Energy  Oscillator  Energy  Oscillator  (eV)  Strength  (eV)  Strength  (eV)  Strength  1 e 2 (10 ) V  1 e 2 (10) V-  1 e 2 (10 ) V  91.0  2.18  124.0  1.09  166.0  0.562  92.0  2.20  126.0  1.04  168.0  0.562  93.0  2.11  128.0  1.03  170.0  0.542  94.0  2.10  130.0  0.986  172.0  0.549  95.0  2.10  132.0  0.948  174.0  0.526  96.0  2.00  134.0  0.908  176.0  0.494  97.0  1.94  136.0  0.879  178.0  0.496  98.0  1.92  138.0  0.848  180.0  0.476  99.0  1.85  140.0  0.835  182.0  0.465  100.0  1.82  142.0  0.801  184.0  0.471  102.0  1.74  144.0  0.773  186.0  0.454  104.0  1.67  146.0  0.755  188.0  0.460  106.0  1.57  148.0  0.726  190.0  0.431  108.0  1.52  150.0  0.702  192.0  0.412  110.0  1.45  152.0  0.682  194.0  0.445  112.0  1.40  154.0  0.685  196.0  0.411  114.0  1.33  156.0  0.671  198.0  0.401  116.0  1.28  158.0  0.613  200.0  0.392  118.0  1.22  160.0  0.608  120.0  1.18  162.0  0.614  122.0  1.15  164.0  0.581  a (Mb)  =  1.0975 x 102-eV1  227 8.2.2 high Resolution Absolute Photoabsorption Oscillator Strength Measurements for Molecular Nitrogen (12—22 eV) Figure 8.2 shows the absolute optical oscillator strength spectrum for the photoabsorption of molecular nitrogen In the energy region 12—22 eV obtained using the high resolution dipole (e,e) spectrometer (0.048 eV FWHM). Also shown on figure 8.2 is the presently determined low resolution dipole (e,e) data, the earlier low resolution electron Impact based data of Wight et al. [87] and the photoabsorption data of Samson and Haddad [292]. It can be seen in figure 8.2 that the present high resolution (HR) and the various low resolution (LR) data are in good agreement over the continuum region. Similarly in the discrete region the measurements are consistent when the large differences in energy resolution (0.048 eV vs 1 eV FWHM) are taken Into account.  The  present HR data in the continuum 18—22 eV are also in good quantitative agreement with the photoabsorption data of Samson and Haddad [292]. Figures 8.3, 8.4 and 8.5 show expanded views of figure 8.2 in the energy regions 12.4—13.4, 13.2—15 and 15—19 eV respectively. The detailed qualitative spectroscopy of molecular nitrogen is well known from higher resolution optical and electron energy loss spectra and the indicated assignments and energy positions shown are as given in refs. [80,300,304,317]. The most prominent transitions below 15 eV H and 1 correspond to the valence excitations to the b  states, and  g—’Spau) c”u, 3 ( 0 g’ c’flu aJtu) ( P the lowest members of the three 3 and (btu ag) 4  O’flu  Rydberg series. In the energy region 15—17.5 eV,  the spectrum involves mainly transitions to higher members of the  chlu+,  l Rydberg series. The assignments and energy positions for o f H and 1 1 c  228  5 500  •> 4  400 C)  a) a)  3 300  ‘-4  I.  U) U) U)  0  ‘-4  Cl)  C)  ‘-4  C  0  2  200  -4  .—  C)  1-4  0  U)  0  Cl)  100  C)  0  0 12  14  16  18  20  22  Photon energy (eV)  Figure 8.2: Absolute oscillator strengths for the photoabsorption of molecular nitrogen in the energy region 12—22 eV measured using the high resolution dipole (e,e) spectrometer (FWHM=O. 048 eV).  229  I?  5 500 4  0 400  3 300 C.)  0  2  _f•n  .4-i  4 C 0 0  100 0 0  0 12.4  12.8  13.2  Photon energy (cv)  Figure 8.3: Expanded view of figure 8.2 for the photoabsorption of molecular nitrogen in the energy region 12.4—13.4 eV. The assignments are taken from references [300.304,317]. Deconvoluted peaks are shown as dashed lines and the solid line shows the total fit to the experimental data.  230  V  N21  1.6 1  1.2  Ii  c E  II  I  II  I  I  22  33  44  55  66  I  I 6  V  on  1’  2  I  I  I  8  10  12  I 14  I  I  7’7  I  1  I  I  I 12  0  160  22  20  120  24  14  16 0  II  I I  II  b’fI  0  1  1  2 Ii  2  eEu IJ 1 e  +  0 13.2  13.6  14.0  14.4  14.8  Photon energy (eV)  Figure 8.4: Expanded view of figure 8.2 for the photoabsorption of molecular nitrogen in the energy region 13.2—15.0 eV. The assignments are taken from references [300,304,317]. Deconvoluted peaks are shown as dashed lines and the solid line shows the total fit to the experimental data.  Cl) U)  0  bIiEu+  I  0 C) V U)  oil_-lu  l I 18  16  I.  Cl)  +  231  :  tj  0.8  g 2 X  H 2 A  0  0.6  uufldag 2 4  3  4  5  9 2a—nsa  0.4  6O  567  I  I  V i2  80  LN2I I  II III 678  2  B E  +  40  ‘.4  0  0 1.4  0 20  0:  0 0  0 15  16  17  18  19  Photon energy (eV)  Figure 8.5: Expanded view of figure 8.2 for the photoabsorption of molecular nitrogen  in the energy region 15—19 eV. The assignments are taken from references [80,300,3171.  232 these transitions are not shown in figure 8.5 due to heavy overlapping In this region. The autolonization profiles In the energy region 17.1—18.5 eV are due to transitions from the 2 0u—’nsag “window resonances”, and the 2 0u—’ndag Rydberg series [80]. The “window resonances” are caused by destructive quantum mechanical interference with the underlying direct ionization continuum. In the present work integration of the area under each spectral peak will give directly the absolute optical oscillator strength for the respective discrete vibronic transition. Since the energy positions of the peaks are very well known [80,300,304,3 171, a curve fitting program using Voigt—profiles has been used to provide an accurate deconvolution of the partially resolved peaks In the energy region 12.4—14.9 eV. Although they should be slightly asymmetric due to unresolved rotational structure (as observed for example in the very high resolution electron energy loss spectrum obtained by Geiger and Schroder [304]), the peaks are expected to be essentially symmetric at the resolution of the present work. Accordingly symmetric peak profiles have been used in the curve— fitting procedure. The dashed lines In figures 8.3 and 8.4 show the resulting deconvoluted peaks. Absolute optical oscillator strengths obtained from the deconvoluted peak areas are summarized in table 2. The assignments and energy positions shown In table 8.2 are taken from the paper of Geiger and Schroder [304]. The uncertainties of the area determinations (and thus the oscillator strengths) in the present work are estimated to be —5—10% for the relatively strong and well separated peaks in the energy region 12.40—13.27 eV, and -40—20% for the remaining peaks at higher energies.  233  Table 8.2 Absolute optical oscillator strengths for discrete transitions from the ground state of molecular nitrogen in the energy region 12.50—14.86 eV#  Energy  Final  Upper level  Integrated  ( eV)  electronic  vibrational  oscillator  state  number (vt)  strength  12.500  b’fl  0  0.00254  12.575  b’fl  1  0.0113  12.663  b’fl  2  0.0272  12.750  b’fl  3  0.0526  12.835  b’fl  4  0.0861  12.910  c’fl  0  0.0635  12.935  c”2  0  0.195  12.980  b’fl  5  0.00613  13.062  b’fl  6  0.00500  13.100  O’fl  0  13.156  b’fl  7  0.0237  1  0.00147 0.0640  13.185 13.210  c’fl  1  13.260  b’fl  8  13.305  b”Z  5  C  b’fl  9  I  oln  1  13.390  b”2  6  0.00216  13.435  .b’fl  10  0.0147  13.475  c’fl  2  0.0155  13.530  b’fl  11  0.00484  13.345  1 !‘-  J  0.0258  234 Table 8.2 (continued)  Energy  Final  Upper level  Integrated  (eV)  electronic  vibrational  oscillator  state  number (v’)  strength  13.585  ohflu  2  0.0277  13.615  b’fl  12  0.00181  9  0.0128  13.660 b’fl  13.700  13  13.720  3  13.760  10  0.0190 ‘I  > 3  0.00510  13.785  b’fl  14  13.820  O’fl  3  0.0236  13.830  1 b’  11  0.00654  13.870  b’fl  15  13.910  b1 u 1 +  12  13.950  b’fl  16  13.980  c”E  4  0.0496  13.990  c’fl  4  0.00210  13.998  Zu+ 1 b?  13  14.050  fl 1 o  4  0.00620  14.070  b”u  14  0.0341  14.150  b”E  15  0.0409  b”Z  16  c’fl  5  c”2  5  o f 1 l  5  r 14.230  14.275  0.0303  .  0.0632  J 0.00155  235 Table 8.2 (continued)  Energy  Final  Upper level  Integrated  ( eV)  electronic  vibrational  oscillator  state  number (v’)  strength  14.300  17  0.0318  14.330  fI 1 e  0  0.0153  14.350  e”2  0  0.0104  18  0.00326  14.400 14.465  b”D  19  0.0166  14.478  ctlu+  6  0.0135  20  0.0173  14.525 14.585  fI 1 e  1  0.00761  14.680  u+ 1 b?  22  0.00455  c’fl  7  14.720  (  .<  I_  7  0.00547  J  14.737  b”Z  23  0.0102  14.795  bu  24  0.00455  14.839  n=5’fl  0  14.860  e’fl  2  0.0113  # The energy positions and assignments were obtained from ref. [304].  236 Tables 8.3—8.7 summarize the absolute, vibrationally resolved oscillator strengths for the electronic transitions from the ground state to each of the b’H,  l states, along with o f c’H and 1  previously published data [78,79,294—297]. For the overlapping transitions such as v’=9 of b’fl and v’= 1 of o’fl, as shown In table 8.2, the oscillator strength value for each individual transition was estimated from the ratio of the relative band strengths for these states as calculated by Stahel et al. [306]. Similar procedures were employed for the other unresolved states indicated in table 8.2. It can be seen in tables 8.3—8.7 that great variations exist in the absolute vibronic oscillator strengths reported by various groups using different experimental techniques and methods of normalization [78,79,294—297]. The photoabsorption data of Lawrence et al. [78] shown In tables 8.3, 8.5 and 8.6 are more than 30% lower than the present work even though the data were obtained by extrapolating the measured oscillator 13 cm ) in an attempt to account 2 strength values to low pressure (N<10 for the ‘line saturation” effects. However, as has been pointed out in refs. (11 ,37] and discussed in the introduction of this chapter, this kind of extrapolation procedure may lead to large errors in the resulting oscillator strength values since it relies heavily on the least accurate data measured at the lowest pressure. Carter [79] has reported similar measurements for nitrogen as a function of pressure but only extrapolated . Despite the extrapolation the 2 down to a column number N of 1014 cm absolute oscillator strength data reported by Carter [79] still show serious “line saturation” effects for many transitions, and the errors are especially large in the cases of v’=4 of the b’fl state, v’=16 of the blu+ state, v’=O of the  state and v’=O of the c fl state (see tables 8.3—8.6). 1  237  Table 8.3  Absolute optical oscillator strengths for transitions to the vibronic bands of the valence b’H state from the ground state of molecular nitrogen  Energy  Present  James  Zipf and  (eV)  work  et al.  Mclaughlin  [297]t  [2941@  Carter  Lawrence et al.  [791#  [78J  12.500  0  0.00254  0.0014  0.00239  12.575  1  0.01 13  0.0081  0.0139  12.663  2  0.0272  0.0182  0.0311  0.035  12.750  3  0.0526  0.0343  0.0579  0.058  0.02  12.835  4  0.0861  0.0550  0.0922  0.047  0.055  12.980  5  0.00613  0.0029  0.00473  13.062  6  0.00500  0.0027  0.00437  13.156  7  0.0237  0.0153  0.0248  13.260  8  0.0003  0.000506  13.345  9  0.00466*  0.0031  0.0050  13.435  10  0.0147  0.0093  0.0146  0.013  13.530  11  0.00484  0.0032  0.00439  0.0046  13.615  12  0.00181  0.0007  0.00126  0.0042  13.700  13  13.785  14  13.870 13.950  0.019  0.007 0.00290  0.0008  0.00131  15  0.0005  0.000887  16  0.0004  0.000752  + Data were normalized on Lawrence et a!. [78] at v’=4. @ The same set of values was quoted in the article of Zipf and Gorman [2951. Values were obtained at a column number N of 1014 cm . 2 This transition cannot be separated from v= 1 of the o fI state. The value was obtained from the ratio 1 of the relative band strengths of these two states as calculated by Stahel et a!. [3061.  Table 8.4  238  Absolute optical oscillator strengths for transitions to the vibronic bands of the valence bhlDu+ state from the ground state of molecular nitrogen  Energy (eV)  v’  Present  Ajello  Zipf and  work  et al.  MacLaughlin  (2961  1294]  Carter  (79]#  0  1 2 3  4 13.305  5  13.390  6  0.00216  0.00135  0.00123  0.002649  0.00260  0.0075  0.0048  7  0.003409  8  0.022107  13.660  9  0.0128  0.009529  0.0102  13.760  10  0.00220  0.001643  0.00173  13.830  11  0.00654  0.003504  0.00367  13.910  12  0.0303  0.030297  0.0316  13.998  13  0.004443  0.00455  14.070  14  0.0341  0.041825  0.0424  14.150  15  0.0409  0.054902  0.0493  0.034  14.230  16  0.0626*  0.067792  0.0667*  0.025  14.300  17  0.0318  0.037148  0.0368  0.025  14.400  18  0.00326  0.003366  0.00329  14.465  19  0.0166  0.021500  0.0208  14.525  20  0.0173  0.018373  0.0177  21  0  0.019  0.016 0.0076  14.680  22  0.00455  0.005532  0.00522  14.737  23  0.00897  0.009411  0.00880  14.795  24  0.00363  0.003823  0.00356  0.0052  0.0044  Values were obtained at a column number N of 1014 cm . 2 This transition cannot be separated from v=5 of the cI+ state. The value was obtained from the ratio of the relative band strengths of these two states as calculated by Stahel et aL 13061.  *  0.0592 0.0007* 0.0176  0.0285 0 0.0179  0.0496 0.0006* 0.0135  4 5 6  13.980  14.230  14.478  0.0039  . 2 Values were obtained at a column number N of 1014 cm state. The value was obtained from the ratio of the This transition cannot be separated from v= 16 of the b’ relative band strengths of these two states as calculated by Stahel et al. 13061.  0.0207  0.0136  0.0190  3  13.720  0.029  0.14  0.065  0.011  [78]  et aI.  Lawrence  [79]#  Carter  0.0027  0.00199  0.0038  0.00147  1  13.185 2  0.217  0.1567  0.195  0  [294]  [296]  12.935  McLaughlin  et al.  work  t v  Zipf and  Ajello  Present  (eV)  Energy  member of the Rydberg c 2 state from the ground state of molecular nitrogen 1  Absolute optical oscillator strengths for transitions to the vibronic bands of the lowest  Table 8.5  co  C)  5  14.230  0.00210  0.00530  # Values were obtained at a column number N of 1014 cm . 2  4  13.990  3  0.018  0.0172  0.0155  2  13.475  0.0682  0.0640  1  13.210  0.040  0.037  0.0656  0.0635  0  [78]  et al.  Lawrence  [79]#  Carter  [294]  12.910  McLaughlin  work  v’  Zipf and  Present  (eV)  Energy  l state from the ground state of molecular nitrogen c f member of the Rydberg 1  Absolute optical oscillator strengths for transitions to the vibronic bands of the lowest  Table 8.6  C  0.030  0.0329 0.00506 0.00321  0.0236 0.00620 0.00155  3 4 5  13.820  14.050  14.275  . 2 Values were obtained at a column number N fo 1014 cm of the v=9 from separated be cannot * This transition b’l1 state. The value was obtained from the ratio of the relative et at. 1306]. Stahel by as calculated two states these band strengths of  0.021  0.0278  0.0277  13.585  2  1  13.345  0.00049  [79]#  Carter  0.0226*  0  13.100  McLaughlin  work [294]  Zlpf and  Present  0.0211*  v’  (eV)  Energy  member of the Rydberg olH state from the ground state of molecular nitrogen  Absolute optical oscillator strengths for transitions to the vibronic bands of the lowest  Table 87  242 It can also be seen In tables 8.3—8.7 that although the absolute vibronic oscillator strengths reported by Zipf and McLaughlin [294], Ajello et al. [296], James et al. [297] and the present results show variations between each other, the relative oscillator strength values for the vibronic levels of a given electronic transition are reasonably consistent. These differences between the data sets are therefore likely caused by the different ways in which the data have been made absolute. For the b’H vibronic bands, the data of James et al. [297], which were normalized at v’=4 to the value reported by Lawrence et al. [78], are lower than the presently reported values. This observation and the differences with the present work are consistent with the fact that the data of Lawrence et al. [78] still show “line saturation” effects at the lowest pressure used for measurement (see above discussion). The absolute oscillator strength data reported by Zipf and McLaughlin [294] are in general slightly higher than the present results. However, It has to be pointed out that Zipf and McLaughlin [2941 did not make any direct oscillator strength measurement. Their oscillator strength data [294], which were used to calculate the predissociation branching ratios by combining with their measured emission cross sections, were in fact derived from the relative electron impact data of Geiger and Schroder [304] by normalizing on the absolute generalized oscillator strength data of Lassettre and Skerbele [13]. The data reported by Lassettre and Skerbele [13] were in turn obtained from the earlier limiting oscillator strengths work of Silverman and Lassettre [18], which had to be renormalized [13] by multiplying a factor (0.754) in order to correct for an error in the pressure measurements. Ajello et al. [2961 determined  243 absolute oscillator strength data from their own measurements, but their results have a stated uncertainty of 22%. By summing up the appropriate vibronic oscillator strengths shown in tables 8.3—8.7, the total absolute oscillator strengths for the b’fl and bI’u+ excited valence states, and the lowest members of c’I1, c’l2+ and l Rydberg states can be obtained. The results are summarized in o f 1 table 8.8 where previously available experimental [294,296,297,324] and theoretical data [299—303,3061 are also shown for comparison. It can be seen that there are large variations between the reported values. Except fl state, the theoretical data of Bielschowsky et al. 1 in the case of the o [303], calculated using the configuration interaction method, show better agreement with the present results than those calculated using the Hartree—Fock method. The calculations reported by Stahel et al. [3061 only show good agreement with the present values for the c’fl state, while the calculated values for the other states are all lower. The total oscillator strengths for the five excited states reported by Zipf and McLaughlin [2941 are somewhat higher than the presently reported data, which is consistent with the vibrationally resolved results in tables 8.3— 8.7. Similarly, the total oscillator strength value for the b’fl state reported by James et al. [297] is -36% lower than the present value. However, this is consistent with the fact that the normalization [297] was obtained using the vibronic oscillator strength for v’=4 of the b’H state measured by Lawrence et a!. [78], which is lower than the present work by the same amount, as shown in table 8.3. The spectrum above 14.92 eV involves many highly overlapped transitions. Therefore absolute integrated oscillator strengths over small energy intervals in the energy region 14.92—16.91 eV have been  244 Table 8.8 Total absolute optical oscillator strengths for transitions to the Hu and b’lu+ valence states, and the lowest members of the 1 b flu, c’ 1 c u and 1  flu 1 O  Rydberg states from the ground state of  molecular nitrogen  b’fl  C’flu  1 C’  O’fl  Experiment: Present work  0.243  Jamesetal. [297]  0.156  Ajelloetal. [296] ZipfandMcLaughlin[2941  0.278  0.145  0.321 0.283  Chutjianetal. [324]  0.279  0.080  0.223  0.310  0.156  0.317  0.0921  0.10  0.080  0.12  0.026  Theory: Bielschowsky et al. [303] (a) Hartree-Fock  0.68  0.62  0.07  0.06  0.11  (b) CI  0.41  0.31  0.09  0.26  0.15  0.124  0.209  0.141  0.139  0.061  0.0641  0.0493  0.136  Staheletal. [306] KosmanandWallace[3001 Hazi [302]  0.47  Rescignoetal. [2991 Roseetal. [3011  0.11 0.0681  0.32  0.49  0.0591 0.11  0.149  245 Table 8.9 Integrated absolute optical oscillator strengths in selected regions over the energy range 14.92—16.9 1 eV for excitation of molecular nitrogen  Energy range  Integrated oscillator  (eV)  strength  14.92—15.07  0.0139  15.07—15.19  0.0228  15.19—15.30  0.0196  15.30—15.43  0.0245  15.43—15.54  0.0212  15.54—15.74  0.0510  15.74—15.93  0.0606  15.93—16.03  0.0300  16.03—16.11  0.0270  16.11—16.17  0.0115  16.17—16.26  0.0260  16.26—16.33  0.0184  16.33—16.40  0.0156  16.40—16.49  0.0236  16.49—16.70  0.0476  16.70—16.91  0.0426  246 obtained, and these are summarised in table 8.9. Comparison with the previously reported photoabsorption data in this energy range is difficult because of different instrumental energy resolutions and also because of the presence of “line saturation” effects in the photoabsorption data. Finally, it can be noted that the oscillator strength distribution of molecular nitrogen was reviewed earlier by Berkowitz [143], using the experimental data available before 1980. Berkowitz obtained a value of 1.153 for the integrated oscillator strength below 15.56 eV using the data of Lassettre and Skerbele [13] and a value of 0.3299 in the 15.56— 16.76 eV energy region based on the data of Carter [79]. In the present work these integrated values are determined to be 1.173 and 0.3 19, respectively.  8.3 Conclusions In the present work comprehensive oscillator strength measurements have been obtained throughout the UV and soft x-ray energy regions for the photoabsorption of molecular nitrogen. Absolute optical oscillator strengths have been measured in the energy region 11— 200 eV using low resolution dipole (e,e) spectroscopy and TRK sum—rule normalization. The present continuum results are in good agreement with the photoabsorption data reported by Samson and Haddad [292]. Absolute optical oscillator strengths in the 12—22 eV region of discrete excitation have also been measured using the high resolution dipole (e,e) method recently developed in this laboratory. The absolute scale was obtained by normalizing in the smooth continuum region at 20 eV to the absolute photoabsorption value determined using the low resolution  247 dipole (e,e) spectrometer. The transition peaks below 14.9 eV have been deconvoluted to obtain the absolute photoabsorption oscillator strength values for individual vibronic transitions. The presently determined absolute optical oscillator strengths for excitation to the b’H and b’ valence states, and the c’fl, ctu+ and o fl Rydberg states have been 1 compared with previously reported experimental and theoretical data. Large differences between the various reported data sets are observed. However, it is found that the relative oscillator strength values for the vibronic bands determined from the present work and some of the previously reported [294,296.2971 data are reasonably consistent. This suggests that the differences in these cases are most likely due to the different normalization procedures used to establish the absolute scales. In the present work the absolute optical oscillator strength scale has been established by independent procedures. The accuracy of the presently determined absolute optical oscillator strengths for the photoabsorption of molecular nitrogen in the discrete region can be justified by a consideration of the results for the noble gases [37—391 (chapters 4—6) and molecular hydrogen [401 (chapter 7) which have been recently obtained using the same instrumentation and techniques. The present work also clearly demonstrates the existence of serious errors due to “line saturation” (bandwidth) effects in absolute oscillator strength (cross section) determinations for discrete transitions in molecular nitrogen made using Beer—Lambert law photoabsorption techniques, even where the measurements have been made as a function of pressure. Such considerations will be of concern in absolute oscillator strength determinations for all atoms and molecules using Beer—Lambert law photoabsorption methods.  248 Chapter 9  Absolute Optical Oscillator Strengths for the Photoabsorption of Molecular Oxygen (5-30 eV) at High Resolution  9.1 Introduction Since oxygen is the second most abundant species within the earths atmosphere, an accurate knowledge of absolute oscillator strengths (cross sections) for the photoabsorption of molecular oxygen in the valence discrete region is of great importance in aeronomy and in other areas such as nuclear physics, radiation physics and astrophysics. The dissociation and predissociation of molecular oxygen by the absorption of solar radiation can also be used to determine the oxygen density profile at high altitudes and such processes play an important role in atmospheric phenomena such as aurora and dayglow. Molecular oxygen is also of particular theoretical interest and challenge since it is an open shell system. The photoabsorption spectrum of oxygen has been studied extensively. Critical reviews and compilations of the spectroscopic data of oxygen can be found in several papers [46,330,331]. Although Beer— Lambert law photoabsorption methods have often been used to obtain quantitative results for discrete transitions, it has been pointed out [37,46] (see chapter 2) that absolute oscillator strengths (cross sections) measured by direct absorption of photons may be subject to considerable error because of “line saturation” effects due to the finite resolution (bandwidth) of the optical spectrometer. Such effects can be severe for  249 discrete transitions with very narrow natural linewidth and high cross section. For example, Yoshino et al. [55] have noted that the Schumann— Runge (12,0) band of 18 is too sharp for its absolute cross section to be measured by conventional Beer—Lambert law photoabs orption techniques. The Schumann—Runge band system of molecular oxygen, which g to the B 3 - state, has been 3 involves transitions from the ground X studied extensively by many workers. On the low energy side the system consists of sharp discrete transitions with very low oscillator strength, which have been measured by Lewis et al. [332] using the curve of growth method to allow for bandwidth effects. At higher energy In the 7—9.8 eV region the absorption spectrum of oxygen is dominated by the broad and generally featureless Schumann—Runge continuum, for which many Beer— Lambert law photoabsorption measurements of the absolute cross section have been made [333—342]. Ab—initio theoretical calculations have been reported by Buenker and Peyerlmhoff [3431 and by Allison et al. [344] for the oscillator strengths of the Schumann—Runge continuum region, 3 and the taking into account the mixing between the valence B Rydberg E 3 in other notation) states. Allison et al. [344] also 3 (or B’ fl state and reported 3 took into account the contributions from the 1 cross sections and structural features that were consistent with the existing experimental results. Wang et al. [342] performed an experimental absolute photoabsorption measurement of oxygen in the Schumann—Runge continuum region, and by fitting their theoretical calculations to the observed data, they reported potential curves and 3 and mixed transitions moments for the mixed Rydberg—valence B valence—Rydberg E 3 states.  250 On the high energy side of the Schumann—Runge continuum, there are several diffuse bands. The three prominent peaks at 9.96 eV (longest), 10.28 eV (second) and 10.57 eV (third) have been assigned by Yoshimine et al. [345] and Buenker et al. [346] as transitions to the three lowest vibrational levels of the mixed valence—Rydberg E - state. 3 Yoshimine et al. [345], Buenker et al. [3461 and Li et al. [347] have computed the absolute oscillator strengths for these three bands. Beer— Lambert law—type photoabsorption measurements have also been performed for these diffuse bands [334,336,3401, including a recent study by Lewis et al. [348,349], who made measurements on isotopic molecular oxygen (1802) and for the first time analyzed the data using Beutler—Fano type resonance profiles. Electron energy loss spectroscopy (EELS) has also been used to study the electronic excitation spectrum of molecular oxygen [13,16,17,92,350,3511 in the valence discrete region. Since electron impact excitation is non—resonant as described in chapter 2, EELS based methods of determining optical oscillator strengths have the enormous advantage that they are not subject to the limitations of “line—saturation” (i.e. bandwidth) effects which cause difficulties in Beer—Lambert law photoabsorption measurements [37,46]. Using measurements of inelastically scattered electrons obtained at a range of scattering angles, absolute optical oscillator strengths for oxygen in the discrete and continuum regions were derived by Lassettre and co—workers [13,16,17] from extrapo1ation of the measured generalized oscillator strengths to zero momentum transfer. With the use of extremely high impact energy (25 keV) and small scattering angle, Geiger and Schroder [350] reported a very high resolution electron energy loss spectrum of oxygen in the  251 energy loss region 6.8—21 eV, but only relative intensities (not absolute oscillator strengths) were obtained. Huebner et al. [35 1] have reported data In the energy region 6—14 eV which were derived from high resolution electron energy loss measurements obtained at an impact energy of only 100 eV and at a small scattering angle (0.02 rad.). The measured oscillator strengths are questionable in this case [3511 sInce the experimental conditions correspond to a rather large momentum O.O1 and 0.04 a.u. at 6 eV and 14 eV respectively). The (K = transfer 2 absolute scale was established by Huebner et al. [351] by normalizing the spectrum to an average optical value [46] at a single point in the Schumann—Runge continuum region where the photoabsorption measurements were mutually in best agreement. An independent TRK sum rule normalization method was used by Bnon et al. [921 to obtain absolute oscillator strengths for the photoabsorption of oxygen in the energy region 5—300 eV from Bethe—Born converted electron energy loss spectra. These latter results [921 were determined directly at negligible momentum transfer using a low resolution (AE 1 eV FWHM) dipole (e,e) spectrometer with an impact energy of 8 keV and a mean scattering angle of zero degrees. In the presently reported work, the recently developed [36,37] high resolution dipole (e,e) method which has already been applied successfully to measurements for the noble gases [36—39] (see chapters 4—6) and several small molecules [27,40,4 1] (see chapters 7 and 8), has been used to measure directly, at negligible momentum transfer, the absolute oscillator strengths for oxygen in the energy region 6—30 eV at a resolution of 0.048 eV FWHM. The absolute scale has been obtained by normalizing in the smooth continuum at 26 eV to the previously reported  252 absolute oscillator strength value determined by Brion et al. [92] using a low resolution dipole (e,e) spectrometer.  9.2 Results and Discussion The photoabsorption oscillator strengths and spectral assignments of molecular oxygen are conveniently discussed with reference to the ground state molecular—orbital, Independent particle, valence shell electronic configuration, which may be written as:  2 ( lrg) 2 ( 2o)2( 1)( 3Gg) 2 (2ag)  Figure 9.1 shows the presently measured absolute differential oscillator strength spectrum of molecular oxygen measured in the energy region 5— 30 eV by high resolution dipo1e (e,e) spectroscopy at a resolution of 0.048 eV FWHM. Several vibrational progressions are clearly visible. The two other sets of data shown in figure 9.1 are the low resolution (1 eV FWHM) dipole (e,e) data (open triangles) reported earlier at 1 eV intervals by Brion et al. [92] and the photoabsorption data (open circles) measured by Samson and Haddad [292] using a double ion chamber method. The double ion chamber results [292] are not compared with the present work in the region of the sharp autoionizing structure (12—18 eV) because of significant differences in energy resolution and also because the optical measurements may be subject to “line saturation” effects. Therefore the data of reference [2921 are only shown in figure 9.1 in the generally smoother spectral region above 18 eV. It can be seen from figure 9.1 that the present results are in very good quantitative  253  0.4  0.3  Cl)  0.2 20  C  Q Ci)  o  0.1  10  C-)  C 0.0  Photon energy (eV)  Figure 9.1: Absolute oscillator strengths for the photoabsorption of molecular oxygen in the energy region 5—30 eV measured using the high resolution dipole (e,e) spectrometer (FWHM=O.048 eV).  254 agreement with the earlier data of Brion et aL. [921 and also those of Samson and Haddad [292] in the smooth continuum region (where the cross section will be effectively independent of resolution). At lower energies the presently obtained high resolution spectrum is seen to be consistent with the data of Brion et al. [92] given the differences in resolution. The total Integrated oscillator strengths below 18 eV for both the high and low resolution spectra are In very good agreement with each other, giving values of 1.13 and 1. 12 respectively. In the present work, integration of the measured high resolution differential oscillator strength spectrum over a given energy region will give directly the absolute oscillator strength for that region. The uncertainties in the presently reported absolute oscillator strengths are estimated to be ±5%. Figure 9.2 shows an expanded view of figure 9.1 in the energy region 6.5—10 eV showing the absolute oscillator strengths for the Schumann—Runge continuum. The weak Schumann—Runge bands below 7 eV which are several orders of magnitude smaller in oscillator strength than the continuum could not be observed in the present work. In figures 9.2 (a) and (b) the present results are compared with previously published experimental [334—336,338—342,351] and theoretical [342,344] results respectively. Immediately it can be seen from figure 9.2 (a) that the present results are in excellent agreement with most of the other experimental data. The data of Ditchburn and Heddle [335] are much higher than all the other experimental data while those of Goldstein and Mastrup [339] are somewhat lower In the energy region around the continuum maximum. For the experimental work shown in figure 9.2 (a) only the present high resolution dipole (e,e) measurements and the data of Huebner et al. [351] are derived from electron energy loss  (a) 0.20  • x  o • o  0.15  * *  o  255  Experimental measurements  Io  /  Present HR Dipole (e,e) Expt. Goldstein & Mostrup [339] / Ditchburn & Heddle [335] / Wotonobe et ci. [334) / Bloke et ci. [338] / ‘ Cook Metzger & [338] / Huebner et ci. [351] / ‘ Ogawo & Ogowo [340]/ Gibson et ci. [341] / Wang et ci. [342] /  0.10  20  15 x.’ x  x  4  A  Schumann Runge Con t  10  1.  0.05  ,0  5 C C.)  a.)  0  0  0.00 6.5  jJ 1  7.5  8.5  9.5  0  0  0.20  20  C.) 0  0  Ce C.)  o  IC.)  0  .-  Cl)  I-i  0  0.15 15  C 0.10  10  0.05  5  0.00  0  Photon energy (eV)  Figure 9.2: Absolute oscillator strengths for the photoabsorption of molecular oxygen. Expanded view of figure 9.1 in the energy region 6.5—10 eV, showing the Schumann—Runge continuum region. (a) comparison with previously published experimental data [334—336,338—342,351] (b) comparison with theory [342,344]  256 spectra. The remainder are Beer—Lambert law photoabsorption measurements [334—336,338—342] which in this particular energy region should not be subject to “line—saturation” effects due to the broad nature of the Schumann—Runge continuum in oxygen. Note that the data of Huebner et al. [3511 were normalized at the continuum maximum (8.61 eV) to the average of the optical data [46] which were available at that time and therefore reasonable agreement with the photoabsorption data is not surprising. In contrast, the present high resolution dipole (e,e) spectrum was made absolute using the TRK sum—rule normalized low resolution dipole (e,e) work of Brion et al. [921 in the smooth continuum region at 26 eV, which is -17 eV above the Schumann—Runge continuum maximum. The Bethe—Born conversion process (see experimental section 3.3) results in a very large change in relative intensity of the two continua between the original electron energy loss data and the relative optical oscillator strength spectrum. Therefore any inaccuracy in the Bethe—Born conversion factor for the spectrometer would produce spurious oscillator strengths. The validity and accuracy of the Bethe— Born conversion factor for the high resolution dipole (e,e) spectrometer used in the present work has previously been confirmed down to —11 eV by comparison of measurements and highly accurate ab—initio calculations for helium [371 and molecular hydrogen [40]. The results for the Schumann—Runge continuum of oxygen now provide a further stringent test of the accuracy with which the Bethe—Born conversion factor for the high resolution dipole (e,e) spectrometer has been determined and in particular in the region down to 7 eV. This is important to establish since the Bethe-Born conversion factor was obtained from a comparison of high and low resolution dipole (e,e) measurements above 22 eV in the  257 ionization continua of helium [37] and neon [38] (see chapter 3). The Bethe—Born factor below 22 eV was then obtained by curve fitting the measured quantity above 22 eV and extrapolating to lower energies. The excellent agreement of the present work with many previously published photoabsorption measurements of the absolute oscillator strengths in the Schumann—Runge continuum region of oxygen is a very strong indication that the Bethe—Born conversion factor is well characterized for the high resolution dipole (e,e) instrument, even in the low energy loss (photon energy) range. By extrapolating measured relative generalized oscillator strengths to zero momentum transfer, Lassettre et al. [13] obtained an integrated oscillator strength of 0.179 for the Schumann—Runge continuum region, over the range 6.56—9.46 eV, following correction of their previously published data [16,17]. By integrating the same energy region, the present work gives a slightly lower oscillator strength of 0. 169. In the other electron impact based work using low impact energy, Huebner et al. [3511 reported an integrated oscillator strength of 0.161 for the Schumann—Runge continuum. In figure 9.2(b), the present measurements are compared with the theoretical work reported by Allison et al. [344] and Wang et al. [3421. Both sets of calculated data show reasonable agreement with the present work. However, it must be pointed out that Allison et al. [344] employed a semiempirical method in which the calculated potential curve and the transition moment were adjusted in order to reproduce oscillator strength values and structural features consistent with the experimental results [340]. The theoretical results of Wang et al. [342], on the other hand, were obtained by fitting to their own measurements of the  258 Schumann—Runge continuum region. They then reported potential - mixed—Rydberg— 3 - and E 3 curves and transition moments for the B l valence state, which were obtained from 1 f valence states, and also the 3 the fitting procedures. Thus, although the existing theoretical absolute oscillator strength values for the Schumann—Runge continuum region appear to show good agreement with the present work, It should be remembered that both of these theoretical results depend for their success on experimental values. Figures 9.3(a) and (b) show expanded views of figure 9.1 in the energy regions 9.5—15 eV and 14—25 eV respectively. The ionization potentials for the states shown were obtained from the photoelectron work of Edqvist et al. [353]. The first ionization potential due to the ejection of an electron from the ltg orbital occurs at 12.07 1 eV. In figure 9.3(a) several diffuse bands are observed in the energy region from 9.7 eV to just below the first ionization potential. Due to the diffuse nature of the peaks compared with the relatively narrow bandwidth that can be obtained in optical experiments in this energy region, absolute oscillator strengths (photoabsorption cross sections) for these diffuse bands that have been measured using the Beer—Lambert photoabsorption method are expected to be reasonably accurate [334,336,340,348,349]. The three prominent peaks at 9.96, 10.28 and 10.57 eV, corresponding to the longest, second and third bands respectively, have been assigned [345,346] as transitions to the vibrational levels v’0, 1 and 2 of the mixed valence—Rydberg E - state. The absolute oscillator strengths for 3 the diffuse bands in the energy region 9.7—12.07 eV were determined in the present work and the results are summarized in table 9.1 along with previously available experimental [340,349,3511 and theoretical [345—  259  0.2  0.1  £ C.) U) 0 Ci)  a.) Cl)  oI-.  0.0  C.)  o  0  0  (b)  C’)  C  Cl)  02!  —  C.)  •—  0  o  0.3 30  C  0.2 20 02  ofl A Eg 4 Ii b 2  0.1  g B E 2  4 U  —  10  cEU  0  0.0 14  16  20  22  24  Photon energy (eV)  Figure 9.3: Absolute oscillator strengths for the photoabsorptlon of molecular oxygen. The ionization potentials have been obtained from ref. [353]. (a) in the energy region 9.5—15 eV. The assignments of the vibrational levels v’=O, 1 and 2 of the E 2u and 2 3 flu states are taken from the theoretical work of 3 Buenker et al. [346]. (b) in the energy region 14—25 eV.  ?  7  ?  7  v2  v’=l  0.000820 0.000752 0.000497  0.00159 0.00110 0.00210 0.000502 0.00205 0.00163 0.00283  0.000733 0.000606 0.00147 0.000419 0.00169 0.00174 0.00169  10.98—11.17  11.17—11.33  11.33—11.52  11.52—11.59  11.59— 11.74  11.74—11.89  11.89—12.07  0.00242  0.00146  10.71 —10.84 0.000900  0.00140  0.000650  0.000652  10.62—10.71  0.000814  0.000660  0.00147  0.000827  10.44—10.62  2  10.84— 10.98  0.000770  0.00078  0.00804  0.00759  10.17— 10.44  1  v’=O  0.00706  0.00705#  0.001024  0.00833  0.01742 0.00562 0.00061  0.0124 0.00412  0.0157 0.007  # This value was obtained from the average of the Integrated oscillator strengths for 016018 and 180.2 in the energy region 10.19-10.35 eV.  0.0006  0.0007  0.0009  0.0136  0.0103  [3471 eta!. [345J t3461  Ogawa [3401  0.00844  [3491  eta!. [351j  LI et a!. Yoshimine  Buenker et a!.  calculations  Theoretical  Ogawa and  9.75—10.17  Lewis et a!.  Huebner  photoabsorption methods  methods Present work  Beer-Lambert law  Electron impact based  v’=O  Energy range (eV)  The assignments were taken from ref. [346j.  l 2 f 3  2I1  2[1  3 E  Assignment  Experimental measurements  Absolute optical oscillator strengths  Absolute optical oscillator strengths for the photoabsorption of molecular oxygen in the energy region 9.75—11.89 eV  Table 91  261 347] data. Column two in table 9.1 gives the energy regions over which integration was performed in order to obtain the absolute oscillator strength for each diffuse peak. The absolute oscillator strength values reported by Ogawa and Ogawa [340] were obtained by integrating their Beer—Lambert law photoabsorption data over the same energy regions. It can be seen from table 9. 1 that the present results are consistent with the photoabsorption work of Ogawa and Ogawa [340], as expected (see above). The recent Beer—Lambert law photoabsorption work of Lewis et al. [349] for the second and third bands is also in good agreement with the present work and with that of Ogawa and Ogawa [340]. For the lowest (E - (v0)) band, the data reported by Lewis et al. [348] are only 3 for the energy region 9.95—9.98 eV compared with 9.75—10.17 eV for both the present work and that of Ogawa and Ogawa [340]. Hence the data of Lewis et al. [348] cannot be compared directly with the present work in this region. However, as demonstrated in the work of Lewis et aL. [348], their absolute cross sections in the limited energy region 9.95— 9.98 eV are in excellent agreement with the measurements of Ogawa and Ogawa [3401 and thus also with the present work. The electron impact based oscillator strength data reported by Huebner et al. [3511 are in general higher than the present results and the data of Ogawa and Ogawa [340]. It should be noted that the accuracy of the Bethe—Born factor used by Huebner et al. [3511 was not known over a wide energy range. In addition they employed an impact energy of only 100 eV to measure the energy loss spectrum and this is too low an impact energy to obtain a dipole—only spectrum (i.e. the momentum transfer K is to large). Several g 3 vibronic bands in the X  -  g 3 a’u and X  —  systems in the  energy region 9.8—10.6 eV, which are dipole—forbidden transitions, were  262 observed even in direct photoabsorption measurements [331 ,349]. The intensities of these dipole—forbidden peaks would be expected to be significantly higher in the electron energy loss spectrum of Huebner et al. [351], which would cause higher oscillator strength values for those energy regions involving dipole—forbidden peaks. The present work, using an impact energy of 3000 eV and zero degree scattering angle, does not suffer from this problem. Ab—initio configuration interaction theoretical methods have been used by three groups [345—347] to calculate the absolute oscillatOr strengths for the vibrational levels v’=O, 1 and 2 of the mixed—valence Rydberg E 3 state. The theoretical calculations reported by Yoshimine et al. [345] and Buenker et al. [3461, which assigned the longest, second and third bands as the vibrational levels v=0, 1 and 2 of the mixed valence—Rydberg E 3 state from the calculated energy levels, give oscillator strength values for these three bands which are much higher than the present and other experimental values. The recent work of Li et al. [347] shows better agreement with the present results for the v’= 1 and 2 bands while the value reported by Li et al. [347] for v’=O is even higher than that reported by Yoshimine et al. [345] and Buenker et al. [346]. Buenker et al. [346] also assigned three other peaks at energies of 10.90, 11.24 and 11.55 eV as the vibronic bands v’=O, 1 and 2 of the mixed valence—Rydberg 2 fl state. The calculated [346] oscillator 3 strengths for these three peaks are only slightly higher than the present results as seen in table 9.1. The electron impact data reported by Lassettre et al. [131 give an oscillator strength of 0.020 for the energy region 9.46—10.7 eV while the present estimate for the same energy range is 0.0 185. The total oscillator strength sum up to the first  263 ionization potential (12.07 eV) was determined to be 0.198 in the present work, which Is exactly the same value as was reported by Huebner et al. [351]. However, it should be remembered that the oscillator strength sum below 9.46 eV reported by Huebner et al. [351] Is slightly lower than that In the present work, while in the energy region 9.46—12.07 eV their reported value is slightly higher. In the energy region 12—17 eV most of the bands in the photoabsorption spectrum of oxygen have not been classified, while from 17—25 eV there are many Rydberg series converging on the various ionization limits shown on figure 9.3(b). The energy positions and the assignments of these Rydberg states can be found In the critical compilation published by Krupenle [3311. Table 9.2 shows the present integrated oscillator strength values over selected energy intervals in the energy region 12.07—18.29 eV. The electron Impact study by Huebner et al. [3511 (which like the present work Is free of “line—saturation” effects) also reported integrated absolute oscillator strength values in the energy region 12.10—14.04 eV. These values [351], also shown in table 9.2, are in general somewhat higher than the present results. The absolute oscillator strength sum in the energy region 12.10—14.04 eV was estimated to be 0.181 by Huebner et al. [351], while the present result for the same energy region is 0.151. The value reported by Huebner et al. [351] is —20% higher than the present result which Is consistent with the generally higher values reported by Huebner et al. [351] from 9.75— 11.89 eV as seen in table 9.1.  In the review paper of Hudson [46], it  was pointed out that much of the Beer—Lambert photoabsorption cross section data for oxygen [354—356] in the energy region 12.10—20.66 eV is subject to bandwidth errors (or “line—saturation” effects) and also  264 Table 9.2 Integrated absolute optical oscillator strengths for the photoabsorption of molecular oxygen over intervals in the energy regIon 12.07-18.29 eV  Integrated absolute optical Energy range (eV)  oscillator strengths Present work  Huebner et al. [3511  12.070  12.240  0.00176  0.00182  12.412  0.00325  0.00379  12.538  0.00611  0.00725  12.673  0.0106  0.01176  12.794  0.0134  0.01483  12.915  0.0149  0.01724  13.026  0.0147  0.01641  13.152  0.0147  0.01567  13.152—13.263  0.0117  0.01390  13.263  13.369  0.00999  0.01186  13.476  0.00861  0.00987  13.577  0.00793  0.01033  13.684  0.00775  0.00952  13.684—13.814  0.00925  0.01166  13.814—13.954  0.00941  0.01424  13.954  14.056  0.00701  0.01027  14.056—14.181  0.00852  14.181  0.00812  12.240 12.412 12.538 12.673 12.794 12.915 13.026  13.369 13.476 13.577  —  —  —  —  —  —  —  —  —  —  —  —  —  —  14.302  265 Table 9.2 (continued)  Integrated absolute optical Energy range (eV)  oscillator strengths Present work  Huebner et al. [351]  14.408  0.00736  14.488  0.00573  14.603  0.00948  14.728  0.0127  14.853  0.0160  14.978  0.0195  15.092  0.0214  15.217  0.0294  15.2 17— 15.332  0.0340  15.332  15.472  0.0427  15.587  0.0310  15.862  0.0614  16.006  0.0282  16.151  0.0266  16.351  0.0345  16.481  0.02 16  16.581  0.0164  17.171  0.147  17.514  0.0897  17.875  0.0882  18.287  0.0740  14.302 14.408 14.488 14.603 14.728 14.853 14.978 15.092  15.472  —  —  —  —  —  —  —  —  —  —  15.587 15.862 16.006 16.151 16.351 16.481 16.581 17.171 17.514 17.875  —  —  —  —  —  —  —  —  —  266 systematic errors. Based on the photoabsorption data reported by Matsunaga and Watanabe [356], the absolute Integrated oscillator strength in the energy region 12.07—16.53 eV was estimated to be 0.724 by Berkowitz [1431. However, we find that a reanalysis of the data of Matsunaga and Watanabe [356] gives an Integrated absolute oscillator strength value of 0.587. This value we have obtained by digitizing figures 1 and 2 of ref. [356]. Alternatively we have obtained a value of 0.685 from the reported [356] numerical oscillator strength values In table 1 of ref. [3561. The difference occurs since the tabulated numerical values reported in the paper of Matsunaga and Watanabe [356] only include one third of their actual experimental data. Thus, Insufficient data are given to obtain an accurate integration of the spectral area. Therefore, It would seem that Berkowitz [143] made use of the limited tabulated numerical values reported by Matsunaga and Watanabe [356] in order to obtain the integrated oscillator strength in the energy region 12.07—16.53 eV. The present dipole (e,e) work for the same region gives an integrated oscillator strength of 0.578, which agrees well with the presently revised value of 0.587 obtained by digitizing the data in figures 1 and 2 reported by Matsunaga and Watanabe [356]. Digitizing the figures of other photoabsorption work reported by Huffman et al. [354] for the energy region 12.07—16.53 eV, an integrated oscillator strength of 0.685 was obtained, which is —20% higher than the value determined in the present work. This is again consistent with the work of Matsunaga and Watanabe [3561, in which they state that the data of Huffman et a!. [354] were 20—30% higher than their measured values in this energy region.  267 9.3 Conclusions Absolute optical oscillator strengths for molecular oxygen have been measured by high resolution dipole (e,e) spectroscopy In the energy region 5—30 eV, which are free of ‘line—saturation” (bandwidth) effects. Absolute optical oscillator strengths for the broad Schumann—Runge continuum region of oxygen determined in the present work are In excellent agreement with most previously reported experimental results. This gives considerable confidence in the accuracy of the previously determined Bethe—Born conversion factor for the high resolution dipole (e,e) spectrometer used in the present work, when extrapolated down to 7 eV. This in turn lends support to the accuracy of the absolute oscillator strengths previously reported for argon, krypton and xenon [39] (see chapter 6), hydrogen [40] (see chapter 7) and nitrogen [41] (see chapter 8) from this laboratory. The electron impact data reported by Huebner et al. [351] for oxygen are in general higher than the present work for the electronic transitions higher in energy than the Schumann—Runge continuum. This may be due to appreciable contributions from dipole forbidden transitions due to the low impact energy of 100 eV, or alternatively to inaccuracies in the Bethe—Born conversion factor employed by Huebner et al. [351]. For the diffuse discrete bands in the oxygen spectrum In the 9.7— 12.071 eV energy region, the presently determined absolute oscillator strengths are in good agreement with the photoabsorption measurements of Ogawa and Ogawa [340]. The present work is also in good agreement with the integrated oscillator strength value reported by Matsunaga and Watanabe [356] in the energy region 12.07—16.53 eV. “Line—saturation”  268 effects which have caused severe difficulties In some of the direct Beer— Lambert law photoabsorption measurements In the valence discrete excitation regions of the electronic spectra of hydrogen [40] (see chapter 7) and nitrogen [41] (see chapter 8) are not found for the transitions studied in the present work in molecular oxygen. This Is probably due to the generally broader nature of the transition peaks In the oxygen spectrum, in contrast to the situation for hydrogen and nitrogen (see chapters 7 and 8). Such broadening is to be expected In oxygen above 12.07 eV (the first ionization potential) due to the short lifetimes of the rapidly autoionizing excited states associated with the higher ionization limits.  269 Chapter 10  Absolute Optical Oscillator Strengths for the Discrete and Continuum Photoabsorption of Carbon Monoxide (7-200 eV) and Transition Moments for the X 1  —  AH System  10.1 Introduction Carbon monoxide is of great importance in astrophysics since it is the second most abundant interstellar molecule after hydrogen. It has been detected in interstellar clouds and also in comets and planetary atmospheres. Quantitative spectroscopic data such as the absolute oscillator strengths (cross sections) for the photoabsorption and photodissociation of carbon monoxide provide valuable Information for the understanding of the formation and properties of interstellar matter [357,3581. Since molecular hydrogen cannot be observed directly in dense opaque regions such as in our galaxy, carbon monoxide has been utilized as a tracer of molecular hydrogen [357,358]. Absolute optical oscillator strengths for the photoabsorption of carbon monoxide in the valence discrete region can also be used to determine molecular abundances in planetary and stellar atmospheres [232]. In electron impact experiments, the excitation cross section at sufficiently high Impact energy is related to the optical oscillator strength. Therefore, the latter quantities can be used to normalize relative experimental electron impact excitation cross sections [359]. Moreover, the absolute electron impact excitation cross sections can be used in combination with the emission cross sections to determine the predissociation yields for  270 carbon monoxide, which are useful quantities in constructing photochemical models of molecular clouds [360]. However, the existing absolute optical oscillator strength (cross section) data for the photoabsorption of carbon monoxide In the valence discrete region show large differences in the magnitudes of the absolute oscillator strengths between the various experimental and theoretical values. In contrast, there is generally better agreement between the various available measurements in the higher energy smooth continuum regions [30]. Absolute optical oscillator strengths for the valence shell discrete transitions of carbon monoxide have been calculated by several groups. Absolute optical oscillator strengths for the discrete transitions from the X’ ground state to the A fl, C 1 Z and B 1 1 excited states have been calculated by Rose et al. [301] and Coughran et al. [361], using an equation—of—motion (or random—phase approximation) method, by Wood [3621, using a configuration interaction (CI) method and by Nielsen et al. [363] using the second order polarization propagator approach (SOPPA). In other work, Lynch et al. [364] have calculated the dipole moments and oscillator strengths for the low—lying valence states of carbon monoxide by applying the multiconfigurational random phase approximation (MCRPA). Padial et al. [365], have constructed pseudospectra of discrete transition frequencies and calculated the oscillator strengths for the discrete and continuum excitations from the occupied molecular orbitals by employing the Stieltjes—Tchebycheff (S—T) technique and separated— channel, static—exchange calculations. Ab initio CI calculations have been performed by Cooper and Lânghoff [366], Kirby and Cooper [367] and Chantranupong et al. [368]. In particular, calculations of the absolute optical oscillator strengths for the transitions to the individual vibronic  271 1 excited states have been reported by 1 and B l, C A f levels of the 1 Kirby and Cooper [367] and Chantranupong et al. [368] while Cooper and Langhoff [3661 have calculated the theoretical radiative lifetimes for those same vibronic states. A large number of experimental photoabsorption studies of carbon monoxide have been made and critical reviews and compilations of the available spectroscopic data can be found in refs. 130,46,369—37 1]. Photoabsorption methods [372—392] have been commonly employed and quantitative measurements based on the Beer—Lambert law [376,379,380,385—388,39 1,392] have provided much of the existing absolute optical oscillator strength data. However, as pointed out earlier by Hudson [46] and discussed in further detail recently by Chan et al. [37,411 (see chapter 2) the Beer—Lambert law is only strictly valid in the hypothetical situation of infinite experimental energy resolution (i.e. zero bandwidth). Thus in practice Beer—Lambert law photoabsorption data for discrete transitions will be subject to so—called ‘line—saturation’ effects (i.e bandwidth—linewidth interactions) which lead to errors in the derived oscillator strengths. These arise from the logarithmic transform involved in Beer—Lambert law photoabsorption methods and the resonant nature of photon induced excitation. Since the peaks in the vibronic 1 excited states of carbon 1 and C l, B A f spectra for production of the 1 monoxide have extremely narrow natural linewidths, the absolute oscillator strengths measured for these bands using Beer—Lambert law photoabsorption techniques may be expected to exhibit severe “line— saturation” effects. For instance, the oscillator strengths for the fl excited state measured by Lee and Guest 1 vibrational bands of the A [387] using the Beer—Lambert law are found to be an order of magnitude  272 higher than those reported by Myer and Samson [385] which were measured at a lower resolution. While Lee and Guest [387] correctly stated that the cross sections at the peak maxima would be affected by the monochromator bandwidth, their claim that the integrated cross section over the molecular band (I.e. the Integrated oscillator strength) would be independent of the bandwidth Is Incorrect. This Is convincingly demonstrated in refs. [37,391], where it is shown that It Is not only the peak maximum that is affected by the incident bandwidth, but also more importantly the integrated cross section for the transition, which will be smaller than the true value. These spurious effects are further illustrated by the fact that the photoabsorption oscillator strength value reported by Lee and Guest [387] for production of the v’=O level of l state is found to be only —50% of the value obtained by Lassettre A f the 1 and Skerbele [69] using an electron impact based method. In other more recent photoabsorption work, Eidelsberg et al. [392] and Letzelter et al. [388] have reported discrete oscillator strengths for carbon monoxide excitation in the VUV energy regions 8.00—9.92 eV and 10.78—14.01 eV respectively. In order to minimize the “line saturation” effects involved in using Beer—Lambert law photoabsorption, the integrated absorption was measured in these studies [388,392] as a function of pressure and the integrated cross section was determined at pressures low enough such that the integrated absorption varied linearly with pressure. These procedures used by Eidelsberg et al. [392] and Letzelter et al. [388] are similar to those involved in measuring the integrated cross section at several different pressures and extrapolating to low pressure in an attempt to obtain the true Integrated cross section. However, these kinds of procedures put the most weight on the least accurate data  273 determined at the lowest sample pressures [37,46] and as a result the integrated cross sections measured by Eldelsberg et al. [3921 and by Letzelter et al. [3881 are most likely still subject to errors as was found In the case of nitrogen [37,41] (see chapter 8). Oscillator strengths for the vibrational levels of the A 11 band have also been reported by Rich [393] 1 using absorption measurements based on the shock tube technique and curves of growth analyses. Lifetime measurements [202,251,394—408] have been extensively employed for studying the valence shell discrete transitions of carbon monoxide. However, large discrepancies exist between the various reported experimental values. The lifetimes for the vibronic levels of the fl state have been measured by several groups [251,398—400,406,407]. 1 A It has been found [407] that the decay rates for some of the vibronic +, 3 levels of the A fl state are affected by perturbations from the nearby a’ 1 —, d 3 e z, j1- and D 3 A states. These kinds of perturbations cause the 1 measured lifetimes to differ by up to 20% from the true values. Field et a!. [4071 have derived deperturbed lifetimes for the vibronic levels of the fl state and reported a linear dipole moment function from their data. 1 A This function was used by Kirby and Cooper [3671 to calculate the absolute oscillator strengths for photoabsorption from the ground state to the vibronic bands of the A fl state. Furthermore, in order to convert the 1 lifetimes of the vibronic levels of the B 2D and C1÷ bands to oscillator 1 strengths, it is necessary to know the branching ratios for the two systems (B-X, B-A) and (C-X, C-A). Electron impact methods based on electron energy loss spectroscopy have also been applied to study the oscillator strengths for the valence shell discrete [69,107,409] and continuum [87] transitions of  274 carbon monoxide. As pointed out In chapter 2, electron Impact excitation is non—resonant even for discrete transitions, and because no logarithmic transform is needed to obtain the cross section (In contrast to Beer—Lambert photoabsorption) no “line saturation” (I.e bandwidth) errors can occur. Lassettre and Skerbele [69] have measured generalized oscillator strengths (GOS) for selected discrete transitions of carbon monoxide as a function of momentum transfer using electron energy loss spectroscopy and varying the scattering angle. Absolute optical oscillator strengths for the four discrete electronic transitions of carbon monoxide were reported [69] by extrapolating a series of GOS measurements for each transition to zero momentum transfer and normalizing their relative data on the absolute elastic electron cross sections measured by Bromberg [4101. Wight et al. [87], using a 8 keV energy incident electron beam and zero—degree mean scattering angle in a low resolution dipole (e,e) experiment, have determined the photoabsorption oscillator strengths of carbon monoxide in the energy region 7—70 eV. However, the data reported by Wight et al. [871 were made absolute by normalization to previously published absolute photoionization data reported by Samson and Cairns [325] in the smooth continuum region at 30 eV. Furthermore, since the resolution of the spectrum recorded by Wight et al. [87] was only 0.5 eV FWHM, oscillator strengths for the individual vibronic transitions could not be determined in the discrete region of the spectrum. In addition, it appears, from recent investigations using the same apparatus, that Wight et al. [87] did not make adequate corrections for background gases and non—spectral electrons in their measurements.  275 In the present work, the high resolution dipole (e,e) method as recently used to measure absolute photoabsorption oscillator strengths for the discrete transitions of the noble gas atoms [37—39] (see chapters 4—6) and several small molecules [27,40—42,411] (see chapters 7—9), Is now applied to quantitatively study of the valence shell discrete transitions of carbon monoxide. In addition, new wide ranging (7—200 eV) measurements of the photoabsorption absolute oscillator strengths for carbon monoxide have been made using low resolution dipole (e,e) spectroscopy. The absolute scale of the present measurements is established independently of any other measurements by using TRK sum— rule considerations [30]. The accuracy of the high resolution and low resolution dipole (e,e) methods has been confirmed by studies comparing measurements with ‘benchmark” theoretical calculations for helium [371 (see chapter 4) and molecular hydrogen [40] (see chapter 7). In addition, results for molecular oxygen [42] (see chapter 9) and nitrogen [411 (see chapter 8) have supported the accuracy of the energy dependent Bethe—Born conversion factor for the high resolution dipole (e,e) spectrometer when extrapolated down to lower equivalent photon energies than were used for its original determination using measurements for helium [37] and neon [38].  10.2 Results and Discussion The electronic transitions and photoabsorption oscillator strengths of carbon monoxide are conveniently discussed with reference to Its ground state molecular—orbital valence shell independent particle configuration which may be written as  276 5a) 2 ( 4 (4a) hr) 2 (3c) (  10.2.1 Low Resolution Absolute Photoabsorption Oscillator Strength Measurements for Carbon Monoxide (7—200 eV) A relative oscillator strength spectrum was obtained by Bethe—Born conversion of the electron energy loss spectrum measured with the low resolution (—1 eV FWHM) dipole (e,e) spectrometer in the energy region 7—200 eV. The data were least—squares fitted to the function AE over the energy region 90—200 eV. The fit gave B=2.243 and on this basis the fraction of the valence—shell oscillator strength above 200 eV was estimated to be 6.7%. The total area was then TRK sum—rule normalized to a value of 10.3, which includes the total number of valence electrons (10) plus a small estimated correction (0.3) for the Pauli—excluded transitions from the K shells to the already occupied valence shell orbitals [52,53]. Figures 10.1(a) and 10.1(b) show the resulting absolute optical oscillator strengths for carbon monoxide obtained in the present work at low resolution in the energy regions 5—50 and 50—200 eV respectively. Previously reported experimental data [87,292,325,328,329.4 12] are also shown for comparison. Numerical values of the presently determined absolute photoabsorption oscillator strengths for carbon monoxide obtained in the present work from 7—200 eV are summarized in table 10. 1. It can be seen in figures 10. 1(a) and 10. 1(b) that the present results are in extremely good agreement with the photoabsorption data reported by Samson and Haddad [292]. The data reported by Lee et al.  277  (a)  0.4  Ico! •  Present LR Dipole (e,e) Wight et ol. [87] Dipole (e,e) Samson & Haddad [292] Lee et al. [325] Watson et al. [412] Ph.Abs. Cole & Dexter [329] De Reilhac & Dornany [328)  A  o 0.3 D * -4-  0.2  20  C)  A A A  0.1  10  0.0  LI  S  U)  C  0.10  =  15  25  3  C) C) U) U) Cl) IC)  45  0 A A A  (b)  Icol  C) Cl)  0  30  A.  +  C)  40  •10  0.08 Q  C)  •  Present LR Dipole (e,e) Wight et al. [ 87] Dipole (e,e) Samson & Haddad [292] Lee et al. [325) Ph.Abs. Cole & Dexter [ 329] De Reilhac & Damony t 328]  A 0  0.06  * +  4  0 0 .0 0 .4I 0  6  0.04  4 +  0.02  ‘  +  2  + +  +  ••••••..• •  0  0.00 50  100  150  200  Photon energy (eV)  Figure 10.1: Absolute oscillator strengths for the photoabsorption of carbon monoxide measured using the low resolution (FWHM=1 eV) dipole (e,e) spectrometer (a) comparison with previously reported experimental data [87,292,325,328,329,412] in the energy region 5—SO eV. (b) comparison with previously reported experimental data [87,292,325,328,329] in the energy region 50—200 eV.  278 Table 10.1 Absolute differential optical oscillator strengths for the photoabsorption of carbon monoxide obtained using the low resolution (1 eV FWHM) dipole (e,e) spectrometer (7—200 eV)  Energy  Oscillator  Energy  Oscillator  Energy  Oscillator  (eV)  Strength  (eV)  Strength  (eV)  Strength  eV-l) 2 (1O-  eV2 (1O) 1  eV-l) 2 (10-  7.0  0.00  16.0  23.15  25.0  19.03  7.5  0.35  16.5  22.87  25.5  19.07  8.0  4.24  17.0  24.47  26.0  19.36  8.5  11.40  17.5  24.53  26.5  19.10  9.0  9.48  18.0  23.72  27.0  18.72  9.5  4.98  18.5  21.25  27.5  18.60  10.0  2.14  19.0  20.72  28.0  18.12  10.5  0.97  19.5  20.55  28.5  17.67  11.0  6.25  20.0  19.97  29.0  16.97  11.5  16.57  20.5  20.30  29.5  16.80  12.0  13.43  21.0  20.18  30.0  16.20  12.5  10.95  21.5  20.15  30.5  15.76  13.0  26.97  22.0  20.22  31.0  15.48  13.5  39.50  22.5  19.75  31.5  15.09  14.0  40.19  23.0  19.80  32.0  14.50  14.5  34.16  23.5  19.59  32.5  14.03  15.0  25.82  24.0  19.48  33.0  13.55  15.5  24.20  24.5  19.23  33.5  13.61  279 Table 10.1 (continued)  Energy  Oscillator  Energy  Oscillator  Energy  Oscillator  (eV)  Strength  (eV)  Strength  (eV)  Strength  eV 2 0 ) (11  eV2 0) ( 11  eV-l) 2 (1O  34.0  13.45  45.0  9.62  62.0  5.69  34.5  13.28  45.5  9.82  63.0  5.51  35.0  12.80  46.0  9.39  64.0  5.36  35.5  12.80  46.5  9.31  65.0  5.12  36.0  12.66  47.0  9.24  66.0  4.87  36.5  12.47  47.5  9.01  67.0  4.76  37.0  12.03  48.0  9.13  68.0  4.63  37.5  11.84  48.5  8.94  69.0  4.54  38.0  11.81  49.0  9.01  70.0  4.35  38.5  11.33  49.5  8.84  71.0  4.25  39.0  11.26  50.0  8.63  72.0  4.10  39.5  11.05  51.0  8.42  73.0  4.03  40.0  11.01  52.0  8.17  74.0  3.90  40.5  10.91  53.0  7.75  75.0  3.81  41.0  10.69  54.0  7.56  76.0  3.71  41.5  10.64  55.0  7.32  77.0  3.66  42.0  10.31  56.0  7.00  78.0  3.46  42.5  10.11  57.0  6.85  79.0  3.37  43.0  10.33  58.0  6.56  80.0  3.34  43.5  9.88  59.0  6.40  81.0  3.27  44.0  9.83  60.0  6.07  82.0  3.13  44.5  9.88  61.0  5.88  83.0  3.05  280 Table 10.1 (continued)  Energy  Oscillator  Energy  Oscillator  Energy  Oscillator  (eV)  Strength  (eV)  Strength  (eV)  Strength  eVl) 2 (1O  eV’) 2 (1O  eV’) 2 (1O  84.0  3.03  118.0  1.40  162.0  0.697  85.0  2.85  120.0  1.35  164.0  0.667  86.0  2.82  122.0  1.30  166.0  0.658  87.0  2.79  124.0  1.26  168.0  0.642  88.0  2.75  126.0  1.20  170.0  0.617  89.0  2.63  128.0  1.18  172.0  0.625  90.0  2.58  130.0  1.12  174.0  0.588  91.0  2.46  132.0  1.10  176.0  0.582  92.0  2.51  134.0  1.05  178.0  0.576  93.0  2.37  136.0  1.01  180.0  0.546  94.0  2.35  138.0  0.991  182.0  0.535  96.0  2.28  140.0  0.969  184.0  0.515  98.0  2.15  142.0  0.909  186.0  0.509  100.0  2.10  144.0  0.887  188.0  0.507  102.0  1.98  146.0  0.868  190.0  0.502  104.0  1.88  148.0  0.834  192.0  0.471  106.0  1.77  150.0  0.820  194.0  0.473  108.0  1.72  152.0  0.787  196.0  0.467  110.0  1.65  154.0  0.781  198.0  0.451  112.0  1.58  156.0  0.768  200.0  0.461  114.0  1.51  158.0  0.716  116.0  1.46  160.0  0.702  a (Mb)  =  1.0975 x 1 -eV 2 10  281 [325] are higher than the present data at energies above 30 eV while the data reported by De Reilhac [3281 are —15% lower than the present results at 25 eV and also at energies above 60 eV. The data reported by Cole and Dexter [329] are in general slightly lower than the present work. The earlier electron impact based dipole (e,e) data reported by Wight et at. [87] are -10% higher than the present work. It should be pointed out that the data of Wight et at. [87] were normalized In the smooth continuum at 30 eV on the earlier optical data of Samson and Cairns [3251 and in addition it appears that adequate background subtraction procedures were not employed. The present work is TRK sum—rule normalized and thus independent of any other measurements. The present low resolution data has been used to establish the absolute scale for the high resolution data as described in the following section.  10.2.2 High Resolution Absolute Photoabsorption Oscillator Strength Measurements for Carbon Monoxide (12—22 eV) Figure 10.2 shows the absolute optical oscillator strength spectrum for the photoabsorption of carbon monoxide in the energy region 7—21 eV obtained from the high resolution (0.048 eV FWHM) dipole (e,e) spectrometer. The presently determined low resolution dipole (e,e) data and the photoabsorption data of Samson and Haddad [292] are also shown for comparison. It can be seen in figure 10.2 that the present high resolution (HR) and low resolution (LR) data are in excellent agreement over the continuum energy region. Similarly, in the discrete region the HR and LR measurements are consistent when the large differences in energy resolution (0.048 eV vs 1 eV FWHM) are taken into account. The  282  2.0 200  0  1 .5 IRn IJ  a) (I)  0 (I) Ci) U)  0  1 .0  C)  100  0  0 1-4  0  0.5  0.0  :° 7  9  11  13  15  17  19  21  Photon energy (eV)  Figure 10.2: Absolute oscillator strengths for the photoabsorption of carbon monoxide in the energy region 7—21 eV measured using the high resolution dipole (e,e) spectrometer (FWHM=O.048 eV).  283 present HR data in the continuum 17—21 eV are also in good quantitative agreement with the photoabsorption data of Samson and Haddad [292]. Figure 10.3 shows the absolute optica1 oscillator strength spectrum for the vibronic bands of the A fl state of carbon monoxide in the energy 1 region 7.5—10.5 eV. The energy positions have been taken from the detailed spectroscopic studies reported In refs. [369,370,378]. A curve— fitting program using Voigt profiles has been employed to deconvolute the spectrum and the resulting deconvoluted peaks are shown as the dashed lines in figure 10.3, while the total fit is shown as a solid line. In the present work, integration of each peak area gives directly the absolute optical oscillator strength for the corresponding vibronic transition. Absolute vibronic optical oscillator strengths for v’=0—l2 of the A fl state were thus obtained and the results are summarized in table 1 10.2. Previously reported experimental [69,251,387,392,393,407] and theoretical [367,368] values are also shown for comparison. The uncertainties of the present results are estimated to be —5% for resolved peaks and —10% for unresolved peaks due to additional errors in the deconvolution process. Lee and Guest [3871 obtained spectra for all the vibronic bands of the A fl state using Beer—Lambert law photoabsorption 1 methods. However, only the numerical oscillator strength value for the v’=O vibronic band was reported and that value is -40% lower than the present result. The photoabsorption data reported by Lee and Guest [386] are still subject to “line saturation” effects even though the authors state that their results were independent of the monochromator bandwidth (see discussion in the introduction of the present chapter, and chapter 2 for a more detailed discussion of “line saturation” effects). Eidelsberg et al. [392] recently attempted to avoid “line saturation”  284  0.8 -4  >  a)  89  0.7  70  0.6  0  60 0.5 a.) Cl)  50  0.4  0  = C.) Ci)  0  ci  0  j 40  0.3  30 0.2  p I 0  20 C.) ‘-4  0.1  10  C 0.0  0 7.5  8.0  8.5  9.0  9.5  10.0  10.5  Photon energy (eV)  Figure 10.3: Absolute oscifiator strengths for the photoabsorption of carbon monoxide in the energy region 7.5—10.5 eV at 0.048 eV FWHM. The energy positions are taken from references [369,370,3781. Deconvoluted peaks are shown as dashed lines and the solid line represents the total fit to the experimental data.  0  the  0.0380 0.0429 0.0360 0.0251 0.0155 0.00848 0.00437  0.00108 0.00050 0.00025 0.00010  0.0351  0.0402  0.0347  0.0242  0.0145  0.00805  0.00414  0.00202  0.00095  0.00041  0.00018  0.00009  1  2  3  4  5  6  7  8  9  10  11  12  0.00013  0.00028  0.00065  0.0014  0.0029  0.0059  0.0104  0.0163  0.0258  0.0377  0.0424  0.0337  0.0165 0.0096  (387]  Lee & Guest  0.033  0.027  [3931  Rich  growth  Curves of Lifetime  the X E+— Am 1  0.0358  0.0361  0.0412  0.0343  0.0156  [4071#  etal.  Field  0.0005  0.0011  0.0024  0.0048  0.0091  0.0024  0.0074  0.0146  0.0162  0.0226  0.0111  [2511  Hesser  measurements  of  0.0161  bands  as derived by Kirby and Cooper 13671 using the linear dipole moment reported by Field et at. [407J.  0.00217  0.0200  (3921  (691  0.0162  etal.  Skerbele  dipole (e,e)  Eidelsberg  (Beer—Lambert law)  based work Lassettre &  Photoabsorption  Present HR  vibronic  Experimental results  strengths for  Electron impact  oscillator  0  v’  monoxide  optical  10.2  Absolute  Table  0.0010  0.0168  0.0262  0.0371  0.0462  0.0473  0.0356  0.0148  (3681  etal.  Chantranupang  (1)  Theory  0.0004  0.0009  0.0019  0.0039  0.0075  0.0134  0.0220  0.0316  0.0373  0.0324  0.0155  1367]  Cooper  Kirby &  (II)  transition of carbon  286 effects by determining the integrated cross sections at pressures low enough that the integrated absorption varied linearly with pressure. The photoabsorption data reported by Eidelsberg et al. [392] are In much better agreement with the present work than other optical work [385,387]. The photoabsorption values reported by Rich [393] for the v’= 1 and 2 levels of the A fl state using a shock—tube experiment with a 1 curves—of—growth analysis are —25% lower than the present work. Two sets of vibronic oscillator strength values for the A fl state obtained from 1 lifetime measurements [251 ,407] have been reported. Hesser [251] converted lifetime data to optical oscillator strengths by using the measured vibrational band emission intensities. However, the so— obtained oscillator strength values are much smaller than the presently reported results. In other lifetime work, Field et al. [4071 discussed the discrepancies between different lifetime measurements and determined fl state. They 1 the deperturbed lifetimes for the vibronic bands of the A also derived a linear dipole moment function from the deperturbed lifetimes. Kirby and Cooper [367] then used the linear dipole moment f1 1 reported by Field et al. [4071 to derive oscillator strengths for the A state vibronic bands which are found to be in good agreement with the present work. The only previously reported electron impact based oscillator strength data for the A fl bands of carbon monoxide are from 1 Lassettre and Skerbele [691, who measured generalized oscillator strengths as a function of momentum transfer and obtained optical oscillator strengths by extrapolating to zero momentum transfer. The absolute scale for these measurements [69] was obtained by normalizing on independent measurements of the absolute elastic scattering cross section [410]. The data reported by Lassettre and Skerbele [69] are In  287 general -5—10% higher than the present values and the differences can be largely attributed to the normalization procedures [69]. In theoretical work, two sets of oscillator strength calculations for the vibronic bands of the 1 A f l state have been recently published. The theoretical values reported by Kirby and Cooper [367] are —5—10% lower than the present experimental values, while the theoretical resu1ts reported by Chantranupong et al. [3681 show much greater discrepancies with the present work, in terms of both the absolute magnitudes of the oscillator strengths and also in the shape of the vibrational envelope of the band. The absolute total oscillator strength for the 1 A f l state is obtained by summing the oscillator strengths for all the vibronic bands. Table 10.3 summarizes the present result, where It Is compared with previously reported experimental [69,392,407] and theoretical [301,361— 365,367,3681 values. It can be seen that all the experimental [69,392,407] values, including that obtained in the present work, are In quite good agreement with each other, with values in the range 0.180 to 0.195. In contrast, the theoretical values [301,361—365,367,368] vary from 0.11 to 0.342. The theoretical value reported by Lynch et al. [364] is consistent with the present work while that of Kirby and Cooper Is -9% lower. Figure 10.4 shows the presently measured absolute optical oscillator strength spectrum for photoabsorption to the vibrational levels of the  1 and 1 C E f l excited states of carbon monoxide in the  energy region 10.5—12 eV. The assignments and energy positions have been taken from refs. [369,370,378]. The deconvoluted peaks resulting from a curve fit to the experimental data are shown as the dashed lines in figure 10.4, while the total fit is shown as the solid line. Table 10.4  288 Table 10.3 Absolute total optical oscillator strength for the X 1  -.  A 1 1 1  transition of carbon monoxide  Absolute optical oscillator strength for the 1 A 1 1 state Theory: Chantranupong et al. [368]  0.2250  Kirby and Cooper [367]  0.1636  Lynch etal. [364]  0.18  Nielsen et al. [363]  0.1208  Padialetal. [365]  0.342  Wood [362]  0.24  Coughran et al. [3611  0.14  Rose et al. [301]  0.11  Experiment: Present work  0.1807  Eidelsbergetal. [392]  0. 1941  Field etal. [4071  0.187  Lassettre and Skerbele [69]  0.1945  289  a)  Icol  2.0  0  —*  C’E  200 0  S  C.)  1 .5  E 1 X  —  BE  0  a.)  v=  0  0  150  E 1 1 1  1-1  U)  1  1  1 .0  100  C.) U)  0  0.5  5QP  Ax3  C.)  :1 0 0  C  0.4  0  0.0 10.5  11.0  11.5  1 2.0  Photon energy (eV)  Figure 10.4: Absolute oscillator strengths for the photoabsorption of carbon monoxide in the energy region 10.5—12 eV at 0.048 eV FWHM. The assignments and energy positions are talcen from references [369,370,378. Deconvoluted peaks are shown as dashed lines and the solid line represents the total fit to the experimental data.  0.0181 0.094  0.0127 0.163  0.0024 0.0 153  LeeandGuest[387]  Lassettre and Skebele (69]  0.0025 0.0365 0.0028 0.0619 0.0007  0.0045  Letzelteretal. [388]  0.00353  0.00803  Presentwork  0.0706  0.1200  0.00480  Roseetal. [301]  0.00356  0.0400  0.00300  Coughranetal. [361]  0.1177  0.084  0.060  Wood [362]  0.0050 0.049  0.0110  0.00329  v’=l  0.0274  v’=O  l E f 1  X1  0.00132  0.0495  0.00448  Padialetal. [365]  Experiment:  0.1327  0.00285  0.0018  0.1181  0.0003  0.0021  KirbyandCooperl3674l  Nlelsenetal. [363]  0.0049  v=1  0.0647  v’=O  0.00052  v’=l  0.00508  v’=O  1 B  Absolute optical oscillator strength  fl excited electronic states of carbon monoxide 1 1 and E C  Chantranupongetal. [3681  Theory:  ground state to the  Absolute optical oscillator strengths for the vibronic bands of the transitions from the  Table 10.4  t’) (0 C  291 summarizes the presently measured absolute optical oscillator strengths for the vibronic bands of the  C12+ and E fl excited states. where 1  they are compared with previously reported experimental [69,387,3881 and theoretical [301,361—363,365,367,3681 values. Experimentally, there are many reported lifetime measurements [202,251,394—397,40 1— B and C1+ states. Large variations have been found 406,408] for the 1 among the reported lifetime values. Moreover, In order to convert the lifetime data to absolute oscillator strengths, the branching ratios for the two systems (B-X, B—A) and (C-X, C-A) must be known. Carlson et al. [4061, using the branching ratios measured by Aarts and Dc Heer [359], and Krishnakumar and Srivastava [408], using the branching ratios measured by Dotchin and Chupp [402], have converted their lifetime data to absolute oscillator strength values. However, the branching ratios reported by the two groups [359,402] differ significantly for the (B—X, B— A) system and are slightly different for the (C—X, C—A) system. Thus, different oscillator strength values will be obtained from the same set of lifetime data when using the different branching ratios. For example, from the lifetime data reported by Hesser [69], absolute oscillator strength values of 0.005 4 and 0.119 were obtained respectively for the v=0 band of the B 2 and C1+ states when using the branching ratios 1 reported by Dotchin and Chupp [402] while values of 0.0079 and 0.1350 were obtained when using the branching ratios reported by Aarts and De Heer [359]. For this reason, the data obtained from the lifetime measurements are not shown in table 10.4. A summary of the lifetime measurements and also the converted oscillator strengths using various branching ratios can be found in refs. [406,408]. It can be seen from table 10.4 that, unlike the situation for the A fl state, large variations 1  292 exist among the reported experimental oscillator strength values for the D, C1+ and E 1 B fl states [69,387,3881. The photoabsorption data 1 measured by Lee and Guest [387] are much lower (< 30%) than the present values, presumably due to serious “line saturation” effects as discussed above. The photoabsorption data of Letzelter et al. [388] are also -25—50% lower than the present work. This difference is somewhat surprising since the experimental procedures employed by Letzelter et al. [388] are the same as those used by Eidelsberg et al. [3921 for their measurements on the vibronic bands of the A fl state which are found to 1 be in good agreement with the present work (see table 10.2). In other experimental work, the electron impact based data of Lassettre and Skerbele [691 are found to be much higher than the present results. Turning to theory, absolute vibronic oscillator strengths for the Bl+, C1+ and E fl states have been calculated by several groups 1 [301,361—363,365]. Since the vibrational oscillator strengths for v’= 2 and the higher bands of these states have been calculated to be much smaller (< 1%) than the values for the v’=O and 1 bands [367], the data reported in refs. [301,361—363,365] should be almost equal to the sum of the oscillator strengths for the v’=O and 1 bands determined in the present experimental work. These values are shown in table 10.4. It can be seen that large differences exist between the various theoretical results [301,361—363,365,367,368], and that no single set of theoretical data is consistent with the present work. Only the oscillator strength for the v’=O level of the C 1 state reported by Kirby and Cooper [367], and the oscillator strength sum for the C1+ state reported by Rose et al. [301], are in agreement with the present work.  293 The absolute optical oscillator strength spectrum determined in the present work for the higher energy excited states In the energy region 12—20 eV is shown in figure 10.5. The energy positions of the ionization thresholds have been taken from refs. [369,4131. Detailed assignments of this energy region can be found In refs. [358,386]. Integrated oscillator strengths determined from the present work over small energy ranges are summarised in table 10.5. The photoabsorptlon data reported by Stark et aL. [391] and Letzelter et a1. [388] were obtained at a much higher resolution than the present work. Therefore, the oscillator strengths for several transitions in references [388] and [391], corresponding to the energy ranges shown in table 10.5, have been summed and are compared with the present results. Also shown in table 10.5, the photoabsorption data of Stark et al. [391] were obtained via direct Beer—Lambert law photoabsorption measurements, using a resolution 20 times higher than in the work of Letzelter et al. [3881, and an attempt was made to monitor the “line—saturation effects by comparing the photoabsorption values measured at a variety of pressures. Even under such experimental conditions, “line—saturation” effects were reported for some very sharp features [3911. As shown in table 10.5, the  two sets of photoabsorption data [388,391] are found to be somewhat lower than the present work even though precautions were taken to try to minimize “line—saturation” effects. The oscillator strength distribution of carbon monoxide has been reviewed by Berkowitz [143] using the experimental data available before 1980. Berkowitz obtained an oscillator strength value of 0.792 1 for the energy region between 12 and 14 eV, using the photoabsorption data of Huffman et al. [380], while a value of 0.8 165 was obtained using the photoabsorption data of Cook et al. [3821.  294  1 .2 0%  ,-  120 a.)  E  1.0 100 0 I.  C)  0.8 to  80  a.)  4) Cl) Cl) Cl)  0.6  Cl)  60  0  0 1 C) 0  =  0.4  C)  40  Ci)  Cl)  0  .0  C.,  0.2  20  0.0  0  4  15  17  Photon energy (cv)  Figure 10.5: Absolute oscillator strengths for the photoabsorption of carbon monoxide in the energy region 12—20 eV at 0.048 eV FWHM. The assignments and energy positions of the ionization thresholds are taken from references [369.413].  0 0  295 Table 10.5 Integrated absolute optical oscillator strengths for the photoabsorption of carbon monoxide over energy intervals in the region 12.13-16.98 eV  Integrated absolute optical oscillator_strength Energy range (eV)  Present  Stark et al.  Letzelter  work  [391]  etal. [388]  12.463  0.0113  12.655  0.0270  0.0208  0.0163  12.896  0.0857  0.0438  0.0579  13.001  0.0202  0.0148  0.0138  13.115  0.0365  0.0301  0.0324  13.237  0.0721  0.0538  0.0472  13.364  0.0748  0.0594  0.0569  13.452  0.0337  0.0251  0.0278  13.614  0.0982  0.0719  13.614— 13.780  0.0820  0.0706  13.780  13.867  0.0358  0.0327  14.016  0.0678  14.169  0.0558  14.169— 14.458  0.0900  14.458  14.743  0.0665  14.902  0.0334  12.130 12.463 12.655 12.896 13.001 13.115 12.237 13.364 13.452  13.867 14.016  14.743  —  —  —  —  —  —  —  —  —  —  —  —  —  —  0.00802  296 Table 10.5 (continued)  Integrated absolute optical oscillator_strencth Energy range (eV)  14.902  Present  Stark et al.  Letzelter  work  [3911  etal. [388]  15.085  0.0402  15.296  0.0449  15.443  0.0430  15.621  0.0406  15.780  0.0347  15.939  0.0346  15.939— 16.107  0.0356  16.107— 16.286  0.0386  16.286  16.470  0.04 17  16.658  0.0443  16.822  0.0343  16.978  0.0366  15.085 15.269 15.443 15.62 1 15.780  16.470 16.658 16.822  —  —  —  —  —  —  —  —  —  —  297 The present estimate for the same energy region is 0.640. The photoabsorption data reported by Huffman et al. [380] and Cook et al. [382] are -25% higher than the present result, which Is presumably due to errors in the pressure and/or light Intensity measurements in these direct optical studies. On the other hand, It has been mentioned above (see table 10.5) that the recently reported high resolution photoabsorption data of Stark et al. [391] and Letzelter et al. [388] are somewhat lower than the present work in the energy region —12.1—13.9 eV. Hence, the data of Stark et al. [391] and Letzelter et al. [388] would be much smaller than the data of Huffman et al. [380] and Cook et al. [382] over the same energy region. These large differences In oscillator strengths between different photoabsorption determinations reveal some further difficulties involved in absolute intensity measurements when using the Beer—Lambert law, in addition to the ‘line saturation” effects.  10.2.3 The Variation of Transition Moment with Internuclear Distance for the Vibronic Bands of the X1+  —‘  fl Electronic 1 A  Transition The vibronic band oscillator strength (f’”) for excitation to the A fl 1 state is related to the electronic transition moment  I Re( r’”)  through  equation 7.5 [40,367,368]. In the present work, the absolute optical oscillator strengths (f’o) for the vibronic bands for excitation to the A 11 1 state have been measured directly (see table 10.2). The Franck—Condon factors qv’o and the centroids rv’o can be taken from ref. [392], In which the values were calculated from the deperturbed RKR A 11 potential 1 determined by Field [414] and revised molecular parameters for the  298 Z state [415]. The energies (E’—E’) have been taken from 1 ground X refs. [369,370,378]. 0 Is the statistical weighting factor which is equal to 2 for a —‘H transition. The electronic transition moment  I Re( rv’v”)  Cfl  then be derived from equation 7.5 for each vibronic band. The resulting values of  Re( r”)  are plotted as a function of rv’o in figure 10.6, which  shows the variation of electronic transition moment with Internuclear 1 state. A 1 distance in carbon monoxide for the vibronic bands of the 1 Previously reported experimental [392,407.4161 and theoretical [367,3681 values are also shown for comparison. From the measured deperturbed lifetime data, Field et al. [407] have derived a linear dipole moment function of the form  IRe(rv’o)I  7.48(1—0.683 r’o)  (10.1)  In other work involving laser induced fluorescence measurements to sample the electronic dipole moment at large internuclear distance (1.35—1.80  A),  combined with the data reported by Field et al. [407] at  lower internuclear distance, Dc Leon [4161 has derived an electronic dipole moment function of the form  IRe(rvo)1  1.5741(1  —  1.17722 rv’o+ 0.35013 rv’0 ) 2  (10.2)  As shown in figure 10.6, the dipole moment functions reported by Field et al. [407] (solid line) and De Leon [416] (dashed line) are in good agreement with the present work only for Internuclear distances (rv’o) above 1.1  A,  and their values become much higher than the present  experimental results at low rv’o. The photoabsorption work of Eidelsberg  299  Vibrational quantum number (v’) 12  10  6  8  0  2  4  1 .3  o1  0  1.1  + 1 x  F1 1 >A  0.9 0  0  E  0  I  *  * *  0.7  *  * •  0.5  0  * *  0.3 0.9  Present HR dipole (e,e) Eidelsberg et al. [ 392] Exp* Field et al. [ 407] De Leon [416] Kirby & Cooper [ 367) Chantranupong et al. [ 368 ]Theory  1.1  1.0  1.3  1.2  Internuclear distance rvo  (A)  Figure 10.6: The electronic transition moment IRe(r..o)I in atomic units (a.u.) as a function of the internuclear distance rjO in vibronic bands of the X  —,  Angstroms (A)  fl transition. 1 A  for the  300 et al. [392] shows results similar to the predictions by Field et al. [407] and by De Leon [416]. On the other hand, the theoretical work of Kirby and Cooper 1367] is in very good agreement with the present work over the entire range of study, while the values calculated by Chantranupong e t al. [368] are much higher than the present results.  10.3 Conclusions Absolute optical oscillator strengths for the photoabsorptlon of carbon monoxide have been measured in the energy region from 7—200 eV. The data were TRK sum—rule normalized and thus are independent of any other measurements. Absolute optical oscillator strengths for the fl states have been reported. 1 2 and E 1 l, C12+, B vibronic bands of the 1 A f Good agreement is found (see table 10.2) between the present and some of the previously published experimental [69,392,407] and theoretical fl state. In contrast (see 1 [367] results for the vibronic bands of the A table 10.4) considerable differences are seen for the vibronic band oscillator strengths for the  F1 states. It is noteworthy 1 1 and E B  that severe “line saturation” effects due to incident photon bandwidth are observed in some of the photoabsorption measurements (e.g. refs. [385,387,391]) for the discrete transitions In carbon monoxide. The procedures employed by Letzelter et al. [388] and by Eidelsberg et al. [3921 can lower the errors due to “line saturation” effects in direct Beer— Lambert law photoabsorption experiments, however, these kinds of procedures place the most weight on the least accurate data obtained at low pressure, which may be the reason for the discrepancies between the present work and the data reported by Letzelter et al. [388], even though  301 the data reported by Eidelsberg et al. [392] are consistent with the present work. For the lifetime measurements, accurate branching ratios are necessary in order to obtain reliable absolute optical oscillator strengths. In contrast, the present dipole (e,e) method provides a direct means for measuring the absolute optical oscillator strengths for the discrete transitions of carbon monoxide, free of “line saturation’ effects. The variation of the electronic transition moment with the C—O 1 state derived from the present A [ Internuclear distance for the 1 measurements was found to be in good agreement with the theoretical results of Kirby and Cooper [367].  302 Chapter 11 Absolute Optical Oscillator Strengths for the Photoabsorption of Nitric Oxide (5—30 eV)  11.1 Introduction Absolute optical oscillator strengths for photoabsorption by nitric oxide (NO) in the valence discrete region are of interest in areas such as atmospheric sciences [417,418] and the development of lasers [419]. Nitric oxide is found in air at high temperatures and also occurs in the upper atmosphere. In addition, nitric oxide is a major atmospheric pollutant since it is a product of internal combustion engines and combustion power plants. An accurate knowledge of the nitric oxide concentration is essential for the understanding of atmospheric chemistry [4171. Oscillator strengths for the y 2 2—X (A I 1) absorption bands of nitric oxide have been used to estimate column densities in the mesosphere [418]. They bands have also been considered as the basis of an optically pumped laser involving bound electronic states with inherently narrow linewidths [419]. Below 8 eV, the valence—shell excitation spectrum of nitric oxide consists mainly of discrete transitions belonging to the y f — 2 (A X l), 11—X (B 1 2 1), ô (C2flX2fl) and  £  — 2 (D f X systems. Ory [420] has l)  calculated Franck—Condon factors for the ô and  systems using Morse  oscillator wavefunctions. In the same study [420], the total electronic oscillator strengths for the y,  ó and  E  systems have been derived by  assuming a constant electronic transition moment and using published  303 experimental data for the oscillator strengths of a number of Individual vibronic levels. Cooper [421] has calculated the electronic transition moments for the  and ô systems of nitric oxide using ab inltio  configuration interaction methods. In other work, multireference configuration interaction (MRCI) methods have been used by de Vivie and Peyerimhoff [422] and Langhoffet al. [423,424] to calculate the lifetimes, Einstein coefficients (A) and transition moment functions for excited states of nitric oxide. Rydberg—vaience state Interactions occur between excited bound levels of nitric oxide, and perturbations between the vibronic excited levels of 2 symmetry have been studied by Gallusser and Dressier [425]. The absolute scale of the calculated (perturbed) oscillator strengths reported by Gallusser and Dressier [425] was adjusted by referencing to previously reported experimental values [426]. In addition, the unperturbed oscillator strengths were also calculated [425]. In experimental work, the energy levels of nitric oxide have been studied extensively using photoabsorption methods [427—436], but relatively few studies have been made of the associated oscillator strengths. Critical reviews and compilations of the spectroscopic data up to 1976 can be found in refs. [46,330,437,438]. Beer—Lambert law photoabsorption measurements [46,326,330,439—445] have provided much of the existing absolute optical oscillator strength data for nitric oxide. However, as has been pointed out earlier [37,46] (see chapter 2) Beer—Lambert law photoabsorption data for discrete transitions are t (bandwidth) effects which result In subject to so—called “line—saturation’ the measured oscillator strengths being too small. These spurious effects are more severe for transition with narrow linewidth and high cross section as illustrated in recent studies of the electronic spectra of  304 nitrogen [41] (see chapter 8) and carbon monoxide [43] (see chapter 10). Similar “line saturation” effects can be seen In the photoabsorption measurements of nitric oxide In the energy region 5.39—11.27 eV reported by Marmo 1439]. In the latter work [4391, a decrease In the observed photoabsorption cross sections was found for some of the discrete transitions of nitric oxide at high sample pressure, while this behavior was not observed in the continuum. Improved determinations of the absolute oscillator strengths for the valence discrete transitions of nitric oxide using the Beer—Lambert law were subsequently reported by Weber and Penner [440], Bethke [426] and Hasson and Nicholls [441]. In order to minimize the “line saturation” effects in these studies [426,440,441], the nitric oxide sample was mixed with a very high pressure of noble gas so that the linewidths for the discrete transitions of nitric oxide were collisionally broadened and therefore much smaller than the bandwidth of the spectrometer [426,440,441]. Other measurements of the absolute photoabsorption oscillator strengths for the discrete transitions of nitric oxide have been reported by Mandelman and Carrington [4461 using the resonance—line absorption method, by Callear and Pilling [447) using the curves—of—growth method, and by Pery— Thorne and Banfield [4481 and Farmer et al. [449,450] using the “Hook” method (which measures the rate of change of the refractive Index near an absorption region). Shock tube emission and absorption measurements were also carried out by Keck et aL. [451] and Daiber and Williams [452], respectively, to estimate electronic oscillator strengths for some discrete transitions of nitric oxide. In other work, Mandelman et al. [453] have reported the oscillator strength for the ô (0,0) band by measuring the absolute intensity of the recombination emission.  305 Lifetime measurements [251,394,417,454—467] have been extensively employed for studying various discrete transitions of nitric oxide but differences exist In the measured values. Moreover, In order to convert the lifetime values to oscillator strengths, the branching ratios must be known. The branching ratios can be obtained from relative emission intensities and such measurements have been carried out by several groups [251,461,466—474]. However, the reported branching ratios also show large differences. For example, the branching ratio for the y (0,0) band was measured by Callear et aL. [4691 and Hesser [251] as 0.143 and 0.24 respectively. Electron impact methods based on electron energy loss spectroscopy have also been used to study the discrete and continuum regions of the excitation spectrum of nitric oxide. In early work, Lassettre et al. [4751 measured the electron energy loss spectrum of nitric oxide in the energy region 5—9.5 eV at 50 eV impact energy and zero—degree scattering angle, but no absolute oscillator strengths for the discrete transitions were reported. Later, quantitative low resolution dipole (e,e) work by lida et al. [93] reported absolute oscillator strengths for the photoabsorption of nitric oxide In the energy region 6—190 eV. In this study [93], the absolute scale was established using TRK sum—rule normalization. However, since the resolution of the spectrum recorded by lida et al. [93] was limited to 1 eV FWHM, the oscillator strengths for individual discrete transitions could not be determined. The absolute oscillator strength data reported by lida et al. [93] in the continuum have been compared with direct optical studies [326,445] in the data compilation of Gallagher et al. [30].  306 In the present work, the high resolution dipole (e,e) method, which has recently been used to measure absolute oscillator strengths for the discrete transitions of noble gas atoms [37—391 (see chapters 4—6) and several small molecules [27,40—43,411] (see chapters 7—10), Is now applied to study the valence shell discrete transitions of nitric oxide. The absolute photoabsorption oscillator strengths obtained using the dipole (e,e) method are not subject to “line saturation” effects since e1ectron impact excitation is non—resonant and because no logarithmic transform is required in order to convert the measured experimental quantities to oscillator strengths, in contrast to Beer—Lambert law photoabsorption. The absolute scale of the present high resolution dipole (e,e) measurements is established by normalizing in the smooth photoabsorption continuum at 25 eV to the photoabsorption oscillator strength reported by lida et al. [931. The high reliability of the high resolution dipole (e,e) method has been confirmed by a comparison of the results of the measurements for helium [37] (see chapter 4) and molecular hydrogen [40] (see chapter 7) with highly accurate ab—initio calculations. In addition, the results for molecular oxygen [421 (see chapter 9) are particular relevant to the present work, since they have established the accuracy of the Bethe—Born factor of the high resolution dipole (e,e) spectrometer when extrapolated down to equivalent photon energies as low as 6 eV.  307 112 Results and Discussion The oscillator strength spectra of nitric oxide are conveniently discussed by reference to Its ground state molecular—orbital valence shell independent particle configuration which may be written as (3)2(4)2( 2 1 ( 4 13r) ( 5a) 2r)  Figure 11.1 (solid line) shows the absolute optical oscillator strength spectrum of nitric oxide in the energy region 5—30 eV obtained in the present work using the high resolution (0.048 eV FWHM) dipole (e,e) spectrometer. The low resolution dipole (e,e) photoabsorption data previously determined by lida et al. [93], and the photoabsorption data of Lee et al. [326] and of Gardner et al. [445] are also shown for comparison. It can be seen in figure 11. 1 that the present high resolution (HR) results and the low resolution (LR) data reported by lida et al. [931 are in excellent agreement over the continuum region. Similarly in the discrete region the high and low resolution dipole (e,e) measurements are highly consistent when the large differences in energy resolution (0.048 eV vs 1 eV FWHM) are taken into account.  The  presently obtained HR data in the continuum 21—30 eV are also in good quantitative agreement with the photoabsorption data of Gardner et al. [445], while the data of Lee et al. [326] are 10—15% lower than the present work. Figures 11.2—11.4 are expanded views of figure 11. 1 in the energy regions 5—8.2, 8—13 and 13—22 eV respectively. The assignments and energy positions of the excited states and ionization thresholds have been taken from the detailed spectroscopic studies reported in refs.  308  1 .5 150  0  -4  C.)  a.)  1.0  U)  100 0  1 C.)  C)  0  0  -4  C.) C,)  50  1.4  0  C C.)  0.0  0’ 5  9  13  17  21  25  29  Photon energy (eV)  Figure 11.1: Absolute oscillator strengths for the photoabsorption of nitric oxide in the energy region 5—30 eV measured using the high resolution dipole (e,e) spectrometer (FWHM=O.048 eV).  309  0.14  u) 2 s (B 0.12  I I I  I I I I I I  5  9  7  13  11  I 15  a (cfI)  t4-  ‘2  çDEj  0.10  0  I  I  1  2  INOI  12  10 4-’  C)  3  a.)  8 0.08  Cl) Cj Cl)  0 I-’  C)  6  0.06  0  44-’  0.04  ‘  0  0.02  1.4 A -to  E) 2 (A  1  2  3  2  0  0.00 5  6  7  I  8  Photon energy (eV)  Figure 11.2:  Expanded view of figure 11.1 in the energy region 5—8.2 eV. The assignments are taken from references (425,437J. Deconvoluted peaks are shown as dashed lines and the solid line represents the total fit to the experimental data.  310 0.06  (a)  6  IN  0.05  5  1E X  0.04  4 0.03 3 -  0.02  2  0.01  0  1  —  C) V r  I0  9.0  8.5  8.0  10.0  9.5  0 0 1-. C)  0  INQI  (b)  30j  0 0  -..  20  0.1  10  0  0.0 10  11  12  13  Photon energy (eV)  Figure 11.3:  Expanded view of figure 11.1. The Ionization limit for the X 1 edge Is taken from reference [476]. (a) in the energy region 8—10 eV. (b) in the energy region 10—13 eV.  311  1.6  (a)  160  IN  1.2 • 120  0.8  80 —I  C) ‘—  0.4  40 .  C) C)  -  C) .  U,  15  14  13  o =  0  0.0  U) 0)  o  16  0.4  C) 0)  (b)  o  40  —  Ct  0 Cl) .0 Ct  o  0.3  0  30  0.2  n 3 c  1 w  Q  20  l B f 3  Ah1E 0.1  •10  Afl l b f cE 3  3  w  E 3 b’ 0  0.0 16  18  20  22  Photon energy (eV)  Figure 11.4:  Expanded view of figure 11.1. The Ionization limits are taken from reference [476]. (a) in the energy region 13—16 eV. (b) in the energy region 16—22 eV.  312 [425,437,476]. Figure 11.2 shows the discrete transitions below 8 eV. A curve—fitting program was used to deconvolute the spectrum between 6.25—7.5 eV and the resulting deconvoluted peaks are shown as dashed lines in figure 11.2. The total fit to the data Is shown as the solid line. In the present work, Integration of the peak area gives directly the absolute optical oscillator strength for the corresponding vibronic transition. Absolute vibronic optical oscillator strengths for the discrete transitions in the energy region 5.48—7.44 eV determined in the present work are summarized in table 11. 1. The oscillator strength for the i (5,0) band was obtained by subtracting the leading edge of the tall of the curve fitted to the y (3,0) band from the present experimental data In the energy region 6.194—6.280 eV. The uncertainties in the present results are estimated to be —5—10% for the strong, partially resolved peaks and -  10—20% for the remaining peaks due to the additional errors in the  deconvolution processes. Tables 11.2—1 1 .5 summarize the presently determined absolute vibrationally resolved oscillator strengths for the electronic transitions to the y, 3, ô and  states. Previously reported experimental and theoretical  data are also shown for comparison. For the overlapping f3 (7,0) and ô (0,0) bands (see table 11.1), the oscillator strength for each of the individual transitions (shown in tables 11.3 and 11.4 respectively) was estimated using the ratio of the oscillator strengths for these bands calculated by Gailusser and Dressier [4251 in conjunction with a total oscillator strength for the bands determined from the presently reported spectrum. The oscillator strength contributions of the other overlapping bands such as they (4,0), y (5,0), y (6,0),  (8,0),  I  (10,0) and  are assumed to be negligible compared with the dominant ö and  (13,0) E  peaks,  313 Table 11.1 Absolute optical oscillator strengths for discrete transitions from the ground state of nitric oxide in the energy region 6.48—7.44 eV#  Energy (eV)  Final state (v’,v”)  Oscillator strength  5.481  y  (0,0)  0.000420  5.771  y  (1,0)  0.000824  6.057  y  (2,0)  0.000730  6.256  (3(5,0)  0.000029  6.340  y  (3,0)  0.000356  6.374  (3  (6,0)  0.000037  6.494 6.608  13(7 0) + b (0,0) •y (4,0) +  6.718  13  (8,0)  0.00267  (0,0)  + £  0.000314  13(9,0)  6.782  (3  6.891  ‘y  (10,0)  +  0.00275  ô (1,0)  (5,0) + s (1,0)  0.00601 0.00461  6.939  (3(11,0)  0.000648  7.035  (3(12,0)  0.00209  o  7.063 7.168 7.259 7.342 7.396 7.438  y  (2,0)  (6,0) + (3(13,0) +  13(14,0)  o  (3,0)  (3(15,0) £  (3,0)  0.00308 £  (.2,0)  0.00367 0.000354 0.000976 0.000870 0.00179  The assignments and energy positions have been taken from refs. [425,426,4371.  ( Branching_ratios_and_lifetimes)  Brzozowski et al. [4571  (Branching ratios and lifetimes)  Mohlmann et al. (459]  (Branching ratios)  McGee et al. [4701  (Branching ratios)  Piper and Cowles 1473]  (HR dipole (e,e))  Present work  0.000345  0.000404  0.000323  0.00039  0.000420  0.000829  0.00082  0.000824  0.00247  0.00104  de Vivie and Peyerlmhoff 14221  v’=l  0.000731  v’=O  0.000377  Experiment:  —‘  ) transition in nitric 2 A  0.000750  0.00081  0.000730  0.000620  v’=2  0.000356  v=3  Absolute oscillator strengths for the y (v’,O) band  Langhoffetal. [4231  Theory:  oxide  fl 2 Absolute optical oscillator strengths for the vibronic bands of the y (X  Table 11.2  ( Photoabsorption)  Weber and Penner [440]  ( Ph otoabsorptlon)  Bethke [426]  (Branching ratios and lifetimes)  Hesser [251]  (“Hook” method)  Pery—Thorne and Banfleld [4481  (“Hook” method)  Farmer et al. [449]  Experiment:  Table 11.2 (continued)  0.00041  0.000399  0.00025  0.000364  0.00040  v’=O  0.00088  0.000788  0.00030  0.000809  v’=l  0.00067  0.000673  0.00171  0.000700  v’=2  0.000360  0.000240  v’=3  Absolute oscillator strengths for the y (v’,O) band  01  (‘3  316 Table 11.3 Absolute optical oscillator strengths for the vibronic bands of the  11 2 (X  -  fl) transition in nitric oxide 2 B  Abso1ute oscillator strengths for the Experimental v’  I  (v’,O) band Theoretical  Present work  Bethke [426]  Gallusser and  (HR Dipole (e,e))  (Photoabsorption)  Dressier [4251  0  0  1  0  2  0.00000155  0  3  0.00000461  0  4  0.0000138  0.00001  5  0.000029  0.0000264  0.00002  6  0.000037  0.0000462  0.00004  7  0.000375  0.000350  0.00036  8 9  0.00012 0.000314  0.000358  10  0.00034 0.00003  11  0.000648  0.000362  0.00035  12  0.00209  0.0023 1  0.00245  13  0.00001  14  0.000354  15  0.000870  0.000201  0.00015 0.00071  0.002 14  0.00560  0.002 13  0.002 2  0.00204  0.00578  0.00601  0.006 10  v’=l  0.00274  0.00308  0.00259  v’=2  • The value was obtained by assuming a constant electronic transition moment for the ö bands.  (Photoabsorptlon)  Bethke [426]  (Curve—of growth)  Callear and Piling 14471  (Radiative recombination of N+O)  Mandelmanetal. [4531  (Resonance—line absorption)  Mandelmann and Carrlngton [446]  ( Lifetimes )  Brzozowskietal. (4571  (HR dipole (e,e))  Present work  0.00229  0.00220  Gallusser and Dressier [4251  Experiment:  0.00249  de Vivie and Peyerimhoff [4221  Theory:  v=0  0.000976  0.00098  v=3  Absolute oscillator strengths for the ô (v,0) band  F1 2 Absolute optical oscillator strengths for the vibronic bands of the ô (X  Table 11.4 l) transition in nitric oxide C f 2  cz  (Photoabsorptlon)  Bethke [426]  (Branching ratios and lifetimes)  Hesser [251]  (HR dipole (e,e))  Present work  Experiment:  de Vivie and Peyerlmhoff [422]  Theory:  in nitric oxide  —,  ) transition 2 D  0.00242  0.0019  0.00263  0.00196  vO  0.00460  0.0040  0.00461  0.00245  v’tl  0.00332  0.00367  v’=2  0.00179  v’=3  Absolute oscillator stren ths for the E (v’,O) band  11 2 Absolute optical oscillator strengths for the vibronic bands of the E (X  Table 11.5  319 since the y bands have small oscillator strength values even for the lower vibrational members. In this regard it should also be noted that the calculations performed by Gallusser and Dressler [425] have also reported very small oscillator strength values for the  1  (8,0),  (10,0) and  (13,0)  bands. Similar assumptions concerning contributions from the overlapping bands have also been made to the photoabsorption data reported by Bethke [426]. It can be seen from table 11.2 that the various experimental values for the y bands are generally in reasonable agreement with each other except for those reported by Hesser [251]. Hesser [251], Brzozowski et al. [457] and Mohlmann et al. [4591 have measured both branching ratios and lifetimes while Piper and Cowles [473] and McGee et al. [471] have only measured the branching ratios, and the oscillator strength values reported by these authors [471,473] were obtained by using previously published experimental lifetimes. The data reported by Mohlmann et al. [4591 for the y bands are in excellent agreement with the present work, while the data reported by Piper and Cowles [473] for v’=O and 1 are also consistent with the present work, but their value for v’=2 is slightly higher. In contrast, the values reported by Brzozowski et aL. [4571 and McGee et al. [4711 for v’=O are —20% lower than the present result. The “Hook” method was employed by two groups [448,449]. The value for v’=O reported by Pery—Thorne and Banfield [4481 is slightly lower than the present value. In the other work [4491, the values reported by Farmer et al. [449] show good agreement with the present work for v’=O— 2 while the value for v’=3 is -33% lower. The Beer—Lambert law photoabsorption measurements reported by Weber and Penner [440] and Bethke [4261, which were obtained by collisionally broadening the natural  320 linewidths of the discrete transitions of nitric oxide with noble gases, show very good agreement with the present work. However, the data [426,440] will still be subject to “line saturation” effects (which however may be smaller than other experimental uncertainties in the present cases) since it has been pointed out in ref. [37] (see chapter 2) that “line saturation” effects will always occur since perfect resolution (i.e. zero bandwidth) cannot be obtained. Turning to theory, MRCI methods have been used by de Vivie and Peyerimhoff [4221 and by Langhoffet al. [423]. The values calculated by Langhoffet al. [423] for the y bands are -10— 15% lower than the present work while those reported by de Vivie and Peyerimhoff [422] are much higher than the present results. Table 11.3 shows the present and previously published [425,426] oscillator strength results for the 3 bands of nitric oxide and demonstrates the irregularities in the oscillator strength distributions caused by configuration interactions between the valence and the Rydberg states of 2 fl symmetry. Note that the oscillator strengths calculated by Gallusser and DressIer [4251 were obtained by adjusting the electronic transition moments of the 3 and ô bands by reference to the photoabsorption data reported by Bethke [426]. Hence, the calculated values of Gallusser and Dressier [425] are consistent with the data reported by Bethke [426]. The present results are in reasonable agreement with the data of Bethke [4261 except for the v’= 11 and 14 bands for which the present values are somewhat higher. The larger discrepancies in the cases of these two bands may arise from deconvolution errors. The present and previously published [422,423,426,446,447,453,457] results for the ö bands are shown In  321 table 11.4. It can be seen that the reported experimental and theoretical data are in very good agreement with each other with the exception that the value for v’=O reported by Callear and Pilling [447], using the curve— of—growth method, is much higher than the other results. For the  E  bands as shown In table 11.5, the present results are again In good agreement with the data of Bethke [4261. On the other hand, the lifetime data of Hesser [251] and also the theoretical values of de Vivie and Peyerimhoff [422] are considerably lower than than the present results. Absolute integrated oscillator strengths over selected ranges in the energy region 7.52—9.43 eV are summarized in table 11.6. Marmo [439] has also reported photoabsorption data in this energy region, but the data are not shown in table 11.6 since they are subject to the “line saturation” effects as discussed above. In contrast the present work provides a quantitative determination of oscillator strength below the first ionization threshold. Berkowitz [143] has performed a sum—rule analysis on all experimental oscillator strength data for nitric oxide available before 1980 and obtained an integrated oscillator strength value of 14.17 from the lower limit of the data at 8.86 to infinity. As stated by Berkowitz [143], this analysis therefore implies that the integrated oscillator strength below 8.86 eV is 0.83 by difference (I.e. 15.00 minus 14.17). In contrast, the presently measured integrated oscillator strength sum up to 8.86 eV gives a very different value of 0.0603. The present result therefore strongly suggests that the published data used by Berkowitz [143] misses appreciable oscillator strength at higher energies. In the energy region 10—22 eV, the absorption spectrum of nitric oxide (figures 11.3 and 11.4) consists of several unclassified bands and also numerous  322 Table 11.6 Integrated absolute optical oscillator strengths over the energy region 7.52-9.43 eV in the photoabsorption of nitric oxide  Energy range  Integrated oscillator  (eV)  strength  7.5 17  7.606  0.000615  7.789  0.00235  7.907  0.00 139  8.065  0.00335  8.199  0.00225  8.333  0.00389  8.442  0.00250  8.64 1  0.00598  8.747  0.00259  8.868  0.00375  8.94 1  0.00 168  9.039  0.00255  9.148  0.00297  9.148—9.221  0.00144  9.221—9.323  0.00232  9.323  0.0025 1  7.606 7.789 7.907 8.065 8.199 8.333 8.442 8.64 1 8.747 8.868 8.94 1 9.039  —  —  —  —  —  —  —  —  —  —  —  —  —  —  9.428  323 transitions to the many Rydberg series converging to the triplet and singlet ionization limits corresponding to the ejection of a 5a, 1t or 4o electron. Details concerning the assignments and energy positions of these Rydberg series can be found In refs. [430,432,433]. Above the first ionization potential the discrete peaks are broadened by autolonization and therefore Beer—Lambert law photoabsorption studies In this region would be expected to be less affected by “line saturation” effects. This Is supported by a comparison of the present spectrum (figures 11.3 and 11.4) and the photoabsorption data reported by Watanabe et aL. [443]. Using the data of Watanabe et aL. [443], Berkowitz [143] reported an oscillator strength sum of 1.413 in the energy region 8.86—18.44 eV which Is in good agreement with the present result of 1.435.  11.3 Conclusions Absolute optical oscillator strengths for the photoabsorption of nitric oxide in the valence discrete region 5—30 eV have been measured. Previously reported low resolution sum—rule normalized dipole (e,e) data [931 have been used to establish the absolute scale for the present high resolution measurements. The presently determined absolute scale is thus completely independent of any direct optical data and the oscillator strengths are free of “line saturation” effects. Absolute optical oscillator strengths for the vibrational bands of the y, 3, ô and  E  states are reported.  The results are in generally good agreement with absolute photoabsorption data. This good agreement in the case of nitric oxide arises because in general the oscillator strengths for discrete transitions below the first ionization potential are not large. Furthermore, the  324 pressure broadening techniques used in the Beer—Lambert photoabsorption studies reported by Bethke [4261 enable the “line saturation” effects to be considerably reduced.  325 Chapter 12  Concluding Remarks  A new high resolution dipole (e,e) method has been developed for the measurements of absolute optical oscillator strengths for discrete and continuum transitions throughout the valence shell electronic spectra of gaseous atoms and molecules. The present work has presented absolute optical oscillator strengths for the discrete and continuum excitations of , 2 , N 2 five noble gases (He, Ne, Ar, Kr and Xe) and five diatomic gases (H 02, CO and NO). The new measurements have considerably extended the range of measured absolute oscillator strength data for the above gases. , S-÷n 1 (1 The present results for the discrete excitation transitions P n=2—7) of helium and for the Lyman and Werner bands of hydrogen are in excellent agreement with high—level ab—initio quantum—mechanical calculations. These findings confirm the viability of the high resolution dipole (e,e) method and in particular the accuracy of the Bethe—Born conversion factor determined for the high resolution dipo1e (e,e) spectrometer. The good agreement of the present measurements in the Schumann—Runge continuum region of oxygen with most previously reported experimental results further support the accuracy of the high resolution Bethe—Born conversion factor when extrapolated down to lower energy (7 eV). The results also confirm the validity of the Bethe— Born approximation for high energy electron scattering and the suitability of the high resolution dipole (e,e) method using TRK sum rule normalization for general application to the measurement of optical  326 oscillator strengths for discrete electronic excitations in atoms and molecules at high resolution. The present work has also provided a detailed analysis of the “line saturation” (bandwidth) effects that can occur In quantitative photoabsorption cross section measurements for discrete transitions when using Beer—Lambert law methods. In contrast, the presently developed dipole (e,e) method provides a ready means of oscillator strength measurement for atoms and molecules across the entire valence shell region at high resolution and does not suffer from the problems of “line saturation” effects that can complicate Beer—Lambert law photoabsorption studies. 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