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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 FORELECTRONIC EXCITATIONS OF NOBLE GASATOMS AND DIATOMIC MOLECULESByWing-Fat ChanB. Sc. (Chemistry) The Chinese University of Hong Kong, 1984M. Phil. (Chemistry) The Chinese University of Hong Kong, 1986A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE STUDIESDEPARTMENT OF CHEMISTRYWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIASeptember 1992© Wing-Fat Chan, 1992Signature(s) removed to protect privacyIn presenting this thesisin partial fulfilment ofthe requirements for an advanceddegree at the University ofBritish Columbia, I agreethat the Library shall make itfreely available for referenceand study. I further agree that permissionfor extensivecopying of this thesis forscholarly purposes maybe granted by the head of mydepartment or by hisor her representatives. It isunderstood that copying orpublication of this thesis forfinancial gain shall not be allowedwithout my writtenpermission.(Signature)__________________(2/88)Signature(s) removed to protect privacySignature(s) removed to protect privacyAbstractA new high resolutiondipole (e,e) method isdescribed for themeasurement of absoluteoptical oscillator strengths(cross sections) forelectronic excitationof free atoms and moleculesthroughout the discreteregion of the valence shellspectrum. The technique, utilizingthe virtualphoton field of a fast electroninelastically scattered at negligiblemomentum transfer, avoidsmany of the difficultiesand errors associatedwith the various direct opticaltechniques which have traditionallybeenused for absolute opticaloscillator strength measurements.In particular,the method is free of thebandwidth (line saturation)effects which canseriously limit the accuracy ofphotoabsorption cross sectionmeasurements for discretetransitions of narrow linewidthobtained usingthe Beer-Lambert law(I0/I=exp(n1o)).Since these perturbing“linesaturation” effects are not widelyappreciated and are onlyusuallyconsidered in the context of peakheights a detailed new analysisof thisproblem is presented consideringthe integrated cross section(oscillatorstrength) over the profile of eachdiscrete peak.Using a low resolution dipole(e,e) spectrometer (—1 eV FWHM),absolute optical oscillator strengthsfor the photoabsorptionof the fivenoble gases He, Ne, Ar, Kr andXe have been measured upto 180, 250,500, 380 and 398 eV respectively.The absolute scales for themeasurements of heliumand neon were obtained by TRKsum rulenormalization and it was not necessaryto make the difficultdeterminations of photon flux ortarget density requiredin conventionalabsolute cross sectiondeterminations. Single point continuumnormalization toabsolute optical data was employedfor theHmeasurements of argon, krypton and xenon due to the closelyspace inthe subshells of these targets which cause problems in the extrapolationprocedures required for TRK sum—rule normalization. The newlydeveloped high resolution dipole (e,e) method(0.048 eV FWHM) hasthen been used to obtain the absolute optical oscillator strengths for thevalence discrete excitations of the above five noble gases with theabsolute scale normalized to the low resolution dipole (e,e)measurements in the smooth ionization continuum region. Themeasured dipole oscillator strengths for helium excitation (11S—nP,n=2-7) are in excellent quantitative agreement with the calculationsreported by Schiff and Pekeris (Phys. Rev. 134, A368 (1964)) andbyFernley et al. (J. Phys. B 20, 6457 (1987)). High resolution absoluteoptical oscillator strengths are also reported for the autoionizingresonances, corresponding to the double excitation of two valenceelectrons and/or single excitation of a inner valence electron, of theabove five noble gases.High resolution absolute optical oscillator strengths (0.048 eVFWHM) for discrete and continuum transitions forthe photoabsorption offive diatomic gases (H2,N2,02,CO and NO) throughout the va1ence shellregion are reported. The absolute scales were obtained by normalizationin the smooth continuum to TRK sum rule normalized data determinedusing the low resolution dipole (e,e) spectrometer. Absolute opticaloscillator strengths for the vibronic transitions of the Lyman and Wernerbands of hydrogen, theb’fl and b”Zvalence excited states, thec’H,c?lu+ and o1fl Rydbergstates and thee’H and e”Dstates of nitrogen,the A111, B1 and E1fl states of carbon monoxide, and they (A2—X211),1(B211—Xfl), ô (C2fl—XH) and E (D2—Xfl)systems of nitric oxide,Inwere determined. Absoluteintensities for the Schumann—Rungecontinuum region and forthe discrete bands below the first ionizationpotential of oxygen are alsoreported. The variation of the electronictransition moment with internucleardistance was studied for the Lymanand Werner bands of hydrogen andfor the vibronic bands of the X1_A111 transition of carbonmonoxide. The dipole strengthsof the Lymanand Werner bands ofhydrogen at the equilibrium internucleardistance(0.74 lÀ) are also reported.The present results are comparedwithpreviously published experimentaldata and theoretical calculations. Theresults for molecular hydrogenare in excellent agreement withhigh leveltheory (Allison and Dalgarno, At.Data 1, 289 (1970)).ivTable of ContentsAbstractilTable of ContentsvList of TablesIxList of FiguresxivAcknowledgements1 General Introduction12 Measurement of Absolute Optical Oscillator Strengthsby Photoabsorption and Electron Impact Methods62.1 Photoabsorption Cross Section Measurements via theBeer—Lambert Law62.2 Optical Methods for Determining Absolute OpticalOscillator Strengths for Discrete Transitions92.3 “Line Saturation” Effects in Beer—Lambert LawPhotoabsorption for Discrete Transitions152.4 Electron Impact Methods292.4.1 Theoretical Background for Fast Electron ImpactTechniques302.4.2 Experimental Approach333 Experimental Methods383.1 The Low Resolution Dipole (e,e) Spectrometer383.2 The High Resolution Dipole (e,e) Spectrometer 423.3 Experimental Considerations and Procedures473.4 Energy Calibration523.5 Sample Handling and Background Subtraction534 Absolute Optical Oscillator Strengths for the ElectronicExcitation of Helium554.1 Introduction 554.2 Results and Discussion 56V4.2.1 Low Resolution Optical OscillatorStrengthsMeasurements for Helium564.2.2 High Resolution OpticalOscillator StrengthsMeasurements for Helium634.2.2.1 The Discrete Transition of1S—’nP(n=2—7) 634.2.2.2 The Autoionizing Excited StateResonances 724.3 Conclusions745 Absolute Optical OscillatorStrengths for the ElectronicExcitation of Neon765.1 Introduction765.2 Results and Discussion845.2.1 Low Resolution Measurementsof thePhotoabsorption Oscillator Strengthsfor Neon upto 250 eV845.2.2 High Resolution Measurementsof thePhotoabsorption Oscillator Strengths fortheDiscrete Transitions of Neon Below the2pIonization Threshold925.2.3 High Resolution PhotoabsorptionOscillatorStrengths for Neon in the 40—55 eV Region of theAutoionizing Excited State Resonances1045.4 Conclusion1076 Absolute Optical OscillatorStrengths for the ElectronicExcitation of Argon, Kryptonand Xenon1096.1 Introduction1096.2 Results and Discussion1186.2.1 Low Resolution Measurements ofthePhotoabsorption Oscillator Strengths forArgon,Krypton and Xenon1186.2.1.1 Low Resolution Measurementsfor Argon 1186.2.1.2 Low Resolution Measurements forKrypton 1336.2.1.3 Low Resolution Measurementsfor Xenon 141vi6.2.2 High Resolution Measurements of thePhotoabsorption Oscillator Strengths for theDiscrete Transitions Below the mp IonizationThresholds for Argon (m=3), Krypton (m=4) andXenon (m=5) 1526.2.3 High Resolution Measurements of thePhotoabsorption Oscillator Strengths in theAutolonizing Resonance Regionsdue to Excitationof the Inner Valence s Electrons1766.4 Conclusions1827 Absolute Optical Oscillator Strengths (11—20 eV) andTransition Moments for the Lyman and Werner Bands ofMolecular Hydrogen1847.1 Introduction 18472 Results and Discussion1927.2.1 Absolute Oscillator Strengths 1927.2.2 The Variation of Transition Moment with theInternuclear Distance for the Lyman and WernerBands 2057.3 Conclusions 2128 Absolute Optical Oscillator Strengths for the Discreteand Continuum Photoabsorption of Molecular Nitrogen(11—200eV)2138.i Introduction 2138.2 Results and Discussion 2218.2.1 Low Resolution Absolute Photoabsorption OscillatorStrength Measurements for Molecular Nitrogen(11—200eV) 2218.2.2 High Resolution Absolute PhotoabsorptionOscillator Strength Measurements for MolecularNitrogen (12—22 eV) 2278.3 Conclusions 245vii9 Absolute Optical OscillatorStrengths for thePhotoabsorption of Molecular Oxygen(S-30 eV) 2489.1 Introduction2489.2 Results and Discussion2529.3 Conclusions26710 Absolute Optical Oscillator Strengthsfor the Discreteand Continuum Photoabsorption ofCarbon Monoxide (7—200 eV) and Transition Moments for the Xl+-*AlflSystem26910.1 Introduction26910.2 Results and Discussion27510.2.1 Low Resolution Absolute PhotoabsorptionOscillator Strength Measurementsfor CarbonMonoxide (7—200 eV)27610.2.2 High Resolution Absolute PhotoabsorptionOscillator Strength measurements for carbonmonoxide (12—22 eV)28110.2.3 The Variation of Transition moment withInternuclear Distance for the Vibronic Bands oftheX1—Af1Transition29710.3 Conclusions30011 Absolute Optical Oscillator Strengthsfor thePhotoabsorption of Nitric Oxide (5—30 eV)30211.1 Introduction30211.2 Results and Discussion30711.3 Conclusions32312 Concluding Remarks325References327viiiList of TablesTablePage2. 1 Methods of obtaining optical oscillatorstrengths for discreteelectronic transitions at high resolution 113.1 Sources and stated minimum purity of samples544. 1 Absolute differential optical oscillatorstrengths for heliumobtained using the low resolution (1 eV FWHM) dipole (e,e)spectrometer (24.6—180 eV) 584.2 Theoretical and experimentaldeterminations of the absoluteoptical oscillator strengths for the (1’S—n1P, n=2 to 7)transitions in helium 685. 1 Absolute differential optical oscillator strengths for neonobtained using the low resolution (1 eV FWHM) dipole (e,e)spectrometer (2 1.6—250 eV) 875.2 Theoretical and experimental deteminations of theabsoluteoptical oscillator strengths for the2s2p6—2s2p5(P3/,1/)3s discrete transitions of neon 955.3 Theoretical and experimental deteminations of the absoluteoptical oscillator strengths for discrete transitions of neon(19.5—20.9eV) 975.4 Theoretical and experimental deteminations of the absoluteoptical oscillator strengths for discrete transitions of neon(20.9—21.2eV) 99ix6. 1 Absolute differential optical oscillatorstrengths for thephotoabsorption of argon above the first ionization potentialobtained using the low resolution (1 eV FWHM) dipole(e,e)spectrometer (16—500 eV)1226.2 Absolute differential optical oscillatorstrengths for thephotoabsorption of krytpon above the first ionization potentialobtained using the low resolution (1 eV FWHM) dipole(e,e)spectrometer (14.7—380 eV)1366.3 Absolute differential optical oscillatorstrengths for thephotoabsorption of xenon above the first ionization potentialobtained using the low resolution (1 eV FWHM) dipole(e,e)spectrometer (13.5—398 eV)1456.4 Theoretical and experimental deteminationsof the absoluteoptical oscillator strengths for the3s23p6—’3s23p5(2P312,11)4s discrete transitions of argon 1596.5 Theoretical and experimental deteminationsof the absoluteoptical oscillator strengths for discrete transitions of argon.(a) in the energy region 13.80—14.85 eV (b) in the energyregion 14.85—15.30eV1616.6 Theoretical and experimental deteminationsof the absoluteoptical oscillator strengths for the4s24p6—4s5(P3/2,1/)5s discrete transitions of krypton 1636.7 Theoretical and experimentaldeteminations of the absoluteoptical oscillator strengths for discrete transitions ofkrypton.(a) in the energy region 1 1.90—13.05 eV, (b)in the energyregion 13.05—13.50 eV165x6.8 Theoretical andexperimental deteminationsof the absoluteoptical oscillator strengths forthe5s25p6—’5s25p5(P32,i /2)6sdiscrete transitions of xenon 1676.9 Theoretical andexperimental deteminations ofthe absoluteoptical oscillator strengths fordiscrete transitions of xenon.(a) in the energy region9.80—11.45 eV (b) in the energyregion 11.45—11.80eV1697. 1 Absolute osci1latorstrengths for the vibronic transitionsof theLyman band of molecular hydrogen1967.2 Absolute oscillatorstrengths for the vibronictransitions of theWerner band of molecular hydrogen1977.3 Total integrated absolute oscillatorstrengths for the Lymanand Werner bands of molecularhydrogen 2037.4Dipole strengths De(ro) for the Lymanand Werner bands ofmolecular hydrogen2118. 1 Absolute differentialoptical oscillator strengths forthephotoabsorption of molecularnitrogen obtained using thelowresolution (1 eV FWHM) dipole(e,e) spectrometer (11—200eV)2248.2 Absolute optical oscillatorstrengths for discrete transitionsfrom the ground state ofmolecular nitrogen in the energyregion 12.50—14.68 eV2338.3 Absolute optical oscillatorstrengths for transitions to thevibronic bands of the valence b’flstate from the ground stateof molecular nitrogen237xi8.4 Absolute optical oscillator strengths for transitions to thevibronic bands of the valence bhlZ+ state from the groundstate of molecular nitrogen 2388.5 Absolute optical oscillator strengths for transitions to thevibronic bands of the lowest member of the Rydbergstate from the ground state of molecular nitrogen 2398.6 Absolute optical oscillator strengths for transitions to thevibronic bands of the lowest member of the Rydbergc’Hstate from the ground state of molecular nitrogen 2408.7 Absolute optical oscillator strengths for transitions to thevibronic bands of the lowest member of the Rydberg o1flstate from the ground state of molecular nitrogen 2418.8 Total absolute optical oscillator strengths for transitions to theb’IIand valence states, and the lowest members of thec1fl, c’1 and o1fl Rydberg states from the ground state of244molecular nitrogen8.9 Integrated absolute optical oscillator strengths in selectedregions over the energy range 14.92—16.9 1 eV for excitationof molecular nitrogen 2459. 1 Absolute optical oscillator strengths for the photoabsorption ofmolecular oxygen in the energy region 9.75—11.89 eV 2609.2 Integrated absolute optical oscillator strengths for thephotoabsorption of molecular oxygen over intervals in theenergy region 12.07—18.29 eV 264xii10. 1 Absolute differential optical oscillator strengths for thephotoabsorption of carbon monoxide obtained using the lowresolution (1 eV FWHM) dipole (e,e) spectrometer (7—200eV) 27810.2 Absolute optical oscillator strengths for the vibronic bands oftheX1—’Afltransition of carbon monoxide 28510.3 Absolute total optical oscillator strengths for theX1—’Afltransition of carbon monoxide 28810.4 Absolute optical oscillator strengths for the vibronic bandsfrom the X1ground state to theC1+and E1fl excitedelectronic states of carbon monoxide 29010.5 Integrated absolute optical oscillator strengths for thephotoabsorption of carbon monoxide over energy intervals inthe region 12.13—16.98eV 29511. 1 Absolute optical oscillator strengths for discrete transitions ofnitric oxide in the energy region 5.48—7.44 eV 31311.2 Absolute optical osciilator strengths for the vibonic bands ofthe y (X2fl—’A)transition in nitric oxide 31411.3 Absolute optical osciilator strengths for the vibonic bands ofthe (X2fl—BH) transition in nitric oxide 31611.4 Absolute optical osciilator strengths for the vibonic bands ofthe ô(X2H_C2fl)transition in nitric oxide 31711.5 Absolute optical osciilator strengths for the vibonic bands ofthe (X2fl—’D)transition in nitric oxide 31811.6 Integrated absolute optical oscillator strengths over theenergy region 7.52—9.43 eV in the photoabsorption of nitricoxide 322xiiiList of FiguresFigurePage2. 1 Comparison of the absolute valence shellphotoabsorptionoscillator strength spectra of molecular nitrogen obtained byphotoabsorption and dipole (e,e) experiments in the energyregion 12.4—13.2 eV182.2 Diagrammatic representation of the“line saturation” effectoccuring in Beer—Lambert law photoabsorptionexperiments ... 212.3Variation of integrated peak intensity (NxA4)with columnnumber for different ratios of (incident bandwidth(AE))/(natural absorption line-width (AL))252.4 Variation of the observed integratedcross-section withcolumn number for different AE/AL ratios262.5 Variation of the observed integratedcross-section withcolumn number at AE/AL= 10 for peaks with trueintegratedcross-section273.1 Schematic of the dipole (e,e+ion)spectrometer 403.2 Schematic of the high resolutiondipole (e,e) spectrometer .... 433.3 Flow-chart showing the data recordingand processingprocedures used in determining the absolutedipole oscillatorstrengths for the discrete electronic excitationtransitions(l1S—’nP, n=2-7) of helium504. 1 Absolute dipole oscillator strengths forhelium measured bythe low resolution dipole (e,e) spectrometer from20—180 eV(FWHM=l eV)57xiv4.2 Absolute dipole oscillator strengths for helium measured bythe high resolution electron energy loss spectrometer from20—30 eV (FWHM=0.048 eV)664.3 Absolute dipole oscillator strengths for helium Intheautoionizing resonance regions measured by the highresolution electron energy loss spectrometer. (a) in theenergy region 58—66 eV, (b) in the energy region69—72 eV 735. 1 Absolute oscillator strengths for the photoabsorptionof neonmeasured by the low resolution dipole (e,e) spectrometer(FWHM=leV). (a) 15.7—250 eV, (b) Expanded viewof the 20—60 eV energy region855.2 Absolute oscillator strengths for the photoabsorption of neonmeasured by the high resolution dipole (e,e) spectrometer(FWHM=0.048 eV). (a) 16—26 eV, (b) 19.5—22 eV935.3 Absolute oscillator strengths for the photoabsorption ofneonin the autoionizing resonance region 40—55 eV (FWHM=0.098eV)1066. 1 Absolute oscillator strengths for the photoabsorption of argonin the energy region 10—60 eV1196.2 Absolute oscillator strengths for the photoabsorption ofargonin the energy region 40—240 eV1206.3 Absolute oscillator strengths for the photoabsorption ofargonin the energy region 220—500 eV1216.4 Absolute oscillator strengths for the photoabsorptionofkrypton in the energy region 5—60 eV1346.5 Absolute oscillator strengths for the photoabsorption ofkrypton in the energy region 50—400 eV 135xv6.6 Absolute oscillator strengths for the photoabsorption of xenonIn the energy region 5—60 eV1426.7 Absolute oscillator strengths for the photoabsorption of xenonin the energy region 40—200 eV 1436.8 Absolute oscillator strengths for the photoabsorption of xenonin the energy region 160—400 eV 1446.9 Absolute oscillator strengths for the photoabsorption of argonobtained 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 1536. 10 Absolute oscillator strengths for the photoabsorption ofkrypton obtained using the high resolution dipole (e,e)spectrometer (FWHM=0.048 eV) in the energy region 9—16eV 1546. 11 Absolute oscillator strengths for the photoabsorption ofkrypton obtained using the high resolution dipole (e,e)spectrometer (FWHM=O.048 eV). (a) Expanded view of the12.2—13.6 eV energy region, (b) Expanded view of the 13.5—15.0 eV energy region 1556. 12 Absolute oscillator strengths for the photoabsorption of xenonobtained using the high resolution dipole (e,e) spectrometer(FWHM=0.048 eV) in the energy region 8—15 eV 1566. 13 Absolute oscillator strengths for the photoabsorption ofxenonobtained using the high resolution dipole (e,e) spectrometer(FWHM=0.048 eV). (a) Expanded view of the 11—12 eVenergy region, (b) Expanded view of the 12—13.7 eV energyregion 157xvi6. 14 Absolute oscillator strengthsfor the photoabsorption of argonin the autoionizing resonance region 25—30 eV1786. 15 Absolute oscillator strengths forthe photoabsorption ofkrypton in the autolonizing resonanceregion 23—28.5 eV 1806.16 Absolute oscillator strengths for thephotoabsorption ofkrypton in the autoionizing resonanceregion 20—24 eV 1817. 1 Absolute oscillator strengths for the photoabsorptionofmolecular hydrogen in the energy region11—20 eV measuredby the high resolution dipole (e,e) spectrometer(FWHM=0.048 eV)1937.2 Absolute oscillator strengths for thephotoabsorption ofmolecular hydrogen in the energy region11—14 eV 1947.3 The absolute optical oscillator strengthsfor individual vibronictransitions as a function ofthe vibrational quantum number v’for the Lyman band1997.4 The absolute optical oscillator strengthsfor individual vibronictransitions as a function of the vibrationalquantum number v’for the Werner band2007.5 The electronic transition momentRe(rvo)Iin atomic units(a.u.) as a function of the internuclear distancerv’o inAngstroms(A) for the Lyman band 2077.6 The electronic transition momentIRe(rv’o)Iin atomic units(a.u.) as a function of the internuclear distancerv’o inAngstroms(A) for the Werner band 208xvii8. 1 Absolute oscillator strengths forthe photoabsorption ofmolecular nitrogen measured usingthe low resolution(FWHM=l eV)dipole (e,e) spectrometer.(a) in the energyregion 10—50 eV, (b) in the energy region 50—200 eV2228.2 Absolute oscillator strengths for the photoabsorptlonofmolecular nitrogen in the energy region12—22 eV measuredusing the high resolution dipole (e,e) spectrometer(FWHM=0.048 eV)2288.3 Expanded view of figure 8.2 for the photoabsorption ofmolecular nitrogen in the energy region 12.4—13.4 eV 2298.4 Expanded view of figure 8.2 for the photoabsorptionofmolecular nitrogen in the energy region 13.2—15.0eV 2308.5 Expanded view of figure 8.2 for the photoabsorptionofmolecular nitrogen in the energy region 15—19 eV2319. 1 Absolute oscillator strengths forthe photoabsorption ofmolecular oxygen in the energy region 5—30eV measuredusing the high resolution dipole (e,e) spectrometer(FWHM=0.048 eV) 2539.2 Absolute oscillator strengths for the photoabsorption ofmolecular oxygen. Expanded view of figure 9.1 in the energyregion 6.5—10 eV, showing the Schumann—Runge continuumregion 2559.3 Absolute oscillator strengths for the photoabsorptionofmolecular oxygen. (a) The energy region 9.5—15 eV,(b) Theenergy region 14—25 eV 259xviii10. 1 Absolute oscillator strengths for the photoabsorption of carbonmonoxide 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 27710.2 Absolute oscillator strengths for the photoabsorption of carbonmonoxide in the energy region 7—21 eV measured using thehigh resolution dipole (e,e) spectrometer (FWHM=0.048 eV) 28210.3 Absolute oscillator strengths for the photoabsorption of carbonmonoxide in the energy region 7.5—10.5 eV at 0.048 eVFWHM 28410.4 Absolute oscillator strengths for the photoabsorption of carbonmonoxide in the energy region 10.5—12 eV at 0.048 eVFWHM 28910.5 Absolute oscillator strengths for the photoabsorption of carbonmonoxide in the energy region 12—20 eV at 0.048 eV FWHM 29410.6The electronic transition momentIRe(rvo)Iin atomic units(a.u.) as a function of the internuclear distance rv’o inAngstroms (A) for the vibronic bands of theX1+—b A1fltransition 29911. 1 Absolute oscillator strengths for the photoabsorption of nitricoxide in the energy region 5—30 eV measured using the highresolution dipole (e,e) spectrometer (FWHM=0.048 eV) 30811.2 Expanded view of figure 11.1 in the energy region 5—8.2 eV 30911.3 Expanded view of figure 11.1. (a) in the energy region 8—10eV, (b) in the energy region 10—13 eV 31011.4 Expanded view of figure 11.1. (a) in the energy region 13—16eV, (b) in the energy region 16—22 eV 311xixAcknowledgementsI would like toexpress my sincerethanks to myresearchsupervisor, Dr.C. E. Brion for hisInterest, assistance andencouragementthroughout thecourse of my study.It has been a pleasureto work withhim and withother members in hisresearch group. Specialthanks aredue to Dr. G.Cooper for a lot of help inmy research workand for hishelpful commentsand suggestions onthe writing of mythesis. Thanksare due to Dr. K. H.Sze for introducingme to the highresolutionspectrometer and toDr. W. Zhangand G. R. Burton formany helpfuldiscussions.I would like to thankProfessor M. J.Seaton for sendingme hiscalculated datafor helium and ProfessorJ. A. R. Samsonfor sending mehis measured data forargon, krypton andxenon. Helpful commentsanddiscussions concerningthe present work withProfessor M. J.Seaton,Professor J. A. R.Samson, Dr. W. L. Wieseand Dr. M. Inokutiare alsoackn owleciged.I would liketo thank the staff ofthe mechanicaland electronicworkshops fortheir assistance in maintenancethe spectrometers, inparticular B. Greeneand E. Gomm. Thanksare also due to D. JonesandM. Hatton (Electronicworkshop) for the designand construction ofthefast data buffer.Financial support inthe form of a Universityof British Co1umbiaGraduate Fellowshipis gratefully acknowledged.The research workhasbeen supported byoperating grants fromthe Canadian NationalNetworksof Centres of ExcellenceProgramme (Centresof Excellence in Molecularxxand InterfacialDynamics) andfrom the NaturalSciences andEngineeringResearch Councilof Canada.Finally, Iwish to thank tomy parents andJosanna fortheirpatience andencouragement.This thesisis dedicatedto them.xxi1Chapter 1IntroductionAbsolute optical oscillator strength (cross section) information is ofimportance because of the need to know electronic transitionprobabilities for both valence and Inner shell excitation and ionizationprocesses In many areas of application including plasmas, fusionresearch, lithography, aeronomy, astrophysics, space chemistry andphysics, laser development, radiation biology, dosimetry, health physicsand radiation protection. Such information is also a crucial requirementfor the development and evaluation of quantum mechanical theoreticalmethods and for the modelling procedures used for various phenomenainvolving electronic transitions induced by energetic radiation [1].However, most spectroscopic studies to date for discrete electronicexcitation processes have emphasized the determination of transitionenergies rather than oscillator strengths, since the former quantities aregenerally relatively easier to obtain both experimentally and theoretically.In contrast only rather limited information is available for thecorresponding absolute optical oscillator strengths (or equivalentquantities reflecting transition probability such as cross section, lifetime,linewidth, extinction coefficient, A value etc.) for atoms. In the case ofdiscrete electronic transitions for molecules such quantities areextremely sparse, while for core (inner shell) processes the available dataare even more limited. In particular oscillator strengths are in very shortsupply for transition energies beyond 10 eV where most valence shellelectronic excitation and ionization processes occur. This situation is2partly due to the wellknown inherent difficulties of quantitativework inthe vacuum UV and soft X-rayregions of the electromagneticspectrum(i.e. beyond theL1F cut-off). These and otherlimitations provideconsiderable challenges inboth photoabsorption andphotoemissionstudies. The situation a1soreflects the limitations andapplicationrestrictions involved in othertypes of optical methods such aslifetime,line profile, self absorptionand level crossing techniques.Furthermore,the commonly employed directphotoabsorption methodsusing the Beer—Lambert law transmissionmeasurements are subject toso—called “linesaturation” (bandwidth) effects,which can lead to largeerrors in thederived absolute opticaloscillator strengths for discrete transitions.These spurious effects becomemore severe for transitionswith narrowlinewidth and high cross section. Insuch cases the measuredoscillatorstrengths are too small. Detaileddiscussions of Beer—Lambertlawphotoabsorption and the associated“line saturation” effects aregiven inchapter 2 section 3.From a theoretical standpoint,calcu1ation offers an alternativeapproach to experimental oscillatorstrength determination.However,theoretical ca1culations of oscillatorstrengths involve computationalmethods that require extremely sophisticatedcorrelated wavefunctionsand reasonable accuracy is at presentonly feasible for the simplestatomssuch as hydrogen [21 andhelium [3-9].Electron energy loss spectroscopy(EELS), utilizing the virtualphoton fie1d induced in atarget by fast electrons at negligiblemomentumtransfer, provides an alternativeand versatile means of measuringopticaloscillator strengths for electronictransitions in atoms andmolecules inboth the discrete and continuumregions. Under suchexperimental3conditions the electron energyloss spectra are governed bydipoleselection rules, and for thisreason EELS based methods for opticaloscillator strength determinationare often referred to as dipoleelectronimpact experiments. The theoreticalgroundwork showing thequantitative relationship betweenphotoabsorption measurementsandelectron scattering experimentswas laid earlier, in 1930, byBethe [10],by using the First Bornapproximation. The Bethe—Borntheory has beenfurther discussed by Inokuti [11]and Kim [121 and itsapplication inexperimental studies has been reviewedby Lassettre and Skerbele [131and Brion and Hamnett [14]. Since1960, there has been growinginterest in electron scatteringexperiments partly due torecognition ofthe importance of phenomenainvolving electron—atomand electron—molecule interactions, andpartly due to advances in high—vacuumtechnology, low energyelectron optics, and detectiontechniques such asfast pulse counting using channelelectron multipliers (channeltrons).Electron energy loss experimentshave been applied to themeasurements of absoluteoptical oscillator strength fordiscretetransitions following the pioneeringwork of Lassettre et al. [15—18]andof Geiger [19,20]. In otherwork Van der Wiel and co—workers 121—23]developed a variety of “photonsimulation” experiments usinghigh Impactenergy, small angle electronscattering techniques to determineabsolutedifferential optical oscillatorstrengths in the continuumregion. Inrecent years, the techniquesused by Van der Wiel andhis co—workers[21—23] have been modifiedand further developed hereat the Universityof British Columbia wherea variety of low resolutiondipole electronimpact methods have nowprovided absolute differentialoptical oscillatorstrengths for a wide rangeof valence—shell [24—27] andinner—shell4[28,291 photoabsorptionand photoionizationprocesses.A reviewandcompilationof photoabsorptionand photolonizationdata obtainedbydirect opticaland dipoleelectronimpactmethodsfor smallmoleculesInthe continuumregion hasrecentlybeen publishedby Gallagheret al.[301.In otherwork,a high impactenergy, zero—degreescatteringangle,high resolutionEELS spectrometer[311 was built inthis laboratoryforthe studyof valence—shell[32—341 and inner—shell[32,34,351 electronicexcitationspectraof a varietyof molecules.In the presentwork, theoperationof thisEELS spectrometer[311 has now beenmodifiedtoprovidea new highresolutiondipole (e,e)methodfor the determinationof opticaloscillatorstrengthfor discretephotoabsorptionprocessesinfree atomsand molecules.This newmethodis freeof the spurious“linesaturation”effects thatcomplicatethe measurementof absoluteopticaloscillatorstrengths(cross sections)in Beer—Lambertlaw photoabsorptionexperimentsfor discretetransitions.The methodis applicableto alltransitionsthroughoutthe discretevalenceshell regionof the valenceshell spectrumat high energyresolution(0.048 eVFWHM).The Bethe—Born conversionfactorfor the highresolutiondipole(e,e) spectrometer,developedhere in theUniversityof BritishColumbiahas beendeterminedby calibrationagainsta previouslydevelopedlow resolutiondipole (e,e)spectrometer.The absolutescalesof the presentoscillatorstrengthdata wereobtainedfrom Thomas—Reiche—Kuhn(TRK) sum—rulenormalizationof the Bethe—Born transformedelectron—energy—lossspectraand assuch donot involvethe difficultdeterminationsof photon(or electron)flux or targetdensity requiredin photoabsorptionand othertypes of electronscatteringexperiments.5In chapter 2 of this thesisthe photoabsorption andelectron Impactmethods are compared, togetherwith a consideration of othertechniques for optical oscillatorstrength determination.The presentlyused electron impactbased dipole (e,e) methods are discussedInchapter 3. Absolute optical oscillatorstrengths for photoabsorptionInthe discrete and continuumregions for five noble gases (helium [36,371.neon [38] and argon, kryptonand xenon [39]) and five diatomicgases(hydrogen [40], nitrogen [41],oxygen [42], carbon monoxide [43]andnitric oxide [44]) are presentedfrom chapters 4 through11. Thevariations of electronic transitionmoment with the internucleardistancefor the Lyman and Werner bandsof molecular hydrogen and fortheX1—’Aflbands of carbon monoxideare also discussed In chapters 7and10 respectively. The presentresults are compared with previouslyreported experimental and theoreticaldata from the literature.6Chapter 2Measurement of Absolute Optical OscillatorStrengths byPhotoabsorption and Electron Impact Methods2.1 Photoabsorption Cross Sectionmeasurements via the Beer—Lambert LawIn photoabsorption experiments,quantitative cross sectionmeasurements are governed by the Beer—Lambert law.Consider first thereduction in the photon intensity when a light flux I passesthrough adistance dl containing a sample target of numberdensity ri. The loss ofintensity dl of the incident photon beamis proportional to the distancetravelled dl, the number density ri. of the target, andthe photoabsorptioncross section of the target a(E). The relationshipcan be written asdI=—IoE)nd1(2.1)where the photoabsorption cross sectiono(E) is related to theprobability that a photon of energy E willbe absorbed in passing throughthe target and has the dimension of area.Integrating equation 2.1 overthe path length 1, we obtainI=I0exp(-oE)n1)1 exp(—o(E) N)(2.2)Equation 2.2 is the familiar Beer—Lambertlaw [30,45] where 1 and I arethe incident and transmitted lightintensities, respectively. The7quantity N is equal to ni and is sometimesreferred to as the columnnumber. The Beer—Lambert photoabsorptionmethod can in principlebereadily applied to the complete electronicspectrum of a given atomicand molecular target in both thediscrete and continuum regions.Furthermore, the measurement procedurewould at first seemto be quitestraight forward. Extensivemeasurements using thistechnique havebeen made for atoms andmolecules in the continuumregion. Reviewsand compilations of such crosssection (oscillator strength)data can befound in references [30,45—48].However, in the discrete excitationregion, only limited cross sectioninformation is available fromuse of theBeer—Lambert law photoabsorptionmethods, and most of themeasurements performed arefor molecules. This situation arisesbecause of the large errors whichcan occur in Beer—Lambertlaw crosssection measurements for discretetransitions due to “line saturation”(i.e. bandwidth) effects.These spurious effects are particularlysevere fordiscrete transitions withnarrow natural linewidths and highcrosssections. A comparison ofdifferent optical methodsfor determiningabsolute oscillator strengthsin the discrete excitation regionis given insection 2.2, while the perturbing“line saturation” effects inBeer—Lambert law photoabsorptionare discussed in detail in section 2.3.A dimensionless quantity, namelythe optical oscillator strength,i(E), is also often used in opticalabsorption spectroscopy.The oscillatorstrength is related[49] to the integrated photoabsorption cross sectionc for a discrete transitionthrough the equation (in atomic units):tAll equations are in atomic units.282it(2.3)In quantum mechanics, f°(E) is defined [14] as:No 2f(E)= 2EI(WIrIW0)I (2.4)Swhere E is the excitation energy, r5 gives the coordinates of the Nelectron species, and W and W are the initial and excited statewavefunctions respectively.At sufficiently high photon energies, ionization occurs andtransitions occur from the bound initial state to a continuum final state.Instead of using the integrated photoabsorption cross section, a, andthe optical oscillator strength, 1°, equation 2.3 can be rewritten as [50]2i12df°(E)o(E)= (2.5)c dEwhere a(E) is the photoabsorption cross section as defined earlier anddf°(E)/dE is the differential optical oscillator strength with thedimension of (energy)’. If the energy E is expressed in electron volts(eV) and a(E) is in megabarns (1 megabarn10-18cm2), we haveaGE) [Mbarns] = 109.75df°(E)[eV’](2.6)9Equation 2.6 may be usedfor the interconversion of cross section anddifferential oscillator strength data.The optical oscillator strengths f(E) In thediscrete region anddf(E)/dE in the continuum region havean important property thatisuseful for establishing the absolute intensityscale in the presentlydeveloped dipole (e,e) method (see chapter 3).It has been shown thatfor an N electron species [50,51],f°(E)+fdf°(E) dE = N(2.7)This simply means that the total integratedoptical oscillator strength(i.e. summingover all discrete transitions and integratingover allcontinuum states) is equal to the totalnumber of electrons. Equation 2.7is the famous Thomas-Reiche-Kuhn (TRK)sum-rule which In generalholds for any atomic and molecular system.Generally, a valence shellpartial sum rule is applied and in this casespectral area (i.e. the totaloscillator strength) is normalized to the numberof valence shellelectrons plus a small correction for the Pauliexcluded transitions fromthe core orbitals to the already occupied groundstate valence orbitals[52,53].2.2 OptIcal Methods forDetermining Absolute Optical OscillatorStrengths for Discrete TransitionsA variety of different optically basedmethods have traditionallybeen used for the determination ofmost of the optical oscillator strength10data available for discreteelectronic transitions in the literature.Only alimited amount of data isavailable for atoms and much ofthis is to befound in the importantcompilations published by Wieseand coworkers 154]. Very littleinformation is available formolecules. Theoscillator strength data base is extremelylimited because suchmeasurements are difficultto perform and also becausemost availablemethods suffer from avariety of often serious difficulties and/orlimitations which severely restricttheir range of application.Wiese andco—workers [54] have discussedvarious aspects of the opticalmethodsused for atoms and provideuseful conversion formulaerelating thevarious quantities produced bythe different types of measurements.The most commonly usedoptical measurement techniquesinclude(a) Photoabsorption via theBeer—Lambert law [55], (b)Lifetimemeasurements by level crossingtechniques (including the Hanleeffect) [56,57], (c) Lifetimemeasurements by beam foilmethods [58], (d)Emission profile measurementsfrom 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]. Thestrengths and weaknessesof these methods withregard to theirwidespread general applicationto atomic and molecularelectronicexcitation spectra are summarisedin Table 2.1. Also shownin table 2.1are corresponding considerationsfor theory as well as forelectronimpact based oscillator strengthmethods [67—7 1], includingthe presentwork, as discussed in section2.4 below. Methods (b)—(h)have all beenused but only in selectedfavourable cases involvingrelatively intenseatomic transitions. Howeversuch approaches aregenerally complexandvarious limitations make themunsuitable for widespreadapplicationTable2.1MethodsofobtainingopticaloscillatorstrengthsfordiscreteelectronictransitionsathighresolutionMethodAdvantagesDifficultiesandProblemAreasSuitabilityforGeneralERef.]MolecularStudiesBeer-LambertLaw.Simplerelation,l011=expfrtlop)Bandwidtheffect(linesaturation)duetotheLimitedsuitabilityunderPhotoabsorptionVeryhighresolutionresonantnatureofdiscreteexcitationandfavourablecircumstances1551WidespectralrangeuseoflogarithmicrelationtoobtainStraylight,orderoverlapping.Extrapolationtozerocolumnnumber.LifetimeMethodsNobandwidthproblemBranchingratiosmustbeknown.Notgenerallysuitable[56—581Molecularenergystatesmustbeknown.(i)LevelcrossingGoodforstrongresonancesSlightdependenceoflinewidthon(1-lanleeffect)[56,571backgroundpressure.(ii)BeamfoilUsefulformeanlifetimesofCascadesfromotherstates.[58]excItedstateatomicandionicBlendingofunresolvedspectrallines.levelsTable2.1(continued)MethodAdvantagesDifficultiesandProblemAreasSuitabilityforGeneralLRef.1MolecularStudiesPlasmaemissionNobandwidthproblemOnlygoodforopticallythickemission.DifficultandprofileUncertaintiesincalculatedStarkwidth.notgenerallysuitable159] BeamemissionprofileNobandwidthproblemTimevariationsinDopplerwidth.Difficultand[60]Reliesoncalculatedelectroncollisioncrossnotgenerallysuitablesection.ResonancebroadeningNobandwidthproblemExtrapolationtozeropressure.DifficultandemissionprofileDifferentDopplerwidthcorrespondingtonotgenerallysuitable[611differentexcitationtoupperlevels.SelfabsorptionNobandwidthproblemPossibledeparturefromDopplerprofile.Difficultand[62-64)Re-emissionfromatomsexcitedbynotgenerallysuitableabsorptionofresonancephotons.Table2.1(continued)[65) Opticalphase-matching[66) Electronscattering(Vary9atfixedE0)[67—701Onlygoodforopticallythickabsorptionintheabsenceofcollisionbroadening.Transitionpeakmustnotbeperturbedbycollisioneffects.Refractiveindexofbuffergasatparticularwavelengthmustbeknown.ExtrapolationtoK2=0isproblematical.Tediousprocedureforeachtransition.Absolutescalerequiresexternalprocedures.ExtrapolationtoK2=0isproblematical.Tediousprocedureforeachtransition.Electronopticaleffectsandlensratios.Absolutescalerequiresexternalprocedures.DifficultandnotgenerallysutiableDifficultandnotgenerallysutiableTotalabsorptionMethodAdvantagesDifficultiesandProblemAreasSuitabilityforGeneral(Ref.1MolecularStudiesNobandwidthproblemNobandwidthproblemNobandwidthproblemNobandwidthproblemElectronscattering(VaryE0atfixed0)[711DifficultbutpossibleDifficultforgeneralapplicationTable2.1(continued)MethodAdvantagesDifficultiesandProblemAreasSuitabilityforGeneral(Ref.1MolecularStudiesElectronscatteringNobandwidthproblemStrayelectrons.ReadilyapplicableoverwideHRDipole(e,e)AbsolutescaleviaTRKsumrule.AccuracyofBetheBornconversionfactorspectralrange.Lthiswork)NopressureorincidentfluxsinceB(E)inlowenergyregionisdependentMostdifficultiescanbemeasurementsrequired.onextrapolation.overcomewithverycarefulDirectmeasurementoverwideResolutionlimitedtoAE0.01eVFWHM.experiments.spectralrange.Goodaccuracy.QuantummechanicalVeryaccurateforsmallatoms.ExtensiontolargesystemslimitedbyVerydifficulttoobtaingoodcalculationNoinstrumentaleffects.wavefunctionaccuracyandcalculationaccuracy.13-91Infiniteenergyresolution,methods. Lackofsufficientlyaccurateexperimentaldataforcomparison.15across the complete valenceshell spectral range foratomic and inparticular molecular targets.Although in principle Beer—Lambertlawphotoabsorption measurementswould seem to offer astraightforwardmeans for routinemeasurement of absolute opticaloscillator strengthsfor atomic and moleculartransitions over a widespectral range,application of the method mayoften result in large errorsIn themeasured cross section.Since the limitations ofthis method are notwidely appreciated, thespecial case of the Beer—Lambertlawphotoabsorption methodwill now be discussed indetail.2.3 “Line Saturation”Effects in Beer—LambertLaw Photoabsorptionfor Discrete TransitionsPhotoabsorption via the Beer—Lambertlaw (method (a) in table2.1)can in principle be appliedreadily to the complete valenceshellspectrum of atoms andmolecules, and the measurementprocedurewould seem to be quitestraightforward in principle.While the methodworks well for continuum processes,very few accurate determinationsofabsolute oscillator strengthsfor discrete electronic transitionshaveactually been made usingthe Beer—Lambert law. Thisis because veryserious problems can arise whenBeer—Lambert law discretephotoabsorption spectra areused for absolute intensity(oscillatorstrength) determinations [721rather than just for indicatingthe energylevels. These problems, whichare not always widelyappreciated or wellunderstood, arise from thefinite energy resolution ofany real opticalmonochromator and theresonant nature of discretephotoabsorption. Inparticular, it should be noted thatequation 2.2 is only strictlyvalid for16the unphysical situation of zerobandwidth (i.e. infiniteenergy resolution)as discussed in references [11,37,46,73,74].DiffIculties arise because alogarithmic transform isrequired (equation 2.2) in orderto obtain theabsolute cross—section a(E)from the percentage transmission (l/1)obtained from the experimentalmeasurements. As a result ofthislogarithmic transform the measuredcross section at the characteristicenergy will correspond to a weightedaverage observed cross section(which is often much less than the truecross section a(E)) in situationswhere the bandwidth (BW=AE)Is a significant fraction of, orgreater than,the natural linewidth (LW=AL) fora transition [46,73,74].This limitationand the fact that measured peakcross—sections are often a functionof theinstrument as much as of the target,has been reviewed in somedetail byHudson [46] and commented on byothers [11,75]. The situation ispotentially particularly serious forintense narrow lines in thediscreteregion because of the Bohr frequencycondition and the fact that the lineprofile varies rapidly within theBW unless the latter is very muchnarrower than the naturalLW. Hudson [46] has also discussedthe so—called “apparent pressure” effectand shown how the bandwidth effectscan be minimised (but neverentirely eliminated) by the tediousprocedure of extrapolating peak intensitiesmeasured at a series ofpressures, for each separatetransition, to zero column number N.However, even with suchprocedures, as Hudson [46] correctlypointsout, I approaches 10 as thisoptically thin limit is approachedand thus thegreatest weight is placed on the leastaccurate data! The net result isthat accurate optical oscillatorstrengths often cannot beobtained fromBeer—Lambert law photoabsorptionmeasurements for very sharp,intenselines (for example compare references[55,76—80]). These problems are17likely to be particularly severe in the vacuumUV and soft X—rayregions ofthe spectrum where low lightfluxes, even from monochromatedsynchrotron sources, often requirethe use of wide monochromatorexitslits. These bandwidth effects willoccur when the monochromatorisplaced between the continuum lightsource and the sample cell.Thisarrangement is the usual situation on synchrotronbeam lines (i) becauseof the ultra high vacuum requirements inthe storage ring and themonochromator and (ii) because the monochromatoris usually an integralpart of the beam line facility feedingdifferent possible experimentalarrangements. However, thesespurious bandwidth effects wouldalsoinfluence the measured cross sectionsin the same way if the samplecellwas placed between the source andmonochromator as occurs in manylaboratory—based spectrometer arrangements.Despite the well documented and seriousdeficiencies which cancomplicate the determination ofabsolute optical oscillator strengths fordiscrete transitions using thel3eer—Lambert Law, it is still sometimesused and it can then often result inspurious results which are not alwaysapparently realised by the experimenters. Aparticularly drastic exampleof such “line saturation’ BW effectsoccurs in the vacuum UV absorptionspectrum of N2 [801 illustrated in figure2.1. The vacuum UV spectrumas reported by Gurtler etal. [80] on an absolute scale (figure 2.1(a))hashigh enough resolution to showevidence of rotational effects.Thisoptical absorption spectrum [80] is comparedwith a high impact energy,negligible momentum transfer, highresolution (zE0.O17 eV) electronenergy loss spectrum placedon an absolute scale [37,4 1] in figure2.1(b)over the same energy region. Clearlythere are large differences inrelative intensity between thetwo spectra in the 12.6—13.0 eVrange, andPhoton energy (eV)Figure 2.1: Comparison of the absolute valence shell photoabsorption oscillatorstrength spectra of molecular nitrogen obtainedby Beer—Lambert lawphotoabsorption and dipole(e,e) experiments in the energy region 12.4—13.2eV. (a) Beer—Lambert law absolute photoabsorption spectrum adaptedfromfigure 1 of reference [80] — the dashed lines have beendrawn to show thepositions of the maximum cross—sections of the peaks according to thevalues given in the text of reference [80].(b) Dipole (e,e) spectrum [37,41] —the electron energy loss spectrum was placed on an absolute opticaloscillator strength scale by referencing to the high resolution oscillatorstrength spectrum reported in the present work(see chapter 8).4002I18(a) Photoabsorptionk L.JL300iIII III IL3.2•1•0-864I?•100C.)00Cl)00C.)-800p40600400—F-—-—13.2 13.012.8 12.612.4(b) Dipole (e,e) spectroscopyIE0 =2500eVj= 0.017 eV.1—‘/“b__%__‘20200I — I13.2 13.0 12.8 12.6012.419particularly in the 12.9—13.0eV region. These differencesreflect serious“line saturation” effectsin the optical work Inthe 12.9—13.0 eV regiondue to the finite bandwidthof the incident radiationand the extremelynarrow natural linewidth of theseintense transitions. Ascan be seenfrom figure 2.1 these factors havedramatic effects on thederived opticaloscillator strengths (crosssections). Clearly not onlythe peak heightsbut also the peak areas (and thusthe apparent oscillatorstrengths) aredrastically reduced in the opticalspectrum. In contrastthecorresponding absolute opticaloscillator strength spectrumobtained viaElectron Energy Loss Spectroscopy(EELS) in figure 2.1(b)(see section2.4 following) shows the correctrelative intensities (bandareas) eventhough it is at lower energy resolutionthan the optical work.This largeintensity effect in the electronicspectrum of N2 waspointed out earlierin electron impactstudies by Lassettre [81] andalso by Geiger [82].Subsequently, extrapolation ofvery carefully controlled opticalmeasurements [78,79], made asa function of column numberN, wasfound to give results muchmore consistent with theintensities derivedfrom the EELS measurements [81.821.It is important to note thatthe earlier treatment of “linesaturation”effects by Hudson [46] only emphasizedthe effects of finite BW onthepeak heights of sharp spectrallines (i.e. the cross sectionat the peakmaximum) and how sucheffects may, hopefully, be minimisedbyextrapolation to zero columnnumber. As Hudson [46] hasshown, a 40%error still exists in a peakheight cross section for thesituation whereLW=BW, even at N=0! Howeverit should be remembered thatanaccurately measured oscillatorstrength for a discrete transitionshouldinvolve an integral over thewhole profile of the spectralline and should20not just be assessed from the peak height. The peakarea in aphotoabsorption experiment is also severely Influencedby the BW effects,which results in a significant reduction inboth peak height and peakarea, as can be seen in figure 2.1. This clearly leadsto an Integratedoptical oscillator strength for the transition which issignificantly in errorunless the BW is very narrow compared withthe narrowest features inthe spectrum — regardless of whether ornot such features are resolved!Such errors are therefore likely to be particularlyserious for molecularspectra because of the vibrational and rotational fine structure— as canbe seen in figure 2.1. Since in generaldifferent lines in the samespectrum have different natural LW, the cross sectionperturbations aredifferent for every transition (see again figure 2.1(a) and(b)). Thus thecomplete spectroscopy (i.e. all line widthsand line shapes) must alreadybe known if any meaningful understandingof photoabsorption crosssections for spectral lines is to be obtainedfrom Beer—Lambert lawmeasurements. If such information was available thenof course theoscillator strengths wou1d already be known from the linewidths!Clearlythen, one can never be sure that the correctoscillator strength has beenobtained in a Beer—Lambert law photoabsorptionexperiment unlesseither the information is already availablein some form from othersources, or unless the absolute integrated spectralintensities can beshown to be effectively independent of theBW as well as the columnnumber N.Given the above considerations it is necessaryto extend the peakheight analysis of Hudson [46] to considerthe effects of bandwidth ontheintegrated cross section over the spectralline profile (i.e. peak area) inadiscrete photoabsorption experiment.For example, consider (figure 2.2)21% absorptionof10(AE,E)Econvoluted with triangularbandwidth áEap(tE,E)AA1=A2A34Figure 2.2: Diagrammatic representation of the“line saturation” effects occuring inphotoabsorption experiments when theBeer-Lambert law is used todetermine the Integrated cross-section of adiscrete transition.Gaussian absorption peak% absorptionof10(E)a(E)o(E) = [n\7I0(i..E,E)(]2+2)W2oE,E) = LnI(iE,E)JA2\E\E£F/22the effects of convoluting an assumed Gaussian shaped absorption peak ofnatural linewidth iL with a triangular monochromator bandwidth AE. Inthis case, equation 2.2 can be rewritten asI(AE,E) =I0(tE,E) exp (—(o(AE,E)N) (2.8)The area A1 (see figure 2.2 — left hand side) of the unconvolutedGaussian absorption peak depends linearly on the percentage absorption{(I—I)/I} of10(E) at the peak maximum for a given zL. The area of theGaussian peak is, of course, unchanged by convolution with the bandwidthAE regardless of AE/iL. That is, considering the % absorptionpPi1{I I (E) — 1(E)10(AE,E) — I(AE,E)IdE=dE (2.9)J10(E)or (A1) (A2)However, in order to calculate the photoabsorption cross section a(E), alogarithmic transformation (see equation 2.2) of 1/I is needed. Thelogarithmic transform together with the resonant nature of discreteexcitation by photons is the root cause of the “line saturation” bandwidtheffects and the resulting spurious experimental cross sections whichoften occur in absolute photoabsorption measurements using Beer’s law.In the case of the logarithmic conversion we have for the cross sectionalareas before and after convolution (figure 2.2 — right hand side)23PkI1I0(E)= dE1(E)CO1A4=-______n-i[n=1(AL2+AE2)A3=dE(2.10)PkA4 = fo1zEE)dE= JIndE(2.11)It is found that A3 is always greaterthan A4 unless AE is equal tozero,which is only true of course for the hypotheticalcase of Infinitely narrowbandwidth. In more detailmathematically, area Ai is convoluted bybandwidth AE to yield an area A2 suchthatA1=A2.If area A2 is also aGaussian distribution with full widthat half maximum (FWHM)approximately equal to (tL2+t\E)1/thenunder this circumstance,A1=A2(=1 IS) (where S is a scale factor inorder that we may vary theareaunder the Gaussian peak).After integration of equations 2.10 and 2.11,we obtain1A3=N-(2.12)(2.13)Cnl242I1n2whereU =Comparing eachterm for equation 2.12 and2.13, A3 Is always greaterthan A4 unless AEis zero, and only in this casedoes A3=:A..In figure 2.3, the variationof observed peak area (NxA4)withcolumn number Nfor a given transition is shownfor different AE/ALratios. It showsthat the area becomes smalleras the ratio AE/ALisincreased for the same columnnumber. Figure 2.4 showsthe variation ofintegrated cross sectionfor a given transition obtainedby use of theBeer—Lambert law with columnnumber for differentvalues of LE/AL. Thetrue integrated crosssection (100Mb eV) is onlyattained at N=0 orwhere AE=0 (i.e. infiniteresolution). Figure 2.5 ((a)—(e))shows thevariation of observed integratedcross section with columnnumber atAE/AL=10,calculated for a series oftransitions of different truecrosssection (given at zero columnnumber). Note thatfor each cross sectionthe behaviour is differenteven for a fixed AL. Since ingeneral differentlines will have different naturallinewidths AL, it can be seenthat theeffects and therefore the interpretationof photoabsorptionexperimentscan be very complex indeed.These effects are known asthe “linesaturation” or “apparentpressure’ effects occurringin photoabsorptionexperiments [46].With a very narrow naturallinewidth (i.e. large AE/AL)and a high cross section theproblem is obviously moresevere, in orderto attempt to obtain a resultcloser to the correctcross section, the onlyexperimental approach isthe tedious procedure ofperforming themeasurements for each transitionin the spectrum at aseries of pressuresand extrapolatingto zero column number asshown in figures 2.4 and2.5.VVVIVI-.UC.,0Column number (x lOlócm-2)Figure 2.3: Variation of integrated peak intensity (NxA4)with column number fordifferent ratios of (incident bandwidth (AE))/(natural absorption line-width(AL)), calculated using equations 2.12 and 2.13.250 1 2 34 56V04-UVU)U)U)0IU4)IVCa)VIa)VU)0Figure 2.4: Variation of the observed integrated cross-section with column number fordifferent AE/zL ratios, calculated using equations 2.12 and 2.13. The trueintegrated cross-section is taken to be 100Mb eV.260 1 2 3 4 56Column number(x lOlócm-2)271o0.. 80C)0IC)VIV40VVb.20VI-.C).0o00.00Column number ( x1018cm2)Figure 2.5: Variationof the observed integratedcross-section wIth columnnumber atAE/zL=1O for peakswith true integratedcross-section of(a) 100, (b)50, (c)30, (d) 20 and (e) 10Mb eV. Thecurves were calculated usingequations 2.12and 2.13.0.050.100.1528Such procedures have been used by Lawrence [781 and Carter [79]. Infigure 2.5 we can see that for peaks with the same AE/AL va1ue, thehigher the true cross section, the greater the error in the opticallymeasured cross section at a given column number. Thus It can be seenthat for very narrow peaks of very high cross section, extrapolation toextremely low pressure would be required to obtain the correct crosssection experimentally. However, in an actual experiment, the error InmeasuringI0(tE,E)/I(E,E) increases with decrease In pressure. AsHudson [46] has pointed out, extrapolation procedures put the mOstemphasis on the least accurate data and hence the extrapolated value Islikely to be inaccurate. These extrapolation procedures only minimisethe BW effect and the resulting cross sections may in some cases still besubject to large errors. In such situations direct photoabsorptionmeasurements are meaningless and for example, Yoshino et al. [55] havestated that the (12,0) transition of18jis too narrow to be measuredusing the Beer—Lambert law photoabsorption method.in summary then, the above model calculations Indicate that it Isoften extremely difficult to obtain highly accurate optical oscillatorstrengths for discrete transitions in optical photoabsorption experimentsbased on the Beer—Lambert law, especially for very sharp peaks with highcross section. As such, absolute photoabsorption cross sections obtainedfor discrete transitions using the Beer—Lambert law must always beviewed with some caution because of the possibility of significantsystematic errors due to finite bandwidth effects which in general will bedifferent for every transition. Therefore, widespread application of Beer—Lambert law photoabsorption methods to the study of discrete atomic andmolecular spectra is not practical if accurate cross—sections are desired.29In the following discussion alternativemethods of determining opticaloscillator strengths aredescribed which do not sufferfrom thesespurious bandwidth effects.2.4 Electron Impact MethodsAn alternative and entirely independentapproach to opticaloscillator strength determination,free of spuriousbandwidth effects, isprovided by exploiting thevirtual photon field inducedin a target by fastelectrons. This can be achievedby means of fast electron impactelectron energy loss techniquesat vanishingly small momentumtransfer.The theoretical relation betweenhigh energy electronscattering andoptical excitation has longbeen understood [10].The resonant processof absorption of a photonof energy Ehv(E)+M—’M(2.14)may be compared with thenon—resonant process ofelectron Impactexcitatione(E0) + M—M + e(E0—E)(2.15)Clearly the electron energyloss (E) is analogousto the photon energy E.The Intensity of scattered electronsresulting from the excitationprocessis measured rather than apercentage absorption. Thenon—resonantnature of the electron impactexcitation process togetherwith avoidanceof the logarithmic Beer—Lambertlaw in determiningoscillator strength30(cross section) meansthat the “line saturation”bandwidth problem whichoften complicatesdiscrete photoabsorptionexperiments is eliminatedInthe EELS method [111.2.4.1 TheoreticalBackground for Fast ElectronImpact TechniquesThe process involvingthe collision betweena fast electron andatarget atom or moleculecan be consideredas a sudden but smallperturbation of the targetby the incident electron.The suddentransferof energy and momentumto the target electronsdue to the perturbationresults in excitationswithin the target molecule[11]. Under theseconditions the perturbationis due to an inducedelectric field, sharplypulsed in time andtherefore correspondingbroad in the frequencydomain. This provides a“virtual photon field” ordipole excitation ofconstant flux in thespectral region of interest.A key quantityin theelectron impact methodfor determining opticaloscillator strengthsisthe momentum transfer(K) in the collision.A momentum transferdependent, generalisedoscillator strengthf(K,E), describing thetransition probability, can bedefined as [10,11,141f(K,E) =(2.16)where the quantitieshave the same physicalmeanings as in equation2.4.It can be seen thatequations 2.4 and2.16 are very similar in form.Itwill be shown laterthat equation 2.4 is alimiting case of equation2.16.In the continuumregion, f{K,E) is replacedby dUK,E)/dE, the31differential generalised oscillator strength,which will be used throughoutthe following discussion.In fact, even for discretetransitions thequantity measured at a givenenergy in an actual experimentis alsodf(K,E)/dE, and integrationover the discrete peakarea gives fK,E).Thequantity dfK,E)/dE is related[11] to the differentialinelastic electronimpact cross—sectiond2ae(K,E)/dEdQ# (which is proportionalto theinelastically scattered current)by the equationdf(KE) = !-K2dOe(E)(2.17)dE 2 k dEdQwhere E is the energy lossand k0,k are the incidentand scatteredmomenta respectively. Thevarious momenta are relatedto the polarscattering angle 0 by thecosine ruleK2 = k + k— 2k0kcos0 (2.18)and K=k0—k(2.19)According to the Bethe—Borntheory [10], equation 2.16can be expandedin terms of a powerseries in K2 if 1K is smalldf(KE) = df°(E)+ AK2 + BK4 +... (2.20)#d2ue(K,E)/dEdQas a function of energyloss E is the electron energyloss spectrum atmomentum transfer Kinvolving scatteringinto a solid angle elementdQ.32whereA = (s—2E1E3), B= (+2E1E5—2E284) (2.21)Nmandm =(q:J1(2.22)where df(E IdE is thedifferential optical oscillatorstrength and Em Isthemtorder multipole matrixelement with m= 1 forelectric dipole andm=2 for electric quadrupole,etc..AsIKI—0, the so—called OPTICALLIMIT, which correspondsto zero momentum transfer,can be obtainedfrom equation 2.20[11]df(K,E) df°(E)dE - dE(2.23)Under such conditionsof negligible momentumtransfer dipole selectionrules apply and equation2.17 can be rewrittenasdf°(E)= -L.K2d2øe(E)= B(E)d2Ge(E)(2.24)dE2 kdEdQdEdQThe quantity B(E) iscalled the Bethe—Bornfactor and it can be seenthatit depends onkinematic (i.e. instrumental)factors alone. B(E) relatesthe electron impactdifferential cross—sectionat negligible momentumtransfer to the differentialoptical oscillatorstrength. In an actualexperiment the factor B(E)must also take intoaccount the finite33acceptance angle of the spectrometer about the mean scatteringangle of00.This will be considered in the following section.2.4.2 Experimental ApproachIt is clear from equations 2.17—2.24 that electron impactmeasurements made under appropriate conditionsmay be used to makeabsolute optical oscillator strength measurements if appropriate absolutenormalisation procedures can be established.The momentum transferK, which depends on the impact energy E0, the energy loss E and themean scattering angle 0, can be obtained for a particular experimentalcondition by substitutingk02=2E andk2=2(E0—E) into equation 2.18[14].K2 = 2E0 + 2(E0—E) — 2/2E0-/2(E—E) cosO (2.25)Equation 2.25 can be rearranged to becomeK2 = 2E0 (2— E—2cosO) (2.26)From equation 2.26, it can be seen that if we require K2—’O,E/E0 and 0should be made as small as possible. Under these conditions, we canexpand (1—E/E0)1/2into a binomial series and neglect the contribution ofthe higher terms for small E/E0. In addition, cosO can be made equal to(1_02/2)for small 0. Equation 2.26 can then be simplified to2 22K = 2E0 (x + 0 )(2.27)where x is a dimensionlessquantity and Is equal to E/2E0.Bysubstituting equation2.27 into equation2.24 and integratingover thefinite half angle of acceptance 00of the detector,the Bethe—Bornconversion factor B(E)can be derived for aparticular spectrometergeometry to be [14,83]EEkB(E)= 00in1 + (2.28)t k,Two general approacheshave been used foroptical oscillatorstrength determinationby electron impact:(a) An indirect EELSmethod, pioneeredin the 1960’s by E.Lassettreand co—workers [67—70].involves measurement ofthe relativeintensity for a given transitionas a function of scatteringangle (i.e. ofK2, see equation2.25) at a fixed intermediateimpact energy(typically —500eV). This results in a relativegeneralized oscillatorstrength curve (see equations2.17—2.23) which canbe extrapolatedto K2=O to give anestimate of the relativeoptical oscillator strengthfor the transition.The extrapolation procedureis tedious since aseries of measurementsis required for eachtransition. In additionthe procedure can oftenbe problematical dueto unusual behaviourofthe functional formof fIK) at low K[67] and also due tothe fact thatthe minimum experimentalvalue of K2 was oftenstill quite large [67—35701 sothat a lengthy extrapolation wasrequired. The minimumattainable value of K2 was furtherlimited [67—701 by thefact that thespectrometer could not be operatedat0=00due to interferencefromthe incident primaryelectron beam in the electronenergy lossanalyzer. The relative value ofthe oscillator strength wasusuallymade absolute by reference toconcurrent measurementsof therelative elastic scattering Intensitywhich was in turn normalizedon apublished value of the calculatedor experimental absoluteelasticscattering cross section. Avariation of this extrapolationapproachused by Ross et a!. to studyalkali metals [71], involvedscanning theimpact energy at fixed scatteringangle for each transition.Howeversuch an approach is even moredifficult for general applicationtoquantitative work because ofelectron optical effects onthe scatteredelectron intensities andas a result its use has beenextremely limited.(b) A more direct and versatileapproach which avoids theneed for theundesirable extrapolationprocedures is to choose theexperimentalconditions so that the OPTICAL LIMIT(i.e. K2—’O) is effectivelysatisfied directly [2 1—23].This can be achieved by measuringat highimpact energy E0 (typically3000 eV for valence shellprocesses) anddesigning the electron analyzerand associated electron opticsso thata mean scattering angleof00can be used [83—871. Thistypicallyresults in K2<10-2a.u.. Under suchconditions equation 2.24 issatisfied to better than1% accuracy and an entireEELS spectrumcovering both the discreteand continuum regions canbe scanneddirectly under dipole(optical) conditions. Toobtain a relative optica1oscillator strength spectrumit suffices merely totransform the36relative electron impact differential cross section (at K2—0) by theknown Bethe—Born factor B(E) for the spectrometer. B(E) must takeinto account the effects caused by the finite acceptance angles of theelectron energy loss analyzer (i.e. a spread of K2, see equation 2.28).The relative optical oscillator strength spectrum obtained in this wayhas the correct relative intensity distribution because of the “flat”nature of the virtual photon field [14,88] associated with inelasticallyscattered fast electrons at K2—O [10]. This means that nodetermination of beam flux is required. The relative spectrum can bemade 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 independentand accurate means of obtaining an absolute scale, frequently used inthis laboratory (for some examples see references [24—27,30]), is toobtain the Bethe—Born transformed valence shell EELS spectrum (i.e.d2oe(E)/dEdQ — see equations 2.24 and 2.28) out to high energy loss.The proportion of valence shell oscillator strength from the limit ofthe data to E=cc is estimated by extrapolation of a curve fitted to thehigher energy measurements. The total area of the spectrum is thennormalised to the number of valence shell electrons. This overallprocedure makes use of the valence shell Thomas—Reiche—Kuhn(TRK) sum rule (see equation 2.7). The TRK sum rule normalisationof a Bethe—Born converted EELS spectrum produces an accurateabsolute scale without the need for measurements of beam flux andtarget density which are required in conventional absolute crosssection determinations.37In summary, the selection of experimental conditionscorresponding directly to the optical limit, together with TRK sum rulenormalisatlon, provides an extremely direct and versatile approach whichIs the basis of the dipole (e,e), (e,2e) and (e,e+lon) techniques formeasuring absolute optical oscillator strengths. These three methodsprovide quantitative simulations of tunable energy photoabsorptlon,photoelectron spectroscopy and photolonization mass spectroscopyrespectively [14,30,881. The three dipole electron scattering techniqueshave been used extensively in recent years for total and partial opticaloscillator strength measurements [30] for photoabsorption andphotoionization in the continuum at modest energy resolution (1 eVFWI-IM) for a wide variety of valence shell and inner shell processes (seereferences [24—30] for some recent examples). The modest energyresolution results from using an unmonochromated incident electronbeam of thermal width. At such a low energy resolution the sharp peaksin the valence shell excitation spectra of atoms and molecules are largelyunresolved [24—27] but the spectral envelope nevertheless encloses thecorrect integrated discrete oscillator strength, regardless of thebandwidth, since electron impact excitation (equation 2.15) is non—resonant [11,14,88]. In the high resolution dipole (e,e) method (0.048eV FWHM) developed in the present work a detailed absolute differentialoptical oscillator strength spectrum is obtained throughout the valenceshell discrete region, free of “line saturation” effects.38Chapter 3Experimental MethodsThe complementaryperformance characteristics of twodifferentzero degree, high—impact—energy electron—energy—lossspectrometers (ordipole (e,e) spectrometers), one withlow resolution and aknown Bethe—Born conversion factor, the otherwith high energy resolution, havebeenused to obtain the results reported inthis thesis. Absolute opticaloscillator strengths for the discrete andcontinuum photoabsorptionoffive noble gases and fivediatomic gases have been obtained.Thecombined techniques establish ageneral method suitable forroutineapplication to measurementsof absolute optical oscillatorstrengths forelectronic excitation (i.e. photoabsorption)of atoms and molecules athigh resolution over a wide spectralrange.3.1 The Low Resolution Dipole(e,e) SpectrometerThe present low resolutiondipole (e,e) spectrometeris the non—coincident forward scattering portionof a dipole (e,e÷ion) spectrometerthat has been extensively used inthis laboratory in recent years toobtainhighly accurate photoabsorptionand photoionization continuumtotal andpartial oscillator strengthsfor a large number of moleculartargets [24—301. Thisdipole (e,e+ion) spectrometerwas originally built at the FOMinstitute in Amsterdam [2 1—23,85—87],but was moved to the Universityof British Columbia in1980 where the spectrometerhas been furthermodified [89,901. Detailsof the construction and operationof this39spectrometer can be foundin references [21—23,85—87,89,90].Aschematic diagram of thedipole (e,e+ion) spectrometeris shown infigure 3.1.Briefly, a black and whitetelevision electron gun withan indirectlyheated oxide cathode (Philips6AW59) at —4 kV potential withrespect toground is employed to producea narrow (-1 mm diameter)beam of fastelectrons. The electronbeam is collided with the targetmolecules in acollision chamber whichis at potential of +4 kV. Thus,the kineticenergy of the incident electronsis 8 keV in the interactionregioncontaining the target molecules.The inelastically scatteredelectrons arecollected in a small cone of1.4x104steradiansabout the zero degreemean scattering angle, definedby an angular selectionaperture. Afterpassing through Einzel lensesand a decelerating lens, theelectrons areenergy—analyzed by a hemisphericalelectron analyzer and finallyaredetected by a channel electronmultiplier (Mullard B4 1 9AL)used in thepulse counting mode. Theresolution of this electronenergy lossspectrometer is - 1 eV FWHM.The time—of—flight massspectrometer,consisting of extraction plates,ion lenses and an ionmultiplier, capableof detecting the positive ionsproduced in the collisionchamber isarranged at 90 degrees tothe incident electron beambut thisarrangement (dipole(e,e+ion) spectroscopy) wasnot used in the presentwork. Helmholtz coils andhigh permeability mumetalare employed toshield the scatteringregions from externalmagnetic fields. The use ofturbo molecular pumpsprovides a clean vacuum environmentsuitable forquantitative electron spectroscopy.Recently, some modificationshavebeen made to this dipole(e,e+ion) spectrometer [27,291.A differentialpumping chamber pumpedby a Seiko—Seiki(STP300) magneticlevitation40ELECTRON GUNFigure 3.1: Schematicof the dipole (e,e+ion)spectrometerIn the presentwork, this instrumenthas been usedonly in the dipole(e,e)mode(i.e. the forward electronenergy loss spectrometerhas been employedwithout thetime—of—flightspectrometer).COLLISIONCHAMBER(e,e +ion)SPECTROMETERGASINErANGULAR SELECTIONEINZEL LENSESDECELERATINGLENSTIME OF FLIGHTMASS SPECTROMETERAND ION LENSESPRiMARYBEAM DUMPELECTRON ANALYSER41turbo—molecular pump,was added to the existingspectrometer betweenthe electron gun vacuumchamber and the collisionchamber In order toeffectively isolate the electrongun from the sample gassuch that theoxide cathode of the electrongun will have a longerlife. In addition,theextra differential pumpingchamber also stabilizesthe electron beamandonly slight retuning ofthe beam Is necessarywhen the sampleIsintroduced into the system.The modifications aboveinvolved adding afurther set of quadrupoleelectrostatic deflectorsand a new electronbeam monitoringaperture (—1 mm diameter).The electron gun wasmoved back from the targetregion by -7 cm. Avacuum isolationvalvewas also added betweenthe electron gun andthe differential pumpingchamber and withthis device in place maintenancework can beperformed on eitherthe gun chamber orthe main system withoutlettingthe whole systemup to atmosphericpressure.The experimentalconditions (E08 keVand half—angle ofacceptanceO0=6.7xlO radians)of this low resolutiondipole (e,e)spectrometer satisfythe small momentumtransfer (K) conditionwhenthe energy loss E500 eV according to theBethe—Born theory(seechapter 2). Theelectron energy lossspectrum is then convertedto arelative optical spectrumfrom the knownscattering geometry (E0,E andO)of the spectrometerusing the equation 2.28.The absolutedifferential oscillator strengthscale for the relative opticalspectrum canthen be establishedby using the (partial) TRKsum—rule or by normalizingat a single point inthe smooth continuumto published opticaldata. Thelatter procedure hasonly been used when thesum—rule normalizationprocedures are nottractable because ofclosely spaced innershells42adjacent to thevalence shell (see results forargon, krypton and xenon,chapter 6).3.2 The HighResolution Dipole (e,e)SpectrometerAll the high resolutionspectra reported in thisthesis weremeasured using thehigh resolution dipole (e,e)spectrometer whichwasbuilt earlier by Daviel, Brionand Hitchcock [31] torecord EELS spectra.The design and constructionof this spectrometer.havebeen described Indetail in reference [31].Figure 3.2 shows aschematic diagram ofthehigh resolution dipole(e,e) spectrometer.The following featuresof thespectrometer provideimproved performancein terms of resolution,sensitivity and stability,compared with olderdesigns:(a) Differential pumpingof the four vacuumchambers including theelectron gun, themonochromator, the collisionregion and theanalyzer, alleviates theproblems of surfacecontamination, retuningand frequent cleaningof the system. Thisarrangement ensureslong term stabilityas well as high sensitivityand good resolutionofthe spectrometer. Thevacuum isolation of theelectron gun alsoenhances the studyof thermally unstable compounds.(b) Advanced electronoptics were designed [31]to improve the beamcurrents and alsominimize the effects of scatteringof the incidentbeam from s1it edges andthe surfaces of theanalyzers into thedetector. The largebackground originatingfrom the primaryelectron beam isstrongly suppressed andoperation at zero—degreemean scattering angleis possible withminimial backgroundeffects.MONOCHROMATORFigure 3.2: Schematic of theLegend: A anodeC cathodeCC collision chamberT tubeANALYSERhigh resolution dipole (e,e) spectrometerG grid P1 — P8 aperturesF focusing lensQi — QdeflectorsV valve L1 — L7 lensesHV high voltageD decoupling transformerGAS gas inlet43TURBOPUMP360 L/SSCALEIo 10 20cmTURBO TURBOPUMP PUMP450 L/S 360 L/SL/S liter per second44(c) Large hemisphericalelectron energy analyzers(mean radius R0 =19 cm = 7.5 in) are employed.As a result, high transmissionandhigh resolution atrelatively high pass energycan be attained. Thehigh pass energy in turnpermits the required highimpact energywhile retaining reasonablelens voltage ratios.Briefly, a thoriated tungstenfilament, spot weldedonto anexternally adjustablemount and located just in frontof the grid of anoscilloscope electron gunbody (Cliftronics CE5AH),is heated by a directcurrent to producethermal electrons. Exceptfor the groundedfirst andthird elements ofthe focussing Elnzel lens F,the filament cathode (C),grid (0), anode (A) andthe second elementof the focussing lens F areallfloated on top of—3 kVin the present design. Atwo element lens (Li)Isused to retard the 3keV electron beam (—1 mmdiameter) to therequired pass energy ofthe monochromatorbefore being energy—selectedby a hemisphericalelectron energy analyzer.A virtual slit generated bythe accelerating(voltage ratio 1:20) lens (L2)is located at themonochromator exit. Themonochromated beam isfurther accelerated(x5) by lens (L3) andthen focussed onto theentrance of the reactionchamber. After passingthrough the Einzel lens (L4),the electron beamcollides with the samplemolecules in the collisionchamber which Is atground potential. Thekinetic energy of theincident electrons Is 3 keVin the collision region.The electron beam thenpasses through a zoom,energy—add, lens (L5).The design of the analyzerentrance lenses (L6andL7) is similarto that of the monochromatorexit lenses (L2 and L3)and avirtual slit is employed. Inthe present work, thepass energy of the45analyzer was always set to be equalto that of the monochromator. Theinelastically scatteredelectrons are energy analyzedbefore beingdetected by the channel electronmultiplier (Mullard B4 19AL) which Ismounted just behind theanalyzer exit aperture.Hydrogen—annealedmumetal enclosures located outsidethe vacuum housing providemagnetic shielding invarious regions of the spectrometer.Seiko—Seiki(STP 300 and 400) magneticlevitation turbo molecularpumps have beenused to establish a cleanvacuum environment.The spectrometer is tuned upby using the primary(unscattered)electron beam which isdirected to the cone of thechanneltron withenergy analyzer deflectionvoltages, lens voltages (Lito L7) and theciuadrupole deflectors (Q1toQ).The quadrupole deflectors eachconsistof two pairs of electrostaticplates in the x and y directions.Electrometers are connectedto the apertures (Pi to P8)to monitor thecollimation and directionof the electron beam, whilea floated vibratingreed electrometer (Cary,model 401) is used to measurethe smallcurrents on the cone ofthe channeltron. In the presentwork, the lensvoltages (Li to L7) were recordedafter the initial tuning ofthespectrometer for a given resolution(which is set by passenergy of theenergy analyzers). Thesame lens voltages were thenused for subsequentmeasurements performedat the same energy resolution.This procedurewas used in order to ensurethe same half—angle ofacceptance 00 of theanalyzer/detection system (whichmay be changed by differentlensvoltages) at a given resolution.To obtain an energy lossspectrum, avoltage corresponding to theenergy loss of the inelasticallyscatteredelectrons is added to thelens L5 and to the completeanalyzer anddetection system. The inelasticallyscattered electronsthus regain their46energy loss and are transmitted to thedetector. At the same time, theprimary (incident) electron beam gains thesame energy and is stronglydefocused by the advanced electron opticsat the input of the analyzer.This results in a strong suppressionof the primary, unscattered,beamand permits operation at zero degreescattering angle. High gainpreamplifier and amplifier/discriminator units(PRA models 1762 and1763respectively) are employed to processthe signals coming fromthechanneltron. The signals are collected usinga Nicolet 1073 signalaverager operated in a multichannel scalingmode. The data are thentransmitted to the PDP 11/23 computer which isalso used to control thescanning voltages on L5 and theanalyzer of the spectrometer as wellasthe channel advance of the signalaverager.The energy resolution AE (FWHM) of thespectrometer depends onthe selected pass energies E for both themonochromator (Em) andanalyzer(Ea).The theoretical resolution (neglecting angulareffects) for ahemispherical analyzer is given [9 ii byzEw---—- (3.1)where w is the slitwidth and r is themean radius. For the combiningmonochromator and analyzer the individualresolution functions must beadded quadrature. The observedhalfwidth of the monochromatedandanalyzed primary beam at a pass energy of10 eV is 0.036 eV in excellentagreement with equation 3.1. Under theseconditions the halfwidth ofthe inelastically scattered beam originatingin the collision chamber, issomewhat larger (0.048 eV FWHM) due tothe additional angularspread.473.3 ExperImental Considerationsand ProceduresThe high resolution dipole(e,e) spectrometer had beenusedextensively in recent years forthe measurement of highresolutionvalence shell [32—341, and innershe1l [32,34,35] excitationspectra.However, prior to the presentwork no attempt had beenmade toquantitative measurements ofabsolute oscillator strengthsbecause theBethe—Born factor of the spectrometerwas not known. In order toobtainabsolute optical oscillator strengthsfrom the high resolutionEELSspectra, an absolute scalemust be established, andin addition the energydependent Bethe—Bornconversion factor for thishigh resolutionspectrometer (BHR) mustbe determined. The conversionfactor is inpractice more complexthan that given by the singleexpression inequation 2.24 because itmust account for integrationover the finitespectrometer acceptance anglesabout0=00(see equation 2.28). Asufficiently exact knowledgeof the effective acceptanceangles wouldrequire a very accurateand detailed understandingof the complexelectron optical functionsof the lenses in all regionsof the highresolution dipole (e,e) spectrometeras a function of energyloss.Furthermore, this detailedinformation would be required foreachanalyser/monochromatorpass energy combinationselected to provide agiven energy resolution.Such detailed informationis difficult to obtainwith sufficient precision bymodel calculations for thecomplex electronoptics in this type of instrument.A better and morefeasible approach [37] isto calibrate theintensity responseof the high resolution instrumentand obtain an48empirically determined, relative,Bethe—Born factor by referencing thehigh resolution EELS signal to the knownoptical cross section in thesmooth photolonization continuum spectralregion of a suitable gas. Thiscould be achieved by takingthe ratio of the high resolution EELSintensity to that of an independentlymeasured absolute photoabsorptioncross section, as a functionof energy loss (photon energy). An obviouschoice for this calibration Is helium gas.Recommended experimentalva1ues of absolute photoabsorption cross sectionfor the heliumcontinuum have been tabulated by Marrand West [47] from aconsideration of a large number of publishedoptical experiments. Wehave, however, chosen an alternative andentirely independent approach,in which the high sensitivity low resolution(—1 eV FWHM) dipole (e,e)spectrometer (described In section 3.1), withno monochromator,simpler optics and collision geometry. anda well characterised Bethe—Born factor(BLR) [24—30], has been used to obtain a new wide rangemeasurement of the helium discrete andcontinuum absolutephotoabsorption oscillator strengths, entirely independentof any opticalmeasurement. It has been found [14,30] thatTRK sum rulenormalization of Bethe—Born converted EELSspectra obtained on this lowresolution dipole (e,e) spectrometer providesa highly accurate absolutephotoabsorption oscillator strength scale, withoutthe need for anymeasurement of beam flux or target density.Helium is a particularlysuitable choice for the calibration measurementssince it Is has only asingle (1s2) shell and thus no shell separation or corrections forPauliexcluded transitions are required for theTRK sum rule procedure, incontrast to the situation for more complextargets.49The absolute photoabsorption oscillatorstrengths obtained on thelow resolution dipole (e,e) spectrometermay then be used to generatethe relative Bethe—Bom factor for thehigh resolution instrument bytaking the ratio of the signals In thesmooth continuum region abovethefirst ionization energy of helium, asdescribed above. The relative Bethe—Born factor for the high resolution spectrometercan then be obtained atlower energies by extrapolation of asuitable function (see chapter 4)fitted to the measured factor in the regionabove 25 eV. Finally, theBethe—Born converted high resolution EELSspectrum of helium wasplaced on an absolute scale by singlepoint normalization in thecontinuum (at 30 eV) to the absolute opticaloscillator strengthdetermined using the low resolutiondipole (e,e) instrument. Employingthese procedures, both the Bethe—Borncalibration and the measurementof absolute optical oscillatorstrengths is achieved entirelyindependentlyof any optical techniques.Furthermore, exploitation of theTRK sum ruleavoids the difficulties andlimitations of conventional methods ofabsolutescale determination. The resultingabsolute measurements can thusbeindependently compared with published valuesof measured andcalculated optical oscillator strengthsfor helium. The sequence ofmeasurements and proceduresused in the present work are summarisedby the flow chart shown infigure 3.3.Similar procedures have beenperformed using the measurementsfor neon [38], and the values obtainedforBHRare in excellent agreementwith those using helium. Theaverage of the two determinationsprovidesfurther statistical precision, andthis average value has been usedIn thehigh resolution absolute oscillatorstrength work performed withthehigh resolution dipole (e,e)spectrometer. The averaged BHRalso50Figure 3.3: Flow-chart showingthe data recording andprocessing proceduresused indetermining the absolute dipoleoscillator strengths for thediscreteelectronic excitation transitions(1 ‘S—n1P, n=2—7) ofhelium.51provides increased reliability when the curve above 25 eV is fitted andextrapolated down to equivalent photon energies as low as 5 eV. Thehigh resolution electron energy loss spectra of the three heavier noblegases (Ar, Kr and Xe) and five diatomic gases(H2,N2,02,CO and NO)have been converted to relative oscillator strength spectra using theBi-ijfactor obtained as described above. The absolute scales were thenobtained by normalizing in the smooth continuum to the data determinedusing 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 rulenormalization procedures used to establish the absolute scales for heliumand neon could not be used for the heavier noble gases since thesuccessive atomic inner subshell energy separations are relatively smalland thus a good fit to the valence shell tail is not possible. In thesecircumstances the extrapolation procedures used to estimate the amountof valence shell oscillator strength above a certain energy becomeunreliable. Therefore, the alternative procedure of single pointnormalization to a previously published photoabsorption measurementhas been used to establish the abso1ute scale for argon, krypton andxenon. For the five diatomic gases, low resolution dipole (e,e) oscillatorstrength measurements have been previously reported [86,87,92,93].The TRK sum rule normalization procedures were used to establish theabsolute scale for the measurements of hydrogen [86], oxygen [921 andnitric oxide [93]. In contrast, single point normalization procedureswere used for the earlier reported measurements for nitrogen and carbonmonoxide [871 since the data were only obtained up to 70 eV energy andhence sufficiently accurate extrapolation procedures could not be carried52out. Therefore in the present work,new wide ranging lowresolutiondipole (e,e) measurements of nitrogenand carbon monoxide havebeenperformed up to an equivalent photonenergy of 200 eV. The TRK partialvalence shell sum rule hasnow been employed In order toestablish theabsolute oscillator strength scalefor these new measurementsfornitrogen and carbon monoxide.Thus, the presently determinedabsoluteoptical oscillator strengthdata for all five diatomic gasesat both high andlow resolution are completely independentof any directly obtainedoptical data.For quantitative measurementsit is essential to ensure thatsaturated count rates are obtainedin the channeltron detectors ofbothspectrometers over the fulldynamic range of the signals. Inorder toavoid dead—time errors it was alsonecessary to use a fast data bufferbetween the output of the highresolution spectrometer and the PDP11/23 computer. Since for the high resolution instrumentno fast MCAcompatible with the PDP 11/23 computerwas available, a speciallyadapted Nicolet 1073 signal averagerwas used as the data buffer in thepresent work. Maximum countrates were restricted toa maximum of20000 per second in order to ensurelinearity over the full dynamicrange of the spectra.3.4 Energy CalibrationThe absolute energy scale ofthe electron energy loss spectrum ofhelium measured using the highresolution dipole(e,e) spectrometer wasobtained by referencing tothe21S—’2 1P transition of heliumat 21.218eV. For the other gases, the absolutescale was established in separate53experiments by simultaneous admission of helium and referencing thesample spectrum to the21S21Ptransition of helium at 21.2 18 eV [54].In practice, the calibration corrections were found to be O.015 eV. Theenergy scale for the low resolution dipole (e,e) measurements wasobtained by referencing the energy position of a prominent spectralfeature to the corresponding peak in the high resolution electron energyloss spectrum.3.S Sample Handling and Background SubtractionThe sample gases studied in the present work were obtainedcommercially. Their sources and stated minimum purities aresummarized in table 3.1. No impurities were apparent in the highresolution electron energy loss spectra. Appropriate gas regulators wereused to establish a steady gas flowrate and sample introduction to thespectrometers was achieved using Granville—Phillips series 203 stainlesssteel leak valves. Ambient gas pressures were adjusted to be in the range0.5—2.0 x1O torr and 0.1—1.0 x1O torr for the high resolution and lowresolution spectrometers, respectively, by using the Granville—Phillipsleak valves. It is important to maintain single collision conditions and noevidence for double scattering was found In the energy loss spectrumunder the selected conditions.Contributions to the electron energy loss spectra from backgroundgases remaining at the base pressures (2x10—7torr) of the turbomolecular pumped spectrometers and/or non—spectral electrons wereremoved by subtracting the signals obtained when the sample pressureswere quartered. Such procedures were used because complete remova154of the sample gas wasfound to influence slightlythe tuning of the energyloss spectrometers.Table 3.1: Sources andstated minimum purityof samplesSample SourceStated minimum_______________purity_(%)He Linde99.995Ne Matheson99.99Ar Linde99.998Kr Linde99.995XeMatheson99.995H2 Linde99.95N2 Medigas 99.02Medigas99.0cO Matheson99.5NO Linde98.555Chapter 4Absolute Optical OscillatorStrengths forthe Electronic Excitationof Helium4.1 IntroductionThe availability of very accuratequantum mechanicalcalculations,together with the fact that heliumhas only a K shell and thusa totaloscillator strength of exactly 2, withno corrections needed forPauliexcluded transitions [52,53],makes the dipole excitation ofground statehelium an ideal test casefor the high resolution dipole(e,e) method. Inaddition further consistency checkscan be made involvingoscillatorstrength sums in appropriateregions of the discrete andcontinuumspectrum. In the presentwork, test measurements, involvingacomp1etely independent determinationof the absolute optical oscillatorstrengths for the 1 S—’nPseries (n=2—7) for helium, arecompared withpreviously published experimentaldata for n=2 and 3obtained using arange of optical [56—64]and electron impact [19,68,84]methods. Themeasured results n=2—7 arealso compared for with highlevel quantummechanical calculations employingcorrelated wavefunctions [3—9,54].The present measurementsrepresent the first absoluteexperimentalresults for n=4—7 and veryfew previous measurementsfor n=3 have beenreported. Measurements of theabsolute continuum photoabsorptionoscillator strengths up to 180eV photon energy, includingthe Fanoprofile resonance regionsof double excitations around60 eV and 70 eV,were also obtained andare compared with existingdirect optical56measurements [94—97] and calculations[9,98—100]. The results forhelium are used to establish the viability of the high reso1ution dipole(e,e) method for general application to measurements of absolute opticaloscillator strengths in the discrete valence shell spectral regions ofelectronic excitation for atoms and molecules.4.2 Results and Discussion4.2.1 Low Resolution Optical Oscillator Strength Measurements forHeliumUsing the low resolution dipole (e,e) spectrometer, electron energyloss 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 eVrespectively. The energy resolution was 1 eV FWHM. Absolute opticaloscillator strengths for helium were obtained by Bethe—Born conversion(usingBLR,see figure 3.3) and TRK sum rule normalization (to a value oftwo) of the electron energy loss data as described above. The portion ofthe relative oscillator strength from 180 eV to infinity was first estimatedby extrapolation of a least squares fit to the measured data In the 72—180eV region using a function of the formAE-B(E=energy and A and B arebest fit parameters). The fit gives B=2.5583 and the fraction of the totaloscillator strength above 180 eV was estimated to be 4.65%. The helium11S_21P transition (21.218 eV) was used for calibration of the energyscale of the spectrum and is the only discrete structure resolved at theresolution of this spectrometer. The measured data is recorded in table4.1 and illustrated in figure 4.1 (solid circles). Also shown on figure 4.1>0a)‘-4U)I0.4-’C-)C,)0C-)a.4-’030 —‘,00C.)V20U)U)Cl)0‘-4C.)0a10f571 ft•.0•.1040.3..,Z’P4III,I’IIII20300 320• X 3 67‘i:: Hej•••6.4a...a*0.•to t€o tao• LR Dipole (e,e) this workMarr and West[47)Fernley et al. [9)(sp,22+)Ip.h.••ô .À.,••4•*. ••I010 20 30 40 5060 70 80 90 100Photon energy (CV)Figure 4.1: Absolute dipole oscillatorstrengths for helium measured by the lowresolution dipole (e,e) spectrometer from 20—180 eV(F’WHM=1 eV). Solidcircles are this work, open triangles arephotoabsorption data of Marr andWest[471,solid line is theory, Fernley et al. [91.58Table 4.1Absolute differential optical oscillator strengths for heliumobtainedusing 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(102eV’) (10-2eV1)(102eV-1)24.6 7.05 29.5 5.12 38.0 3.2124.7 6.96 30.0 4.98 38.5 3.1124.8 6.85 30.5 4.92 39.02.9724.9 6.76 31.0 4.65 39.52.8925.0 6.62 31.5 4.57 40.0 2.9025.1 6.71 32.0 4.45 40.5 2.7625.2 6.66 32.5 4.34 41.0 2.7325.3 6.58 33.0 4.26 41.5 2.6325.4 6.58 33.5 4.07 42.02.5425.5 6.55 34.0 3.95 42.5 2.5626.0 6.37 34.5 3.87 43.02.4626.5 6.08 35.0 3.81 43.52.4227.0 5.94 35.5 3.63 44.0 2.3327.5 5.81 36.0 3.55 44.52.2628.0 5.61 36.5 3.49 45.02.2528.5 5.45 37.0 3.40 45.52.2329.0 5.33 37.5 3.32 46.02.1459Table 4.1 (continued)Energy Oscillator Energy OscillatorEnergy Oscillator(eV) Strength (eV) Strength(eV) Strength(10-2eV-1) (102eV1) (102eV1)46.5 2.04 63.0 1.14 83.00.59847.0 1.97 64.0 1.11 84.0 0.56947.5 2.00 65.0 1.08 85.0 0.55748.0 1.92 66.0 1.05 86.0 0.54048.5 1.90 67.0 1.01 87.0 0.52949.0 1.89 68.0 0.968 88.0 0.50849.5 1.75 69.0 0.926 89.0 0.49150.0 1.77 70.0 0.912 90.0 0.47551.0 1.68 71.0 0.869 91.0 0.46452.0 1.63 72.0 0.850 92.0 0.44853.0 1.56 73.0 0.822 93.0 0.42954.0 1.52 74.0 0.785 94.00.42155.0 1.48 75.0 0.757 95.0 0.41256.0 1.43 76.0 0.735 96.0 0.39757.0 1.40 77.0 0.708 97.0 0.38858.0 1.37 78.0 0.698 98.0 0.39359.0 1.43 79.0 0.669 99.0 0.37060.0 1.61 80.0 0.652 100.0 0.36061.0 1.18 81.0 0.632 101.0 0.34162.0 1.11 82.0 0.612 102.0 0.35060Table 4.1 (continued)Energy Oscillator Energy Oscillator Energy Oscillator(eV) Strength (eV) Strength (eV) Strength(1O2eV1) (10-2eV-1) (1O2eV-1)103.0 0.335 136.0 0.168 178.0 0.0856104.0 0.326 138.0 0.162 180.0 0.0824105.0 0.321 140.0 0.155106.0 0.302 142.0 0.147107.0 0.314 144.0 0.144108.0 0.310 146.0 0.138109.0 0.288 148.0 0.136110.0 0.284 150.0 0.130112.0 0.273 152.0 0.125114.0 0.262 154.0 0.123116.0 0.250 156.0 0.118118.0 0.240 158.0 0.112120.0 0.232 160.0 0.109122.0 0.219 162.0 0.106124.0 0.211 164.0 0.106126.0 0.204 168.0 0.0998128.0 0.194 170.0 0.0980130.0 0.187 172.0 0.0932132.0 0.181 174.0 0.0916134.0 0.173 176.0 0.0893o (Mb) = 1.0975 x102-eV161are “recommended values”of the absolute photoabsorption(photolonization) oscillatorstrengths of helium (opentriangles) reportedin the compilation by Marr andWest[471.The values compiledInreference [47] were obtained byMarr and West asfollows: Variousopticalmeasurements of the photoionizationcross sections of helium Indifferentenergy ranges havebeen reported by differentgroups using opticalmethods [45,101,1021. West andMarr [103] have alsothemselvesmeasured the photoionizatlonof helium in the340—40A (35—3 10eV)range using synchrotronradiation. There aresome slight discrepanciesbetween the different datasets in some energyranges. A criticalevaluation of the various crosssection measurementswas carried out[103] by givinga weight to the variousdata sets according to criteriasuchas the scatter of data points,performance andquality of themonochromator used .. .. etc. Then all the data wascombined and the“best values” wereobtained by fitting polynomialsto the weighed datapoints. The resultingabsolute photoionizationcross section data forhelium and also forother noble gases in the vacuumUV and soft x—rayregions were then tabulated [471.It can be seen fromfigure 4. 1 that the presentlyreported BetheBorn converted, TRK sumrule normalised, low resolutiondipole (e,e)results are generally in goodquantitative agreement withthe absolutephotoabsorption data recommendedby Marr and West [47], fromaconsideration of a range ofpublished results. Itshould be noted that thedipole (e,e) and directphotoabsorption techniquesare physicallydifferent and also that theassociated methods of obtainingthe absolutescales are completelydifferent. The goodagreement therefore providesconvincing proof of thevalidity of the Bethe—Borntheory and the62quantitative equivalence of the dipole (e,e) and photoabsorption(photolonization) methods at leastin the continuum region. In theregion near 60 eV the dipole (e,e) datashow evidence of the well knowndouble excitation resonances of helium whereas the Marrand West data[47] were obtained by fitting a smooth curve through the resonanceregion. Notwithstanding the excellent overall quantitativeagreementsome small differences in shape are apparent. In particular,the Marrand West data [47] are slightly below and slightly abovethe present datain 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 (crosssection) calculations for helium recently reported by Fernleyet aL. [9](solid line). The calculated data [9] have been shifted up in energyby0.280 eV as the first ionization energy of helium calculated by Fernleyetal. [9] is 0.280 eV lower than the accurately known spectroscopicvalue(24.59 eV). It can be seen that the oscillator strength calculations[91 arein excellent agreement with the present dipole (e,e)measurements.Similar calculations were reported earlier by Cooper[104] and by Belland Kingston [105].The presently obtained low resolution dipole (e,e) measurements(table 4.1, figure 4.1) have been used to obtain the Bethe—Bornconversion factor(BHR) for the high resolution spectrometer and fornormalization of the high resolution spectrum of helium (at 30 eV). Thehigh resolution oscillator strength results are presented in the followingsection.634.2.2 High ResolutionOptical Oscillator Strength MeasurementsforHelium4.2.2.1 The DiscreteTransitions1S—’nP(n=2 to 7)Using the high resolution electronenergy loss spectrometer.electron energy loss spectra ofhelium were obtained at an Impactenergyof 3000 eV in the energyloss range 20—60 eV at a resolutionof 0.048 eVFWHM and in the range20—100 eV at resolutions of0.072, 0.098, 0.155and 0.270 eV FWHM. The data havebeen processed using theprocedures outlined in section3.3. The intensity of the high resolutionelectron spectrum at eachenergy loss in the smooth continuumregionabove 25 eV was divided by the absoluteoptical oscillator strengthsmeasured by the LR dipole(e,e) spectrometer (see section 4.2.1,table4.1 and figure 4.1). This quotientprovided a relative Bethe--Bornconversion factor (BHR, see figure 3.3)for the high resolution instrumentin the energy range above25 eV. In order to extend this Bethe—Bornfactor to the excitation regionbelow 25 eV, the quotienthas been fittedto a suitable function (which effectivelyrepresents the Bethe—Borncorrection factor for the HR spectrometer)over the energy range 28-60eV, which can then be extrapo1atedto lower energy. This fittingand theextrapolation must be done verycarefully if correct experimentaldipoleoscillator strengths are to be obtainedin the discrete excitationregiondown to 21 eV for heliumand to even lower energies (5 eV)for otheratoms and molecules. Inparticular the effects of finiteangular resolutionabout the forward scatteringdirection must be properlyaccounted for inthe Bethe—Born conversionfactor if it is to be accurateover the long64extrapolation down to 5 eV. Therefore theeffects of angular resolutionmust be accounted for in someway in the fitting function[14]. In thereal situation of finite acceptance angles,the Bethe—Born conversionfactor has been derived as shownin equation 2.28. At sufficiently highimpact energy andk0—k, equations2.24 and 2.28 can be combined togived2Oe(E)/2— /dEdQ— a1 100A— 0/ —ALA I +(4.1)df(E)/ x/dEwhere F(E) is equal to 1 /B(E) and a is a constant.Thus we might expecta function of the form of the right hand side ofequation 4.1 to fit theratio of the high resolution electron energy lossspectrum to the absoluteoptical oscillator strength. While the use of equation4.1 gave a quitereasonable fit, in practice a further improvedfit to the ratio F(E) in thecontinuum (28—60 eV) was obtained by addingan energy dependent termto the constant a on the right hand side of equation4.1 to gived2e(E)/2F(E)= /dEdQ= a + cEin 1 + (4.2)dfo(E)/E/dEIn this equation a and c are constants. (F(E) is equal to 1/Bj —see figure 3.3). Values of a, c and00were determined from a leastsquares best fit. The value of the half angle0was found to beapproximately 0.17 degrees. At each resolutiona function of this form65fitted the data very well over the range 28—’60 eV and was extrapolatedto lower energies in order to convertd2cTe(E)/dEdQ for the discretetransitions in helium to a relative optical oscillator strength scale. Theeffectiveness of the extrapolation method employed has been examinedby comparing the shapes of the photoabsorption oscillator strengthcurves down to 5 eV for a range of molecules(02 [42],NO [441 and alsoN20, CO2 and H20 [1061), obtained using the high resolution dipole (e,e)method, with those obtained earlier using the low resolution dipole (e,e)method [30]. The oscillator strength distributions of the high and lowresolution dipole (e,e) spectra are consistent for each molecule forenergies down to 5 eV when the differences in energy resolution areconsidered. Further confirmation of the accuracy of the high resolutionBethe—Born conversion factor at low energies is provided by the very goodagreement between the high resolution dipole (e,e) and photoabsorptionmeasurements for02 [421and NO [441. It should be noted that the exactform ofBHJchanges for the different resolution settings of thespectrometer. TheseBi-mfactors will be used for future oscillatorstrength measurements of other atoms and molecules.The high resolution energy loss spectra of helium were multipliedby the appropriate BHR function in order to obtain relative opticaloscillator strength spectra which were then normalised in the continuumregion at 30 eV using the absolute data of table 4.1, as determined usingthe low resolution spectrometer. A typical result at an energy resolutionof 0.048 eV FWHM is shown in figure 4.2, which is the first reportedabsolute optical oscillator strength spectrum of helium covering therange n=2—7 of the optically allowed discrete transitions (11S—nP)preceding the first ionization threshold. Over the near threshold-4•>a.)‘Stoa)1U)I0C.)U)0C)C0.—C.)V11)U)U)0‘-4C.)0‘-40I6620 2224 2628 30Photon energy (eV)Figure 4.2:Absolute dipole oscillatorstrengths for helium measured by the highresolution electron energyloss spectrometer from 20—30 eV (FWHM=0.048eV). Solid line above theionization edge on X8 spectrum isphotoabsorption data fromMarr and West [47] and Fernley et al.19].67continuum region (24.6—30 eV) there is excellent quantitative agreement(see Insert to figure 4.2) between the present work and thephotoabsorption measurements compiled by Man and West [47] andalsothe continuum calculations reported by Fernley et al. [91 (the dataofreferences [9,47] are both represented by the samesolid line).Transitions up to n=7 for the n1P series are resolved.A very small peakbarely visible at 20.6 eV represents a contributionfrom the dipoleforbidden 1l5_.2 istransition due to the finite (but very small)momentum transfer of the dipole (e,e) experiment. This non—dipolecontribution is less than 0.5 percent of the 21P peak.Integration of the peak areas in each spectrum, such as that infigure 4.2, provides a measure of the absolute oscillator strengthsforeach discrete transition in the1S—’n’P series. An analysisof thespectra obtained at a series of different energy resolutionsresults in thevalues shown in table 4.2. The uncertainties quoted representthescatter in the measurements made at differentresolutions. The absoluteuncertainty is estimated to be —5%. Other than the relativevalues forn=3 and 4 reported by Jongh and Eck [62], previously reportedwork(see table 4.2) has been confined to absolute values for n=2 anda fewmeasurements [19,57,64,85] for n=3. The present data whichextend ton=7 represent the first measured values above n=3.Various othercalculated and measured values for the helium 1 seriesare shownin table 4.2. Immediately it can be seenthat the present high resolutiondipole (e,e) measurements are in excellent agreement across therange ofn values with the calculations for heliumreported by Schiff and Pekeris[4], Fernley et al. [9] andothers [3,5—8,54] (see table 4.2). The earlierelectron impact measurements of Lassettre et al. [68] for n=2 andofTable4.2Theoreticalandexperimentaldeterminationsoftheabsoluteopticaloscillatorstrengthsforthe(11S—’nlP,n=2to7)transitionsinheliumtOscillatorStrengthforTransitionfrom11StoTotaltoIonization2’P31p41p51p61P7’PThresholdA.Theory: Fernley,TaylorandSeaton(1987)[910.28110.074340.030280.015240.0087340.005469Schiff,PekerisandAccad(1971)[810.27620.0730.0300.015Welss(1967)[710.27600.07320.0303Greenetal.(1966)[510.275620.072940.029590.014840.008460.00525DalgarnoandParklnson(1966)[610.2760.07340.02990.01510.00860.00540.424Wiese,SmithandGlennon(1966)[5410.27620.07340.03020.01530.008480.00593SchiffandPekeris(1964)1410.027620.00734DalgarnoandStewart(1960)[310.2700.07460.03040.01530.00878C)Table4.2(continued)OscillatorStrengthforTransitionfrom11StoTotaltoIonization21P31P41P51P61P71PThresholdB.Experiment Presentwork(HRdipole(e,e))TsurubuchletaL(1989)[641(Selfabsorption)WesterveldandEck(1977)1631(Selfabsorption)Backxetal.(1975)[851(Electronimpact)*BurgerandLurio(1971)1571(Lifetime:Level-crossing)JonghandEck(1971)[621(Selfabsorption)#Lassettreetal.(1970)[681(Electronimpact)MartinsonandBickel(1969)[581(Lifetime:Beamfoil)0.0152(0.0003)0.00892(0.0005)0.00587(0.0003)0.0741(0.0007)0.071(0.003)0.073 0.073(0.005)0.076(0.004)0.0303(0.0007)0.029(0.002)0.431(0.006)0.4210.280(0.007)0.273(0.008)0.262(0.018)0.276 0.275(0.007)0.276 0.269(0.01)0.27(0.01)0) CDTable4.2(continued)OscillatorStrengthforTransitionfrom11toTotaltoIonization21P31P41P51P6’P71PThresholdB.Experiment:(continued)FryandWllliams(1969)156)0.273(Lifetime:Hanleeffect)(0.011)LlnckeandGriem(l.966)(59J0.26(Plasmasemissionprofile)(0.07)KorolyovandOdintsov(1964)16010.28(Beamemissionprofile)(0.02)0.26(0.012)KuhnandVaughan(1964)16110.37(Resonancebroadeningemissionprofile)(0.03)Gelger(1963)11910.3120.0898(Electronimpact)(0.04)(0.006)+EstimateduncertaintiesInexperimentalmeasurementsareshowninbrackets.*Relativemeasurementsnormaltzedtothetheoreticalvalueforn=2reportedbySchiffandPekeris(1964)141.#Relativemeasurementsnormalizedtothetheoreticalvalueforn=2reportedbyWeiss(1967)[7).C71Backx et al. [85] forn=3 respectively,are reasonably consistentwith thepresent more comprehensivework. The slightlylower value obtainedforn=2 by Lassettreet al. [68] may reflectthe difficulties of extrapolationtoK2=O (see section 1.4).The electron impact datafor n=2 and 3 reportedby Geiger [19]show large departures fromthe present data andalsofrom the calculations[3—9,54]. This couldpartly be due to thenormalization procedureused by Geiger [191,which was based onelasticscattering values, butas Lassettre [681 haspointed out the ratioof thevalues for n=2 and 3reported by Geiger showsa significant departurefrom the ratio of thecalculated oscillatorstrength values[3—9,54]. Thevarious optical measurementsare in almost all casesrestricted to n=2[56,58—61,63] and ingeneral are reasonablyconsistent with the presentmeasurements andwith theory [3—9,541.The Hanle effectmeasurementfor n=2 reported byFry and Williams [56]and the level crossinglifetimemeasurements reportedfor n=2 and 3 by Burgerand Lurio [57]wouldseem to be the mostaccurate opticaldeterminations. Tothe best of ourknowledge, noBeer—Lambert law photoabsorptionmeasurementshavebeen reported for thehelium discrete transitions,probably due to thebandwidth!un ewidth difficulties or“line—saturation” effectsdiscussed insection 2.3. Such effectswould be particu1arly difficultto avoid for theintense and extremelynarrow lines in thehelium resonanceseries. Theself—absorption methodused by Jongh andEck [62], Westerveldand Eck163] and Tsurubuchiet al. [64] is notsubject to “line saturation”effectsbut unfortunately likemost other optical methodsit is restricted in itsapplication to the lowern values. A furtherinteresting check onthepresently reported datais the integrated oscillatorstrength for thediscrete region up tothe first ionizationthreshold. The valueof 0.43172obtained in the present workis in good agreementwith earlier estimatesof 0.424 [6], 0.421 [85] and0.427 [851.4.2.2.2 The AutoionizingExcited State ResonancesThe energies and profiles ofthe well—known autoionizingdoublyexcited state resonancesof helium in the 5 9—72 eVenergy region havebeen previously studied insome detail both experimentally[94—97,107]and theoretically [98—100,108].In the present work,this regioncontaining the autoionizingresonances was remeasuredusing the HRdipole (e,e) spectrometerat medium resolution. Bydividing the HRelectron energy lossspectrum at each energyloss in the smooth regionsof the continuum by the absoluteoptical oscillator strengthmeasured bythe LR dipole (e,e) spectrometer(see section 4.2.1, table 4.1and figure4.1) valuesof BHR in the energy regionof the autolonizingresonanceswere obtained. A fittedcurve through these pointspermittedinterpolated valuesofBHRto be obtained in acontinuous form throughoutthe resonance region. TheBethe—Born convertedrelative opticaloscillator strength spectrumwas norma1ised in thesmooth continuumregion at 75 eV usingthe absolute photoabsorptionoscillator strengthdata from table 4.1,as determined by theLR dipole (e,e) spectrometer.The present results forthe absolute optical oscillatorstrengthsthroughout the region ofthe autoionizing doublyexcited state resonancesbelow the He(2s) andHe(3s) thresholds areshown in figures 4.3(a)and(b) respectively.In figure 4.3(a) theabsolute oscillator strengthsfor the autoionizingresonances below theHe(2s) threshold calculatedby Fernley etat. [9]fl:273[Hel(sp,2n+)lpo3 45[60.050.040.030.020.010 000.0150.0100.00564 66>-‘C,)CC.)Cl)CC.)Figure 4.3:54320C.)1VCl)Cl)ci,0C0I-I015Ci)001.00.5(b)[He(Sp,33+)1P0(sp,34+)1P°69 70 7172Photon energy (eV)Absolute dipole oscillatorstrengths for helium in theautolonizingresonance regions measuredby the high resolutionelectron energy lossspectrometer. (a)in the energy region 58—66 eV;solid circles are thiswork,solid line is data from Fernleyet al. 19] (convolutedwith the presentexperimental bandwidthof 0.115 eV), (b) in theenergy region 69—72 eV;solid circles are this work,solid triangles aredata of Kossmannet al.197],open squares are data of Lindleet al. [96], solid lineIs theory. Gersbachberet al. [99].74(solid line) have beenconvoluted with a Gaussianof 0.115 eV FWHM,which was used torepresent the experimentalenergy resolution. Theenergy scale of the datacalculated by Fernleyet al. [9] has beenshifted by+0.280 eV to give a correctenergy scale, It canbe seen that there isgenerally excellent agreementin both the shapes andmagnitudes of theresonances between theconvoluted calculationsof Fernley et al. [9](solidline) and the presentexperimental work(dots) except for the minimumof the (sp,22÷)IPOstate. Slight differences inthe energies ofthemaxima of the resonancesare also observed.The energies of the maximaof the (sp,2n+)iporesonances for n=2to 5 have been determinedIn thepresent work to be 60.150,63.655, 64.465 and 64.820eV respectively.These values are ingood agreement withprevious experimentaldeterminations [94,95,97,98,100].The autoionizing resonances(sp,33+) and (sp,34+)1P° were alsoobserved in the presentwork. In figure 4.3(b),the present data (dots)iscompared with other experimentalresults by Lindle et al.[96] (opensquares) and by Kossmannet al. [97] (solid triangles)both of whomnormalised their resultsat 68.9 eV using the Marrand West tabulateddata [47]. The solid lineon figure 4.3(b) representstheoretical valuescalculated by Gersbacheret al.[991.4.3 ConclusionsThe present high resolutiondipole (e,e) measurementsof opticaloscillator strengths forthe discrete excitationtransitions (11S—n’P,n=2—7), the autoionizingdoubly excited state resonancesand also thephotoionizationcontinuum have considerablyextended the rangeof75measured absolute oscillatorstrength data for the photoabsorptionofhelium. The presentlyreported results are all inexcellent quantitativeagreement with state of theart quantum mechanicalcalculations carriedout using correlatedwavefunctions [4—9] and areconsistent with mostoptical and other measurementsfor those few transitionswhere previousexperimental data were available.These findings confirm thevalidity ofthe Bethe—Born approximationand the suitability of thehigh resolutiondipole (e,e) methodusing TRK sum rule normalizationfor generalapplication to the measurementof optical oscillator strengthsfordiscrete electronic excitationsand ionization inatoms and molecules.The dipole (e,e) methodtherefore provides a versatileand accuratemeans of oscillator strengthmeasurement acrossthe entire valence shellregion at high resolution and doesnot suffer from the problems of“linesaturation” (bandwidth)effects that can complicateBeer—Lambert lawphotoabsorption studiesfor discrete transitions.76Chapter 5Absolute Optical OscillatorStrengths forthe Electronic Excitationof Neon5.1 IntroductionAbsolute optical oscillatorstrengths for discreteand continuumelectronic excitation of neonare important quantitiesin areas such asradiation physics, plasma physicsand astrophysics. For instance,Auerand Mihalas [1091 have usedNe I oscillator strength datato re—evaluatethe abundances ofneon in the B stars. Recently therehas also beenstrong interest in the energylevels and oscillator strengthsof neon—likesystems because of theirapplication in the developmentof soft X—raylasers [110]. Discrete oscillatorstrengths also provide asensitive test foratomic structure calculations,since the simple LS and j—jcouplingschemes are not strictly applicablefor neon and some sortofintermediate coupling schememust be used instead [111].In contrast tothe situation for helium,the photoionization cross sectionmaximum ofneon is not at threshold,showing a significant departurefrom hydrogenicbehavior due to more prominentelectron correlations. Cooper [104]hascalculated the oscillatorstrength distribution for theouter atomicsubshefl of neon by assuming anelectron moving in an effectivecentralpotential similar to theHartree—Fock potential. McGuire[112],approximating the Herman—Skilimancentral field with a seriesof straightlines, has computed the photoionizationcross section of neon withthecontinuum orbitals calculatedfrom the approximate potential.Kennedy77and Manson [1131, utilizing Hartree—Fock wave functionswith completeexchange, Luke [1141. employing a multi—configuration close couplingmethod for the wavefunctions, Burke and Taylor [1151, using the R—matrix theory, and Amus’ya et al. [116] applying the RPAE(random—phaseapproximate with exchange) method have also calculated photolonizationcross sections for neon. Relativistic random—phase approximation(RRPA) calculations carried out by Johnson and Cheng [1171showed thatrelativistic effects are small in neon and gave results in good agreementwith the non—relativistic RPAE results of Amu&ya et al. [116].Parpia etal. [118] have also reported the photoionization crosssections of theouter shells of neon using the re1ativistic time—dependent local—densityapproximation (RTDLDA) method, which is closely related to the RRPAmethod of Johnson and Cheng [1171. Although thecalculated values aremuch improved with the inclusion of electroncorrelation, somediscrepancies (>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 photolonizationmeasurements for neon in the continuum performed using the Beer—Lambert law [45,47,102,103,119—1221 show good agreementwith eachother in terms of the shape (i.e. relative cross section). However, thevarious reported values of the absolute cross sections in the continuumshow substantial differences (—10%), probably due todifficulties Inobtaining sufficiently precise measurements of the sampletarget densityin a ‘windowless’ far UV system. In addition, inadequatelyaccounted forcontributions from stray light and/or higher order radiation willaffectmeasured cross sections. Lee and Weissler [119], and Ederer and78Tomboulian [120] have measured the photoabsorption crosssection ofneon using discharge lamp line sources in the energyranges 15.5—54,and 20—155 eV respectively. Lee and Weissler [119] recordedtheabsorption photometrically in a grazing incidence vacuum spectrograph.Ederer and Tomboulian [120] have made measurements combiningtheconventional photographic recording method with a Geiger—Mullercounter for selected wavelengths. Samson [45,121,122] hasdesigned anextremely effective double ion chamber technique which iscapable ofmeasuring very accurate photoionization cross sections usingeither lineor continuum sources. Using this apparatus Samson [45,121,122]hasreported measurements for neon in the range 21.6—310 eV.Saxon [1241reviewed the limited neon photoabsorption data available in 1973andprovided a sum rule analysis which suggested that the measuredcrosssections were reasonably accurate. Wuilleumier and Krause[125] derived2p, 2s and is subshell partial photoionizationcross sections bycombining photoelectron branching ratio studies using x—ray line sourceswith existing total photoabsorption measurements. In additioncontributions from multiple ionization were estimated [125]. With theadvance of synchrotron radiation (SR), an intense and continuous lightsource became available for measuring the photoionization crosssectionsof atoms and molecules up to high energies. However with SRsourcesvery careful work is required to correct for the effects of contributionsfrom stray light and higher order radiation on absolute cross sectionmeasurements [126—1281. Watson [102] obtained photoionizationcrosssections for neon in the 60—230 eV photon energyrange. West and Marr[103] not only used synchrotron radiation to make absolute absorptionmeasurements for neon over the range 36—310 eV, but also gave acritical79evaluation of existing publishedcross section data and obtainedrecommended weighted—averagevalues [47] throughout the vacuumultraviolet and X—ray region.Electron impact based techniques[21,23,1231have also been employed toobtain photoionization crosssections of neon. By approximatingthe generalized oscillator strength(f(K,E) where K=momentumtransfer and E=energy) as theopticaloscillator strength U(E)) usingan impact energy 500—1000eV andcollecting the inelasticallyscattered electrons at small angles,Kuyatt andSimpson [123] converted the electronenergy loss spectrum ofneon (upto 100 eV energy loss) to arelative photoabsorption cross sectioncurve.Using high electron impactenergy (10 keV) and the calculatedscatteringgeometry of the beam toobtain the relative Bethe—Born factor,electronenergy loss results at small momentumtransfer have been convertedtorelative photoionization cross sectionsfor neon by Van der Wiel [21].Vander Wiel and Wiebes [23]have also studied multiple photoionizationofneon using the same method. Therelative optical oscillatorstrengthdata obtained by the electron impactmethods described above werenormalized using a literaturevalue of the absolute photoabsorptioncrosssection at a single energy.Apart from the difficulty ofmeasuring an accurate sampledensity,Beer—Lambert law photoabsorptionmeasurements for the discreteexcitation region of neon may alsobe subject to serious errors dueto so—called “line—saturation” (i.e.bandwidth) effects [36,37,46,72] (seechapter 2) since the neon valenceshell (2p) electronic transitionshaveextremely narrow naturalline—widths [65, 129—137]. Theseeffects aremost significant when thecross section is large and where thebandwidthof the incident radiationis greater than the naturalline—widths of the80spectral lines being measured. In such situations the oscillatorstrengths(cross sections) may be much smaller (by as much as anorder ofmagnitude) than the true values unless careful measurementsare made asa function of pressure [37,46]. Detailed discussions and quantitativeassessments of “line saturation” effects have been givenin refs. 137,461.Other experimental methods for optical oscillator strengthdeterminationwhich avoid the “line saturation” problemsinclude profile analysis[129,1381, self absorption [62,139,140], total absorption [65], and lifetime measurements [130—137], as well as the completely independentapproach afforded by electron impact basedmethods using electronenergy loss spectroscopy[20,36,37,141,1421. These various optical andelectron impact methods have been used in earlier reported worktoobtain absolute optical oscillator strengths for neon in the discreteregion, but the measurements have beenmainly restricted to the 16.67 1eV (f1) and 16.848 eV (f2) resonance lines correspondingto the(2s22p6—’2s5(P3/2,/2)3s) transitions. Korolevet al. [1291 measuredthe transition probability of the f2 line from the natural broadeningprofile, while Lewis [138] studied the pressure broadeningprofile andgave the oscillator strengths for both the f1 and f2 resonance lines.Therelative self—absorption method was used by Jongh and Eck[62] tomeasure the oscillator strength of the f2 resonance line using thecalculated 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 thef1 and f2resonance lines. Aleksandrov et al. [65] employed the total—absorptionmethod to obtain oscillator strengths for various lines in the 20—8Onm(15.5—62 eV) range. Radiative lifetimes for some of the resonance81transitions of neon have been determined using: a) a pulsed electronsource for excitation and studying the resulting photon decay curve[130,1311; b) the beam foil method [132, 1331; c) the level—crossingtechnique [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 obtainedlifetimes can then be converted to the optical oscillator strengths for therespective transitions. In electron impact based studies, Geiger[20]obtained the sum of the absolute photoabsorption oscillator strengths forthe f1 and f2 resonance lines at low resolution by measuring both theelectron elastic scattering cross section and the small—angle inelasticscattering cross section at very high impact energy (25 keV) andnormalising on known absolute values of the elastic scattering crosssection. Later, Geiger [141] obtained the ratio (f2/f1)of the oscillatorstrengths of the resonance lines using a high resolution electron energyloss spectrometer, and by combining the values obtained from the lowresolution spectrometer with this ratio he obtained values for theindividual oscillator strengths for the two resonance lines. The electronimpact method has also been employed by Natali et al. [142] to measurediscrete optical oscillator strengths of neon. The unpublished results ofNatalietal. [142] are quoted in refs. [139,143].A variety of discrete oscillator strength calculations have beenreported for neon. Cooper [104], employing a one electron centralpotential model, Kelly [144], using the Slater approximation to theHartree—Fock method, and Amus’ya et al. [145], applying the RPAEmethod, have calculated the oscillator strengths for the transitions fromthe ground state of neon to the2s22p5(P312,112)nsand nd states. Other82calculations of the oscillator strengths for individual transitions from theground state to various2s22p5(P3/)nsand nd states, and also to2s22p5(P1/2)ns’ and nd’ states, have likewise been reported, but In mostcases these are only for the transitions to the2s22p5(P3/2)3s (fi)and2s22p5(P1/2)3s’ (f2) states. The oscillator strengths of the f1 and f2resonance lines were calculated by Gold and Knox [1461 using theHartree Fock equation based on experimental energies and dipole matrixelements computed from theoretical atomic wavefunctions. Gruzdev[111], using the techniques of intermediate coupling and values of thetransition integral obtained from the Coulomb approximation, hasreported the oscillator strengths for the f1 and f2 resonance lines. Aymaret al. [1471 calculated Ne I transition probabilities and lifetimes with theintroduction of an effective operator for the angular part of thewavefunctions and a parametrized central potential for the radial part ofthe wavefunctions. Gruzdev and Loginov [148] carried out a calculation ofthe radiative lifetimes of several levels of neon with a many—configurationapproximation using Hartree—Fock self—consistent field wavefunctions.Albat and Gruen [149] have reported the excitation cross section of thelowest resonance level of neon using a Cl calculation based on theorthogonal set of orbitals obtained from a ground state Hartree—Fockcalculation. The time dependent Hartree—Fock equations were alsoemployed by Stewart [150,151] to study the excitation energies andbound—bound oscillator strengths for atoms isoelectronic with neon overa wide range of energies. Aleksandrov et al. [65] not only reportedmeasurements for the discrete oscillator strengths of neon by the total—absorption method, but have also calculated oscillator strengths for thesame discrete lines of neon based on an intermediate—coupling scheme83with the electrostatic, spin—orbit, and effective Interactions Included inthe energy matrices. An examination of the various experimental[62,65,129—1401 and theoretical [104,111,144—151] studies reveals aconsiderable spread in oscillator strength values for a given transition,even in the case of the Intense f1 and f2 resonance lines of neon.Recently, we have reported a new, highly accurate, electron Impactmethod [36,37] (see chapters 2—4) for obtaining absolute photoabsorptionoscillator strengths for discrete excitation processes over a wide spectralrange at high resolution. In chapter 4, helium was used to check theaccuracy of the new high resolution method [37]. Excellent agreementwas found between experiment and theory for the He1S—’nP(n=2—7)series as well as in the photoionization continuum and doubly excitedstate resonance regions [36,371. The new high resolution dipole (e,e)method is now applied to the electronic transitions for neon. In thischapter, we also report measurements of the absolute photoabsorptioncontinuum oscillator strengths up to 250 eV. The absolute scale has beenobtained by TRK sum rule normalization and is thus completelyindependent of any direct optical measurement. The absolute(photoabsorption) oscillator strengths for the dipole—allowed electronictransitions of neon from the 2p6 subshell to lower members of the2.s22p5ns and 2s22p5nd(2P312,112)manifolds have been obtained fromhigh resolution dipole (e,e) spectra of neon normalised on the lowresolution results in the smooth continuum region. The presentmeasurements are compared with other published experimental andtheoretical data. Absolute optical oscillator strengths have also beenobtained in the energy range 43—55 eV in the region of the Beutler—Fanoautoionization resonance profiles arising from processes involving single84excitation of a valence 2s electron as well as processes due to doubleexcitation of 2p electrons.5.2 Results and Discussions5.2.1 Low Resolution Measurements of the PhotoabsorptionOscillator Strengths for Neon up to 250 eVA relative photoabsorption spectrum of neon was obtained byBethe—Born conversion of an electron energy loss spectrum measuredwith the low resolution dipole (e,e) spectrometer from 15.7 to 250 eV.This was then least squares fitted to the functionAE—Bover the energyrange 120—250 eV, and extrapolation of the formula gave the relativephotoabsorption oscillator strength for the valence shell from 250 eV toinfinity. The fit gave B= 1.959 and the fraction of the total valence shelloscillator strength above 250 eV was estimated to be 17.6%. The totalarea was then TRK sum rule normalized to a value of 8.34, correspondingto 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 theresulting absolute optical differential oscillator strengths for thephotoabsorption of neon below 250 eV. Also shown in figure 5.1(a) arepreviously reported theoretical and experimental data from the literature[23,45,102,103,112,113,116,118,121,152]. Figure 5.1(b) is anexpanded view (on an offset vertical scale) of the spectrum in the energyregion 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 the85Figure 5.1: Absolute oscillator strengths for the photoabsorption of neonmeasured bythe low resolution dipole (e,e) spectrometer (FWHM=1 eV). (a) 15.7—250 eVcompared with other experimental [23,45,47,102,103,121,152] andtheoretical [112,113,116,118] data. (b) Expanded view ofthe 20—60 eVenergy region compared with other experimental [23,45,47,103,121,152] andtheoretical [112—116,118] values. Note offset vertical scale.(a)[Ne]0AI*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]cv0C)IC—.-C.)0C.)01816141210864201098765450 10018161412108640C.)20C)0087200 250CC(b)INelC.x.0D••A• Present work LR dipole (ce)West & Mcrr [47,103]o Samson[45121]Van der Wiel & Wiebes[23)*Henke et al. [152]xBurke & Taylor [115]CLuke [114]Amusya et a!. [106]—— Kennedy & Monson [113)- —— McGuire [112]Parplo et a!. [118]6520 25 30 35 40 45 50 55Photon energy (eV)6086absolute photoabsorption oscillator strengths for neon obtained In thepresent 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 presentlyreported Bethe—Born converted, TRK sum rule normalized resultsobtained from the low resolution spectrometer are generally in quitegood quantitative agreement with the measurements of Samson [45,121],the compilation data of Henke et al. [152] and the earlier electron impactbased measurements by Van der Wiel and Wiebes [23]. The data ofSamson [45,121] and Henke et al. [152] are slightly higher than thepresent work in the energy region 60—150 eV, while the results reportedby Van der Wiel and Wiebes [23] are lower at energies above 180 eV. Thephotoionization oscillator strengths for neon measured by Watson [102] Inthe energy range 60—230 eV are larger than all other reportedexperimental data below -200 eV but are in better agreement at higherenergies. West and Marr [103] measured photoionization cross sectionsfor neon in the energy range 36—3 10 eV using synchrotron radiation andgave a critical evaluation of several published cross section data (includingthe data of Samson [45,121] and Watson [102]) which they used to obtain“best weighted—average” values [47] throughout the vacuum ultraviolet andX—ray spectra1 regions. However the West and Marr measured andcompiled values [47,103] are significantly higher than the present dataand than the other experimental data from Samson [45,121], Henke etal. [152], and Van der Wiel and Wiebes [231 in the energy range 35—200eV.The calculated photoionization cross sections for neon generallyshow great differences in absolute values between calculations using thedipole—length and dipole—velocity forms. The dipole—length data have87Table 51Absolute differential optical oscillator strengthsfor neon obtained usingthe low resolution (1 eV FWHM) dipole (e,e)spectrometer (2 1.6—250cv)Energy Oscillator Energy OscillatorEnergy Oscillator• (eV) Strength (eV) Strength(eV) Strength(10-2eV-1) (10-2eV-1) (102eV-1)21.6 5.75 23.3 6.52 25.07.2221.7 5.88 23.46.73 25.5 7.4221.8 5.82 23.5 6.6926.0 7.4621.9 5.86 23.6 6.77 26.5 7.5822.0 5.98 23.7 6.8027.0 7.6722.1 6.00 23.8 6.8227.5 7.7622.2 6.05 23.9 6.74 28.07.6922.3 6.10 24.0 6.97 28.57.9522.4 6.15 24.1 7.02 29.07.9922.5 6.22 24.2 7.05 29.57.9822.6 6.25 24.3 7.07 30.08.0922.7 6.35 24.4 7.07 30.58.0322.8 6.40 24.5 7.11 31.08.0522.9 6.47 24.6 ‘7.13 31.58.1323.0 6.60 24.7 7.1432.0 8.0823.1 6.55 24.8 7.1832.5 8.0823.2 6.55 24.9 7.1433.0 8.0688Table 5.1 (continued)Energy Oscillator Energy OscillatorEnergy Oscillator(eV) Strength (eV)Strength (eV) Strength(10-2eV-1) (102eV1)(102eV-’)33.5 8.10 43.57.32 57.0 6.1734.0 8.00 44.07.29 58.0 6.0834.5 8.14 44.5 7.2759.0 5.9935.0 8.08 45.0 7.4560.0 5.8635.5 7.96 45.5 7.3261.0 5.8336.0 7.88 46.07.06 62.0 5.7136.5 7.83 46.5 7.0163.0 5.6937.0 7.90 47.0 6.9664.0 5.5937.5 7.92 47.5 7.0465.0 5.4338.0 7.86 48.0 6.9166.0 5.3538.5 7.80 48.56.91 67.0 5.3139.0 7.73 49.0 6.8968.0 5.2439.5 7.76 49.5 6.7869.0 5.1340.0 7.72 50.0 6.7570.0 5.0340.5 7.62 51.0 6.7071.0 4.9941.0 7.52 52.0 6.5972.0 4.9341.5 7.50 53.0 6.4973.0 4.8842.0 7.42 54.0 6.3774.0 4.7842.5 7.39 55.0 6.2975.0 4.7343.0 7.35 56.0 6.3076.0 4.59.89Table 5.1 (continued)Energy Oscillator Energy Oscillator Energy Oscillator(eV) Strength (eV) Strength (eV) Strength(102eV1) (1O2eV’) (1O2eV1)77.0 4.52 97.0 3.37 117.0 2.3978.0 4.48 98.0 3.25118.0 2.3679.0 4.41 99.0 3.22 119.0 2.4680.0 4.33 100.0 3.19 120.0 2.3681.0 4.28 101.0 3.18 122.0 2.2882.0 4.22 102.0 3.09 124.02.2383.0 4.16 103.0 3.10 126.0 2.1784.0 4.07 104.0 2.99 128.0 2.0985.0 4.06 105.0 2.94 130.0 2.0286.0 3.92 106.0 2.84 132.0 1.9987.0 3.89 107.0 2.83 134.0 1.9388.0 3.84 108.0 2.90 136.0 1.8889.0 3.78 109.0 2.81 138.0 1.8290.0 3.72 110.0 2.71 140.0 1.7791.0 3.65 111.0 2.67 142.0 1.7392.0 3.59 112.0 2.63 144.0 1.6993.0 3.60 113.0 2.59 146.0 1.6294.0 3.51 114.0 2.67148.0 1.5895.0 3.44 115.0 2.58 150.0 1.5796.0 3.46 116.0 2.55 152.0 1.5290Table 5.1 (continued)Energy Oscillator Energy OscillatorEnergy Oscillator(eV) Strength (eV)Strength (eV) Strength(10-2eV)(1O2eV)(1O2eV)154.0 1.46 194.0 0.915234.0 0.649156.0 1.44 196.00.887 236.0 0.635158.0 1.39 198.00.906 238.0 0.614160.0 1.38 200.0 0.857240.0 0.596162.0 1.32 202.0 0.848242.0 0.612164.0 1.31 204.0 0.826244.0 0.595166.0 1.29 206.0 0.823246.0 0.607168.0 1.25 208.00.786 248.0 0.581170.0 1.21 210.0 0.792250.0 0.572172.0 1.16 212.0 0.791174.0 1.14 214.0 0.771176.0 1.13 216.0 0.736178.0 1.11 218.0 0.740180.0 1.08 220.0 0.724182.0 1.06 222.0 0.700184.0 1.00 224.0 0.703186.0 1.00 226.0 0.706188.0 0.981 228.0 0.678190.0 0.971 230.0 0.684192.0 0.929 232.0 0.649o(Mb) = 1.0975x102eVl91better agreement with the experimentalvalues than the dipole—velocitydata. The dipole—length dataof McGuire [112], obtained using theH artree—Fock—Slater approach withthe Herman—Skiliman central field,show good agreement with thepresent experimental values fromthe 2pionization threshold to 35 eV, but aresignificantly higher in theregion35—210 eV. Kennedy and Manson [113],employing Hartree—Fockfunctions with complete exchange,have also reported calculations of thephotoionization cross sections of neonfrom the 2p ionizationthresholdup to 400 eV. Their dipole—lengthdata [113] give lower results belowthe 2s threshold and becomemuch higher at higherenergies whencompared with the present experimentalvalues. Both the McGuire [1121and Kennedy and Manson [113] datashow a lower calculated 2s thresholdenergy than other theoretical [115]and experimental [153,154] work.The dipole—length data calculatedusing a Hartree—Fock core asreportedby Luke [114] (see figure 5. 1(b)) areconsiderably higher than allotherreported experimental and theoreticaldata. The R—matrix theorydipole—length results of Burke and Taylor[115] show good agreement withtheexperimental values at the 2p ionizationthreshold but agreementbecomes worse at higherenergies, although below the 2s ionizationthreshold there is less than 10%difference with the experimentalvalues(note offset intensity scale in figure5.1(b)). Amus’ya et al. [1161,usingthe RPAE method, report veryclose agreement between the dipole—length and dipole—velocity results.However the RPAE calculation [116]shows a shift of several electron—voltsfrom experiment in thephotoionization cross section maximum andalso the energy of the 2sionization threshold for neon. Thepredicted oscillator strengths[116]are also considerably larger thanexperiment in the energy region40—10092eV. Since the valuescalculated by Johnson and Cheng[117] using theRRPA method showgood agreement with thosecalculated by Amus’ya etal. [116] using the non—relativisticRPAE method, onlyvalues fromAmus’ya et al. [116] are shownon figure 5.1. Except inthe region nearthe maximum, the valuescalculated by Parpia et al.[118] using theRTDLDA method show betteragreement with experimentthan the othertheoretical data [112—117].5.2.2 High ResolutionMeasurements of thePhotoabsorptionOscillator Strengths forthe Discrete Transitionsof NeonBelow the 2p IonizationThresholdHigh resolution electron energyloss spectra of neon atresolutionsof 0.048, 0.072 and0.098 eV FWHM in the energyrange 16—26 eV weremultiplied by the appropriate BHRfunctions for the highresolution dipole(e,e) spectrometer (see section3.3) to obtain relativeoptical oscillatorstrength spectra which werethen normalized inthe smooth continuumregion at 25 eV using theabsolute data of table 5.1, asdetermined in thepresent work with the lowresolution spectrometer.Figure 5.2(a) showsthe typical absolute differentialoptical oscillator strengthspectrum ofneon over the range16—26 eV at an energyresolution of 0.048 eV FWHM.Figure 5.2(b) is an expandedview of the spectrum In theenergy region19.5—22 eV showing thedipole—allowed electronic transitionsfrom the2s22p6configuration ofneon to members ofthe2s22p5(P3/2,l/2)nsandnd manifolds. Verysmall peaks, barelyvisible at 18.96 and 20.38eV,represent contributions fromthe dipole forbidden2s22p6—’2s5(P3/2,1/2)3pand 4p transitions respectively.These non—43.9324003002001000C.)U)CU)U)0C.)C0::>.5IC40.4o0.3D.20.10.0Figure 5.2: Absolute oscillator strengths for the photoabsorption of neon measured bythe high resolution dipole (e,e) spectrometer (FWHM=O.048 eV).Assignments are from reference [1551. (a) 16—26 eV. (b) 19.5—22 eV withdeconvoluted peaks shown as dashed lines.201020.5 21.0Photon energy (eV)094dipole transitions which occurbecause of the finite but very smallmomentum transfer(K2<0.Ola.u.) of the dipole(e,e) experiment, are allless than 0.3 percent ofthe f2 peak. The positionsand assignments[155] of thevarious members of thenl and nl’ series are indicatedonfigure 5.2. Above 19eV the peaks have beendeconvoluted as indicated(figure 5.2(b)) to obtain theseparate oscillator strengthsfor the varioustransitions. Since thepeak energies of the nd[ 1/21and nd[3/2] stateswhich converge to the same 2P312limit are very close,especially athigher n values, the twotransitions have been treatedas single peak inthe deconvolution.For peaks in the experimentalspectrum which can be completelyresolved such as the f1and f2 resonance lines (I.e.the 3s, 35’ lines, figure5.2(a)), integration ofthe peak areas providesa direct measure oftheabsolute optical oscillatorstrengths for the individualdiscrete electronictransitions. For the higherenergy peaks which cannotbe completelyresolved, absolute oscillator strengthshave been obtained fromthedeconvoluted peak areas asshown in figure 5.2(b).The accuracy of thepresently developed methodis confirmed by the consistencyof theoscillator strengths determinedfor given transitionsat the threedifferent resolutions. Theresults obtained from theanalysis of thespectrum at the highestresolution (0.048 eV FWHM)are given in tables5.2, 5.3 and 5.4. The uncertaintiesare estimated to be —5% forthelower energy resolved transitionsand lO% for those suchas 6s, 6s’, 5dand 5d’ at higher energiesdue to additional errorsinvolved indeconvoluting the peaks.Also shown in tables 5.2,5.3 and 5.4 are theabsolute oscillator strengthvalues for several discreteelectronicTable 5.2Theoretical and experimental determinations of the absolute opticaloscillator strengths for the 2S22p6*2s22p5(2P3,2,l,2)3S discretetransitions of neonOscifiator strength for transition from2s22p6—’2s5mwhere m=[P312]3s__(i’)I[2P112]3s’__(f)A. Theory:Amus’ya(1990)[145]0.163*Kelly (1964) [144]0.188*Cooper (1962) [10410.163*Aleksandrovetal.(1983)[65] 0.01060.141Stewart (1975) [1501 0.159Albat and Gruen (1974) [149] 0.0113 0.149Gruzdev and Loginov (1973) [1481 0.01060.139Ayrnaretal. (1970) [147](a) dipole length 0.01210.16 1(b) dipole velcity 0.01000.130Gruzdev (1967) [111] 0.0350.160Gold and Knox (1959) [1461(a)wavefunction 0.011 0.110(b) semi-empirical0.0 12 0.12 1B. Experiment:Present work (HR dipole(e,e)) 0.01 18 0.159(0.0006) (0.008)Tsurubuchiet al.(1990)[140] 0.0122 0.123(Absolute self-absorption) (0.0006) (0.006)Aleksandrovetal. (1983) [651 0.012 0.144(Total absorption) (0.003) (0.024)95Table 5.2 (continued)Oscillator strength for transition from2s22p6—..2s 5m where m=[2P312]3s (f1) [2P112]3s’ (f2)B: Experiment: (continued)Westerveldetal. (1979)1139] 0.0109 0.147(Absolute self-absorption) (0.0008) (0.0 12)Bhaskar and Luiro (1976) [134] 0.0122 0.148(Lifetime: Hanle effect) (0.0009) (0.0 14)Knystautas and Drouin (1974) [1321 0.0078 0.161(Lifetime: Beam foil) (0.0008)(0.011)Irwinetal. (1973) [13310.158(Lifetime: Beam foil) (0.006)Natalietal.(1973)[142] 0.0120.158(Electron impact)Jongh and Eck (1971) [62]0.134(Relative self-absorption) (0.01 0)Kazantsev and Chaika (1971) [1351 0.0138(Lifetime: Hidden alignment) (0.0008)Geiger(1970)[20,l4ll 0.009 0.131(Electron impact) (0.002) (0.026)Lawrence and Liszt (1969) [130] 0.00780.130(Lifetime: Delay coincidence) (0.0004) (0.0 13)Lewis(l967)[138]0.012 0.168(Pressure broadening profile)(0.002) (0.002)Korolevetal. (1964)1129] 0.160(Natural broadening profile)__________________— (0.0 14)tEstimated uncertainties in experimental measurements are shown in brackets.*Total oscillator strength (fj+f2).96Table5.3Theoreticalandexperimentaldeterminationsoftheabsoluteopticaloscillatorstrengthsfordiscretetransitionsofneon(19.5—20.9eV)1Oscillatorstrengthfrom2s22p°—’2s22p5mwheremis(2P312)4s(2P1/2)4s’(2P312)3dI(2P172)3d’(2P312)5I(2P1/2)5s’(2P312)4d(2P112)4d’A:Theory: Amusya(1990)f145]*0.0280.021Kelly(1964)11441*0.0290.0360.0080.025Cooper(1962)1104]0.0260.0370.0090.020Aleksandrovetal.(1983)[6510.01240.01600.01760.00640.00600.00430.00910.0041Stewart(1975)[150)0.02600.0238GruzdevandLoginov(1973)[1481#0.01210.01640.00810.00580.0046Klose(1969)(1311(1)ICandHFS0.0032(11)ICandCF0.0037Klose(1969)[1581(1)ICandHFS0.0156B:Experiment: Presentwork(HRdipole(e,e))0.01290.01650.01860.006650.006370.004610.009440.00439(0.0006)(0.0008)(0.0009)(0.00033)(0.00032)(0.00023)(0.00047)(0.00022)Aleksandrovetal.(1983)[65j0.01450.01850.02220.00820.00830.00490.01470.005(Totalabsorptlon)(0.0035)(0.006)(0.0046)(0.0029)(0.0031)(0.0017)(0.0036)(0.002)(0Table5.3(continued)Oscillatorstrengthfrom2s22p6—2s22p5mwheremIs(2P312)4s(2P1/2)4s(2P312)3d(2P112)3d(2P312)5s(2P112)5s’(2P312)4d(2P112)4d’B:Experiment:(continued)Westerveldetal.(1979)[139]0.01280.01530.00640.00610.0042(Absoluteself-absorption)(0.0010)(0.0012)(0.0005)(0.0005)(0.0003)Ducloy(1973—74)113710.0153(Lifetime:Laserirradiation)(0.0030)Natalletal.(1973)[142]0.0130.0160.0170.0060.0060.00430.00850.0043(Electronimpact)Klose(1970)[131]0.0040(Lifetime:DelaycoincIdence)(0.0003)LawrenceandLiszt(1969)[130](Lifetime:Delaycoincidence)(1)0.00860.01300.02170.00640.00570.0042(0.0010)(0.0020)(0.0022)(0.0010)(0.0010)(0.0010)(2)@0.01340.01780.00680.00620.0048(0.0010)(0.0025)(0.0010)(0.0010)(0.0010)DecompsandDumont(1968)E13610.01640.00598(Lifetime:LaserIrradIation)(0.0020)(0.00023)fEstimateduncertaintiesInexperimentalmeasurementsareshowninbracketssummedoscillatorstrengthasindicated#LlfetlmedataconvertedbyWesterveldeta!.1139)tooscillatorstrengthsusingtransitionprobablltiesreportedinrefs.11561and1157)@RecalculatedbyWesterveldetat.1139]usingbranchingratiosreportedInrefs.11481,(156),and1157)CDTable5.4Theoreticalandexperimentaldeterminationsoftheabsoluteopticaloscillatorstrengthsfordiscretetransitionsofneon(20.9—21.2eV)+Oscillatorstrengthfrom2s22p6—’.2s22p5mTotalwheremisto(2P312sf(2Pi2s’(2P312)5dj(2P112)5d’IonizationA:Theory:Kelly(1964)11441*0.0030.018Cooper(1962)11041*0.0040.011Aleksandrovetal.(1983)[6510.00310.00180.00500.0024B:Experiment:Presentwork(HRdipole(e,e))0.003300.001560.005430.002290.292(0.00030)(0.00016)(0.00054)(0.00023)(0.015)Aleksandrovetal.(1983)[65]0.00450.003(Totalabsorption)(0.0019)(0.001)Natalletal.(1973)[142]0.277(Electron_Impact)tEstimateduncertaintiesinexperimentalmeasurementsareshowninbrackets*summedoscillatorstrengthasindicatedCD CD100transitions 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 theoscillator strength values for the f1 resonance line calculated by differenttheoretical approaches (0.010—0.012) and these results [65,111,146—1491 correspond closely with the presently reported experimental value(0.0118). However, for the f2 resonance line there is substantial variationin 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 thepresently reported experimental value (0.159) for f2. Other theoreticalcalculations [65, 146—149] for the f2 resonance line give lower oscillatorstrengths. Cooper [104], Kelly [1441 and Amus’ya [145] have reportedcalculated summed (nl +nl’) oscillator strengths for transitions from2s22p6to several2s22p5(P3/2.1/2)ns or nd states. For the 2p—’(3s+3s’)transitions (table 5.2), the summed absolute optical oscillator strengths(i.e.f1+f2)calculated by Cooper [104] and Amusya [145] are slightly lowerwhile the value of Kelly [144] is slightly higher than the presentlyreported 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 forthe2p—(Ss+S&) and 2p—(6s+6s’) transitions the data of Cooper [104] andKelly [144] are slightly lower. For the 2p—’(3d+3d’), 2p—(4d÷4d’) and2p—’(5d+5d’) transitions the Cooper [104] and Kelly [1441 data aresignificantly higher while the Amus’ya [145] data for the 2p—(3d+3d’)transitions are slightly lower when compared with the presentexperimental results. The calculated f2 value reported by Gruzdev [111]101using intermediate coupling techniques Is consistent with the presentlyreported value while the f1 value Is much higher than all the other valuesquoted in table 5.2. The calculated data reported by Aleksandrov et at.[651 using an intermediate—coupling scheme are more comprehensiveand comparison with the presently reported experimental data ispossible for individual transitions up to the 6s, 6&, 5d and 5d’ states asshown in tables 5.2, 5.3 and 5.4. Immediately It can be seen that thecalculated data of Aleksandrov et at. [65] are in good agreement with thepresently reported values except for the f1 and f2 values for which theirdata are slightly lower. Gruzdev and Loginov [148] have calculated theradiative lifetimes of several transitions of neon using an intermediatetype coupling and the Hartree—Fock self—consistent field method.Westerveld et at. [139] have converted the lifetime data of Gruzdev andLoginov [148] to oscillator strength values using transition probabilitiesreported by Gruzdev and Loginov in refs [156,157] and these values showgood agreement with the present work for oscillator strength values ofthe 4s, 4s’, 5s and 5s’ lines, while their value for the 3d’ line is slightlyhigher. Stewart [1501, using fully—coupled time dependent Hartree—Fockequations, has reported calculated oscillator strength values for the 4s’and 3d lines which are considerably higher than the presentexperimental results. Klose [131], using intermediate coupling and aHartree—Fock—Slater calculation (IC—HFS), and intermediate coupling andthe central field approximation (IC—CF), has reported two oscillatorstrength values for the 5s’ line but both values are considerably lowerthan the presently reported experimental values. In a second paper,Kiose [158] reported an oscillator strength for the 4s’ line from an IC—102HFS calculation whichis slightly lower than thepresent experimentalresult.Turning now to aconsideration of the variousexperimentalresults,it can be seen fromtables 5.2, 5.3 and 5.4 thatthe presently reporteddata are In very goodagreement over the wholediscrete regionwith theearlier electron impactbased results of Nataliet al. [142]. Thelatterunpublished results [142]have been quoted inreferences [139] and[143]. Thehigh resolution data reportedby Aleksandrov etal. [65], usingthe total absorptionmethod, have rather largeuncertainties andagreement with the presentdata is good for the f1 andf2 resonance linesbut generally poorer forthe higher transitions.The measured absoluteoscillator strengths [651for the discrete transitionsat higher energy aresignificantly higher thanthose determinedin the present work (seetables 5.3 and 5.4). Theself—absorption methodwas used by threegroups [62,139, 1401 and thereported values rangefrom 0.123 to 0.147for the absoluteoscillator strength of the f2resonance line. Allthesevalues are lower than thepresent value of 0.159.Agreement betweendifferent groups usingthe self—absorption methodis generally betterforthe f1 resonanceline where the value of Tsurubuchlet al. [140] isconsistent with the presentwork, and that obtainedby Westerveld et al.[139] is slightlylower but still within thequoted uncertainty.Westerveldet al. [1391 havealso measured oscillatorstrengths for the transitionsfrom the ground stateto the2s22p5(P3/2)4sand 5s states, andalso tothe2s22p5(P112)4s’, 5s’and 3d’ states. Theirresults [1391 for thesetransitions all show verygood agreement withthe present work.Lifetime measurementsusing various experimentalprocedures[130—137] show good agreementfor the absolute oscillatorstrength of103the f2 resonance line withthe present data, with the exceptionof ref.[130]which is —20% lower. Forthe f1 resonance line theresult ofKazantsev and Chaika[135] is somewhat higher andthe values reportedby Knystautas andDrouin [132], and by Lawrenceand Liszt [130] aremuch lower than mostother reported values which arein closeagreement with the present work.In the case of discretetransitions athigh energy (table 5.3), the Lawrenceand Liszt [130] values areslightlylower than the presentwork except for the transitionsto the2s22p5(P312)3d and2s22p5(P1/2)3d’ states. Westerveldet al. [1391have re—evaluatedthe lifetime data of Lawrence andLiszt [130] using thetransition probabilitiescalculated by Gruzdev andLoginov [148,156.157]and it is note—worthy thatthe re—evaluated oscillatorstrength values arein all cases in better agreementwith the present work.The absoluteoscillator strength for the5s’ line determined by Kiose [131]using adelayed coincidence methodis slightly lower than the presentvaluewhile that determined byDecomps and Dumont [136]is -33% higher.For the 4s’ line, the valuesof Decomps and Dumont [136]and Ducloy[1371 are bothconsistent with the presentlyreported experimentalmeasurement.With the use of a high resolutionelectron impact spectrometer,Geiger [141] measured theintensity ratio of the f2/f1 resonancelinesgiving a value consistent withthe ratio derived from the presentdata.However, the total absoluteoptical oscillator strengthsum for the tworesonance lines obtained[141] in Geiger’s earlier work [20],which wasnormalized on the elastic electronscattering cross section,is about 20%lower than the presently reportedvalue. The absolute oscillatorstrengthsobtained from line profile analysisfor f1 and f2 by Lewis [138]and for f2 by104Korolev et al. [1291 are ingood agreement (see table 5.2)with thepresent work. Finally,the total discrete oscillator strengthsum up to21.6 16 eV, which Is the middlepoint between the 2P3/ and2P112ionization thresholds of neon, hasbeen determined in the presentworkto be 0.292 compared withestimates of 0.277 reportedby Natali et al.[142] and 0.4 reported byWest and Marr [103]. The lattervalue wouldseem to be too high.5.2.3 High Resolution PhotoabsorptionOscillator Strengths for Neonin the 40-55 eV Region ofthe Autoionizing ExcitedStateResonancesThe spectroscopy (i.e. theenergy levels) of the autoionizingexcitedstate resonances of neoninvolving excitation of a 2s electronand alsodouble excitation of 2p electrons,has been studied in somedetailexperimentally [65,154,159].However, prior to the presentquantitativework no detailed high resolutionabsolute intensity measurementshavebeen reported for neon inthis region. Similar absoluteintensitymeasurements in the doubleexcitation region for helium inexcellentagreement with theory [9] haverecently been reported from thislaboratory for helium [37](see section 4.2.2.2). Inthe present study, theelectron energy loss spectrum inthe 40—55 eV energy region ofneon wasmeasured with the use ofthe high resolution dipole (e,e)spectrometer ata resolution of 0.098 eV FWHM.This was then convertedto a relativeoptical oscillator strengthspectrum by multipling with the BHRfunction(see section 3.3). Normalizationwas performed in the smoothcontinuum region at 55eV using the absolute opticaloscillator strength105data given in table 5.1, asdetermined by the low resolutiondipole (e,e)spectrometer. The presenthigh resolution absolute dipoleoscillatorstrengths (solid circles) are shownin figure 5.3. The fewphotoabsorption (absolute) datapoints earlier reported bySamson[45,1211 Inthis region are seen from figure5.3 (open circles) to bereasonably consistent with the presenthigh resolution dipole (e,e)results.As shown in figure 5.3, theenergies(±0.005 eV) of the maximaofthe transitions corresponding toexcitation of the 2s electrons to npsubshells with n=3 to 6, andthe double excitation transitionof 2pelectrons to the 3s3p configurationof neon have been determinedin thepresent work to be 45.550,47.127, 47.677 and 47.975,and 44.999 eVrespectively. These energies arein good agreement with the highresolution experimental studiesreported by Codling et al. [154]and byAleksandrov et al. [651, aswell as with the multi—configurationclosecoupling calculations ofLuke [1141. For peaks observedat higherenergies in the present work,the assignments and energypositions ofthe excited state resonancesshown in figure 5.3 aretaken from thephotoabsorption data reported byCodling et al. [154]. A smallpeak (X) at43.735 eV has not been reportedin previous photoabsorptionmeasurements [65,154,159],but it should be noted thatthe publishedspectra in all of these measurementsdid not extend below 44eV.However, a threshold electronimpact study by Brion andOlsen [1601 anda lower electron impactenergy (400 eV) study ofthe ionizationcontinuum of neon by Simpsonet al. [161] also detected apeak at —43.7eV and it was suggested thatthis was probably due toexcitation to the2s2p63s state which hadearlier been reported [162] tobe at 43.65 eV.1060.1112F>I1%eI2s22p6—42s2p(S112)np1 10.10___________I I I2s22p6—42s4(’D)3p(P)ns456 0—3 40.09_____________I lIIto3 4 56(1D)3s(2D)np 9.)0.08 X0‘.4‘-43P3d(P3pC.)P,3d8‘-4700.07 0II-I,— tI‘-4600Cl) 0.0600 —2s22p4(3P)3s(P312)np I3P3d2D3pCl)1S3s(2S3p2sP)3s(112)npP53p 2D 3dS)3p2P3S 600053 56.-_______________0—2s22p4(3P)3p(P)ns 50.04 I40 4555Photon energy (cv)Figure 5.3: Absolute oscillator strengths for the photoabsorption of neonin theautoionizing resonance region 40—55 eV (FWHM=0.098 eV) measured bythehigh resolution dipole (e,e) spectrometer. Solid circles are thiswork andopen circles are photoabsorption data reported by Samson [45,121].Assignments are from reference [154]. Note offset vertical scale.107However, it seems unlikely that the forma1ly dipole forbidden transition2s22p6—’2s2p3swould be so prominent at the very low momentumtransfer (K2=0.014 a.u.) corresponding to the present experimentalconditions of high impact energy (3 keV) and zero degree meanscattering angle. This peak at 43.735 eV is also too high in energy to bedue to any double scattering processes involving below edge outer valenceprocesses.5.3 ConclusionsThe present absolute oscillator strength data for neon, unlike theoptical measurements, are subject to the stringent constraints of the TRKsum rule and are considered to be of high accuracy. Optical oscillatorstrengths for the discrete transitions involving valence 2p electrons andalso for the photoionization continuum up to 250 eV have been measuredfor neon. The presently reported results were compared with theory andalso with earlier reported experimental data, all of which are lesscomprehensive than the present work. The accuracy of the earlierunpublished electron impact data of Natali et al.[142] at lower impactenergy (i.e. large momentum transfer) in the discrete region isconfirmed. Unlike the situation for helium, theoretical calculations forthe absolute oscillator strengths of neon in both the discrete andcontinuum regions show a wide spread of values. The present dataprovide a critical test for these quantum mechanical calculationsthroughout the spectrum and especially for the valence 2p discreteelectronic excitations such as the f1 and f2 resonance lines. The firsthigh resolution absolute optical oscillator strengths have been obtainedfor the autolonizing excited state and doubly excited state resonanceregion (40—55 eV) involving 2s excitation and double excitation, andIt Ishoped that these measurements will stimulate calculation In this region.108109Chapter 6Absolute Optical Oscillator Strengths for the ElectronicExcitation of Argon, Krypton and Xenon6.1 IntroductionSimilar to the situation for neon [104,112,113,115—118,163] (seechapter 5), the photoionization cross section maxima of argon andkrypton [112,113,115—118,163,1641 are shifted to energies above theionization threshold, showing significant departure from the hydrogenicmodel. While this departure is not so obvious for xenon [113,116—118,1631 it does nevertheless show significant non— hydrogenicbehaviour. In addition minima (sometimes called Cooper minima) havebeen observed in the photoionization cross sections of argon, krypton andxenon[104,112,113,115—118,163—165]. Instead ofusinga pureCoulomb nuclear potential, Cooper [104], employing a more realisticpotential similar to the Hartree—Fock potential for the outer subshell ofeach atom, and also both Manson and Cooper [165] and McGuire [1121,starting with Herman-Skiliman central potentials, have been able totheoretically reproduce the maxima above the threshold and also theexistence of the minima in the photoionization cross sections startingfrom one—electron approximations. However the above calculations givenarrower peaks shifted in energy relative to the experimental crosssections, with the cross sections at the peak maxima two or three timeshigher than the experimental values. The 4d shell in xenon is anexample where significant discrepancies between experimental and110theoretical results have been observed. It has been found that electroncorrelation is important in many cases [113, 115—118,163,164,166].Starace [164] has computed the photoionizatloncross sections of argonand xenon starting from a local Herman—Skillman central field andincluding final—state correlation. Amus’ya et al. [116], employing therandom—phase approximation with exchange (RPAE), Kennedy andManson [113], using Hartree—Fock functions with exchange, Burke andTaylor [115], applying the R—matrix theory, and Zangwill and Soven [163],using density—functional theory, have also calculatedthe photoionizationcross sections of the noble gas atoms. The relativisticrandom—phaseapproximation (RRPA) [117] and the relativistic time—dependent local—density approximation (RTDLDA) [118], two methods whichare closelyrelated, have also been applied to calculation of the photoionizationcrosssections of the outer shells of argon, krypton and xenon.Recently,Rozsnyai [166] has reported the photoionization crosssections of the 3pand 3d electrons in krypton and the 4d electrons inxenon based on aself—consistent Dirac—Slater model including the effect of the hole intheionized shell. With the inclusion of electron correlation, the calculatedphotoionization cross sections [115—118,163] are generally in betteragreement with experiment, however some discrepancies(>20%) stillremain between the experimental and theoreticalvalues in certainenergy ranges.Experimentally, photoabsorption and photoionization cross sectionmeasurements in the ionization continuum regions of argon, krypton andxenon have been widely performed using Beer—Lambert lawphotoabsorption and the double ion chamber methods[45,47,48,102,103,167—179]. Line—emitting light sources [45,167,169—111172,175,178,179] have most commonly been used. The Hopfleldcontinuum [168,173], generated by a repetitive, condensed dischargethrough helium, provides a useful continuum source In the energy region11.3—21.4 eV. With the advance of synchrotron radiation an Intense andcontinuous light source has become avaflable for measuring thephotoionization cross sections of atoms and molecules up to highenergies [47,48,102,103,174,176,177]. However, contributions fromstray light and higher order radiation have to be carefully assessed andthe measurements appropriately corrected if synchrotron radiation is tobe used as the light source for accurate absolute cross sectionmeasurements [126—128]. Photographic plates [167,1721, Geigercounters [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 ofdifferent geometries have been constructed [45,173,176,178,179] andphotoionization cross sections of the sample gases have been obtainedfrom the length of the ion collector plates, the sample target density andthe current flowing from the collector plates. These Beer—Lambert lawmeasurements give good agreement for the individual noble gases Interms of the shapes of the continua. However the absolute values of thephotoabsorption cross sections in the continua typically show substantialdifferences (—10%), especially at higher energies, due to difficulties inobtaining precise measurements of the sample target density in a‘windowless’ far UV system and also due to contributions from stray lightand/or higher order radiation. By using the dipole excitation associatedwith inelastic scattering of electron beams of high impact energy (10keV) and small scattering angle, the single and multiple photoionization112of argon [221, krypton andxenon [1801 has been studied usingelectron/ion coincidence techniques.Relative optical oscillatorstrengths were obtained [22,1801by Bethe—Born conversion ofelectronscattering data and absolute scaleswere established by normalizingat asingle energy to previously published [451abso1ute photoabsorptioncrosssections.For the excitation of the heaviernoble gas atoms in thediscreteregion, several theoretical oscillatorstrength calculationshave beenreported. Cooper [1041, employinga one electron central potentialmodel, and Amus’ya [145],applying the RPAE method, havecalculatedoscillator strengths for the transitionsfrom the ground states tothems2mp5(P3/2,l,2)nsand nd states where n>mand m is 3, 4 and 5 forargon, krypton and xenonrespectively. Calculations of theoscillatorstrengths for the separatetransitions from the ground stateto thems2mp5(P3/2)nsand nd states, and thems2mp5(P1,2)ns’and nd’ stateshave also been reported [111, 147,151,181—189],but mostly thesecalculations only give oscillatorstrengths for thems2mp5(P3,2)(m+ 1)sandms2mp5(P1,2)(m+ 1)s’ states [111,147,181—183,151,186—1891.Theoretical discrete oscillatorstrength values have beenreported byKnox [181] for argon, and Dow andKnox [182] for krypton andxenon.The first [1811 set of datais based solely on solvingthe Hartree—Fockequations while the second[182] is based on experimentalenergies withthe dipole matrix elementscomputed from the Hartree—Fockwavefunctions. Gruzdev[ill] has reported the oscillatorstrengths ofresonance lines in the spectra ofAr I, Kr I and Xe I atomsusing thetechnique of intermediatecoupling with the transitionintegral obtainedfrom the Coulomb approximation.Kim et al. [1831, usingHartree—Fock113wavefunctions without freezing of the core orbitals, have calculated thegeneralized oscillator strengths of the Xe I resonance lines, which in theoptical limit gave optical oscillator strengths for these transitions. Aymaret al. [147] calculated Ar I, Kr I and Xe I transition probabilities andlifetimes using a least—squares fit procedure on energy levels for theangular part of the wavefunctions and a parametrized central potential forthe radial part of the wavefunctions. Lee and Lu [184], who havedetermined three sets of parameters: eigen—quantum defects,transformation matrices and excitation dipole moments by fitting toexperimental data, have reported a semi—empirical calculation of discreteoscillator strengths for argon. Later, Lee [185] calculated the sameparameters by solving the many—electron Schrodinger equation for anatom within a limited spherical volume. The radiative lifetimes of thelevels of Ar I [186] and Kr 1 [1871 have been calculated by Gruzdev andLoginov using an intermediate coupling scheme with radial integralsobtained from Hartree—Fock functions. Albat et al. [188], carrying outBorn and four—state “close coupling” calculations, have reported oscillatorstrengths for the low lying argon levels while Stewart [1511, usingsimplified time—dependent Hartree—Fock calculations, has reported theoscillator strength for the (3p61S—’3p54s 1P) transition of argon. Aymarand Coulombe [189] have computed the transition probabilities andlifetimes for Kr I and Xe I spectra using a central field model which takesinto account intermediate coupling and configuration mixing.Since the valence shell electronic transitions of noble gas atomshave extremely narrow natural line—widths, absolute oscillator strengthmeasurements for the discrete regions of the argon, krypton and xenonphotoabsorption spectra via the Beer—Lambert law are not viable since114significant errors may arise due to so—called “line—saturation” (i.e.bandwidth) effects. Detailed discussions of “line—saturation” effects andtheir Implications for absolute photoabsorptlon oscillator strength (crosssection) measurements have been given in refs. [36,37,46,72] (seechapter 2). Several alternative experimental methods for determiningdiscrete optical oscillator strengths which avoid “line—saturation”problems have been reported. However, in most cases these methodsare somewhat complex and also are often severely restricted in theirrange of application so that only a very few transitions can be studied for agiven target [37]. In the cases of argon, krypton and xenon, othertechniques which have been used include the self—absorption method[62,64,139,140], the total (optical) absorption method [190—192], thelinear 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 theelectron excitation function [208] and electron Impact methods[20,141,209—216]. The relative self—absorption method has been used byJongh and Eck [62], while the absolute self—absorption method has beenused by Westerveld et al. [1391 and Tsurubuchi et al. [64,140]. Oscillatorstrengths for the resonance lines of krypton and xenon have beendetermined 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 oscillatorstrengths for the resonance lines of krypton, while in a further paperthey reported the oscillator strength for one resonance line (8.434 eV) ofxenon by determining the refractive index of xenon using the spectralline—shift method [194]. The radiative lifetimes of the resonance115transitions of the noble gases havebeen determined using: a)the beam—foil method [199]; b) the zero—fIeldlevel—crossing technique (Hanleeffect) [195]; (c) study of the photondecay curve using a pulsed electronexcitation source [196—198,200]or pulsed light source [2011; (d)electron—photon delayed coincidencetechniques [202]. Bystudying thepressure—broadening profiles of thenoble gas resonance lines,severalgroups [138,203—2061 have reportedtheir oscillator strengths.With thedevelopment of lasers, a phase—matchingtechnique involvingfocusedbeams for optical wave—mixing becamepossible and oscillator strengthsfor the resonance lines Inthe noble gases have beendetermined usingthese techniques by Kramer et al.[207] for xenon and by Ferrellet al.[66] for krypton and xenon. Byanalyzing the electron excitationfunction,McConkey and Donaldson [2081have reported optical oscillatorstrengthsfor the resonance linesof argon. Electron impactbased methods havealso been employed for measuringthe discrete optical oscillatorstrengths of argon, kryptonand xenon. By using very highImpact energy(25—32 keV) and very smallscattering angle (-.-1x10- rad),Geiger[20,141,210,212,213] obtained opticaloscillator strengths for theresonance lines of the noblegases by converting electron energylossspectra to relative optical spectraand normalizing on the elasticdifferential cross section.In other electron impact work Liet al. [2141for argon, Takayanagi et al. [215]for krypton, and Delage andCarette[2111 and also Suzuki etal. [216] for xenon, havereported opticaloscillator strengths for resonancelines in the heavier noblegases byextrapolating the generalized oscillatorstrengths of lines, measuredatdifferent scattering angles and atlow electron impact energy, tozeromomentum transfer. Delage andCarette [211] normalized theirdata on116one of the transition peaks of xenon that was measured by Geiger[2101,while Lietal. [214], Takayanagietal. [2151 andSuzukietal. [2161normalized their data on the elastic scattering cross section. Theunpublished electron Impact work of Natali et aL. [1421 for the opticaloscillator strengths of the noble gases has been quoted In references[139,212,1431.Consideration of the various experimental and theoretical oscillatorstrength values published to date for argon, krypton and xenon showsthat there is a large body of existing information for the continuumregions. In contrast there is relative little information available in thevalence shell discrete region. For the discrete spectra of argon, kryptonand xenon only the transitions to thems2mp5(P3/2)(m+ 1)s andms2mp5(P1,2)(m+1)s’ states, where m is 3, 4 and 5 respectively, havebeen studied in any detail and even for these considerable variations inoscillator strength values have been reported. In the case of argon theoptical oscillator strength data available in 1975 was reviewed byEggarter [217] for both the discrete and continuum regions up to 3202eV. On the basis of the information available Eggarter[217] listedrecommended optical oscillator strength values for argon.In chapters 4 and 5, we have reported detailed and comprehensivemeasurements for helium [37] and neon [38] respectively. These resultswere obtained using a recently developed highly accurate high resolutionelectron impact based method for obtaining absolute optical oscillatorstrengths for the discrete, continuum and autoionizing resonance regionsin atoms and molecules. This method [37,38] is not subject to the “linesaturation” effects which can cause serious errors in Beer—Lambert lawphotoabsorption experiments when the bandwidth is comparable to or117larger than the naturallinewidth. The methodinvolves combiningmeasurements obtained usinga high resolution (0.048eV FWHM) dipole(e,e) spectrometer in conjunction witha lower resolution(—1 eV FWHM)dipole (e,e) instrument.The absolute oscillatorstrength scales forhelium and neon wereobtained by TRKsum rule normalizationand werethus completely independentof any direct optical measurement.Thesame general methodis now applied to provideindependent and wide—ranging measurementsof the absolute photoabsorptionoscillatorstrengths for the discrete,continuum andautoionizing resonanceregionsof argon, krypton andxenon. However,in practice the TRK sumrulenormalization procedureswhich were employedfor helium [37] andneon[38] are difficult to apply for the heaviernoble gases due to difficultiesincarrying out the necessarylengthy valence shell extrapolations.Thesedifficulties arise becauseof the smaller energy separationsbetween thedifferent subshellsof the argon, krypton andxenon atoms comparedwiththe relatively simple electronicconfigurations of heliumand neon. Theabsolute scales of thepresently reporteddata have therefore beenobtained by normalizingon recently reportedhigh precisionphotoabsorption oscillatorstrengths measuredat helium and neonresonance line photonenergies by Samsonand Yin [178]. In thischapter, we nowreport measurementsof (i) absolute photoabsorptioncontinuum oscillatorstrengths for argon,krypton and xenon upto 500,380 and 398 eV respectively,(ii) absolute photoabsorptionoscillatorstrengths for the discretedipole allowed electronictransitions from themp6 subshells to 1evelsof the lower membersof the ms2mp5nsandms2mp5nd(2P312,112)manifolds where n>m andm is 3, 4 and 5 forargon, krypton and xenonrespectively, and(iii) absolute photoabsorption118oscillator strengths in the regions of the Beutler—Fano autoionizationresonance profiles involving excitation of the inner valence mselectrons.The results are compared with previously published experimental andtheoretical data in regions where such data are available.6.2 Results and Discussion6.2.1 Low Resolution Measurements of the PhotoabsorptionOscillator Strengths for Argon, Krypton and XenonRelative photoabsorption spectra of argon, krypton and xenon wereobtained by Bethe—Born conversion of electron energy loss spectrameasured with the low resolution dipole (e,e) spectrometer(see chapter3) from 10—500 eV, 8—380 eV and 7—398 eV forargon, krypton andxenon respectively. The relative spectra were normalized at21.2 18 eVfor argon and krypton and at 16.848 eV for xenon using therecentlypublished photoionization data of Samson and Yin [178]. Theuncertainties of the present low resolution dipole (e,e) work areestimated to be -5%. The results for argon, krypton andxenon arepresented in the following separate sections.6.2.1.1 Low Resolution Measurements for ArgonFigures 6.1—6.3 show the presently measuredabsolute opticaloscillator strengths for the photoabsorption of argon.The correspondingnumerical values in the energy region 16—500 eV aresummarized in table6.1. Of the three noble gases (argon, krypton and xenon)studied in thepresent work, the photoionization cross sections of argon havebeenFigure 6.1: Absolute oscillator strengths for thephotoabsorption of argon in the energyregion 10-60 eV. (a) comparison with otherexperimental data[22,45,47,103,152,171,176,218]. The discrete regionbelow 16 eV is shown athigh resolution in figure 6.9. The resonancesIn the region 26—29.2 eVpreceding the 3s’ edge are shown at high resolutionin figure 6.14. (b)comparison with theory [112,113,115—118,163,164].119>CSV1.4U)‘.40—C)Cl)0C.).-04030201006050403D20100(a) Experimental measurements_____3s1IA1• Present work (E = 1 eV FWHM)West & Morr [47,103]‘0 Sornson [45]*Henke et ci. [152]A Von der Wiel & Wiebes[22]xCorison et ci. [176]0Modden et ci. [218)• Rustgi [171)x.•cy•*• •I I I10 20 30 40 50 60(b) Comparison with theoryIAiJ0• Present work (Expt.)—— Storoce [164]— Burke end Tcyior [115]3p 3s’Amu&yc et ci. [116]—— Kennedy end Mcnson [113]..-+0 McGuire [112]1:— Zcngwiii & Soven [163]+ Johnson & Cheng [117]aPorpia et ci. [fl8]• :\\s•.••1•.-.-:403020100C.)U)r Cl)U)0‘.4C)0‘.460504030201001 0 20 30 40 50 60Photon energy (eV)2.52.0• Present work (E = 1 eV FWHM)West & Mcrr [47,103]* Henke et ci. [152]* Lukirskii end Zimkinc [169)A Van der Wie? & Wiebes [221o Samson et ci. [179)Amusyc et ci. [116]- —— Kennedy & Manson [113]G McGuire [112]-4>VC—ISV1I.ci)C=.-0Cl)C0401202.50•‘)f —L.LIC.)U)U)U)1.5o3-C-)01.0k0.5/1 .5_____________________________1 .00.50.00.040240Figure 6.2: Absoluteoscillator strengthsfor the photoabsorptionof argon in the energyregion 40—240 eV comparedwith other experimental [22.47.103,152,169,1791and theoretical [112,113,116]data.8b 120160 200Photon energy (eV)I.rI‘I1212p1I’• Present work (E = 1 eV FWHM)West & Marr [47,103]* Henke et ol. [1521* Lukirski and Zimkno [169]A Von der Wiel & Wiebes [22)Amusyo et al. [116]—— Kennedy & Monson [113]o McGuire [112]rI-S>c;IV0Sa)U)1-40C)U)0C.?654320AA2s1A65Cl)U)A U).t-01.4C)3C4:i*1I I260 300 340 380420 460 500220Photon energy (eV)Figure 6.3: Absolute oscillator strengths forthe photoabsorption of argon In theenergy region 220—500 eV compared withother experimental[22,47,103,152,169] and theoretlcal[112,113,1161data.122Table 6.1Absolute differential opticaloscillator strengths forthephotoabsorption of argon abovethe first ionization potentialobtainedusing the low resolution (1 eV FWHM)dipole (e,e) spectrometer (16—500 cv)Energy OscillatorEnergy OscillatorEnergy Oscillator(eV) Strength (eV)Strength (eV) Strength(102eV-l) (10-2eV-1)(102eV-1)16.0 27.74 17.731.05 19.4 32.0216.1 27.96 17.831.09 19.5 32.1916.2 28.16 17.930.86 19.632.3516.3 28.4818.0 30.87 19.732.5216.4 28.5518.1 31.33 19.832.7116.5 28.94 18.231.15 19.932.2316.6 28.95 18.331.57 20.032.4916.7 29.25 18.431.67 20.1 32.5116.8 29.2518.5 31.81 20.232.3616.9 29.52 18.631.61 20.3 32.3817.0 29.71 18.731.73 20.4 32.7117.1 29.9918.8 31.78 20.532.4017.2 29.9718.9 32.19 20.632.5817.3 30.30 19.032.03 20.7 32.9117.4 30.25 19.132.02 20.8 32.9417.5 30.39 19.232.51 20.9 32.5717.6 30.7319.3 32.41 21.032.75123Table 6.1 (continued)Energy Oscillator EnergyOscillator EnergyOscillator(eV) Strength (eV)Strength (eV)Strength(1O-2eV-1) (l0-2eV-1)(102eV1)21.1 32.6228.5 24.50 38.54.3821.2k 33.0029.0 23.37 39.03.8421.3 32.72 29.522.24 39.53.5121.4 32.8930.0 19.8440.0 3.0321.5 33.09 30.518.66 41.0 2.4821.6 33.1631.0 17.85 42.01.97021.7 32.80 31.517.08 43.01.52121.8 32.86 32.016.25 44.0 1.31222.5 32.90 32.515.19 45.0 1.14123.0 32.36 33.013.81 46.00.99123.5 32.16 33.512.69 47.0 0.95624.0 31.6634.0 11.73 48.00.90524.5 31.49 34.510.50 49.0 0.90625.0 31.24 35.09.89 50.00.88325.5 31.08 35.59.02 51.00.90926.0 30.63 36.08.28 52.00.92326.5 29.02 36.57.20 53.00.94627.0 25.76 37.06.34 54.00.97727.5 26.06 37.55.71 55.0 1.00928.0 25.7138.0 5.04 56.01.036124Table 6.1 (continued)Energy Oscillator Energy Oscillator Energy Oscillator(eV) Strength (eV) Strength (eV) Strength(10-2eV-l)(102eV’) (102eV-1)57.0 1.059 77.0 1.373 97.0 1.27858.0 1.078 78.0 1.374 98.0 1.24459.0 1.094 79.0 1.376 99.0 1.24860.0 1.110 80.0 1.366 100.0 1.24161.0 1.146 81.0 1.371 102.0 1.23662.0 1.175 82.0 1.371 104.0 1.21963.0 1.196 83.0 1.359 106.0 1.18264.0 1.223 84.0 1.363 108.0 1.17165.0 1.245 85.0 1.353 110.0 1.15466.0 1.259 86.0 1.341 112.0 1.13967.0 1.278 87.0 1.340 114.0 1.11268.0 1.290 88.0 1.338 116.0 1.10169.0 1.314 89.0 1.337 118.0 1.08170.0 1.316 90.0 1.322 120.0 1.07471.0 1.325 91.0 1.312 122.0 1.04372.0 1.341 92.0 1.310 124.0 1.03573.0 1.347 93.0 1.304 126.0 1.01174.0 1.348 94.0 1.288128.0 0.99975.0 1.364 95.0 1.288 130.0 0.97576.0 1.365 96.0 1.288 132.0 0.963125Table 6.1 (continued)Energy Oscillator EnergyOscillator Energy Oscillator(eV)Strength (eV) Strength(eV) Strength(10-2eV-1) (10-2eV-1)(10-2eV1)134.0 0.936 174.00.665 214.0 0.495136.0 0.920 176.00.654 216.0 0.487138.0 0.910 178.0 0.658218.0 0.480140.0 0.895 180.0 0.636220.0 0.484142.0 0.879 182.00.609 222.0 0.459144.0 0.857 184.0 0.614224.0 0.455146.0 0.851 186.00.593 226.0 0.470148.0 0.829 188.00.606 228.00.446150.0 0.816 190.00.579 230.0 0.436152.0 0.793 192.0 0.566232.0 0.439154.0 0.789 194.00.569 234.0 0.457156.0 0.784 196.00.552 236.0 0.425158.0 0.762 198.00.550 238.0 0.408160.0 0.737 200.00.548 240.0 0.405162.0 0.740 202.0 0.530240.5 0.412164.0 0.726 204.00.538 241.0 0.404166.0 0.696 206.00.521 241.5 0.402168.0 0.701 208.0 0.514242.0 0.409170.0 0.687 210.00.506 242.5 0.406172.0 0.689 212.0 0.485243.0 0.416126Table 6.1 (continued)Energy Oscillator EnergyOscillator EnergyOscillator(eV) Strength (eV)Strength (eV)Strength(1O2eV-1)(1O-2eV1) (1O2eV1)243.5 0.439253.5 3.93 263.53.35244.0 0.578254.0 3.90 264.03.36244.5 0.849 254.53.89 264.53.34245.0 0.774 255.03.81 265.03.36245.5 0.593 255.53.78 265.5 3.34246.0 0.609256.0 3.76 266.03.34246.5 1.049 256.53.69 266.53.35247.0 1.615 257.03.65 267.03.35247.5 1.838 257.53.63 267.5 3.36248.0 2.00 258.03.58 268.0 3.34248.5 2.30 258.53.57 268.5 3.33249.0 2.69 259.03.55 269.0 3.27249.5 3.13 259.53.48 269.5 3.22250.0 3.42 260.03.49 270.0 3.19250.5 3.59 260.53.43 270.5 3.14251.0 3.77 261.03.40 271.0 3.08251.5 3.86 261.53.44 271.5 3.07252.0 3.94 262.03.39 272.0 3.07252.5 3.94 262.5.3.38 272.53.04253.0 3.97 263.03.36 273.03.03127Table 6.1 (continued)Energy Oscillator Energy Oscillator Energy Oscillator(eV) Strength (eV)Strength (eV) Strength(1O-2eV-1) (1O-2eV-1)(1O-2eV-l)273.5274.0274.5275.0275.5276.0276.5277.0277.5278.0278.5279.0279.5280.0281.0282.0283.0284.0285.0286.03.023.023.012.992.962.972.962.962.912.922.912.902.922.892.882.872.852.872.842.85287.0288.0289.0290.0291.0292.0293.0294.0295.0296.0297.0298.0299.0300.0301.0302.0303.0304.0305.0306.02.832.832.832.812.792.792.772.762.742.762.752.742.712.712.732.702.672.672.672.66307.0308.0309.0310.0311.0312.0313.0314.0315.0316.0317.0318.0319.0320.0321.0322.0323.0324.0325.0326.02.672.642.622.632.632.622.622.632.592.572.592.592.572.592.592.602.662.702.742.74128Table 6.1 (continued)Energy Oscillator Energy OscillatorEnergy Oscillator(eV) Strength(eV) Strength (eV) Strength(10-2eV-l) (10-2eV-1)(10-2eV-1)327.0 2.70 347.02.44 384.0 2.11328.0 2.74 348.0 2.41 386.0 2.06329.0 2.69 349.0 2.46 388.02.03330.0 2.69 350.0 2.44390.0 2.07331.0 2.65 352.0 2.40 392.0 2.03332.0 2.61 354.0 2.38 394.0 2.01333.0 2.64 356.0 2.35 396.01.971334.0 2.62 358.0 2.31398.0 2.01335.0 2.61 360.0 2.28 400.0 1.983336.0 2.58 362.0 2.30402.0 1.898337.0 2.56 364.0 2.27 404.01.931338.0 2.52 366.0 2.27 406.0 1.917339.0 2.54 368.0 2.21 408.01.869340.0 2.54 370.0 2.22 410.0 1.891341.0 2.52 372.0 2.22412.0 1.875342.0 2.52 374.0 2.18414.0 1.854343.0 2.48 376.0 2.17 416.0 1.839344.0 2.50 378.0 2.14 418.0 1.820345.0 2.43 380.0 2.14420.0 1.778346.0 2.47 382.02.11 422.0 1.827129Table 6.1 (continued)Energy Oscillator Energy Oscillator Energy Oscillator(eV) Strength (eV) Strength (eV) Strength(102eV1) (10-2eV-1)(102eV1)424.0 1.784 458.0 1.597 492.01.374426.0 1.769 460.0 1.587 494.01.411428.0 1.805 462.0 1.605 496.01.400430.0 1.743 464.0 1.578 498.01.364732.0 1.724 466.0 1.528 500.0 1.346434.0 1.686 468.0 1.532436.0 1.728 470.0 1.507438.0 1.751 472.0 1.532440.0 1.677 474.0 1.501442.0 1.675 476.0 1.523444.0 1.655 478.0 1.453446.0 1.637 480.0 1.471448.0 1.601 482.0 1.482450.0 1.604 484.0 1.436452.0 1.606 486.0 1.454454.0 1.635 488.0 1.452456.0 1.608 490.0 — 1.437tnormalized to ref. [1781 at 21.218 eVo(Mb) = l.0975x102-eV1130previously studied in the greatest detail. Figures 6.1(a)and 6.1(b) showthe presently measured absolute optical oscillator strengthsfor thevalence shell photoabsorption of argon in the energy region10—60 eValong 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 higherresolution data fromSamson [45] and Carlson et al.[176] in the 26—29 eV autoiOnizlng regionhave been omitted to permit clearercomparison with the present lowresolution data. The data reported by Samson [45] andCarlson et al.[176] in the continuum autoionizationregions will be compared with thepresent data obtained from the high resolutiondipole (e,e) spectrometerin section 3.3 below. West and Marr [103] havemade absolutephotoabsorption measurements for argon overthe range 36—310 eV andhave given a critical evaluation of existingpublished cross section data toobtain recommended (weighted—average)values throughout the vacuumultraviolet and x—ray regions. These values[47,103] did not take Intoaccount previously published data in theautoionizlng region (26—29 eV)and simply reported interpolated smoothcross sections throughout theautoionizing region. From figure 6.1(a) it can be seenthat all theexperimental data including the present low resolutionresults show asimilar shape for the continuum and areIn generally good quantitativeagreement. The data from Madden et al. [218]are slightly higher thanother experimental values in the vicinity of25 eV. In contrast to theexperimental data, the theoretical values forargon show substantialdifferences in terms of both the shape and the absolutevalues of thecross sections when compared with thepresent results (see figure6.1(b)). The one—electron calculation byMcGuire [112] gives much131higher cross sections just above the 3p threshold and the cross sectionsdrop very quickly to a very low value before reaching the Cooperminimum at —50 eV. Even with the inclusion of electron corre1ation, thecalculations reported by Starace [164] and by Kennedy and Manson [1131still show large discrepancies with the present and other measuredvalues. Since relativistic effects in argon are small, the RPAE calculationof 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 otherexperimental values below 30 eV and are somewhat lower in the energyregion 30—50 eV. The values reported by Parpia et al. [1181 using theRTDLDA method give excellent agreement with the presently reportedexperimental values above 25 eV, but in common with most of the othertheoretical work there still exist some discrepancies with theexperimental data in the energy region between the 3p threshold and thecross section maximum.Figure 6.2 shows the presently measured absolute photoabsorptionoscillator strengths for argon from 40 to 240 eV just below the innershell 2p excitations of argon. Other previously reported experimentaland theoretical data that are available in this energy region are also shownfor comparison. The present data are in generally good agreement withthe compilation data reported by Henke et al. [152] and West and Marr[47,103]. The photoabsorption data of Lukirskii and Zimkina [169] andthe earlier electron impact data of Van der Wiel and Wiebes [22] givelower values at energies above 120 eV. The values measured recently bySamson et al. [179] using a double ionization chamber in the energyregion 40—120 eV are slightly lower than the present work. In132theoretical work, the one—electron calculation of McGuire [112], whichshows very high cross sections just above the 3p threshold (figure 6.1(b))gives very good agreement with the present results from an energy justabove the Cooper minimum to 240 eV (figure 6.2). The RPAEcalculations reported by Amus’ya et aL. [116] show a similar shape in thecontinuum to the present measurements, but the theoretical values areslightly lower from 40 to 150 eV and become increasingly lower above150 eV. The photoionization cross sections calculated by Kennedy andManson [113] show large discrepancies with the present and all otherexperimental data and furthermore the predicted position of theCooperminimum is - 15 eV too high in energy.Figure 6.3 shows the presently measured absolute photoabsorptionoscillator strengths for argon in the energy region from 220 to 500 eVwhere excitation and ionization of the argon 2s and 2p electronstakeplace on top of the valence shell continuum. The limited previouslypublished experimental and theoretical data in this energy regionare alsoshown in figure 6.3 for comparison. Unlike the situation below 240 eV,the agreement between the available experimenta1 data is poor in thisenergy region. It can be seen in figure 6.3 that the data reportedbyLukirskii and Zimkina [169] and the compilation data of Henke et al.[1521 are —10—25% lowerthan the present results. The data of West andMarr [47, 103], which are slightly higher than the presentlyreportedvalues in the energy region 250—290 eV, are lower by more than30% atenergies above 320 eV. The theoretical calculations reported byKennedyand Manson [1131, which show considerable discrepancieswith theexperimental data below 240 eV, exhibit very good agreement with thepresently measured values in the energy region 270—500 eV,while the133calculations 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 KryptonFigures 6.4 and 6.5 show the presently measuredabsolute opticaloscillator strengths for the photoabsorptionof krypton. Table 6.2summarizes the numerical absolute oscillator strengthvalues in theenergy region 14.7—380 eV. In figures 6.4(a) and 6.4(b), the presentlymeasured valence shell photoabsorption oscillator strengths for kryptonin the energy region 5—60 eV are compared with the previously reportedexperimental and theoretical values, respectively.The earlier reportedphotoionization data of Samson[451 are slightly lower than the presentwork in the energy region from the 4p threshold to 30 eV. Theweighted—average values reported in the West and Marr compilation[47,1031, which included the data from Samson [45], show similarbehavior to the original Samson data[45]. In contrast, the most recentdata reported by Samson et al. [179] show excellent agreement with thepresently reported values. As shown in figure 6.4(b), the situation for thetheoretical cross sections of krypton when compared with theexperimental data is similar to that for argon (in figure 6.1(b)). Eventhough agreement between theoretical and experimental values is betterat higher energies, difficulties still remain in describing the behavior ofthe photoionization cross sections just above the 4p threshold and in theregion 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 momentumFigure 6.4: Absolute oscillator strengths for the photoabsorption of krypton in theenergy region 5-60 eV. (a) comparison with other experimental data[45,47,103,152,1801. The discrete region below 15 eV is shown at highresolution in figure 6.10. The resonances in the region 24.5—27.5 eVpreceding the 4s edge are shown at high resolution in figure 6.15. (b)comparison with theory 1112,113,116—118,163].‘34—>CC.)U)I0C.)U)0C.)C7010 20 3040 50 60.00C.)C)U)U)U)01-4C.)0-4I006050403D20107060Present work (Expt.)Amuyso et ci. [116]—— Kennedy & Monson [113]O McGure [112)Zongwiii & Soven [163)+ Johnson & Cheng Eli?]oPorpia et ci. [118](b) Comparison with theory4sIIr1.01-S50•40•3020•101’O0--20 30 40 50 60Photon energy (eV)Figure 6.5: Absolute oscillator strengths forthe photoabsorption of krypton in theenergy region 50—400 eV compared with otherexperimental[47,103,152,170,177,180]andtheoretjcal[112,113,116,166]data.3d13p13s1H,-0VCl)0.—C)Cl)0C)7654320135Kr!4XAX*AAXI ‘•----XAA>A***• Present work (E = 1 eV FWHM)•7A West & Marr[47,103]A El—Sherbini& Van der Wiel [180]* Lukirskii et at. [170]1-1/ < • Land & Watson [177]\** Henkeet at. [152]Amuy’so et ci. [116]- —— Kennedy & Manson [113]O McGuire C 112]xRozsnyio [1 661AXAX50 100 150 200 250 300 350 400Photon energy (eV)136Table 6.2Absolute differential optical oscillator strengths for thephotoabsorption of krypton above the first ionization potential obtainedusing 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(10-2eV1) (10-2eV1) (102eV1)14.7 40.22 16.4 41.41 18.1 39.8214.8 40.16 16.5 41.81 18.2 39.9614.9 40.56 16.6 41.04 18.3 39.5515.0 40.42 16.7 41.46 18.4 39.6515.1 40.64 16.8 41.62 18.5 39.5815.2 40.50 16.9 41.76 18.6 40.0015.3 41.25 17.0 40.77 18.7 39.6415.4 41.13 17.1 41.02 18.8 39.3515.5 41.41 17.2 41.63 18.9 38.5915.6 41.46 17.3 41.53 19.0 38.4015.7 41.49 17.4 40.70 19.1 38.5315.8 41.22 17.5 40.67 19.2 38.8315.9 41.28 17.6 40.65 19.3 37.9816.0 41.20 17.7 41.07 19.4 38.4116.1 41.73 17.8 40.70 19.5 38.3216.2 40.78 17.9 40.26 19.6 38.3816.3 41.57 18.0 40.70 19.7 37.57137Table 6.2 (continued)Energy OscillatorEnergy OscillatorEnergy Oscillator(eV)Strength (eV) Strength(eV) Strength(10-2eV-1) (1O2eV1)(1O2eV1)19.8 37.7625.0 25.8135.0 9.3019.9 37.8525.5 25.5735.5 8.3320.0 37.4626.0 24.2236.0 7.7720.1 36.8026.5 23.3736.5 7.3920.2 36.7927.0 22.9937.0 6.9220.3 37.3327.5 21.1437.5 6.2820.4 36.9828.0 20.38 38.05.8520.5 35.6528.5 19.8538.5 5.6520.6 35.4229.0 17.9239.0 5.1520.7 35.3929.5 17.0439.5 4.8120.8 35.0930.0 16.0840.0 4.4720.9 35.0330.5 15.4741.0 4.1034.90 31.014.96 42.03.6621.5 35.1531.5 14.0143.0 3.1222.0 33.5732.0 12.6944.0 2.7422.5 32.4932.5 12.3045.0 2.4923.0 31.3833.0 11.5846.0 2.1723.5 30.7933.5 10.7847.0 1.98324.0 29.6234.0 10.2048.0 1.78724.5 28.1234.5 9.6949.0 1.675138Table 6.2 (continued)Energy Oscillator Energy Oscillator Energy Oscillator(eV) Strength(eV) Strength (eV) Strength(102eV1)(102eV’) (102eV1)50.0 1.475 70.0 0.551 110.0 1.56651.0 1.319 72.0 0.527 112.0 1.68452.0 1.220 74.0 0.528 114.0 1.79753.0 1.135 76.0 0.505 116.01.87854.0 1.057 78.0 0.499118.0 2.0055.0 1.014 80.0 0.494 120.0 2.1456.0 0.880 82.0 0.497 122.02.2757.0 0.862 84.0 0.494 124.0 2.3858.0 0.818 86.0 0.489 126.0 2.5259.0 0.788 88.0 0.508 128.0 2.6760.0 0.737 90.0 0.565 130.02.7861.0 0.722 92.0 1.064 132.02.8962.0 0.679 94.0 1.088134.0 3.0163.0 0.657 96.0 1.138 136.0 3.1764.0 0.667 98.0 1.170 138.0 3.2665.0 0.599 100.0 1.171 140.0 3.3366.0 0.645 102.0 1.199142.0 3.4767.0 0.605 104.0 1.252144.0 3.5368.0 0.582 106.0 1.327 146.0 3.6269.0 0.553 108.0 1.444148.0 3.70139Table 6.2 (continued)Energy OscillatorEnergy Oscillator EnergyOscillator(CV) Strength (eV)Strength (eV)Strength(1O2eV1)(1O2eV1) (1O2eV’)150.0 3.75 190.04.40 230.04.55152.0 3.84 192.04.33 232.04.57154.0 3.91194.0 4.32234.0 4.46156.0 3.94196.0 4.41 236.04.46158.0 4.02 198.04.36 238.04.49160.0 4.01 200.04.31 240.0 4.46162.0 4.05202.0 4.32 242.04.40164.0 4.14204.0 4.32 244.04.37166.0 4.18206.0 4.30 246.04.36168.0 4.12 208.04.34 248.0 4.34170.0 4.19 210.04.41 250.0 4.32172.0 4.25 212.04.43 252.0 4.28174.0 4.35 214.04.50 254.0 4.29176.0 4.27 216.04.54 256.0 4.26178.0 4.25 218.04.59 258.0 4.25180.0 4.32 220.04.61 260.0 4.21182.0 4.35 222.04.59 262.0 4.20184.0 4.29 224.04.61 264.0 4.14186.0 4.28 226.04.60 266.04.17188.0 4.31 228.04.57 268.04.09140Table 6.2 (continued)Energy OscillatorEnergy OscillatorEnergy Oscillator(eV) Strength (eV)Strength (eV) Strength(102eV-1) (10-2eV1)(102eV1)270.0 4.07308.0 3.79 346.03.21272.0 4.11310.0 3.75348.0 3.24274.0 4.04312.0 3.73350.0 3.25276.0 4.05 314.03.68 352.03.34278.0 4.01316.0 3.68 354.03.21280.0 4.03318.0 3.67 356.03.15282.0 3.96320.0 3.63 358.03.25284.0 3.97322.0 3.56 360.03.16286.0 3.91 324.03.54 362.03.14288.0 3.98 326.03.58 364.03.17290.0 3.92328.0 3.54366.0 3.09292.0 3.98330.0 3.48 368.03.02294.0 3.95332.0 3.48370.0 3.00296.0 3.94334.0 3.41 372.02.97298.0 3.92336.0 3.40 374.02.97300.0 3.88 338.03.43 376.03.02302.0 3.86340.0 3.41378.0 2.93304.0 3.90 342.03.33 380.02.91306.0 3.83344.0 3.34_________ _______normalized to ref. [178] at21.218 eVa (Mb) = 1.0975 x102eV1141barrier which separates the inner well and outer well states. Thephotoionizatlon cross sections reach a maximum value at -180 eV whichis —90 eV above threshold. Figure 6.5 shows the presently measuredphotoionization cross sections of krypton in the energy region50—400 eVwhich includes not only the 3d ionization threshold but alsothe 3s (-290eV) and 3p (-220 eV) thresholds as well. The optical data of West andMarr [47,103], Land and Watson [1771, and Henke et al. [152]show 10—15% higher values than the present work around the 3d crosssectionmaximum, while the values of Lukirskii et al. [1701 are lower by morethan 25%. The electron impact data of El-Sherbini and Van der Wiel[180] agree very well with the presentwork. The one—electroncalculation of McGuire [112] gives cross sections which are too high. Incontrast all theoretical calculations which include electroncorrelation[113,116,166] adequately describe the behavior of the photoionizationoscillator strength of the 3d—electrons. In particular the RPAE data ofAmus’ya et al. [116] show extremely good agreement with thepresentdata.6.2.1.3 Low Resolution Measurements for XenonFigures 6.6—6.8 show the presently measured absolute opticaloscillator strengths for the photoabsorption of xenon andtable 6.3summarizes the corresponding absolute oscillator strengthvalues in theenergy region 13.5—398 eV. Figures 6.6(a) and 6.6(b) show thepresentlymeasured photoabsOrption oscillator strengths for xenon in the energyregion 5—60 eV along with previously reported experimental andtheoretical data respectively. It can be seen from figure 6.6(a) that thePhoton energy (eV)Figure 6.6: Absolute oscillator strengths for thephotoabsorption of xenon In theenergy region 5—60 eV. (a) comparisonwith other experimental data[45,48,179,,180]. The discrete region below13.5 eV is shown at highresolution in figure 6.12. The resonances inthe region 20.5—27.4 eVpreceding the 5s1 edge are shown at highresolution in figure 6.16. (b)compared with theory [113,116—118,1631.(a) Experimental5p1measurements807060505s11420ADPresent work (E= 1 eV FWHM)West & Morton [48)Samson [45]Et—Sherbini & Van der Wiel [ 180]Samson et ci. [179]-,C-tV1.4U)1-42=C.)Cl)0C.)10 20 30 40 50 6040302010090807060504030201Dwith theory5s’.00C.)VU)U)U)0C.)0‘.40U),0008070605040302010090807060504D3020100Ix(b) ComparisonS.• —/34.• Present work (Expt.)Amt.syo et ci. [116]- —— Kennedy & Manson [113]— ZcngwHi & Soven [163]+ Johnson & Cheng [117]Porpia et ci. [118].... . ... •1’D 20 30 40 50601433020100(a) Experimental measurementsIxA• Present work (E = 1 eV FWHM)**West & Morton [48)* AEl—Sherbini & Von der Wiel [180]***• Land & Watson [177)* Ederer [172)•• * Hansel et CI.[174]C Samson et 01. [179]•* Lukirskii et ci. [170]• .I*•4d’. AJ.c4AA40CVU)1C——VU)CC.)4-iC302010CC.)VU)CC.)00U)C080 120 160 2b0(b) Comparison with theoryIxel30Present work (Expt.)—— Staroce [164]Amuyso et ci. [116)—— Kennedy & Monson [113Zongwiii & Soven [163]Porpio et cI. [118)x Rozsnyia [14p1100-xxxxx\10120Photon energy (cv)1 60 200F’Igure 6.7: Absolute oscillator strengthsfor the photoabsorption of xenon in theener’ region 40—200 eV. (a) comparison with other experimental data[48,170,,172,174,179,,180,]. (b) comparison with theory[113,116,118,163,164,166].• Present work (E = 1eV FWHM)West & Morton [ 48]A EI—Sherbini & Von der WieI 1 180]U Land & Watson [ 177]* Lukirskii et al. 1 1 701—— Kennedy & Manson [113]—CC—.—C.)Cl)C—C-)02.52.01 .51 .00.50.01442.502.0 +.C-)VU)U)r:1)1.5 0I001 fl•4-0U)L).J00.0XciA4s\*_——\. — ——*..‘ \••fl_..o••.•St ___AA A AAAA160 200 240280 320360 400Photon energy(eV)Figure 6.8: Absolute oscillator strengths for the photoabsorptionof xenon In theenergy region 160—400 eV compared with other experimental[48,17,0,177,180] and theoretical[1 13] data.145Table 6.3Absolute differential opticaloscillator strengths for thephotoabsorption of xenon above the firstionization potential obtainedusing the low resolution (1 eV FWHM)dipole (e,e) spectrometer(13.5—398 cv)Energy Oscillator EnergyOscillator Energy Oscillator(eV) Strength (eV)Strength (eV)Strength(102eV’) (102eV1)(102eV1)13.5 58.35 15.254.37 16.9 47.1113.6 58.29 15.353.74 17.045.6313.7 57.96 15.454.25 17.1 45.8213.8 57.9815.5 53.62 17.244.4813.9 57.80 15.653.16 17.344.7014.0 57.53 15.752.20 17.4 44.1614.1 56.71 15.852.65 17.5 44.7414.2 56.95 15.951.86 17.6 43.8014.3 56.62 16.051.64 17.7 44.0914.4 56.8616.1 51.07 17.843.5814.5 56.34 16.250.88 17.9 42.7314.6 56.58 16.350.84 18.0 42.0114.7 56.34 16.449.54 18.1 41.4414.8 55.87 16.548.68 18.240.8814.9 54.59 16.648.20 18.3 41.0715.0 54.4716.7 48.41 18.440.6215.1 54.16 16.8k47.44 18.5 40.43146Table 6.3 (continued)Energy Oscillator Energy Oscillator Energy Oscillator(eV) Strength (eV) Strength (eV) Strength(102eV1) (1O2eV1) (1O2eV1)18.6 40.28 24.0 19.62 34.0 4.0218.7 39.55 24.5 18.13 34.5 3.6918.8 38.70 25.0 16.17 35.0 3.2818.9 38.84 25.5 15.22 36.0 3.1119.0 37.61 26.0 14.78 37.0 2.7719.1 37.49 26.5 13.20 38.0 2.4919.2 37.00 27.0 12.39 39.0 2.2319.3 36.96 27.5 11.39 40.0 2.0519.4 36.19 28.0 9.59 41.0 1.94419.5 35.28 28.5 8.97 42.0 1.78919.6 34.60 29.0 8.27 43.0 1.69619.7 33.83 29.5 7.72 44.0 1.66420.0 33.04 30.0 7.17 45.0 1.57820.5 31.21 30.5 6.54 46.0 1.49321.0 27.93 31.0 6.12 47.0 1.40721.5 26.88 31.5 5.80 48.0 1.39822.0 24.88 32.0 5.28 49.0 1.34122.5 24.01 32.5 4.95 50.0 1.31423.0 22.08 33.0 4.48 51.0 1.24323.5 20.84 33.5 4.26 52.0 1.219147Table 6.3 (continued)Energy Oscillator Energy Oscillator Energy Oscillator(eV) Strength (eV) Strength (eV) Strength(102eV1) (102eV1) (102eV1)53.0 1.203 86.0 14.25 126.0 8.9054.0 1.201 88.0 15.91 128.0 8.1555.0 1.160 90.0 17.80 130.0 6.9456.0 1.153 92.0 18.96 132.0 6.7357.0 1.178 94.0 20.30 134.0 5.3658.0 1.145 96.0 21.19 136.0 4.5559.0 1.137 98.0 21.83 138.0 4.1960.0 1.148 100.0 22.33 140.0 3.4162.0 1.124 102.0 22.05 142.0 3.0364.0 1.177 104.0 21.67 144.0 2.8266.0 1.900 106.0 21.41 146.0 2.4368.0 2.33 108.0 20.40 148.0 2.4170.0 2.71 110.0 19.37 150.0 2.1172.0 3.36 112.0 18.23 152.0 1.83874.0 4.36 114.0 17.39 154.0 1.70276.0 5.66 116.0 16.45 156.0 1.55478.0 7.38 118.0 13.91 158.0 1.45480.0 8.92 120.00 12.66 160.0 1.36682.0 10.29 122.0 11.96 162.0 1.29784.0 11.99 124.0 10.29 164.0 1.241148Table 6.3 (continued)Energy Oscillator Energy Oscillator Energy Oscillator(eV) Strength (eV) Strength (cv)Strength(102eV1) (102eV1)(102eV1)166.0 1.189 206.0 0.974 246.0 1.277168.0 1.130 208.0 0.983 248.0 1.265170.0 1.111 210.0 1.037 250.0 1.284172.0 1.056 212.0 1.072 254.0 1.305174.0 1.031 214.0 10.90 258.0 1.319176.0 0.999 216.0 1.092 262.0 1.315178.0 1.015 218.0 1.159 266.0 1.315180.0 0.986 220.0 1.114 270.0 1.323182.0 0.983 222.0 1.154 274.0 1.342184.0 0.982 224.0 1.151 278.0 1.341186.0 0.977 226.0 1.181 282.0 1.365188.0 0.977 228.0 1.190 286.0 1.339190.0 0.972 230.0 1.188 290.0 1.347192.0 0.960 232.0 1.197 294.0 1.350194.0 0.981 234.0 1.194 298.0 1.363196.0 0.984 236.0 1.235 302.0 1.337198.0 0.979 238.0 1.258 306.0 1.356200.0 0.990 240.0 1.248 310.0 1.340202.0 0.969 242.0 1.263 314.0 1.338204.0 0.995 244.0 1.267 318.0 1.321149Table 6.3 (continued)Energy OscillatorEnergy Oscillator EnergyOscillator(eV) Strength(eV) Strength(eV) Strength(1O2eV1)(1O2eV1)(1O2eV1)322.0 1.322382.0 1.249326.0 1.332386.0 1.208330.0 1.306390.0 1.207334.0 1.297394.0 1.208338.0 1.313398.0 1.175342.0 1.309346.0 1.302350.0 1.288354.0 1.300358.0 1.283362.0 1.241366.0 1.264370.0 1.254374.0 1.279378.0 1.237normalized to ref. [1781 at16.848 eVa(Mb) 1.0975x102-eV1150present data are in excellent agreement with the recent work of Samsonet al. [179] over the entire energy range shown. The data from the Westand Morton compilation [48] are much higher than the present work justabove 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 andCheng [1171 show better agreement with the present work than do thenon—relativistic RPAE data of Amus’ya et al. [116]. which give muchhigher cross sections just above the 5p threshold. The calculationsreported by Zangwill and Soven [163] in the 15-25 eV region usingdensity—functional theory show very good agreement with the presentwork. In contrast other theoretical calculations yield less satisfactoryresults particularly below 20 eV.Photoionization cross sections for the 4d—subshell of xenon havebeen studied extensively both experimentally and theoretically. Figures6.7(a) and 6.7(b) show the presently measured photoabsorption oscillatorstrengths of xenon in the energy region 40—200 eV. It can be seen fromfigure 6.7(a) that the values obtained in the present work are slightlylower than other experimental data in the energy region around the 4dionization cross section maximum. The data from Lukirskii et al. [170],Ederer [172] and El—Sherbini and Van der Wiel [180] give the highestoscillator strengths in this region. All one—electron calculations[112, 165] are in severe disagreement withexperiment and are notshown in figure 6.7(b). This disagreement is not surprising in view ofthe many—electron effects which influence the 4d cross sections. Themore complex calculations [113,116,118,163,164,166] which Includeelectron correlation achieve closer agreement with experimental values.151In figure 6.7(b) it can be seen that the theoretical calculations Includingelectron correlation give photolonization cross sections reasonablysimilar In shape to the present experimental work. However, the crosssection maxima reported by Starace [1641, Kennedy and Manson [113]and Rozsnyai [166] are shifted to higher energy. The calculationsreported by Zangwill and Soven [163] and Parpla et al. [118] showreasonable agreement with the present work, although the calculatedvalues are slightly higher.Figure 6.8 shows the presently determined photoabsorptionoscillator strengths for xenon in the energy region 160—398 eV. Thereare few previously reported data in this energy region. The data from theWest and Morton compilation [48] are lower than the present values inthe energy region 160—200 eV but show good agreement with thepresent work at higher energies. Similar to the results obtained fromthe data reported by Lukirskii and Zimkina [1691 for argon and byLukirskii et al. [170] for krypton, the data reported by Lukirskii et al.[1701 for xenon are lower than the present values at energies higherthan160 eV. The earlier dipole electron impact data of El—Sherbini and Vander Wiel [180] show large statistical errors in this energy region, and aremuch lower than the present work above 200 eV. The calculation byKennedy and Manson [1 13], also shown in figure 6.8, shows fairagreement with experiment above 200 eV.1526.2.2 High Resolution Measurements of the PhotoabsorptionOscillator Strengths for the Discrete Transitions Below themp Ionization Thresholds for Argon (m=3), Krypton (m=4) andXenon (m=5)High resolution electron energy loss spectra at resolutions of0.048, 0.072 and 0.098 eV FWHM in the energy range 11—22 eV forargon, 9—22 eV for krypton and 8—22 eV for xenon were multiplied by theappropriate Bethe—Born factors for the high resolution dipole (e,e)spectrometer (see refs. [37,38] and chapter 3) to obtain relative opticaloscillator strength spectra which were then normalized In the smoothcontinuum regions at 21.218 eV for argon and krypton, and at 16.848 eVfor xenon using the absolute data determined by Samson and Yin [178].Figures 6.9—6. 13 show the resulting absolute differential optical oscillatorstrength spectra of argon, krypton and xenon at a resolution of 0.048 eVFWHM. The dipole—allowed electronic transitions from the ms2mp6configurations of argon, krypton and xenon with m=3, 4 and 5respectively, to members of thems2mp5(P3/21/2)nsand nd manifolds(where n>m) were observed. The positions and assignments [155] of thevarious members of the nl and ni series are indicated in the figureswhere the nd[1/2] and nd[3/2] states which converge to the samelimit are labelled as nd and n respectively. For peaks in theexperimental spectrum which are completely resolved such as the 4s and4& resonance lines of argon, integration of the peak areas provides adirect measure of the absolute optical oscillator strengths for therespective individual discrete electronic transitions. For states at higherenergies which cannot be completely resolved, absolute oscillator0IJL.)C.)0‘-4C.)0I0VJ00153700600500400300‘-I0I02Photon energy (eV)0Figure 6.9: Absolute oscillator strengths for the photoabsorption of argon obtainedusing the high resolution dipole (e,e) spectrometer (FWHM=O.048 eV). Theassignments and energy positions are taken from reference [155]. (a)11—18eV. (b) Expanded view of the 13.5—16.5 eV energy region. The deconvolutedpeaks are shown as dashed lines.500400300 0C.)020000154I!Figure 6.10:12Photon energy (eV)Absolute oscillatorstrengths for thephotoabsorption ofkrypton obtainedusing the high resolutiondipole (e.e) spectrometer(FWHM=0.048 eV) inthe energy region 9—16eV. The assignmentsand energypositions aretaken from reference[155].C.—0120 ,0015521 .220-.Q0Q00.80.40.08040Figure 6.11:14.5Photon energy (eV)Absolute oscillator strengths for the photoabsorptionof krypton obtainedusing the high resolution dipole (e,e) spectrometer (F’WHM=O.048eV). Theassignments and energy positions are taken from reference[155]. (a)Expanded view of the 12.2—13.6 eV energyregion. The deconvoluted peaksare shown as dashed lines. (b) Expanded view of the 13.5-15.0eV energyregion.156I I 11111111112I86s 5d 5d7s Sd6dBsP3/iXe1-- II II II8006s 5d7s 6d8s7d1/2 0C)600c,0C)‘-4o44000C.)00 22000C.)0I____________0I •8 10 1214Photon energy (eV)Figure 6.12: Absolute oscillatorstrengths for the photoabsorption of xenon obtainedusing the high resolution dipole (e,e) spectrometer(FWHM=0.048 eV) inthe energy region 8—15 eV. The assignmentsand energy positions aretaken from reference[1551.o1.6001.2200 ,00 0.—C.)0IC.)0.—0160120157500400300080.40.0Photon energy (eV)Figure 6.13:80400Absolute oscillator strengths for the photoabsorption of xenon obtainedusing the high resolution dipole (e,e) spectrometer (FWHM=O.048 eV). Theassignments and energy positions are taken from reference [155]. (a)Expanded view of the 11—12 eV energy region. The deconvoluted peaks areshown as dashed lines. (b) Expanded view of the 12—13.7 eV energy region.158strengths have been obtained from fitted peak areas as shown in thefigures, according to least squares fits of the experimental data.Thesame fitting procedures have been applied to the spectra obtained at thethree different experimental resolutions. The consistencyof theoscillator strength values obtained for given transitions at thedifferentresolutions confirms the accuracy of thefitting procedures and therespective Bethe—Born factors determined as describedin refs. [37,38]and chapter 3. Tables 6.4—6.9 summarize the optical oscillator strengthsfor the discrete transitions of the three noble gases obtained from theanalyses of the spectra (figures 6.9—6.13) at the highest resolution(0.048eV FWHM). The uncertainties are estimated to be -5% for resolvedtransitions and 1O% for unresolved peaks such as the 5s, 5s’, 3dand 3d’excited states of argon due to the additional errors involved indeconvoluting the peaks. Other previously reported experimentalandtheoretical oscillator strengths for the discrete electronictransitions ofthe three noble gases are also shown in the tables for comparison.Figure 6.9(a) shows a typical absolute differential optical oscillatorstrength spectrum of argon obtained at a resolution of 0.048 eV FWHMover the energy range 11—18 eV. Figure 6.9(b) showsan expanded viewof the spectrum in the 13.5—16.5 eV energy region including the fittedpeaks corresponding to partially resolved or unresolved states. Sincemost 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) andTable 6.4159Theoretical and experimental determinations of the absolute optical oscillatorstrengths for the3s23p6—’3s5(P3/2,1/2)4s discrete transitionsofargontOscillator strength for transition Oscillatorfrom3s23p6—*.3s5mwhere m is strength(2P312)4s (a1) (2P1,)4s’ (a2) ratio(11.614eV)#(11.828 eV) (al/a2)A. Theory:Amus’ya (1990) [1451 0.298Cooper (1962) [104] 0.33Stewart (1975) [151] 0.270Albatetal. (1975) [188] 0.048 0.188 0.255Gruzdev and Loginov(1975)[1861 0.06 1 0.231 0.264Lee(1974)[185] 0.059 0.30 0.197LeeandLu(1973)[184] 0.080 0.210 0.381Aymaretal. (1970)[147](a) dipole length 0.07 1 0.286 0.248(b) dipole velocity 0.065 0.252 0.258Gruzdev(1967)[111] 0.075 0.15 0.500Knox (1958) [181](a)wavefunction 0.052 0.170 0.306(b) semi-empirical 0.049 0.200 0.245B. Experiment:Present work (HR dipole(e,e)) 0.0662 0.265 0.250(0.0033) (0.013)Tsurubuchietal. (1990) [140] 0.057 0.213 0.268(Absolute self-absorption) (0.003) (0.011)L,ietal. (1988) [143] 0.058 0.222 0.261(Electron impact) (0.003) (0.02)Chornayetal. (1984) [202] 0.065(Lifetime: electron-photon (0.005)coincidence)Westerveld et al. (1979) [139] 0.063 0.240 0.263(Absolute self-absorption) (0.005)(0.02)Geiger (1978) [213] 0.066 0.255 0.259(Electron_impact)Table 6.4 (continued)160Oscillator strength for transition Oscillatorfrom3s23p6-.3s5mwhere m is strength(2P312)4s(ai) (2P112)4s (a2) ratio(11.614 eV) (11.828 eV) (al/a2)B: Experiment: (continued)Valleeetal. (1976) [206] 0.0510.210 0.243(Pressure broadening profile) (0.00 7) (0.030)Kuyatt (1975) [219] 0.067 0.267 0.251(Electron impact)Copley and Camm (1974) [205] 0.076 0.283 0.269(Pressure broadening profile) (0.008) (0.024)Irwinetal. (1973) [199] 0.083 0.350.237(Lifetime: beam foil) (0.027) (0.130)Natalietal. (1973) [142] 0.070 0.278 0.252(Electron impact)McConkey and Donaldson (1973) 1208] 0.096(Electron excitation function) (0.02)Jongh and Eck (1971) [62] 0.22(Relative self-absorption) (0.02)Geiger (1970) [141] 0.047 0.186 0.253(Electron impact) (0.009) (0.037)Lawrence (1968) [198] 0.0590.228 0.259(Lifetime: Delay coincidence) (0.003)(0.02 1)Morack and Fairchild (1967) [197] 0.024(Lifetime: delayed coincidence) (0.003)Lewis (1967) [138] 0.063 0.2780.227(Pressure broadening profile) (0.004) (0.002)Chamberlainetal. (1965) [209] 0.049 0.181 0.271(Electron_impact)_________________ _________________ ___________+Estimated uncertainties in the experimental measurements are shown in parentheses.Summed oscillator strength (a1+a2).Table6.5(a)Theoreticalandexperimentaldeterminationsoftheabsoluteopticaloscillatorstrengthsfordiscretetransitionsofargonintheenergyregion13.80—14.85eVOscillatorstrengthfrom3s23p6—..3s23p5mwheremIs(2p312)3d(2P3/2)Ss(2P3i2)3.(2P1/2)5s(2P112)3d(2P312)4d(2P312)6s(13.864eV)t(14.090eV)(14.153eV)(14.255eV)(14.304eV)(14.711eV)(14.848eV)A:Theory: Lee(1974)118510.00160.0450.0450.0390.1280.00260.023LeeandLu(1973)1184)0.00110.0340.0530.0250.110.00310.014B:Experiment: Presentwork(HRdipole(e,e))0.00130.02640.09140.01260.1060.00190.0144(0.0001)(0.0026)(0.0091)(0.0013)(0.011)(0.0002)(0.0014)Westerveldetal.(1979)113910.000890.0250.0790.01060.086(Absolutese1fabsorpt1on)(0.00007)(0.002)(0.006)(0.0008)(0.007)Geiger(1978)12131<0.00250.0320.1080.01080.097(Electronimpact)Natalletal.(1973)142]0.00100.0280.0920.01240.1100.0040.0094(Electronimpact)Wieseetal.(1969)]540.02680.0930.01190.0106(Lifetimedatafromref.1198))Lawrence(1968)(19810.0280.0930.0130.107(Lifetime:delayed(0.002)(0.006)(0.003)(0.015)coincidence)Estimateduncertaintiesintheexperimentalmeasurementsareshowninparentheses.ridandnrefertothendl1/21andnd)3/21statesrespectivelywhichconvergetothesame2P312limit.Thetransitionenergieswereobtainedfromref.11551.@ValuesobtainedbyreanalyzingthelifetimedataofLawrence(1968)1198I.Table6.5(b)Theoreticalandexperimentaldeterminationsoftheabsoluteopticaloscillatorstrengthsfordiscretetransitionsofargonintheenergyregion14.85—15.30eVtOscillatorstrengthfrom3s23p6—..3s23p5mwhere111isTotal(2P312)4d..(2P112)4d(2P112)6s’(2P312)5d(2p312)7(2P3i2)5.to(14.859eV)t(15.004eV)(15.022eV)(15.118eV)(15.186eV)(15.190eV)IonizationA:Theory:Lee(1974)118510.0360.82LeeandLu(1973)118410.0390.0320.013B:Experiment: Presentwork(HRdipole(e.e))0.04840.02090.02210.00410.04260.859(0.0048)(0.0021)(0.0022)(0.0004)(0.0043)(0.0043)Natalietal.(1973)114210.0480.0150.02240.00320.01390.02340.827(Electron_impact)EstimateduncertaintiesIntheexperimentalmeasurementsareshowninparentheses.ndandndrefertothendl1/21andndl3/2}statesrespectivelywhichconvergetothesame213,2limit.Thetransitionenergieswereobtainedfromref.11551.163Table 6.6Theoretical and experimental determinations of the absolute optical oscillatorstrengths forthe4s24p6—.4s5(2P3/2.1 /2)5S discrete transitions of kryptontOscillator strength for transition Oscillatorfrom4s24p6—4s5mwhere m is strength(2P312)5s (b1) (2P1/)5s’ (b2) ratio(10.033eV)#(10.644 eV)(b11b2)A. Theory:Amusya (1990) [145] 0.353Cooper (1962) [1041 0.405Aymar and Coulombe (1978)[189](a) dipole length 0.1760.177 0.99(b)dipolevelcity 0.193 0.172 1.12Geiger (1977) [2121 0.250 0.143 1.748Gruzdev and Loginov (1975) [1871 0.190 0.177 1.073Aymaretal. (1970) [147](a) dipole length 0.2 15 0.2 15 1.000(b) dipole velcity 0.185 0.164 1.128Gruzdev(1967)[llll 0.200.20 1.000Dow and Knox (1966) [1821(a)wavefunction 0.138 0.1361.015(b) semi-empirical 0.1520.153 0.993B. Experiment:Present work (HR dipole(e.e)) 0.214 0.1931.109(0.011) (0.010)Tsurubuchiet al. (1990) [1401 0.155 0.1391.115(Absolute self-absorption)(0.01 1) (0.010)Takayanagietal.(1990)[2151 0.143 0.127 1.126(Electron impact) (0.015) (0.0 15)Table 6.6 (continued)Oscillator strength for transition Oscillatorfrom4s24p6—’4s5mwhere m is strength(2P3/2)5s (b1) (2P1/2)5s’ (b2) ratio(10.033 eV) (10.644 eV) (biIb2)B: Experiment: (continued)Ferrelletal. (1987)166] 0.180(Phase-matching) (0.027)Matthiasetal. (1977) [2011 0.208 0.197 1.056(Lifetime: resonance fluoresonance) (0.006) (0.006)Geiger (1977) [2121 0.195 0.173 1.127(Electron impact)Natalietal.(1973)[142] 0.212 0.191 1.110(Electron impact)Jongh and Eck (1971) [621 0.142(Relative self absorption) (0.015)Geiger(1970)[141] 0.173 0.173 1.000(Electron impact) (0.035) (0.035)Griffin and Hutchson (1969) [1921 0.187 0.193 0.969(Total absorption) (0.006) (0.009)Chashchina and Shrieder (1967) [193] 0.21 0.21 1.000(Linear absorption) (0.05) (0.05)Lewis (1967) [138] 0.204 0.184 1.109(Pressure broadening profile) (0.02) (0.02)Wilkinson(1965)[190] 0.159 0.135 1.178(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 (b1+b2).164Table6.7(a)Theoreticalandexperimentaldeterminationsoftheabsoluteopticaloscillatorstrengthsfordiscretetransitionsofkryptonintheenergyregion11.90—13.05eVtOscillatorstrengthfrom4s24p6—4s24p5mwheremis(2p3/2)4d*(2P3,12)4d(2P312)6s(2P312)5d(2P112)4d’(2P112)6s’(12.037eV)#(12.355eV)(12.385eV)(12.870eV)(13.005eV)(13.037eV)A:Theory:Geiger(1977)[21210.01440.09730.1080.01140.04380.0065B:Experiment: Presentwork(HRdipole(e,e))0.00530.08240.1540.01400.04350.0105(0.0003)(0.0082)(0.015)(0.0014)(0.0044)(0.0011)Geiger(1977)1212]0.00550.06490.1420.0140.04390.015(ElectronImpact)Natalietal..(1973)1142]0.00440.08170.1520.01380.04200.0056(Electron_impact)Estimateduncertaintiesintheexperimentalmeasurementsareshowninparentheses.*ndandnrefertothend]1/21andnd[3/21statesrespectivelywhichconvergetothesame2P312limit.Thetransitionenergieswereobtainedfromref.[155].0)Table6.7(b)Theoreticalandexperimentaldeterminationsoftheabsoluteopticaloscillatorstrengthsfordiscretetransitionsofkryptonintheenergyregion13.OS—13.50eVOscillatorstrengthfrom4s24p6—’4s24p5mwheremisTotal(2p312)5*(2P312)7s(2P312)6d(2P3/2)6d.(2P312)8sto.(13.099eV)#(13.114eV)(13.350eV)(13.423eV)(13.437eV)ionizationA:Theory:Geiger(1977)(21210.09600.04360.00250.03070.0163B:Experiment: Presentwork(HRdipole(e,e))0.06100.1130.00150.04390.02031.126(0.0061)(0.011)(0.0002)(0.0044)(0.0020)(0.056)Geiger(1977)121210.1870.00420.054(Electronimpact)Natalietal.(1973)[142J0.1190.0480.00240.02950.02901.10(Electron_impact)EsthnateduncertaintiesintheexperimentalmeasurementsareshownInparentheses.tmndandnrefertothend[1/21andnd[3/21statesrespectivelywhichconvergetothesame2P312limit.Thetransitionenergieswereobtainedfromref.[1551.— C)167Table 6.8Theoretical and experimental determinations of the absolute optical oscillatorstrengths forthe5s25p6—’5s5(2P3/2.1 /2)6S discrete transitionsof xenonOscillator strength for transition Oscillatorfrom5s25p6—’5s5mwhere m is strength(2P3/)6s (cj) (2P112)6s’ (c2) ratio(8.437eV)#(9.570 eV)(c1/c2)A. Theory:Amus’ya (1990) [145] 0.403Aymar and Coulombe (1978) [1891(a) dipole length 0.282 0.306 0.922(b) dipole velcity0.294 0.270 1.089Geiger (1977) [212] 0.28 0.3650.767Aymaretal. (1970) [147](a) dipole length 0.273 0.235 1.162(b) dipole velcity 0.176 0.118 1.492Kimetal.(1968)[183] 0.212 0.189 1.122Gruzdev(1967) 1111] 0.28 0.25 1.120Dow and Knox (1966) 1182](a) wavefunction 0 194 0.147 1.320(b) semi-empirical 0.190 0.1701.118B. Experiment:Present work (HR dipole(e.e)) 0.273 0.1861.468(0.014) (0.009)Suzukietal.(1991)1216] 0.222 0.158 1.405(Electron impact) (0.027) (0.019)Ferrell et al. (1987) [66] 0.260 0.191.368(Phase-matching) (0.05) (0.04)Table 6.8 (contInued)Oscillator strength for transition Oscillatorfrom5s25p6—i.5s5mwhere m Is strength(2P312)6s (c1) (2P112)6s’ (c2) ratio(8.437eV)#(9.570 eV) (cj/c2)B: Experiment: (continued)Matthiasetal. (1977) [201] 0.263 0.229 1.148(Lifetime: resonance fluoresonce) (0.007)(0.007)Geiger (1977) [212] 0.26 0.191.368(Electron impact)DelageandCarette(1976)[211] 0.183 0.169 1.083(Electron impact)Natalietal. (1973) [142] 0.272 0.189 1.439(Electron impact)Wieme and Mortier (1973) [200] 0.213 0.180 1.183(Lifetime: resonance imprisonment)(0.020) (0.040)Geiger (1970) [141] 0.26 0.191.368(Electron impact)Griffin and Hutchson (1969) [192] 0.194(Total absorption) (0.005)Lewis (1967) [138] 0.256 0.238 1.071(Pressure broadening profile) (0.008) (0.0 15)Wilkinson (1966) [191] 0.260 0.2700.963(Total absorption) (0.020) (0.020)Anderson (1965) [1951 0.256 0.238 1.076(Lifetime: level-crossing) (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).168Table6.9(a)TheoreticalandexperimentaldeterminationsoftheabsoluteopticaloscillatorstrengthsfordiscretetransitionsofxenonIntheenergyregion9.80-11.45eV+Oscillatorstrengthfrom5s25p6—5s25p5mwheremIs(2P312)5d(2P312)5d.(2P312)7s12P312)6d(2Pl/2)6d.(2P3/2)8s(2P3/2)7d(9.917eV)#(10.401eV)(10.593eV)(10.979eV)(11.163eV)(11.274eV)(11.423eV)A:Theory: GeIger(1977)[212]0.02370.5500.07690.00250.09400.01260.0190B:Experiment: Presentwork(HRdipole(e,e))0.01050.3790.0859<0.0010.08350.02220.0227(0.0005)(0.019)(0.0043)(0.0084)(0.0022)(0.0023)Ferrelletal.(1987)[66]0.3700.088(Phase-matchIng)(0.07)(0.01)Krameretal.(1984)(20710.098(Phase-matching) Geiger(1977)[212]0.00950.3950.09680.00250.08620.02360.0217(ElectronImpact)DelageandCarette(1976)121110.0190.395@0.1100.1230.0320.027(Electronimpact)Natalletal.(1973)[14210.0120.3810.090.0020.0820.0210.021(Electron_impact)EstimateduncertaintiesIntheexperimentalmeasurementsareshownInparentheses.ndandn4refertotheadi1/21andndl3/21statesrespectivelywhichconvergetothesame2P312limit.#Thetransitionenergieswereobtainedfromref.11551.@TbJsvaluewasnormalizedtotheexperlmentalvalueofGeiger(1977)1212).CD.Table6.9(b)Theoreticalandexperimentaldeterminationsoftheabsoluteopticaloscillatorstrengthsfordiscretetransitionsofxenonintheenergyregion11.45-11.80eVOscillatorstrengthfrom5s25p6—’5s25p5mwheremIsTotal(2p12)7(2P3/2)95(2P1/2)Sd’(2P3/2)8d(2P3/2)8(2P3/2)lOsto(11.495eV)#(11.583eV)(11.607eV)(11.683eV)(11.740eV)(11.752eV)ionizationA:Theory: Geiger(1977)(21210.00240.00090.2060.01550.1230.0169B:Experiment: Presentwork(HRdipole(e.e))<0.001<0.0010.1910.00880.09670.02881.606(0.019)(0.0009)(0.0097)(0.0029)(0.080)Geiger(1977)[21210.0040.0060.2050.00960.1230.02041.640®(Electronimpact)DelageandCarette(1976)(21110.2510.171(ElectronImpact)Natalletal.(1973)[142]0.00030.0010.l860.006fo.ioo0.015(Electronimpact)IIEstimateduncertaintiesIntheexperimentalmeasurementsareshownInparentheses.ndandnhjrefertothead)1/2)andnd(3/21statesrespectivelywhichconvergetothesame2P312limit.Thetransitionenergieswereobtainedfromref.11551.®ThisvalueIsquotedInref.I143J.C1714&(a2)resonancelines#,the results for these two lines are presentedseparately in table 6.4. Immediately it can be seen that there are greatvariations in the oscillator strength values reported for the 4s and4s’lines in both experimental work and also in the theoreticalcalculations.However, experimental work gives a reasonably consistent result(-0.25)for the oscillator strength ratio (ai /a2) as shown In the fourth column oftable 6.4. This suggests that systematic errors, such as uncertaintiesInmeasuring the target density or errors in normalizing thedata, may bethe cause of the large variations in the absolute values. The summedabsolute optical oscillator strength (i.e. al+a2) calculated by Cooper[104],using a one—electron approximation, (value of Cooper) agreesvery wellwith the sum of the presently measured values (0.33 1) while thevalue(0.298) reported by Amus’ya [1451 using the RPAE method isslightlylower. The calculated data reported by Aymar et al. [147] for ai and a,and the value reported by Stewart [151] for a are consistent withthepresent work. The calculations by Knox [181] and by Albat etal. [188]give very low values. Experimentally, the oscillator strength valuesreported by three groups [62,139,140] using the self—absorptionmethodare all lower than the present values by 5—20%. Lifetimemeasurementsperformed by Irwin et al. [199] using the beam foil method showvaluesfor ai and a much higher than the present work, whilethe value of alreported by Morack and Fairchild [197], who used a delayed coincidencemethod, is much lower than all other experimental values. Thevaluesmeasured by Copley and Camm [205] and by Lewis [138] fromanalyses of#The designations al,a2; b1,b2; and c1,c; are used for conveniencein the present workfor the respective ns, ns’ resonance lines of argon, krypton and xenon,respectively.172the pressure broadening profiles are consistent with the present work.Several electron impact based experimental methods have beenemployed for deriving the absolute oscillator strengths foraland a. Thevalues 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 presentwork. However the unpublished data of Natali et aL.[1421, the data ofKuyatt [219] which are quoted in the compilation of Eggarter[2171, andthe later work of Geiger [213] which has been quoted in refs. [139,143],show quite good agreement with the presently measured values. In acompilation published by Wiese et al. [54] values ofaianda2(not shownin 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 thediscrete 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 beenpublished, but both show substantial differences with the presentlyreported and most other experimental data. The lifetime measurementsof Lawrence [198], obtained using a pulsed electron source, show goodagreement with the present values for the 5s, 3d, 5s’ and 3d’ transitionlines. A reanalysis of the lifetime data of Lawrence [198] by Wiese et al.[54] gave absolute oscillator strength values for the above four transitionlines which are also consistent with the present work. Similar to thesituation for the 4s and 4s’ resonance lines, the self—absorption data forother lines at higher energies measured by Westerveld et al. [139] arelower than the present values. A more comprehensive data set wasreported in the electron impact based work of Natali et al. [142], and theoscillator strength values for most of the more intense lines are173consistent with the present work. The total discrete osci1lator strengthsum up to the2P312 ionization threshold of argon has been determined Inthe present work to be 0.859, a value which agrees within 5% withestimates of 0.82 calculated by Lee [1851 and 0.827 measured by Natali etal. [1421. In the earlier compilation reported by Eggarter [2171, the totaldiscrete oscillator strength of argon was estimated to be 0.793 on thebasis of the more limited data available at that time.Figure 6.10 shows the presently determined absolute differentialoptical oscillator strength spectrum for krypton over the energy range 9—16 eV. Figures 6.11(a) and 6.11(b) show expanded views of thespectrum in the energy regions 12.2—13.6 eV and 13.5—15 eV,respectively. Since higher members of the ns’ and nd’ series whichconverge to the 2P112 Ionization threshold are above the 2P312 ionizationthreshold, autoionizing resonance profiles are observed as shown infigure 6.11(b) due to the interaction between the discrete and continuumstates. The absolute optical oscillator strengths for the individualdiscrete electronic transitions of krypton determined in the presentwork are summarized in tables 6.6 and 6.7. There are considerablevariations between the various experimental and theoretical oscillatorstrength values for both the 5s (b1) and the 5s’ (b2) resonance lines ascan be seen in table 6.6. However, on the basis of the oscillator strengthratio (b11b2)the reported data can be divided into two groups. For onegroup the ratio is close to 1 while for the other it is — 1.1. The summedabsolute optical oscillator strength (i.e. 0.405 forb1+b2)computed byCooper [1041 is consistent with the present value (0.407). The values ofb1 and b2 calculated by Dow and Knox [182] are too low compared withthe present and most other experimental work. Similar to the situation174for argon the self—absorption data reported by Tsurubuchi et al. [1401 forb1 and b2 and Jongh and Eck [62] for b2 are lower than the presentlyreported values. The experimental data of Ferrell et al. [661 obtainedusing the phase—matching method, that of Matthias et al. [2011, whichwas determined by measuring the lifetimes of the radiative fluorescence,the data of Natali et al. [142], who applied the electron Impact basedmethod and the data of Lewis [138], which were obtained by studying thepressure broadening profiles, are all In good agreement with thepresently reported oscillator strength values for b1 and b2 The absoluteoptical oscillator strength values for transitions at higher energies areshown in tables 6.7(a) and 6.7(b). The theoretical data available arelimited to the semi—empirical calculations reported by Geiger [2121. Onlythe value for the 4d’ resonance line computed by Geiger [2121 agreeswith the present results. Previously published data obtained byapplication of electron impact based methods [142,212] together withthe present dipole (e,e) work provide the only available optical oscillatorstrength data for the discrete transitions of krypton at higher energies.Generally quite good agreement for the absolute optical oscillatorstrength values is observed among the different electron impact methodsfor most of the transition lines. The total discrete oscillator strength upto the 2P312 ionization threshold is determined to be 1.126 in thepresent work compared with an estimate of 1.10 reported by Natali et al.[1421.Figure 6.12 shows the high resolution absolute differentialoscillator strength spectrum of xenon obtained in the present work overthe energy region 8—15 eV. Figures 6.13(a) and 6.13(b) show expandedviews of the spectrum in the energy regions 11—12 eV and 12—13.7 eV175respectively. Broad autoionizing resonance profiles of higher members ofthe ns’ and nd’ series above the 2P312 limit are observed as can be seen infigure 6.13(b). Tables 6.8 and 6.9 summarize all the discrete absoluteoptical oscillator strengths values for xenon determined in the presentwork along with various previously reported theoretica1 and experimentaldata. It can be seen from table 6.8 that there are large variations In theoscillator strengths reported for the 6s(ci)and 6s(c2)resonance lines.The oscillator strength ratio ofci/c2also shows considerable variationfrom 0.767—1.492 for theory and 0.963—1.468 for experiment. Sometheoretical data show agreement of eitherci[111,147,189,212] orc2[183] with the present work. However, no single set of theoretical dataare consistent with the present work for both theciandc2values.Experimentally, the phase—matching data of Ferrell et al. [66], and theelectron impact data of Geiger [141,2 121 and Natali et al. [142] showgood agreement with the presently reportedciandc2values. Therecently reported data of Suzuki et al. [216] are --20% lower than thepresent values. Similar discrepancies were observed in the cases of theaiand a2 transitions of argon and thebiand b2 transitions of kryptonbetween the present work and absolute oscillator strengths reported bythe same group [214,2151 (see above). The absolute data for the discretetransitions at higher energies are shown in tables 6.9(a) and 6.9(b). Thephase—matching data of Ferrell et al. [66] show excellent agreement forthe 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 slightlyhigher. Other more comprehensive data for the discrete transitions ofxenon at higher energies have all been measured by electron impactbased methods [142,211,212]. It can be seen that the oscillator176strengths determined in the present work are in excellent agreementover 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 Indeconvoluting the peak. The data of Geiger [2121 are consistent with thepresent work for most of the transitions, while the data of Delage andCarette [2111, which have been normalized on the 5d line from the dataof Geiger [212], show considerable variations compared with thepresently reported values. Finally, the total oscillator strength sum up tothe 2P312 ionization threshold of xenon was determined to be 1.606 inthe present work, which is in good agreement with the estimate of 1.640reported by Geiger [212].6.2.3 High Resolution Measurements of the PhotoabsorptionOscillator Strengths in the Autoionizing Resonance Regionsdue to Excitation of the Inner Valence s ElectronsThe profiles and relative cross sections of the autoionizing excitedstate resonances of argon, krypton and xenon involving the excitation ofan inner valence ms electron have been previously studied in some detailexperimentally [45,176,218,220—226]. Although double excitationprocesses have also been reported in these energy regions [218,221—223], these transitions are extremely weak and they are not specificallyidentified 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 gaseswere 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 resulting177relative optical oscillator strength spectra were then normalized In therespective smooth continua at 21.218 eV for argon and krypton, and at16.848 eV for xenon using the absolute data determined by Samson andYin [178].Figure 6.14 shows the resulting absolute optical oscillator strengthspectrum of argon in the energy region 25—30 eV. The absolute datareported by Carison et al. [176] (crosses) using synchrotron radiation andSamson [45,220] (open circles) employing a double Ionization chamberare also shown in figure 6.14. Only the assignments for the transitionsinvolving excitation of a 3s electron to an np states are shown. Theenergy positions of the resonances as indicated in the manifold on figure6.14 are taken from the high resolution photoabsorption data reported byMadden et al. [218]. The data of Carison et al. [176] show a slight shift inenergy scale with respect to the present work, which may be due toerrors 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—26eV. However, the Samson data are higher than the present work above29 eV while the data of Carison et al. [176] are lower. It seems likelythat “line saturation” effects, which have been discussed in detail in refs.[36,37,46,72] are observed in the direct optical data reported bySamson[45,220] for the 3s—’np transitions. Since the widths of the 3s—’nptransition 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—’4ptransition, the data of Samson [45,220] show a lower minimum than thepresent data, which is consistent with the higher experimentalFigure 6.14: Absolute oscillator strengths for the photoabsorption of argon in theautoionizing resonance region 25—30 eV. The solid circles represent thepresent work (FWHM=0.048 eV), the open circles and crosses represent thephotoabsorption data reported by Samson 145,220] and Carison et al.[176], respectively. The assignments and energy positions are taken fromreference [218].IAn2 61-z623s 3p S0—4 3sp ‘ S112)np0I0.50.40.3-0.20.1 -0.0-I I IIIII4 5 6 7 8917850CAfl .J.4-iC)U)Cl)Cl)30oIC)C: ‘:•‘:Ixx, ,,0..025Present workCarison et al. [ 176)oSamson [45,220]26 27 28 29 30Photon energy (eV)179resolution of Samson [45,2201. However, for the narrower 3s—’5ptransition, the present work (which cannot show “line saturation” effects)gives a lower minimum than the Samson data [45,220]. Thisobservationstrongly suggests the presence of “line—saturation” effects at largern dueto the finite bandwidth of the optical experiments [45,220]. Thesamephenomenon is observed for the transitions to the higher npstates.Figure 6.15 shows the presently determined high resolutionabsolute optical oscillator strength spectrum of krypton in theenergyregion 23—28.5 eV along with the reported absolute data ofSamson[45,2201. The assignments and energypositions for the 4s—’nptransitions are taken from Codling and Madden [221,223]. Thereare twoJ= 1 components for the transition 4s24p6‘So— 4s4p6(251/2)np,whereone Rydberg series is labelled as n and the other one is labelled as,asshown in figure 6.15. Onlyfl=.and .fj for the latter series areunambiguously assigned [221—223]. The ‘line—saturation” effectsthat areobserved in the optical data reported by Samson [45,220] for argon arealso seen in the corresponding direct optical data for krypton.The effectis especially severe for the 4s—’7p transition. Samson [45,220]and otherworkers, using direct optical methods [22 1—223,2261, have reported apeak(Q)at 24.735 eV which was not observed In the presentwork.The presently determined high resolution absolute opticaloscillator strength spectrum of xenon in the energy region 20—24 eV isshown In figure 6.16. The figure also shows the photoionizationcrosssections for xenon in this energy range reported by Samson [451,whichare significantly lower than those determined in the present work.Theassignments and energy positions for the 5s—’np transitions are takenfrom the data reported by Codling and Madden [221,223]. Onlyone1800.5KrI50a.)____‘-r0.404s24p6 1S0 — 4s4p6(2S112)np•4QH I IIII 0s.Q3. 5 5 66 789101/200a.)30C)07‘-400.2•=CL)—C.) 00___________0o IPresent workI0.1 °Samson [45,2201 10oC.) I.0&0.00I• I23 24 2526 27 28Photon energy (eV)Figure 6.15: Absolute oscillator strengths for the photoabsorption of krypton In theautoionizing resonance region 23—28.5 eV. The solid circles represent thepresent work (FWHM=0.048 eV), the open circles represent thephotoabsorption data reported by Samson [45,220]. The assignments andenergy positions are taken from references [221,223].Figure 6.16: Absolute oscillator strengths for the photoabsorption of krypton in theautoionizirig resonance region 20—24 eV. The solid circles represent thepresent work (FWHM=0.048 eV), the open circles represent thephotoabsorption data reported by Samson [45]. The assignments andenergy positions are taken from references [221,223].622 615s 5p S0 — 5s5p(S1/2)npI0.50.40.30.20.10.0XciII1/2181300I-IC)020.1010I I III•%%%9.6 78 9 100 •4Av.40•—— .0.. 0. •V.“... ..00 000000Present work1oSamson[]I20 2122 23Photon energy(eV)2’4182Rydberg series of the twoJ= 1 components ofthe 5s—’np transitionsconverging to the 2S112 Ionizationthreshold has been assigned[221—2231.6.3 ConclusionsComprehensive absolute differentialoptical oscillatorstrength datafor argon, krypton and xenon inboth the discrete andcontinuum regionshave been reported, includingmeasurements at highresolution. Thepresent work represents the completionof the measurementsfor thenoble gas series using thehigh resolution dipole (e,e)method recentlydeveloped for measuring absoluteoptical oscillator strengthsfor a widerange of transitionsin atoms and molecules. TheTRK sum—rulenormalization methodwhich was used for heliumand neon could notbeused for argon. krypton andxenon due to the smaller energyseparationsbetween the different subshellsof the atoms. Therefore, singlepointnormalization on very accuratephotoabsorption measurementshas beenused. The presently reportedresults are compared withtheory and alsoother earlier reported experimentaldata. In the continuumregions thevarious experimental valuesgenerally show reasonableagreement at lowenergy while there are certainvariations at high energy.With theinclusion of more electroncorrelations and moresophisticatedcalculations, the theoreticaldata are in better agreementwithexperimenta1 values. Inthe discrete region a widespread of values isseen for the resonanceline oscillator strengths alarid a2 of argon, b1andb2 of krypton and c and c2of xenon in both experimentand theory. Fordiscrete transitions at higherenergies there is a shortageof theoretical183data. Electron impact based methods have thus far provided most of theabsolute optical oscillator strength data for the valence shell discretespectra. Generally, the present measurements are in quite goodagreement with the earlier unpublished electron impact based data ofNatali et al. [1421 which were obtained at lower impact energy.Absoluteoptical oscillator strengths for the autoionizing excited state regionsinvolving mainly the inner valence s—electrons of the three noble gaseshave also been obtained. The previously publishedphotoionization data ofSamson [45,220] in this energy range show evidence of substantial “linesaturation effects.184Chapter 7Absolute Optical OscillatorStrengths (11—20 eV)and Transition Momentsfor the Lyman andWerner Bands of MolecularHydrogen7.1 IntroductionAn accurate knowledgeof absolute transitionprobabilities forelectronic excitation isessential for a quantitativeunderstanding of theinteraction of energeticradiation with matter.Very few accurateabsolute optical oscillatorstrength (cross section)measurements havebeen reported for molecularphotoabsorption processesat high resolutionparticularly in thediscrete excitation region,below the first ionizationpotential. Even in thecase of the simplest molecule,molecularhydrogen, such informationis quite limited fordiscrete transitions.Absolute oscillator strengthmeasurements requireextremely preciseandcarefully controlled techniquesand in particular directoptical methodsusing the Beer—Lambertlaw can be subject to seriousquantitative errors.However a much largerbody of absolute oscillatorstrength informationexists for the photolonizationcontinuum since experimentalmethods inthese energy regionsare generally more straightforwardin theirapplication [301. Interms of theoretical work thereare few calculationsof absolute oscillatorstrengths. Such calculationsare limited by the lackof a sufficientlyaccurate knowledge of molecularwavefunctions and alsoby the shortage ofprecise absolute experimentaldata for the evaluationand testing of thetheoretical methods. Bothof these concerns are185addressed by recent advances made in electron impact basedspectroscopies. Firstly, electron momentum spectroscopy [227] hasprovided detailed measurements of electron momentum distributionswhich have led to the evaluation and design of new molecularwavefunctions of unprecedented accuracy (for example see refs. [228—2311). The growing availability of Improved molecular wavefunctionsshould lead to greater accuracy in calculated oscillator strengths.Secondly, high resolution dipole (e,e) spectroscopy [37—391 has beendemonstrated to provide a versatile experimental method for theaccurate determination of optical oscillator strengths for atomic andmolecular discrete photoabsorption processes over broad ranges ofexcitation energy (see chapters 4—6 and refs. [27,36—39]).Hydrogen is an important constituent of the solar and planetaryatmospheres and therefore a quantitative understanding of theinteraction of molecular hydrogen with energetic radiation Is of greatInterest in astrophysics, astronomy and space sciences [232,233]. Forexample, the absolute oscillator strength for photoabsorption Is anessential quantity in the determination of molecular abundances frominterstellar molecular absorption lines [2321. Furthermore, absoluteoptical oscillator strengths can be used to provide an absolute scale forrelative measurements of electron impact cross sections. For Instance,the theoretica1 absolute optical oscillator strengths for hydrogen reportedby Allison and Dalgarno [234] were employed by De Heer and Carriere[235] to normalize their measured relative emission cross sections formolecular hydrogen, while Shemansky et al. [236] established absolutecross sections for the Lyman and Werner bands from absolute oscillatorstrengths derived from the lifetime measurements of Schmoranzer et al.186[2371 andthe relative transition probabilities calculated by AllisonandDalgarno [2341. The photoabsorption of molecularhydrogen below thefirst ionization potential is dominated bythe Lyman and Werner bands.However, only a very few rather incompleteexperimental studies of theirabsolute oscillator strengths for excitation fromthe ground state havebeen reported in the literature. Furthermore,the available oscillatorstrength measurements show somediscrepancies with each other andwith theory, although the energy levels ofthese bands are well known[238].Molecular hydrogen is the simplest neutralmolecule and it is thusof fundamental interest since quantummechanical calculations arepossible with greater accuracy than for other molecularsystems. TheLyman and Werner bands, which correspondto the transitions from theground X state to the 2pa, B and 2pr, C ‘Hstates respectively,have been the subject of several theoreticalInvestigations. Mulliken andRieke [239], employing the LCAO.-MOmethod, have reported ca1culatedoscillator strengths for the Lyman and Werner bandsusing the dipolelength operator. Shull [240] repeated the samecomputation using thedipole velocity operator. A theoretical investigationof the oscillatorstrengths of the Lyman band was carriedout by Ehrenson and Phillipson[241] with severalImproved ground state wavefunctions usingdipolelength, velocity and acceleration operators. By solvinga one—electronSchrodinger equation, Peek and Lassettre [242]constructed acorrelation diagram for hydrogen for several statesand reported theoscillator strength values corresponding tothe Lyman and the sum of theLyman and Werner bands. Miller and Krauss [243]approximated theHartree—Fock orbitals by a linear combinationof Gaussian—type atomic187orbitals and calculated the inelastic electron scattering differential crosssections and oscillator strengths of the Lyman, Werner and several otherbands in hydrogen. The theoretical Franck—Condon factors for thehydrogen Lyman band system have been computed by Geiger andTopschowsky [244] employing the Wentzel—Kramers—Brillouin (WKB)approximation, by Nicholls [2451 using the Morse potential function, andby Halmann and Laulicht [246] and Spindler[247,248] based on Rydberg—Klein—Rees (RKR) potential functions. From a consideration of previouslypublished experimental electron energy loss data [244,249,250] andlifetime measurements [251], it has been suggested [252] that theelectronic transition moment for the Lyman band varies considerablywith internuclear separation (r). Using the wavefunctions of Matsen andBrowne [253] and Browne and Matsen [254], Browne [252] has computedthe electronic transition moment as a function of r for the Lyman band,while Rothenberg and Davidson [255], employing the highly accuratewavefunctions of Kolos and Wolniewicz [256], have also reported thevariation of electronic transition moment with r for several transitions ofmolecular hydrogen. In an earlier paper Dalgarno and Allison [257]reported calculations of the vibronic band oscillator strengths for theLyman system. These calculations used the potentials developed by Kolosand Wolniewicz [256,258] in conjunction with the asymptotic formulae ofKolos [2591 and Chan and Dalgamo [2601. Dalgamo and Allison [257] alsoadopted transition moments reported by Schiff and Pekeris[4] at r=0, byRothenberg and Davidson [2551 at r= 1 .4a0 and r=2.0a0,and by Browne[2521 at large values of r. Using the more accurate transition momentsreported by Wolniewicz [2611 for both the Lyman and Werner systems,Allison and Dalgamo [262] later repeated calculations similar to those188reported earlier by Dalgarno and Allison [2571. Morecomprehensivecalculated data, Including the transition probabilitiesfor the Lyman andWerner bands, were further reported by Allison andDaigarno [234]. Thedependence of electronic transition moment on Internucleardistancewas investigated at large r values experimentally by Schmoranzer [263]for the Lyman band and by Schmoranzer and Geiger [2641 for theWernerband based on measurements of the optical emission intensity fromelectron impact excited hydrogen molecules. Theseresults are In goodagreement with the theoretical predictions by Wolniewicz [261].Dressier and Woiniewicz [265] have recomputed the transitionmomentsfor the Lyman and Werner bands using the most accurate wavefunctionsavailable after 1969 and the results are in excellent agreement withtheearlier work of Wolniewicz [2611. In other work Arrighini et al.[266]computed the inelastic scattering of fast electrons from theground stateof hydrogen and reported the total integratedabsolute dipole oscillatorstrengths for the Lyman and Werner bands and also for some otherhigher Rydberg states within the random—phase approximation(RPA) andTamm—Dancoff approximation (TDA). The transition probabilities fortheindividual bands of the transitions from the ground state Xto thehigher lying 3pa, B’1and 3pit, D‘flustates were also calculated byGlass—Maujean [267]. In 1975 Gerhart [2681 reviewed theexistingoptical oscillator strength and photoabsorption data for molecularhydrogen and recommended some revisions on thebasis of sum ruleconsiderations.Much less information on discrete optical oscillator strengthsformolecular hydrogen is available from experiment due to thedifficulties ofconducting absolute optical cross sectiondeterminations. For example,189direct Beer—Lambert law photoabsorption experiments have apparentlynot been used for absolute optical oscillator strength measurements formolecular hydrogen because, even at high experimenta1 resolution(narrow incident band—width), the extremely narrow natural line—widthsof the transitions can result in severe “line—saturation” effects asdiscussed for example in refs. [37,46] (see chapter 2). Experimentallythe discrete valence transitions of hydrogen have been studied quiteextensively by photo—emission [269—271] and also by photoabsorptlon andphotoionization [272—278] methods. However, the opticalphotoabsorption and photoionization studies have been mostly limited todeterminations of the energy positions of the discrete transitions ratherthan of the absolute optical oscillator strengths (i.e. transitionprobabilities), presumably because of the possibility of “line—saturation”effects. In an attempt to allow for such effects photoabsorptionmeasurements with a ‘curve of growth analysis”, which relates themeasured equivalent width to the line oscillator strength, have beenemployed by Haddad et al. [2791 and by Hesser et al. [280,281] tomeasure the oscillator strengths for a few vibrational levels of the Lymanband. The same approach has been used by Fabian and Lewis [282] tomeasure the oscillator strengths of the Lyman and Werner bands below13.8 eV. In the same way Lewis [283] has measured the oscillatorstrengths of the Lyman and Werner bands for the higher vibrational levelsabove 13.8 eV and also the B’—X and the D—X bands. In otherphotoabsorption experiments Glass—Maujean, Breton and Guyon [284—286] attempted to take into account the effects of the bandwidth of themonochromator on the measured linewidths of the discrete transitionsby using Doppler profiles and they reported the photoabsorption190probabilities for several discrete transition peaks. However the resultsare restricted to very high vibrational levels of the Lyman and Wernerbands close to the dissociation limit. Integrated (total) absolute oscillatorstrengths for the Lyman and Werner bands have also been reported byHesser [251] using the phase—shift technique to measure the radiativelifetimes of hydrogen.Electron impact based methods have been previously applied to thestudy of the discrete transitions of molecular hydrogen[244,249,250,288—291]. Lassettre and Jones [2881 obtained absoluteoptical oscillator strengths in the continuum region of hydrogen byextrapolating the generalized oscillator strengths, determined at a rangeof different scattering angles, to zero momentum transfer. Direct,forward scattering, electro.n impact studies of hydrogen at very highimpact energy and with very high resolution (0.007—0.040 eV FWHM)have been reported in the discrete region by Geiger [249], Geiger andTopschowsky [2441 and Geiger and Schmoranzer [2501. These relativeintensity measurements [244,249,250] were subsequently placed on anabsolute scale using calculated and measured elastic cross sections [2491.By measuring the elastic and inelastic differential cross sections atdifferent scattering angles with a resolution of —1 eV FWHM, Geiger [2491has also reported the sum of the total integrated oscillator strengths forthe Lyman and Werner bands. These integrated values [249] were thenused for normalization of the high resolution electron energy loss spectra[244,249,250]. However it should be noted that the elastic relativedifferential cross sections measured by Geiger [2491 were normalized ontheoretical values. In addition the relative intensities produced by theWien filter type of EELS spectrometer used by Geiger and co—workers191[244,249,250] have, in somecases, proved to be significantly inerror(see for example the discussionin ref. [37] and chapter 4 forhelium,where results including thoseof Geiger et al., are compared).Suchdiscrepancies may be due to intensityperturbations caused by fringemagnetic fields from the Wien filters. Inthis regard the three setsofelectron impact data reported by Geiger etal. for hydrogen[244,249,250]show differences In the (relative)Intensities determinedfor the Lyman and for theWerner bands. These results[244,249,250]are also in serious disagreement withsome of the optical work[251,279,281,282] and also, in the caseof the Werner bands, with theory[234,262].The HR dipole (e,e) method[37,38] (described in this thesis inchapter 3) is particularly useful for studyingdiscrete electronictransitions over a wide (photon) energyrange and therefore, In view ofthe existing discrepancies anduncertainties outlined above, it has beenused in the present work to make anindependent absolutedetermination of the opticaloscillator strengths for the Lyman andWerner band (discrete) transitions andalso in the ionization continuumin the electronic spectrumof molecular hydrogen. The absolutescalewas obtained by normalizingto earlier reported absolute optical oscillatorstrengths in the continuumregion, as determined using a low resolution(LR) dipole (e,e) spectrometerand TRK sum rule considerations [86].These LR dipole (e,e) measurements inthe continuum [86] are inexcellent agreement with direct photoabsorptionresults [292] obtainedwith the double ion chambermethod.1927.2 Results andDiscussion7.2.1 AbsoluteOscillator StrengthsFigure 7.1 shows theabsolute differentialoptical oscillatorstrength(photoabsorption) spectrum ofmolecular hydrogen inthe (photon)energy region 11—20eV obtained in the presentwork at a resolution of0.048 eV FWHM. Theentire spectrum has beenplaced on an absolutescale by normalization at18 eV to the previouslyreported absolutephotoabsorption data of hydrogenobtained by Backx etal. [86] using lowresolution dipole (e,e) spectroscopy.It can be seen from figure7.1 thatboth the shape and magnitudeof the present oscillatorstrengthdistribution in the ionizationcontinuum are highlyconsistent with theearlier reported lowresolution dipole (e,e)work of Backx et al. [86]andalso with the directphotoabsorption measurementsreported by Samsonand Haddad [292]over the continuum regionshown (see also ref.[30]).Furthermore, in the discreteregion the present highresolution andearlier low resolution [861dipole (e,e) measurementsare mutuallyconsistent when thelarge difference in energyresolution (i.e. 0.048 eVFWI-IM and 1 eV FWHMrespectively) is taken intoaccount.Figure 7.2 whichshows an expanded viewof figure 7.1 in the 11—14 eV energy regioncomprising mainly theabsolute differential opticaloscillator strengthspectrum for the Lymanand Werner bands in moredetail. The Lymanand Werner bands arethe two strongestelectronictransitions of molecularhydrogen and correspondto transitions fromtheX1gground state to the 2po,B1+and 2pit, C 1fl statesrespectively.The positions of thevibrational levels shownin figures 7.1 and7.2 are1 .51.0‘4.4-J‘40=— 0.0000.0Figure 7.1:150100 000‘400‘40IAbsolute oscillator strengths for the photoabsorption of molecularhydrogen in the energy region 11—20 eV measured by the high resolutiondipole (e,e) spectrometer (FWHM=0.048 eV). The assignments are takenfrom references [270,272—274].193IIIIIIIIIIIIIIIII’IIII I_.irrcnI I I I I I IIC1llWernerPresent work (HR Dipole (e,e))Backx et al. [86] (LR Dipole (e,e))oSamson & Haddad [ 292] (Ph.Abs.)H2XE5017Photon energy (eV)019I I I I Iv=0 2 41 +BELyman1H21I I I I I I— I I6 8 10 12 14I I Iv’=O 1 2 3toVCl)0I I I16 18 20 22I I I4 5 6 7WernerC1fl1.51 .00.50.0194150 •0VCl)Cl)Cl)0inr $-0050jV’=O1B11 12 13 140Photon energy (eV)Figure 7.2: Absolute oscillator strengths for the photoabsorptlon of molecularhydrogen in the energy region 11—14 eV. The assignments are taken fromreferences [270,272,273]. Deconvoluted peaks are shown as dashed linesand the solid line represents the total fit to the experimental data.195taken from the earlierreported optical spectroscopicdata of Dieke [270]for v’=0—17 of the Lymanband and for v=0—4 of theWerner band, andfrom the photoabsorptiondata of Namioka [272,273] forv’= 18—22 of theLyman band, for v’=5,6 ofthe Werner band and forv’=O, 1 of the B’band. It can clearly beseen that the shapes of thevibronic peaks (v’=O—6) of the Lyman band are slightlyasymmetric due torotational finestructure as observed in the veryhigh resolution electronenergy lossspectra reported by Geigerand Topschowsky [2441 andby Geiger andSchmoranzer [250]. In thepresent work, integrationof the peak areacorresponding to a particulardiscrete vibronic transitionwill givedirectly the absoluteoptical oscillator strength forthat transition. Sinceall the peaks are expectedto be asymmetric because ofrotationalbroadening, asymmetricpeak profiles were used to fitthe spectrum infigure 7.2. The fittedpeaks also incorporate theInstrumental energyresolution (0.048 eV FWHM).The resulting deconvolutedpeaks and totalfitted spectrum areshown as the dashed andsolid lines respectively Infigure 7.2. The presentabsolute optical oscillator strengthvaluesobtained by deconvolutingthe (asymmetric) peak areasfor individualvibronic transitions of theLyman and Werner bandsare summarized intables 7.1 and 7.2 respectively.Previously reported experimentaloscillator strength values [250,279,281,282]and the more accuratecalculated data of Allisonand Dalgarno [234,262], whichincluded thedependence of electronictransition moment on internucleardistance rare also shown for comparison.For the three sets ofelectron impactdata reported by Geigerand co—workers [244,249,250],the absolutescales of the data were obtainedby normalizing to the sumof the totalintegrated oscillator strengthof the Lyman and Wernerbands [244] as196Table 7.1Absolute oscillator strengths for the ‘vibronic transitions of the Lyman band of molecularhydrogenAbsolute optical oscillator strengths for transitions fromExcited v’=0 of X 12g to v of B‘+(Lyman band)state Dipole (e,e) experiments Direct optical measurementsTheoryvibrational Present Geiger and Fabian and Hesser et a!. Haddad et a!. Allison andlevel (v’) work Schmoranzer Lewis12811 12791 Dalgarno12501 12821 1234.26210 0.00154 0.00175 0.0019 0.0016891 0.00575 0.00545 0.00519 0.013 0.0057902 0.0114 0.00994 0.0115 0.024 0.011563 0.0177 0.0165 0.0176 0.037 0.017554 0.0228 0.0210 0.0245 0.03 0.022505 0.0263 0.0238 0,0258 0.025716 0.0276 0.0264 0.027047 0.0276 0.0267 0.026738 0.0254 0.0232 0.025239 0.0236 0.0222 0.0229810 0.0200 0.0203 0.0203511 0.0174 0.0181 0.0176412 0.0153 0.0155 0.0150413 0.0122 0.0128 0.0114 0.0120.0126614(0.0101)*0.0104 0.0105515 0.00794 0.00825 0.0101 0.0073 0.00873016 0.00687 0.00703 0.00787 0.005 0.00718517 0.00531 0.00612 0.00575 0.0042 0.00589118 0.00468 0.00552 0.00482019 0.00384 0.00425 0.00344 0.0023 0.00393920 (0.00308) 0.00329 0.0032 1921 0.00267 0.00263222 0.00209 0.002 154*Interpolated values.Table7.2AbsoluteoscillatorstrengthsforthevibronictransitionsoftheWernerbandofmolecularhydrogenExcitedstatevibrationallevel(v’)012 3 4 5 6Presentwork0.0454 0.0718 0.0695 0.0544# 0.0387 0.0255 0.0165GeigerandSchmoranzer[250]0.0348 0.0592 0.0555 0.0437 0.0337 0.0210 0.0153FabianandLewis[282]0.0592 0.0642 0.0442 0.0317 0.0224 0.017AllisonandDalgamo[234,262]0.04760 0.07482 0.06982 0.05472 0.03874 0.02598 0.01700Absoluteopticaloscillatorstrengthsfortransitionsfromv=0ofX1g’tovtofC1I](Wernerband)Dipole(e,e)experimentsDirectopticalTheorymeasurementCD#Thecontributionfromtheoverlyingv’=14componentoftheLymanbandhasbeensubtracted.198determined in separate lowresolution experiments, whichwere In turnnormalized on calculatedelastic cross sections. Of thesethreeexperiments [244,249,2501 onlythe highest resolutiondata reported byGeiger and Schmoranzer [250]are shown in tables 7.1and 7.2. It shouldbe noted that the data of refs. [244]and [249] show muchmore scatterthan those of ref. [2501. Theuncertainties of the presentresults areestimated to be ±5% for fully resolvedpeaks, and ±7—15% for thepartially resolved peaks because ofthe additional errors Inthedeconvolution procedures. Dueto overlapping bands thevalues of v’= 14and 20 for the Lyman bandas shown in table 7.1 wereobtained in thepresent work by interpolation.Also the value for v’=3 forthe Wernerband shown in table 7.2was obtained by subtractingthe contributionfrom the underlying v’= 14component of the Lyman band.These peaks(i.e. for v’=14 and 20 ofthe Lyman band and v’=3for the Werner band)were then generated using acomputer program and are shownalongwith the directly fitted peaks asdashed lines in figure 7.2.A direct comparison ofoscillator strength values as afunction ofvibrational quantum numbers,given by the different experimentalstudies[250,279,281,282] and thetheoretical data reportedby Allison andDalgarno [234,2621, is shownin graphical form for theLyman and Wernerbands in figures 7.3 and 7.4respectively. For the Lyman bandit can beseen immediately fromfigure 7.3 that the presently obtainedexperimental absolute oscillatorstrength results are in excellentquantitative agreement withthe theoretical work reportedby Allison andDalgarno [234,2621 over theentire range of vibrationalquantum numbersshown. The calculated datareported by Allison and Dalgarno[234,262]are slightly lower at v’=5—7and become slightly higherfor v’=13—18 but1990.040.030.020.010.00Vibrational quantum number (v’)Figure 7.3:The absoluteopticaloscillator strengthsfor individualvibronic transitionsas a functionof thevibrational quantumnumber v’ for theLyman band.ICd)0—C)Cd)0C)c4C*1H21*•Present worka Fabian & Lewis[ 282]* Haddad et al. [279]Hesser et al. [ 281 ]Geiger & Schmoranzer [250]Allison & Dalgarno [ 234,262]Lyman BandsçBu+02468 lb 12 14 16 18 2b 22•Present workCFabian & Lewis [ 282]Geiger & Schmoranzer [ 250]Allison & Dalgarno [ 234,262]Vibrational quantum number (v’)200aa)C,)I0—C)Cl)0C)00.080.060.040.020.001H21AAACWerner BandsX1Eg * C1Hu4aFigure 7.4: Theabsolute opticaloscillator strengthsfor individualvibronictransitionsas a function of thevibrationalquantum numberv’ forthe Wernerband.201are still within theestimated experimental uncertaintiesof the presentwork. The electron impactdata of Geiger and Schmoranzer [2501areslightly lower than the presentwork for v’=2—5 and v’=8 butare In goodagreement for higher v’ values.Apart from the electron impactbasedwork of Geiger and Schmoranzer [250],three sets of data (seefigure 7.3)obtained from photoabsorptlonmeasurements using acurve of growthanalysis [279,281,282] providedthe only other source ofabsolutevibronic oscillator strengthsfor the Lyman band prior to thepresentwork. However, these threesets of optical data [279,281,282]onlyencompass a few of the vibrationallevels and give ratherinconsistentresults (see figure 7.3). Of thesestudies only the work reported byFabian and Lewis [2821 is in reasonableagreement with theory[234,262]as seen in figure 7.3.The Fabian and Lewis [282]data are also generallyconsistent with the presentlyreported values but the dataare much lesscomprehensive than the presentwork which covers theentire range ofthe vibrational numbers fromv=0 to 22. Haddad et al. [279]and Hesseret al. [2811 report only a few valuesmostly at low and high vibrationalnumber respectively, and theseshow large discrepancies withthepresent data and with theory [234,2621.It has been suggested [2821thatthe apparently high valuesobserved by Haddad et al. [2791above v’=O maybe due to errors in thepressure measurements.Absolute optical oscillator strengthsfor the Werner band are shownin figure 7.4. It can be seenthat the presently obtained experimentaloscillator strength valuesare again in excellent agreementwith thetheoretical predictions byAllison and Dalgarno [234,262] exceptpossiblyfor v’0 and 1 where the calculatedvalues are slightly higher butnevertheless still well within theestimated uncertainties ofthe present202experiment. The only other absolute experimental data available for theWerner band of hydrogen prior to the present work are from the electronimpact work of Geiger and Schmoranzer [250] and the optical work byFabian and Lewis [282] respectively. However It can be seen from figure7.4 that for v’=O to 5, both sets of data [250,282] are much lower thanthe present results and only for v’=6 are their values In reasonableagreement with the present work and with theory.The absolute oscillator strength value for the v’=O component of theB’ ç’ band at 13.702 eV (see figure 7.2) is estimated to be 0.00384 inthe present work. The transition probability for this vibronic band hasbeen calculated by Glass—Maujean [267] to be 0.238x108sec1 and thiscorresponds 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 andWerner bands are estimated in the present work to be 0.301 and 0.34 1respectively. These estimates were obtained as follows: For the Lymanband the value was obtained from the summation of the absolute oscillatorstrength values for v’=0—22 as shown in table 7.1. The total absoluteoscillator strength for the Werner band was obtained from the summationof the absolute oscillator strength values for v’=0—6 determined from thepresent experimental work (0.322), plus the sum for v’=7—13 ascalculated [234,262] by Allison and Dalgarno (0.0 19) to give a total of0.341. Table 7.3 summarizes the present results along with all thepreviously reported total absolute oscillator strengths for the Lyman andWerner bands. The present data are in good agreement with thetheoretical estimates of Allison and Dalgarno [234,262] and also withthose of Arrighini et al. [266] which were obtained using the TDA andTable 7.3203Total integrated absolute oscillator strengths for the Lyman and Werner bandsof molecular hydrogenTotal integrated absoluteReference oscillator strengthsLyman band Werner bandTheory:Arrighini et al. 12661(i) TDA 0.3090 0.3615(ii) RPA 0.2863 0.3451Allison and Dalgarno 1234,2621 0.311 0.356Browne 12521 0.28Rothenberg and Davidson 12551(1) dipole length 0.286 0.343(ii) dipole velocity 0.287 0.380Miller and Krauss 12431 0.2 79 0.330Peek and Lassettre [242] 0.28 0.276Ehrenson and Phillipson [2411 0.27ShullI24O] 0.18 0.42Mulliken and Rieke 12391 0.24 0.38Experiment:Present work 0.30 1 0.34 1(dipole (e,e))Geiger and Schmoranzer [2501 0.29 0.28(electron impact)Hesser et al. [281] 0.29(optical: curve of growth)Hesser [2511 0.51 0.71(lifetimes)204RPA methods. Onlythree other sets of measurements havereported forthe total integrated absolute oscillatorstrengths. The Integrated valuereported in the electron impact workof Geiger and Schmoranzer [2501isslightly lower than the present valuewhile their value for the Wernerband Is -20% lower. The totalintegrated value for the Lymanband asestimated by Hesser et al. [281], using thecurve of growth analysis, Isalso just slightly lower than the presentwork. However, valuesobtainedfrom the lifetime data reported byHesser [2511 are much higherthan allthe other reported experimental andtheoretical values for both theLyman and the Werner bands, whichis likely caused by the variationofelectronic transition momentwith internuclear distance r, sincetheemission observed by Hesser [2511occurs at large r.In the present work, the total integratedoscillator strength sumfor all transitions below thefirst ionization potential (15.43eV [274]) ofhydrogen is estimated to be 0.836.Arrighini et al. [266]have reportedoscillator strength values for theLyman and Werner bands, andalsoseveral higher members of theRydberg1uand 1fl states. By adding upthe oscillator strengths for all thosestates below the first ionizationpotential of hydrogen that werecalculated by Arrighini et al. [266],valuesof 0.926 and 0.862 were obtainedfor the TDA and RPA computationalmethods respectively. The valuereported using the RPA method Isconsistent with the present result(0.836) while that reported usingtheTDA method is appreciably higher.2057.2.2 The Variation of Transition Moment with the InternuclearDistance for the Lyman and Werner BandsThe vibronic band oscillator strengths(f’”)for the Lyman andWerner systems of molecular hydrogen can be written as [262];2G=(E-E,,)‘vV” (7.1)whereP’” =Pv’I1e(’)I)2(7.2)In these equations 0 is the statistical weighting factor which is equal toone for the Lyman bands and two for the Werner bands, E’—E’ is thetransition energy in atomic units and PV’V’ is the band strength. Thequantity Re(r) is the electronic transition moment which is a function ofthe internuclear distance r, and p’ and q,” are the vibrationaleigenfunctions of the excited and ground states respectively.The dependence of the electronic transition moment on theinternuclear distance for both the Lyman and the Werner bands can beobtained from the presently reported absolute vibronic oscillatorstrengths. Equation 7.2 can be rewritten as [250,2821= Re(rvtvi)2qTT(7.3)where(7.4)206In equation 7.3, r’” is the internuclear distance at which the transitionv”—’vttakes place andqv’v’is the Franck—Condon factor. Combiningequations 7.1 and 7.3, we obtain2=Re(rvivi)q,v, (75)In the present work, thef’ovalues have been measured directly(see tables 7.1 and 7.2) for both the Lyman and the Werner bands so thatif we take Franck—Condon factors (i.e.qv’ovalues) from the calculateddata of Allison and Dalgarno [262],ITe( rv’o)Imay be derived. Theenergies(E—E’)have been taken from the optical data of Dieke [270]and Namioka [272,273]. Therv’ovalues have been obtained by digitizingthe data of Allison [293], which are shown in analog form as a privatecommunication in the article by Fabian and Lewis [282]. The resultingvalues ofIRe( rv’o)Iare plotted as a function ofrv’oin figures 7.5 and 7.6for the Lyman and Werner bands respectively. These figures thereforeshow the variation of electronic transition moment with internucleardistance in hydrogen for the Lyman and Werner bands. Previouslyreported experimental work [250,282] and theoretical calculations[243,252,255,26 1] are also shown for comparison. The data of Millerand Krauss [243] and Wolniewicz [261] were obtained by digitizing thedata from the figures reported in their paper. It can seen from figure 7.5that the presently determined variation of the electronic transitionmomentIRe( rv’o)Iwith the internuclear distancerv’ois in generally goodagreement with the theoretical work of Wolniewicz [261], except atr’o—0.96A(v=0), where the present value is slightly lower. TheVibrational quantum number(v’)Internuclear distance rvo (A)Figure 7.5: Theelectronic transitionmomentIRe(rj)I in atomic units (a.u.) as afunction of theinternuclear distancer,’O in Angstroms (A) for theLymanband.2072018161412 109Lynian BandsX1E — B1EH21-Sz1.501.3a.)0E0.4J0.9Cl)::D**0:6• Present workGeiger & Schmoranzer [250]DFabicn & Lewis [282]Wolniewicz [261]- — —— Miller & Krauss [243]*Browne [252] Length* Browne [252] Velocity0.7 0.8 0.9 1Vibrational quantum number (v’)Internuclear distance rvo (A)Figure 7.6: The electronic transition momentIRe(rv’o)Iin atomic units (a.u.) as afunction of the internuclear distance ro in Angstroms (A) for the Werner208. 2 1 0Werner BandsXgC1Hu**F040E0.—C.)00V0.9 -0.80.70.60.5jr - -*99[H21C**Present workGeiger & Schmoranzer [250]Fabian & Lewis [282]Wolniewicz [261 ]Miller & Krauss [243]Rothenberg & Davidson [255] LengthRomenberg & Davidson [255] VelocityI I I • I0.6 0.7 0.8 0.9 1 .0band.209calculated data reported by Millerand Krauss [243] are somewhathigherthan the present work.The dipole length data reported byBrowne [2521are lower than the presentresults while their dipole velocitydata areslightly higher. The electron impactwork of Geiger and Schmoranzer[250] and the optical work of Fabianand Lewis [282] are alsoconsistentwith the present work but bothsets of data exhibit morescatter. From aleast—squares fit of a straight lineto the present data, thedependence ofelectronic transition moment withinternuclear distance in the range0.63—0.96A for the Lyman band isfound to be:Re(rv=0.l42+ 1.l17r0(7.6)In figure 7.6 the presentresults for the Werner band are alsoseento be generally in rathergood agreement with the theoreticalvaluescalculated by Miller and Krauss [243]and Wolniewicz [261]. Thedipolelength data calculated byRothenberg and Davidson [2551are alsoconsistent with the presentwork while their reported dipolevelocitydata are slightly higher. The resultsderived from the electron impactwork of Geiger and Schmoranzer [2501are considerably lower thanboththe present work and theory[243,261]. Except for the value atr’o—0.66A,the data for the Werner bandreported In the optical work ofFabian and Lewis [282] arealso much lower than the presentlyreportedvalues. A linear least—squares fitof the presently obtained data In therange 0.66—0.89A givesRe(rvi&0.456 + 0.378rt0(7.7)210The dipole strengths De(r0) at equilibrium internuclearseparationr0 have been investigated both experimentally [244,249,250,282]andtheoretically [239-243,252,255,261] by several groups.This quantity isdefined as [250,282]:De(ro)= GIR1o)I2 (7.8)where 0 Is the statistical weighting factor as defined above.In the present work, the transition moment at theequilibriuminternuclear distance r0 for the Lyman and Werner bandscan becalculated from equations 7.6 and 7.7 respectively by settingr’o=r0=0.741A. From equation 7.8 the dipole strengths are determinedto be 0.94 for the Lyman band and 1.08 for the Wernerband. Table 7.4summarizes the present results and showsa comparison with otherpreviously reported experimental [244,249,250,282] and theoreticaldata[239—243,252,255,26 1]. For the Lyman band the previously publishedexperimental results [244,249,250] and the present workshow goodagreement with each other except for the value reportedby Geiger [249]which is - 10% lower. For the Werner bandall the previously reportedexperimental values [244,249,250,282] arelower 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 goodagreement with the present values for boththe Lyman and the Wernerbands. The other calculated values show significant differencesfrom thepresent results.Finally it should be noted that the dependenceof the electronictransition moment on the internucleardistance and also the dipoleTable 7.4 211Dipole strengths De(ro) for the Lyman and Wernerbands ofmolecular hydrogenReferenceDipole strengths De( r0) in a.u.Lyman band Werner bandTheory:Wolniewicz [261] 0.961.10Browne [252](i) dipolelength 0.78(ii) dipole velocity1.04Rothenberg and Davidson [255](i) dipolelength 0.91 1.06(ii) dipole velocity0.92 1.18Miller and Krauss 1243] 1.001.08Peek and Lassettre 12421 0.970.81Ehrenson and Phillipson 1241] 0.85Skull 1240] 0.601.33Milliken and Rieke [239] 0.771.21Experiment:Present work 0.941.08(dipole (e,e))Fabian and Lewis [2821 0.960.92(optical: curve of growth)Geiger and Schmoranzer [250] 0.980.89(electron impact)Geiger and Topschowsky [244]0.95 0.92(electron impact)Geiger 1249] 0.841.03(electron impact)212strength at the equilibriuminternuclear distancedetermined in thepresent work for both theLyman and Wernerbands are consistent withthe theoretical work byRothenberg and Davidson [255], byWolnlewicz[2611 and byMiller and Krauss [243].It should be pointedout that someof these calculations [255,261]were used by Allisonand Dalgarno[234,262] intheir calculation of theabsolute oscillator strengthsfor theLyman and Wernerbands.7.3 ConclusionsAbsolute optical oscillatorstrengths for molecular hydrogenhavebeen measured in the energyregion 1 1—20 eV. Theabsolute scale wasobtained by normalizingin the photoabsorption continuumregion at 18eV to the absolute value determinedby Backx et al. [86] usinglowresolution dipole (e,e) spectroscopyand TRK sum rule normalization.Absolute optical oscillator strengthsfor the vibronic transitionsof theLyman and Werner bandshave been determined.The presently reportedexperimental oscillatorstrength data are in verygood agreement withthe theoretical valuesreported by Allison and Dalgarno [234,262]for theLyman and Werner bands.The optical data of Fabian andLewis [2821agree with the presentresults for the Lyman bandbut are more than 10%lower for the Werner band.The variations of the electronictransitionmoments of the Lyman andWerner bands of hydrogen withinternucleardistance derived from thepresent measurements arefound to be in verygood agreement with theoreticalcalculations [243,255,261].213Chapter 8Absolute Optical Oscillator Strengths for the Discrete andContinuum Photoabsorption of Molecular Nitrogen (11—200 eV)8.1 IntroductionNitrogen is the most abundant molecule In the earth’s atmosphereand photoabsorption, photodissociation and photoionization processesresulting from its interaction with solar UV radiation play an Importantrole in the energy balance of the earth’s upper atmosphere. In additionthe predissociation of electronically excited states of nitrogen is theprinciple process by which molecular nitrogen is dissociated in theatmosphere by solar radiation and by electron impact. Absolute opticaloscillator strengths for nitrogen in the discrete valence region provideinformation on the excitation cross sections, and these together withemission cross section data can be used to determine the predissociationcross sections and emission yields [294—297] of electronically excitedstates of nitrogen.Transition energies and absolute optical oscillator strengths forexcitation from the ground state of nitrogen to various Rydberg stateshave been calculated by a number of authors [298—303]. However, thesecalculations are at the level of electronic but not vibrational resolution.Duzy and Berry [298] based their calculation on a Hartree—Fockwavefunction for the ground state of nitrogen and excited statewavefunctions derived from an irredu cible—tensorial one—centerrepresentation of the effective potential of the nitrogen ion core.214Calculations have also been reported by Rescigno et al. [299] using theStieltjes—Tchebycheff moment—theory technique and by Kosman andWallace [300] using the multiple scattering model. Absolute opticaloscillator strength calculations for the transitions from the ground stateto the valence b’H and b’‘istates and some low—lying Rydberg stateshave been performed by Rose et al. [301] using the equation—of—motionmethod, by Hazi [3021 using the semi—classical impact—parameter methodand by Bielschowsky et al. [3031 using extensive ab inltio calculationswith highly correlated configuration interaction wavefunctions.Irregularities in the vibronic energy levels and intensity distributionsassociated with theb’Hand b’ excited valence states have beenobserved experimentally [304,305], which has been attributed tohomogeneous configuration interaction of the b’fl and b’ states withthe first two members of the c’H and Rydberg states, respectively.By first fitting the eigenvalues of a vibronic interaction matrix to theobservations, Stahel et al. [306] have reported vibronic energies,elgenvectors, B values and relative oscillator strengths for the b’fl andexcited valence states and the c’H,chl+ and o1fl Rydbergstates, based on a matrix optimization with direct solutions of coupledoscillator equations. The effects of configuration interaction on thenitrogen spectrum have been discussed in detail by Lefebvre—Brion andField [307] and also by Carroll and Hagim [308].The photoabsorption of molecular nitrogen in the valence discreteregion has been the focus of many experimental studies and a largeamount 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 opticaloscillator strength215(cross section) values in the valence discrete region. However,very largedifferences in the relative peak intensities for the discretetransitions ofnitrogen in the energy region 12.5—13.2 eV were observedbetweendifferent Beer—Lambert law photoabsorption measurements[76—80,313,316] and also with optical oscillatorstrength determinationsbased on a variety of electron energy loss experiments[11,37,81,82,304].At first it was thought that the discrepancies weredue to the failure ofthe Born approximation used to interpret the electronimpact basedexperiments. However, Lawrence et al. [78] subsequentlyremeasuredthe absolute oscillator strengths for several discreteexcitations ofmolecular nitrogen using Beer—Lambert law photoabsorptiontechniquesin the same energy region at several different samplepressures, andfound that the measured oscillator strengths showedlarge variations withsample pressure. Extrapolating to small values of thecolumn number(i.e. low pressure), the resulting oscillator strengthvalues [78] werefound to be much more consistent with the relativeintensities of thepeaks obtained earlier by Lassettre et al. [81] and by Geigeret al.[82,304] from electron energy loss experiments. Following theseobservations the difficulties involved in using Beer—Lambertlawphotoabsorption for studies of discrete excitations wererealised [11,46].A detailed quantitative analysis and theoretical investigation of thebandwidth effects and associated errors inBeer—Lambert lawphotoabsorption has been given by Chan et al.[37] (see chapter 2). Chanet aL [37] also demonstrate that the bandwidtheffects will be manifest inthe peak areas as well as the peak heights inoscillator strengthdeterminations for discrete transitions. These difficultieswith the Beer—Lambert law, which can lead to very large errors in measured oscillator216strengths, are caused bythe finite bandwidth of the opticalspectrometer.Severe “line saturation”effects are likely to occur particularlywhen themeasured discrete transition has avery narrow natural line—widthandhigh cross section. In such casesthe measured optical oscillatorstrengths are likely to be too smalleven when very carefulBeer—Lambertlaw studies are made as a functionof pressure. Thesedifficulties couldalso be minimlsed in principle Ifextremely high optical resolutioncouldbe obtained [321], but itshould be noted that this requiresIn practicethat the spectrometer bandwidthbe very much narrower than thenaturallinewidth of any spectral line beingstudied. Since electronImpactexcitation is non—resonant, such“line saturation” or bandwidtheffectscannot occur in optical oscillatorstrength determinationsbased onelectron energy loss measurements [11 ,30,37].In particular, the dipole(e,e) method is ideally suited forthe accurate determinationofphotoabsorption oscillator strengthsthroughout the discreteandcontinuum spectral regions [37].In contrast, the Beer—Lambertlawoptical absorption spectrum canexhibit a very variable relativeintensityprofile throughout the discreteregion depending on the experimentalresolution (bandwidth) since differentelectronic transitions ingeneralhave different natural line—widths.These spurious effects areparticularwell illustrated by a comparison ofthe optical oscillator strength spectraobtained by the electron energyloss [37] and Beer—Lambert lawphotoabsorption [80] methods formolecular nitrogen in the VUVregionas shown in figure 2. 1(see chapter 2). It can be seen thatboth therelative band strengths and theabsolute intensities are dramaticallydifferent in the two spectra in the12.4 to 13.0 eV region. Theintensities are essentially correctin the electron energy lossspectrum in217figure 2. 1(b), whereas bandwidth/linewidthInteractions result In severeintensity perturbations Inthe synchrotron radiation Beer—Lambertlawphotoabsorptlon intensities of reference[80] shown In figure 2.1(a).It IsInstructive to note that Itwas In this specific spectral region thatLawrence et al.[78] made photoabsorption studies as a function ofpressure [37,461 in an attempt to avoidthe bandwidth effects. It can beseen from figure 3 of reference[78] that the relative intensities of thefour transitions at 958 A(12.942 eV), 960 A (12.9 15 eV), 965A (12.848eV) and 972 A (12.756 eV) are drasticallyaltered in different ways(reflecting their different naturalllnewidths and different true crosssections) as the column number(pressure) is reduced. At the lowestcolumn number at which measurementswere made [78], the derivedoscillator strength orderand relative magnitudes are consistent withtherelative intensities in the electronenergy loss based measurement shownin figure 2.1(b) of the presentwork. However, the errors barsin figure 3of ref. [781 are necessarily very largeat the lowest pressures at whichoscillator strength measurements weremade, and as a result the absolutemagnitudes of the oscillator strengthsare still significantly in error (seesection 8.2.2 below of the presentwork). It Is clear that the errors aredifferent for every transition becauseof the different natural linewidths.In addition, extrapolation of optical datato low pressure places the mostemphasis on the least accuratedata obtained at the lowest pressures.Therefore, as a result of finitebandwidth considerations, oscillatorstrength measurements obtainedby Beer—Lambert law photoabsorptionmethods must, at best, be regardedwith extreme caution since It Is clearthat very large errors can occurin the measured oscillator strengths evenwhere measurements are madeas a function of pressure. Conversely,the218efficacy of Bethe—Bornconverted electron energyloss spectra, obtaineddirectly using dipole (e,e)spectroscopy at negligiblemomentum transfer,as a means of obtainingaccurate optical oscillatorstrengths in both thediscrete [27,37,38—40]and continuum [30]regions has now beenwellestablished.The preceding perspectivesconcerning the accuraciesof varioustypes of absolute photoabsorptionoscillator strengthdetermination areimportant when consideringthe results of otherstudies using suchinformation. For example,the extreme ultravioletemission fromnitrogen excited byelectron impact has beenstudied by Zlpf andMcLaughlin [2941 for thetwo excited valence statesand several Rydbergstates. Similar studies havealso been made by Zipfand Gorman [295]and by James et al. [297]for the b’fl state, and byAjello et al. [296] forthectlu+and b’1 Rydberg states.In these studies theemission crosssections and the predissociationbranching ratios forthese states werereported. The excitationcross sections, whichwere used to obtainthepredissociation branchingratios from the measuredemission crosssections, were derived frompreviously published opticaloscillatorstrengths [13,78,304]. Zipfand McLaughlin [294]and Zipf and Gorman[295]obtained optical oscillator strengthva1ues from the re1ativeelectronscattering data of Geigerand Schroder [3041,with correction for thescattering geometryof the spectrometer andalso taking into accounttheabsolute generalized oscillatorstrength data of Lassettreand Skerbele[13].James et al. [297] convertedthe excitation crosssections reportedby Zipf and Gorman [2951for the b’fl vibrationalstates at an Impactenergy of 200 eV to thosewhich would be obtainedat an impact energyof 100 eV and normalizedthe data using the absoluteoptical oscillator219strength value for the (4,0) transition reported by Lawrence et al.[78].Ajello et al. [296] obtained optical oscillator strengths for the c’1andb’1u+ states fromtheir own experimental measurements using therelative flow technique and by applying the modified Born approximationformulation to the measured absolute emission cross sections.As indicated above, electron impact methods based on electronenergy loss spectroscopy have also been applied to study the discreteelectronic transitions of nitrogen[13,15,18,81,82,87,304,322—324].Experimental conditions of low electron impact energy and variablescattering angle have been employed by several groups[13,15,18,322—324]. In these studies generalized oscillator strengths as a function ofmomentum transfer (angle) for various discrete transitions weredetermined and optical oscillator strengths were obtained byextrapolating the generalized oscillator strengths to zero momentumtransfer 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 valencediscrete region by using very high incident impact energies (25—33 keV)and small scattering angles (1—4 xlO-4radians), no absolute oscillatorstrengths were derived. In other work Wight et aL. [871 reportedabsolute dipole oscillator strengths for the photoabsorption of nitrogen Inthe limited energy region 10—70 eV using low resolution dipole (e,e)spectroscopy with 8 keV impact energy and zero—degree mean scatteringangle. However, the absolute scale was obtained by Wight et al.[87] bynormalizing in the smooth continuum at 32 eV to the absolutephotoabsorption data previously reported by Samson and Cairns[325]. Inaddition, the resolution of the spectrum reported by Wight et al. [87] was220limited to 0.5 eV FWHM and as a result absolute optical oscillatorstrengths for the Individually resolved discrete vibronic transitions ofmolecular nitrogen could not be determined.In summary, direct photoabsorption studies of the oscillatorstrengths for the discrete excitation of molecular nitrogen are clearly Inerror due to “line saturation’ effects, while earlier high resolutionelectron impact studies have provided only relative Intensities or In othercases Involve uncertainties due to the necessary extrapolations to zeromomentum transfer. Definitive absolute photoabsorption oscillatorstrength measurements in the discrete region of nitrogen at highresolution should however be possible by electron energy lossmeasurements obtained directly at the optical limit, with the absolutescale 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 fordiscrete 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 nowapplied to the valence shell discrete transitions of molecular nitrogen.The excellent agreement obtained between experimental and theoreticaloptical oscillator strengths for “benchmark” targets such as helium [37](see chapter 4) and molecular hydrogen [40] (see chapter 7) hasconfirmed the high accuracy of the high resolution dipole (e,e) method.In order to independently establish the absolute oscillator strength scalefor molecular nitrogen, comprehensive new low resolution dipole (e,e)measurements have also been made in the energy range 10—200 eV andthese data have been placed on an absolute scale by valence shell TRKsum rule normalization.2218.2 Results andDiscussionThe photoabsorptlonoscillator strengths andspectral assignmentsfor molecular nitrogenare conveniently discussedwith reference to theground state molecular—orbital,independent particle,valence shellelectronic configuration,which may be writtenas:(2ag)2(2a)2( l3rtU)4(3ag)28.2.1 Low ResolutionAbsolute PhotoabsorptionOscillator StrengthMeasurements for MolecularNitrogen (11—200 eV)A relative valenceshell oscillator strengthspectrum was obtainedby Bethe—Born conversionof the electron energyloss spectrum measuredusing the low resolution (—1eV FWHM) dipole (e,e)spectrometer in theenergy region 11—200 eV. Thedata were least—squaresfitted to thefunction AE over theenergy region 90—200 eV. Thefit gave B=2.283and on this basis the fractionof valence—shell oscillatorstrength above200 eV was estimatedto be 5.6%. The total areawas then valenceshellTRK sum—rule normalizedto a value of 10.3, whichincludes the totalnumber of valenceelectrons (10) plus a smallestimated correction (0.3)for the Pauli—exciudedtransitions from the coreorbitals to the alreadyoccupied groundstate valence orbitals [52,53].Figures 8.1(a) and (b)show the resulting absoluteoptical oscillator strengthspectra of nitrogenin the energy regions10—50 and 5.0—200 eV respectively,compared withpreviously reported experimentaldata [87,175,292,326—329].Numericalvalues of the absolutephotoabsorption oscillatorstrengths for nitrogen2220.6(a)1N2160• Present work dipole (e,e)Wight et ci. [87] dipole (ee)0.4 0 Samson & Hoddod [292]Lee et ci. [326]40Watson et ci. [327] Ph Abs+ De Rellhoc & Domony [328]*Cole & Dexter [329]0.2°20£0C)a)U)U): 0.0a 0a) 010 20 30 40 50U)0.10(b)JN2j10— A—C)* 0U)0o0.08*82C)__________________o• Present work dipole (e,e)*Wight et ci. [87] dipole (ce)0.060 Samson & Hoddod [292]6Lee et ci. [326]+ De Reilhac & Damany [328]0.04* Cole & Dexter [329] Ph Abs* Denne [175]0.0202•at..“M0.00.50 100150 200Photon energy (eV)Figure 8.1: Absolute oscillator strengthsfor the photoabsorption of molecular nitrogenmeasured using the low resolution (FWHM=1eV)dipole (e,e) spectrometer(a) comparison with previously reportedexperimental data [87,292,326—329]in the energy region 10—50 eV.(b) comparison with previously reportedexperimental data [87,175,292,326,328,329]In the energy region 50—200 eV.223obtained at low resolutionin the present work from 11—200eV aresummarized in table 8. 1. It Is Importantto note that In the discreteregion the low resolution data Intable 8.1 represent an Integralover theunresolved transitions. More detailedquantitative Information onthediscrete region is available fromthe high resolution spectra(see section8.2.2 below).Immediately It can be seen infigures 8.1(a) and 8.1(b) thatthepresent results are in goodagreement with the photoabsorptioncontinuum data reported earlierby Samson and Haddad [292].The datareported by Cole and Dexter [329]are slightly lower than thepresentwork while those reported byDenne [1751 In the energyregion 150—195eV are —50% lower. The earlierelectron impact based dipole(e,e) datareported by Wight et al. [87] areslightly lower than the presentwork Inthe energy region 18—35 eVbut become higher In the energyregionabove 50 eV up to the limitof their measurements at70 eV. However, itshould also be pointed outthat the relative data of Wight et al.[87] werenormalized in the smooth continuumat 32 eV to the direct opticalphotoabsorption data reported muchearlier by Samson and Cairns [325]..In contrast the present workis valence shell TRK sum—rule normalizedand is thus independent of any othermeasurements. The presentlyobtained low resolution photoabsorptiondata has been used to establishan absolute scale for thehigh resolution measurementsdescribed in thefollowing section.224Table 8.1Absolute differential optical oscillator strengths for the photoabsorptionof 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(10-2eV)(102eV)(102eV)11.0 0.00 20.0 21.83 29.0 20.5611.5 0.08 20.5 21.21 29.5 19.9512.0 5.03 21.0 20.83 30.0 20.1412.5 31.74 21.5 20.76 30.5 18.8413.0 49.14 22.0 21.39 31.0 18.3513.5 42.02 22.5 22.47 31.5 17.8914.0 43.06 23.0 23.05 32.0 17.2114.5 31.61 23.5 23.52 32.5 16.6915.0 21.23 24.0 22.64 33.0 16.1415.5 24.14 24.5 21.62 33.5 15.7216.0 26.57 25.0 21.69 34.0 15.0416.5 25.71 25.5 21.66 34.5 14.9417.0 24.04 26.0 21.57 35.0 14.2217.5 23.56 26.5 21.08 35.5 14.0918.0 23.31 27.0 21.17 36.0 13.4118.5 23.33 27.5 21.04 36.5 12.7419.0 22.52 28.0 21.34 37.0 12.4519.5 22.16 28.5 20.92 37.5 12.30225Table 8.1 (continued)Energy Oscillator Energy Oscillator Energy Oscillator(eV) Strength (eV) Strength (eV) Strength(102eV1)(10-2eV1)(102eV1)38.0 12.27 49.0 9.08 70.04.0638.5 11.76 50.0 8.81 71.0 3.9439.0 11.26 51.0 8.68 72.0 3.8339.5 11.09 52.0 8.41 73.0 3.7540.0 10.78 53.0 8.03 74.0 3.6240.5 10.85 54.0 7.71 75.0 3.4741.0 10.55 55.0 7.47 76.0 3.3541.5 10.37 56.0 7.14 77.0 3.3342.0 10.15 57.0 6.82 78.0 3.1842.5 10.16 58.0 6.53 79.0 3.0643.0 10.02 59.0 6.37 80.0 3.0643.5 9.85 60.0 6.00 81.0 3.0044.0 9.81 61.0 5.78 82.0 2.9044.5 9.79 62.0 5.52 83.0 2.7945.0 9.69 63.0 5.31 84.0 2.7045.5 9.68 64.0 5.11 85.0 2.5846.0 9.51 65.0 4.89 86.0 2.5546.5 9.27 66.0 4.60 87.0 2.5247.0 9.37 67.0 4.49 88.0 2.4447.5 9.31 68.0 4.34 89.0 2.3948.0 9.22 69.0 4.22 90.0 2.32226Table 8.1 (continued)Energy Oscillator Energy Oscillator Energy Oscillator(eV) Strength(eV) Strength (eV) Strength(102eV1) (10-2eV-1) (102eV1)91.0 2.18 124.0 1.09 166.0 0.56292.0 2.20 126.0 1.04 168.0 0.56293.0 2.11 128.0 1.03 170.0 0.54294.0 2.10 130.0 0.986 172.0 0.54995.0 2.10 132.0 0.948 174.0 0.52696.0 2.00 134.0 0.908 176.0 0.49497.0 1.94 136.0 0.879 178.0 0.49698.0 1.92 138.0 0.848 180.0 0.47699.0 1.85 140.0 0.835 182.0 0.465100.0 1.82 142.0 0.801 184.0 0.471102.0 1.74 144.0 0.773 186.0 0.454104.0 1.67 146.0 0.755 188.0 0.460106.0 1.57 148.0 0.726 190.0 0.431108.0 1.52 150.0 0.702 192.0 0.412110.0 1.45 152.0 0.682 194.0 0.445112.0 1.40 154.0 0.685 196.0 0.411114.0 1.33 156.0 0.671 198.0 0.401116.0 1.28 158.0 0.613 200.0 0.392118.0 1.22 160.0 0.608120.0 1.18 162.0 0.614122.0 1.15 164.0 0.581a (Mb) = 1.0975 x102-eV12278.2.2 high Resolution AbsolutePhotoabsorption Oscillator StrengthMeasurements for Molecular Nitrogen (12—22eV)Figure 8.2 shows the absolute opticaloscillator strength spectrumfor the photoabsorption of molecularnitrogen In the energy region12—22eV obtained using the high resolution dipole (e,e)spectrometer (0.048eV FWHM). Also shown on figure 8.2is the presently determinedlowresolution dipole (e,e) data, the earlier lowresolution electron Impactbased data of Wight et al. [87] and the photoabsorptiondata of Samsonand Haddad [292]. It can be seen in figure8.2 that the present highresolution (HR) and the various low resolution(LR) data are in goodagreement over the continuum region. Similarlyin the discrete regionthe measurements are consistent when thelarge differences in energyresolution (0.048 eV vs 1 eV FWHM) are takenInto account. Thepresent HR data in the continuum18—22 eV are also in good quantitativeagreement with the photoabsorption data ofSamson and Haddad [292].Figures 8.3, 8.4 and 8.5 show expandedviews of figure 8.2 in theenergy regions 12.4—13.4, 13.2—15 and15—19 eV respectively. Thedetailed qualitative spectroscopy of molecularnitrogen is well knownfrom higher resolution optical andelectron energy loss spectra andtheindicated assignments and energy positionsshown are as given in refs.[80,300,304,317]. The most prominenttransitions below 15 eVcorrespond to the valence excitationsto the b1H and states, andthe lowest members of the three(30g—’Spau) c”u,(3ag’PJtu) c’fluand (btu4ag) O’flu Rydberg series. Inthe energy region 15—17.5 eV,the spectrum involves mainly transitions tohigher members of thechlu+,c1H ando1fl Rydberg series. The assignments and energy positionsfor228•>a)‘-4I.Cl)‘-4C-4.—C)Cl)0C)300500400C)a)U)U)U)0‘-4C)02001-40U)10054320 0Photon energy (eV)Figure 8.2: Absolute oscillator strengths for thephotoabsorption of molecularnitrogenin the energy region 12—22 eV measured using the highresolution dipole(e,e) spectrometer (FWHM=O. 048 eV).12 14 16 18 20 225000400300C.)0_f•n .4-iC4001000229543I?2012.4 12.8 13.2Photon energy (cv)0Figure 8.3: Expanded view of figure 8.2 forthe photoabsorption of molecular nitrogenin the energy region 12.4—13.4 eV. Theassignments are taken fromreferences [300.304,317]. Deconvoluted peaks areshown as dashed linesand the solid line shows the total fit to theexperimental data.1600C)VU)Cl)120U)0230N211’onII I I44 55 66I I I I l I12 14 16 18 201 2II I22 33I I I I6 8 10I I I I Ib’fI12 14 161.6V1.2VI.Cl)10Ii +c E7’7oil_-lu22 24bIiEu+II I I II0 0 1 1 2 2Ii+eEue1IJ13.2 13.6 14.0 14.4 14.8Photon energy (eV)0Figure 8.4:Expanded view offigure 8.2 for thephotoabsorption ofmolecular nitrogenin the energyregion 13.2—15.0eV. The assignmentsare taken fromreferences [300,304,317].Deconvoluted peaksare shown as dashedlinesand the solid lineshows the totalfit to theexperimental data.Figure 8.5:800_________6O4001.402000Expanded view of figure 8.2 for the photoabsorptionof molecular nitrogenin the energy region 15—19 eV. The assignmentsare taken from references[80,300,3171.231X2g A2HLN2I0.8:tj 0.6Vi20.4‘.400:2uufldag3 4 567I III I III4 5 6782 +2a—nsa9BE15 16 17 18Photon energy (eV)019232these transitions are not shown in figure 8.5 due to heavy overlapping Inthis region. The autolonization profiles In the energy region 17.1—18.5eV are due to transitions from the20u—’nsag “window resonances”, andthe20u—’ndag Rydberg series [80]. The “window resonances” are causedby destructive quantum mechanical interference with the underlyingdirect ionization continuum.In the present work integration of the area under each spectralpeak will give directly the absolute optical oscillator strength for therespective discrete vibronic transition. Since the energy positions of thepeaks are very well known [80,300,304,3 171, a curve fitting programusing Voigt—profiles has been used to provide an accurate deconvolutionof the partially resolved peaks In the energy region 12.4—14.9 eV.Although they should be slightly asymmetric due to unresolved rotationalstructure (as observed for example in the very high resolution electronenergy loss spectrum obtained by Geiger and Schroder [304]), the peaksare expected to be essentially symmetric at the resolution of the presentwork. Accordingly symmetric peak profiles have been used in the curve—fitting procedure. The dashed lines In figures 8.3 and 8.4 show theresulting deconvoluted peaks. Absolute optical oscillator strengthsobtained from the deconvoluted peak areas are summarized in table 2.The assignments and energy positions shown In table 8.2 are taken fromthe paper of Geiger and Schroder [304]. The uncertainties of the areadeterminations (and thus the oscillator strengths) in the present workare estimated to be —5—10% for the relatively strong and well separatedpeaks in the energy region 12.40—13.27 eV, and -40—20% for theremaining peaks at higher energies.Table 8.2233Absolute optical oscillator strengths for discrete transitionsfrom theground state of molecular nitrogen in the energy region12.50—14.86eV#Energy Final Upper level Integrated( eV)electronic vibrational oscillatorstate number (vt) strength12.500 b’fl 0 0.0025412.575 b’fl 10.011312.663 b’fl 20.027212.750 b’fl 3 0.052612.835 b’fl 4 0.086112.910 c’fl 0 0.063512.935 c”2 0 0.19512.980 b’fl 5 0.0061313.062 b’fl 6 0.0050013.100 O’fl 013.156 b’fl 70.023713.185 1 0.0014713.210 c’fl 10.064013.260 b’fl 813.305 b”Z 5Cb’fl 9 113.345!‘- 0.0258Ioln 1J13.390 b”2 6 0.0021613.435 .b’fl 100.014713.475 c’fl 2 0.015513.530 b’fl 110.00484234Table 8.2 (continued)Energy Final Upper level Integrated(eV) electronic vibrational oscillatorstate number (v’) strength13.585ohflu2 0.027713.615 b’fl 12 0.0018113.660 9 0.012813.700 b’fl1313.720 3 0.019013.760 10‘I>0.0051013.785 b’fl 14 313.820 O’fl 3 0.023613.830 b’1 11 0.0065413.870 b’fl 1513.910b11u+12 0.030313.950 b’fl 1613.980 c”E 4 0.049613.990 c’fl 4 0.0021013.998b?1Zu+1314.050o1fl4 0.0062014.070 b”u 14 0.034114.150 b”E 15 0.0409rb”Z 1614.230 c’fl 5. 0.0632c”2 5J14.275o1fl5 0.00155235Table 8.2 (continued)Energy Final Upper level Integrated( eV)electronic vibrational oscillatorstate number (v’) strength14.300 17 0.031814.330e1fI0 0.015314.350 e”2 0 0.010414.400 18 0.0032614.465 b”D 19 0.016614.478ctlu+6 0.013514.525 20 0.017314.585e1fI1 0.0076114.680b?1u+22 0.00455(c’fl714.720.<0.00547I_7J14.737 b”Z 23 0.010214.795 bu 24 0.0045514.839 n=5’fl 0 0.011314.860 e’fl 2#The energy positions and assignments were obtained from ref.[304].236Tables 8.3—8.7 summarize theabsolute, vibrationally resolvedoscillator strengths for the electronictransitions from the ground stateto each of the b’H, c’Hand o1flstates, along withpreviously published data [78,79,294—297].For the overlappingtransitions such as v’=9 of b’fl and v’=1 ofo’fl,as shown In table 8.2,the oscillator strength value for eachindividual transition was estimatedfrom the ratio of the relative band strengthsfor these states as calculatedby Stahel et al. [306]. Similarprocedures were employed for theotherunresolved states indicated in table8.2. It can be seen in tables8.3—8.7that great variations exist inthe absolute vibronic oscillator strengthsreported by various groups usingdifferent experimental techniquesandmethods of normalization [78,79,294—297].The photoabsorption data of Lawrence etal. [78] shown In tables8.3, 8.5 and 8.6 are more than30% lower than the present workeventhough the data were obtained byextrapolating the measured oscillatorstrength values to low pressure(N<1013 cm2)in an attempt toaccountfor the ‘line saturation” effects.However, as has been pointed outin refs.(11 ,37] anddiscussed in the introduction of thischapter, this kind ofextrapolation procedure may lead tolarge errors in the resultingoscillator strength values since itrelies heavily on the least accuratedatameasured at the lowest pressure.Carter [79] has reported similarmeasurements for nitrogen as afunction of pressure but only extrapolateddown to a column number N of1014cm2. Despite the extrapolationtheabsolute oscillator strength datareported by Carter [79] still showserious“line saturation” effects for manytransitions, and the errors areespeciallylarge in the cases of v’=4 of the b’flstate, v’=16 of theblu+ state, v’=Oof the state and v’=O of the c1flstate (see tables 8.3—8.6).Table 8.3 237Absolute optical oscillatorstrengths for transitions to the vibronicbands of the valenceb’H state from the ground state of molecularnitrogenEnergy Present James Zipf andCarter Lawrence(eV) work et al. Mclaughlin et al.[297]t [2941@ [791#[78J12.500 0 0.00254 0.0014 0.0023912.575 1 0.01 13 0.0081 0.013912.663 2 0.0272 0.0182 0.03110.03512.750 3 0.0526 0.0343 0.05790.058 0.0212.835 4 0.0861 0.0550 0.09220.047 0.05512.980 5 0.00613 0.0029 0.0047313.062 6 0.00500 0.00270.0043713.156 7 0.0237 0.0153 0.02480.01913.260 8 0.0003 0.00050613.345 90.00466*0.0031 0.005013.435 10 0.0147 0.0093 0.0146 0.01313.530 11 0.00484 0.0032 0.004390.004613.615 12 0.00181 0.00070.00126 0.004213.700 130.00713.785 14 0.00290 0.0008 0.0013113.870 15 0.0005 0.00088713.950 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 andGorman [2951.Values were obtained at a column number N of 1014 cm2.This transition cannot be separated from v= 1 of theo1fI state. The value was obtained from the ratioof the relative band strengths of these two states ascalculated by Stahel et a!. [3061.Table 8.4238Absolute optical oscillator strengths for transitions to the vibronic bands ofthe valence bhlDu+ state from the ground state of molecular nitrogenEnergy Present Ajello Zipf and Carter(eV) v’ work et al. MacLaughlin(2961 1294](79]#0123413.305 5 0.00135 0.0012313.390 6 0.00216 0.002649 0.00260 0.00757 0.0034098 0.02210713.660 9 0.0128 0.009529 0.0102 0.004813.760 10 0.00220 0.001643 0.0017313.830 11 0.00654 0.003504 0.0036713.910 12 0.0303 0.030297 0.0316 0.01913.998 13 0.004443 0.0045514.070 14 0.0341 0.041825 0.042414.150 15 0.0409 0.054902 0.0493 0.03414.230 160.0626*0.0677920.0667*0.02514.300 17 0.0318 0.037148 0.0368 0.02514.400 18 0.00326 0.003366 0.0032914.465 19 0.0166 0.021500 0.020814.525 20 0.0173 0.018373 0.0177 0.01621 0 0.007614.680 22 0.00455 0.005532 0.00522 0.005214.737 23 0.00897 0.009411 0.0088014.795 24 0.00363 0.003823 0.00356 0.0044Values were obtained at a column number N of 1014 cm2.This transition cannot be separated from v=5 of the cI+ state.The value was obtained from the ratio of therelative band strengths of these two states as calculated by Stahelet aL 13061.Table8.5AbsoluteopticaloscillatorstrengthsfortransitionstothevibronicbandsofthelowestmemberoftheRydbergc121statefromthegroundstateofmolecularnitrogenEnergyPresentAjelloZipfandCarterLawrence(eV)vtworketal.McLaughlinetaI.[296][294][79]#[78]12.93500.1950.15670.2170.0650.1413.18510.001470.00380.0019920.00270.01113.72030.01900.01360.02070.02913.98040.04960.02850.059214.23050.0006*00.0007*0.003914.47860.01350.01790.0176ValueswereobtainedatacolumnnumberNof1014cm2.*Thistransitioncannotbeseparatedfromv=16oftheb’state.ThevaluewasobtainedfromtheratiooftherelativebandstrengthsofthesetwostatesascalculatedbyStaheletal.13061.C) coTable8.6AbsoluteopticaloscillatorstrengthsfortransitionstothevibronicbandsofthelowestmemberoftheRydbergc1flstatefromthegroundstateofmolecularnitrogenEnergyPresentZipfandCarterLawrence(eV)v’workMcLaughlinetal.[294][79]#[78]12.91000.06350.06560.0370.04013.21010.06400.068213.47520.01550.01720.018313.99040.002100.0053014.2305#ValueswereobtainedatacolumnnumberNof1014cm2.CTable87AbsoluteopticaloscillatorstrengthsfortransitionstothevibronicbandsofthelowestmemberoftheRydbergolHstatefromthegroundstateofmolecularnitrogenEnergyPresentZlpfandCarter(eV)v’workMcLaughlin[294][79]#13.10000.0004913.34510.0211*0.0226*13.58520.02770.02780.02113.82030.02360.03290.03014.05040.006200.0050614.27550.001550.00321ValueswereobtainedatacolumnnumberNfo1014cm2.*Thistransitioncannotbeseparatedfromv=9oftheb’l1state.ThevaluewasobtainedfromtheratiooftherelativebandstrengthsofthesetwostatesascalculatedbyStaheletat.1306].242It can also be seen Intables 8.3—8.7 that although the absolutevibronic oscillator strengths reported byZipf and McLaughlin [294],Ajello et al. [296], James et al. [297]and the present results showvariations between each other, therelative oscillator strength valuesforthe vibronic levels of a given electronic transitionare reasonablyconsistent. These differences between thedata sets are therefore likelycaused by the different ways in whichthe data have been made absolute.For the b’H vibronic bands, the dataof James et al. [297], which werenormalized at v’=4 to the valuereported by Lawrence et al. [78],arelower than the presently reportedvalues. This observation and thedifferences with the present workare consistent with the fact thatthedata of Lawrence et al. [78] still show “linesaturation” effects at thelowest pressure used for measurement(see above discussion). Theabsolute oscillator strength datareported by Zipf and McLaughlin [294]are in general slightly higher thanthe present results. However, Ithas tobe pointed out that Zipf and McLaughlin [2941did not make any directoscillator strength measurement.Their oscillator strength data [294],which were used to calculate thepredissociation branching ratios bycombining with their measuredemission cross sections, were infactderived from the relative electronimpact data of Geiger and Schroder[304] by normalizing on the absolutegeneralized oscillator strength dataof Lassettre and Skerbele [13].The data reported by Lassettre andSkerbele [13] were in turn obtainedfrom the earlier limiting oscillatorstrengths work of Silverman andLassettre [18], which had to berenormalized [13] by multiplying a factor(0.754) in order to correctforan error in the pressure measurements.Ajello et al. [2961 determined243absolute oscillator strengthdata from their ownmeasurements, but theirresults have a stated uncertaintyof 22%.By summing up theappropriate vibronic oscillatorstrengths shownin tables 8.3—8.7, the totalabsolute oscillator strengthsfor the b’fl andbI’u+ excited valence states, and thelowest members of c’I1,c’l2+ando1fl Rydberg states can beobtained. The results aresummarized intable 8.8 where previouslyavailable experimental[294,296,297,324]andtheoretical data [299—303,3061are also shown forcomparison. It can beseen that there arelarge variations between thereported values. Exceptin the case of the o1fl state,the theoretical data ofBielschowsky et al.[303], calculatedusing the configurationinteraction method,show betteragreement with the presentresults than thosecalculated using theHartree—Fock method. Thecalculations reported byStahel et al. [3061only show good agreementwith the presentvalues for the c’fl state,while the calculated valuesfor the other states areall lower. The totaloscillator strengths for thefive excited states reportedby Zipf andMcLaughlin [2941 are somewhathigher than the presentlyreported data,which is consistentwith the vibrationally resolvedresults in tables 8.3—8.7. Similarly, the total oscillatorstrength value for the b’flstatereported by Jameset al. [297] is -36% lower thanthe present value.However, this is consistentwith the fact that the normalization[297] wasobtained using the vibronicoscillator strength for v’=4of the b’H statemeasured by Lawrence eta!. [78], which is lower thanthe present workby the same amount, asshown in table 8.3.The spectrum above 14.92eV involves many highly overlappedtransitions. Therefore absoluteintegrated oscillator strengthsover smallenergy intervals in the energyregion 14.92—16.91eV have been244Table 8.8Total absolute optical oscillator strengths for transitions to theb1Hu andb’lu+ valence states, and the lowest members of thec1flu, c’1uandO1flu Rydberg states from the ground state ofmolecular nitrogenb’fl C’flu C’1 O’flExperiment:Present work 0.243 0.278 0.145 0.279 0.080Jamesetal. [297] 0.156Ajelloetal. [296] 0.321 0.223ZipfandMcLaughlin[2941 0.283 0.310 0.156 0.317 0.0921Chutjianetal. [324] 0.100.080 0.12 0.026Theory: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 0.15Staheletal. [306] 0.124 0.209 0.141 0.139 0.061KosmanandWallace[3001 0.0641 0.0493 0.136Hazi [302] 0.47 0.11Rescignoetal. [2991 0.0681 0.0591 0.149Roseetal. [3011 0.32 0.49 0.11245Table 8.9Integrated absolute optical oscillator strengths in selected regionsover the energy range 14.92—16.9 1 eV for excitation of molecularnitrogenEnergy range Integrated oscillator(eV) strength14.92—15.07 0.013915.07—15.19 0.022815.19—15.30 0.019615.30—15.43 0.024515.43—15.54 0.021215.54—15.74 0.051015.74—15.93 0.060615.93—16.03 0.030016.03—16.11 0.027016.11—16.17 0.011516.17—16.26 0.026016.26—16.33 0.018416.33—16.40 0.015616.40—16.49 0.023616.49—16.70 0.047616.70—16.91 0.0426246obtained, and these are summarisedin table 8.9. Comparisonwith thepreviously reported photoabsorptiondata in this energy rangeis difficultbecause of different instrumentalenergy resolutions andalso because ofthe presence of “line saturation”effects in the photoabsorptiondata.Finally, it can be notedthat the oscillator strengthdistribution ofmolecular nitrogen was reviewed earlierby Berkowitz [143], usingtheexperimental data available before1980. Berkowitz obtained avalue of1.153 for the integrated oscillatorstrength below 15.56 eV usingthedata of Lassettre and Skerbele [13]and a value of 0.3299 inthe 15.56—16.76 eV energy region basedon the data of Carter [79].In the presentwork these integrated valuesare determined to be 1.173and 0.3 19,respectively.8.3 ConclusionsIn the present work comprehensiveoscillator strengthmeasurements have beenobtained throughout the UV and softx-rayenergy regions for the photoabsorptionof molecular nitrogen.Absoluteoptical oscillator strengthshave been measured inthe energy region 11—200 eV using low resolutiondipole (e,e) spectroscopy and TRKsum—rulenormalization. Thepresent continuum results are ingood agreementwith the photoabsorptiondata reported by Samson and Haddad[292].Absolute optical oscillatorstrengths in the 12—22 eVregion of discreteexcitation have alsobeen measured using the high resolutiondipole (e,e)method recently developedin this laboratory. The absolutescale wasobtained by normalizing in thesmooth continuum regionat 20 eV to theabsolute photoabsorption valuedetermined using the low resolution247dipole (e,e) spectrometer.The transition peaks below 14.9eV have beendeconvolutedto obtain the absolute photoabsorptionoscillator strengthvalues for individualvibronic transitions.The presently determinedabsolute opticaloscillator strengthsfor excitation to theb’H and b’valence states, andthec’fl,ctu+and o1fl Rydberg stateshave beencompared with previouslyreported experimentaland theoretical data.Large differences betweenthe various reported datasets are observed.However, it is foundthat the relative oscillatorstrength valuesfor thevibronic bandsdetermined from the presentwork and some of thepreviously reported[294,296.2971 data are reasonably consistent.Thissuggests that the differencesin these cases are mostlikely due to thedifferent normalization proceduresused to establish the absolutescales.In the present work theabsolute optical oscillatorstrength scale hasbeen established byindependent procedures.The accuracy of thepresently determined absoluteoptical oscillator strengthsfor thephotoabsorptionof molecular nitrogenin the discrete region can bejustified by a considerationof the results forthe noble gases[37—391(chapters 4—6) and molecularhydrogen[401 (chapter 7) which have beenrecently obtained usingthe same instrumentationand techniques. Thepresent work also clearlydemonstrates the existenceof serious errorsdue to “line saturation”(bandwidth) effects in absoluteoscillator strength(cross section) determinationsfor discrete transitionsin molecularnitrogen made usingBeer—Lambert law photoabsorptiontechniques, evenwhere the measurementshave been made as a functionof pressure. Suchconsiderations will be ofconcern in absolute oscillatorstrengthdeterminations for allatoms and molecules usingBeer—Lambert lawphotoabsorptionmethods.248Chapter 9Absolute Optical Oscillator Strengths for the Photoabsorption ofMolecular Oxygen (5-30 eV) at High Resolution9.1 IntroductionSince oxygen is the second most abundant species within theearthsatmosphere, an accurate knowledge of absolute oscillatorstrengths (cross sections) for the photoabsorption of molecular oxygen inthe valence discrete region is of great importance in aeronomy and inother areas such as nuclear physics, radiation physics and astrophysics.The dissociation and predissociation of molecular oxygen by theabsorption of solar radiation can also be used to determine the oxygendensity profile at high altitudes and such processes play an importantrole in atmospheric phenomena such as aurora and dayglow. Molecularoxygen is also of particular theoretical interest and challenge since it isan open shell system.The photoabsorption spectrum of oxygen has been studiedextensively. Critical reviews and compilations of the spectroscopic dataof oxygen can be found in several papers [46,330,331]. Although Beer—Lambert law photoabsorption methods have often been used to obtainquantitative 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 considerableerror because of “line saturation” effects due to the finite resolution(bandwidth) of the optical spectrometer. Such effects can be severe for249discrete transitions with verynarrow natural linewidth and highcrosssection. For example,Yoshino et al. [55] have notedthat the Schumann—Runge (12,0) band of18is too sharp for its absolutecross section to bemeasured by conventional Beer—Lambertlaw photoabsorptiontechniques.The Schumann—Runge bandsystem of molecular oxygen,whichinvolves transitions from the groundX3g to the B3-state,has beenstudied extensively by manyworkers. On the low energyside the systemconsists of sharp discretetransitions with very low oscillatorstrength,which have been measured by Lewiset al. [332] using thecurve of growthmethod to allow for bandwidtheffects. At higher energy Inthe 7—9.8 eVregion the absorption spectrumof oxygen is dominated bythe broad andgenerally featureless Schumann—Rungecontinuum, for which manyBeer—Lambert law photoabsorption measurementsof the absolute cross sectionhave been made [333—342].Ab—initio theoreticalcalculations have beenreported by Buenker andPeyerlmhoff [3431 and byAllison et al. [344] forthe oscillator strengths ofthe Schumann—Runge continuumregion,taking into account the mixingbetween the valence B3and theRydberg E3 (or B’3 inother notation) states. Allison etal. [344] alsotook into account the contributionsfrom the 13fl state andreportedcross sections and structuralfeatures that were consistent withtheexisting experimental results.Wang et al. [342] performedanexperimental absolutephotoabsorption measurement ofoxygen in theSchumann—Runge continuumregion, and by fitting theirtheoreticalcalculations to the observed data,they reported potential curvesandtransitions moments forthe mixed Rydberg—valence B3and mixedvalence—Rydberg E3states.250On the high energy side of the Schumann—Runge continuum, thereare several diffuse bands. The three prominent peaks at 9.96 eV(longest), 10.28 eV (second) and 10.57 eV (third) have been assigned byYoshimine et al. [345] and Buenker et al. [346] as transitions to the threelowest vibrational levels of the mixed valence—RydbergE3-state.Yoshimine et al. [345], Buenker et al. [3461 and Li et al. [347] havecomputed the absolute oscillator strengths for these three bands. Beer—Lambert law—type photoabsorption measurements have also beenperformed for these diffuse bands [334,336,3401, including a recentstudy by Lewis et al. [348,349], who made measurements on isotopicmolecular oxygen (1802) and for the first time analyzed the data usingBeutler—Fano type resonance profiles.Electron energy loss spectroscopy (EELS) has also been used tostudy the electronic excitation spectrum of molecular oxygen[13,16,17,92,350,3511 in the valence discrete region. Since electronimpact excitation is non—resonant as described in chapter 2, EELS basedmethods of determining optical oscillator strengths have the enormousadvantage that they are not subject to the limitations of “line—saturation”(i.e. bandwidth) effects which cause difficulties in Beer—Lambertlawphotoabsorption measurements [37,46]. Using measurements ofinelastically scattered electrons obtained at a range of scattering angles,absolute optical oscillator strengths for oxygen in the discrete andcontinuum regions were derived by Lassettre and co—workers [13,16,17]from extrapo1ation of the measured generalized oscillator strengths tozero momentum transfer. With the use of extremely high impact energy(25 keV) and small scattering angle, Geiger and Schroder [350] reporteda very high resolution electron energy loss spectrum of oxygen in the251energy loss region 6.8—21eV, but only relative intensities(not absoluteoscillator strengths) wereobtained. Huebner et al.[35 1] have reporteddata In the energy region6—14 eV which were derivedfrom highresolution electron energy lossmeasurements obtained atan impactenergy of only 100 eV andat a small scattering angle(0.02 rad.). Themeasured oscillator strengthsare questionable in this case [3511sIncethe experimental conditions correspondto a rather largemomentumtransfer (K2=O.O1 and0.04 a.u. at 6 eV and 14 eVrespectively). Theabsolute scale was establishedby Huebner et al. [351] bynormalizing thespectrum to an averageoptical value [46] at a singlepoint in theSchumann—Runge continuumregion where the photoabsorptionmeasurements weremutually in best agreement.An independent TRKsum rule normalizationmethod was used by Bnonet al. [921 to obtainabsolute oscillator strengthsfor the photoabsorption ofoxygen in theenergy region 5—300eV from Bethe—Born convertedelectron energy lossspectra. These latter results [921were determined directlyat negligiblemomentum transfer using alow resolution (AE 1 eV FWHM)dipole (e,e)spectrometer with an impactenergy of 8 keV and a meanscatteringangle of zero degrees.In the presently reportedwork, the recently developed[36,37]high resolution dipole(e,e) method which has alreadybeen appliedsuccessfully to measurementsfor the noble gases [36—39](see chapters4—6) and several smallmolecules [27,40,4 1] (seechapters 7 and 8), hasbeen used to measure directly,at negligible momentumtransfer, theabsolute oscillator strengthsfor oxygen in the energy region6—30 eV at aresolution of 0.048 eV FWHM.The absolute scale has beenobtained bynormalizing in the smooth continuumat 26 eV to the previouslyreported252absolute oscillator strength value determinedby Brion et al. [92] using alow resolution dipole (e,e) spectrometer.9.2 Results and DiscussionThe photoabsorption oscillatorstrengths and spectral assignmentsof molecular oxygen are conveniently discussedwith reference to theground state molecular—orbital, Independentparticle, valence shellelectronic configuration, which maybe written as:(2ag)2(2o)2( 1)( 3Gg)2(lrg)2Figure 9.1 shows the presently measuredabsolute differential oscillatorstrength spectrum of molecularoxygen measured in the energy region 5—30 eV by high resolution dipo1e (e,e)spectroscopy at a resolution of0.048 eV FWHM. Several vibrational progressionsare clearly visible. Thetwo other sets of data shown in figure 9.1are the low resolution (1 eVFWHM) dipole (e,e) data (open triangles)reported earlier at 1 eVintervals by Brion et al. [92] and thephotoabsorption data (open circles)measured by Samson and Haddad [292] usinga double ion chambermethod. The double ion chamberresults [292] are not compared withthe present work in the region of the sharpautoionizing structure (12—18eV) because of significant differencesin energy resolution and alsobecause the optical measurementsmay be subject to “line saturation”effects. Therefore the data of reference [2921are only shown in figure 9.1in the generally smoother spectralregion above 18 eV. It can be seenfrom figure 9.1 that the present results arein very good quantitative253200.40.3Cl) 0.2CQCi)o0.1C-)C0.0Figure 9.1:Absolute oscillatorstrengths for thephotoabsorption of molecularoxygenin the energy region5—30 eV measured usingthe high resolutiondipole (e,e)spectrometer(FWHM=O.048 eV).10Photon energy (eV)254agreement with the earlier data of Brion et aL. [921 and also those ofSamson and Haddad [292] in the smooth continuum region (where thecross section will be effectively independent of resolution). At lowerenergies the presently obtained high resolution spectrum is seen to beconsistent with the data of Brion et al. [92] given the differences inresolution. The total Integrated oscillator strengths below 18 eV for boththe high and low resolution spectra are In very good agreement with eachother, giving values of 1.13 and 1. 12 respectively. In the present work,integration of the measured high resolution differential oscillatorstrength spectrum over a given energy region will give directly theabsolute oscillator strength for that region. The uncertainties in thepresently reported absolute oscillator strengths are estimated to be ±5%.Figure 9.2 shows an expanded view of figure 9.1 in the energyregion 6.5—10 eV showing the absolute oscillator strengths for theSchumann—Runge continuum. The weak Schumann—Runge bands below 7eV which are several orders of magnitude smaller in oscillator strengththan the continuum could not be observed in the present work. Infigures 9.2 (a) and (b) the present results are compared with previouslypublished experimental [334—336,338—342,351] and theoretical[342,344] results respectively. Immediately it can be seen from figure9.2 (a) that the present results are in excellent agreement with most ofthe other experimental data. The data of Ditchburn and Heddle [335] aremuch higher than all the other experimental data while those ofGoldstein and Mastrup [339] are somewhat lower In the energy regionaround the continuum maximum. For the experimental work shown infigure 9.2 (a) only the present high resolution dipole (e,e) measurementsand the data of Huebner et al. [351] are derived from electron energy loss(a) Experimentalmeasurements255jJ10C.)00CeC.).-C,05CC.)a.)0Cl)0 o0I-C.)0I-i0• Present HRDipole (e,e) Expt./xGoldstein & Mostrup [339]/Ditchburn & Heddle [335]/o Wotonobe et ci. [334)/Bloke et ci. [338]/ ‘• Metzger & Cook [338]/o Huebner et ci. [351]/ ‘* Ogawo & Ogowo [340]/* Gibson et ci. [341]/o Wanget ci. [342]/x.’xx2015100.200.150.100.050.000.200.15Io41.ASchumann RungeCon t6.5 7.5 8.59.520151050.100.050.00Figure 9.2: Absolute oscillatorstrengths for the photoabsorptionof molecular oxygen.Expanded viewof figure 9.1 in the energyregion 6.5—10 eV, showing theSchumann—Runge continuumregion. (a) comparison withpreviouslypublished experimentaldata [334—336,338—342,351](b) comparison withtheory [342,344]Photon energy (eV)0256spectra. The remainder are Beer—Lambert law photoabsorptionmeasurements [334—336,338—342] which in this particular energy regionshould not be subject to “line—saturation” effects due to thebroad natureof the Schumann—Runge continuum in oxygen. Note thatthe data ofHuebner et al.[3511 were normalized at the continuum maximum (8.61eV) to the average of the optical data[46] which were available at thattime and therefore reasonable agreementwith the photoabsorption datais not surprising. In contrast, the present high resolutiondipole (e,e)spectrum was made absolute using the TRK sum—rule normalizedlowresolution dipole (e,e) work of Brion et al.[921 in the smooth continuumregion at 26 eV, which is -17 eV above the Schumann—Rungecontinuummaximum. The Bethe—Born conversion process (see experimentalsection 3.3) results in a very large change in relative intensityof the twocontinua between the original electron energy loss data and the relativeoptical oscillator strength spectrum. Therefore any inaccuracy in theBethe—Born conversion factor for the spectrometer would producespurious oscillator strengths. The validity and accuracy of the Bethe—Born conversion factor for the high resolution dipole (e,e) spectrometerused in the present work has previously been confirmeddown to —11 eVby comparison of measurements and highly accurateab—initio calculationsfor helium [371 and molecular hydrogen[40]. The results for theSchumann—Runge continuum of oxygen now provide a further stringenttest of the accuracy with which the Bethe—Born conversion factor for thehigh resolution dipole (e,e) spectrometer has been determined and inparticular in the region down to 7 eV. This is importantto establishsince the Bethe-Born conversion factor was obtainedfrom a comparisonof high and low resolution dipole (e,e) measurements above22 eV in the257ionization continua of helium[37] and neon [38] (see chapter 3). TheBethe—Born factor below 22 eV wasthen obtained by curve fitting themeasured quantity above 22eV and extrapolating to lower energies. Theexcellent agreement of the present workwith many previously publishedphotoabsorption measurements ofthe absolute oscillator strengths in theSchumann—Runge continuum regionof oxygen is a very strong indicationthat the Bethe—Born conversion factor iswell characterized for the highresolution dipole (e,e) instrument, evenin the low energy loss (photonenergy) range.By extrapolating measured relative generalized oscillator strengthsto zero momentum transfer, Lassettre et al.[13] obtained an integratedoscillator strength of 0.179 for the Schumann—Rungecontinuum region,over the range 6.56—9.46 eV, following correctionof their previouslypublished data [16,17]. By integrating thesame energy region, thepresent work gives a slightly lower oscillatorstrength of 0. 169. In theother electron impact based work using low impactenergy, Huebner etal. [3511 reported an integrated oscillatorstrength of 0.161 for theSchumann—Runge continuum.In figure 9.2(b), the present measurements are comparedwith thetheoretical work reported by Allisonet al. [344] and Wang et al. [3421.Both sets of calculated data show reasonableagreement with the presentwork. However, it must be pointedout that Allison et al. [344] employeda semiempirical method in whichthe calculated potential curve and thetransition moment were adjustedin order to reproduce oscillatorstrength values and structural featuresconsistent with the experimentalresults [340]. The theoreticalresults of Wang et al.[342], on the otherhand, were obtained by fittingto their own measurements of the258Schumann—Runge continuum region.They then reported potentialcurves and transition momentsfor theB3-and E3-mixed—Rydberg—valence states, and also the 13flvalence state, which were obtainedfromthe fitting procedures. Thus,although the existing theoreticalabsoluteoscillator strength values for the Schumann—Rungecontinuum regionappear to show good agreementwith the present work, It shouldberemembered that both of these theoreticalresults depend for theirsuccess on experimental values.Figures 9.3(a) and (b) showexpanded views of figure 9.1 intheenergy regions 9.5—15 eV and14—25 eV respectively.The ionizationpotentials for the states shownwere obtained from thephotoelectronwork of Edqvist et al. [353]. Thefirst ionization potential dueto theejection of an electron from theltg orbital occurs at 12.07 1eV. Infigure 9.3(a) several diffusebands are observed in theenergy region from9.7 eV to just below the first ionizationpotential. Due to the diffusenature of the peaks comparedwith the relatively narrowbandwidth thatcan be obtained in optical experimentsin this energy region,absoluteoscillator strengths (photoabsorptioncross sections) forthese diffusebands that have been measuredusing the Beer—Lambert photoabsorptionmethod are expected to bereasonably accurate [334,336,340,348,349].The three prominent peaksat 9.96, 10.28 and 10.57eV, correspondingto the longest, second andthird bands respectively, havebeen assigned[345,346] as transitions tothe vibrational levels v’0, 1 and2 of themixed valence—Rydberg E3-state. The absolute oscillatorstrengths forthe diffuse bands in theenergy region 9.7—12.07 eV were determinedinthe present work and the resultsare summarized in table 9.1along withpreviously available experimental [340,349,3511and theoretical [345—2590.20.1£C.)U)0Ci)a.)oI-.Cl)0.0C.)0o__0C’)Cl)C—0C.)•— 0.3 o30C0.2200.1100.0 0Photon energy (eV)Figure 9.3: Absoluteoscillator strengths for thephotoabsorptlon of molecularoxygen.The ionization potentialshave been obtained fromref. [353]. (a) in theenergy region 9.5—15 eV.The assignments of thevibrational levels v’=O,1and 2 of theE32u and23flu states are taken from thetheoretical work ofBuenker et al. [346]. (b) in the energyregion 14—25 eV.(b)02!02oflA2Iib4Eg B2EgU4 —cEU1 4 1 6 20 22 24Table91Absoluteopticaloscillatorstrengthsforthephotoabsorptionofmolecularoxygenintheenergyregion9.75—11.89eVAbsoluteopticaloscillatorstrengthsExperimentalmeasurementsTheoreticalAssignmentEnergyrange(eV)ElectronimpactbasedBeer-LambertlawcalculationsmethodsphotoabsorptionmethodsPresentworkHuebnerLewiseta!.OgawaandBuenkereta!.YoshimineLIeta!.eta!.[351j[3491Ogawa[3401t3461eta!.[345J[3471E3-v’=O9.75—10.170.008440.0010240.008330.01360.01030.01742110.17—10.440.007590.008040.00705#0.007060.01570.01240.00562210.44—10.620.0008270.001470.000780.0007700.0070.004120.00061710.62—10.710.0006520.0006500.00066010.71—10.840.001460.002420.001402[1v’=O10.84—10.980.0008140.0009000.0008200.0009?10.98—11.170.0007330.001590.0007522I1v’=l11.17—11.330.0006060.001100.0004970.0007711.33—11.520.001470.0021023flv211.52—11.590.0004190.0005020.000611.59—11.740.001690.00205?11.74—11.890.001740.0016311.89—12.070.001690.00283Theassignmentsweretakenfromref.[346j.#ThisvaluewasobtainedfromtheaverageoftheIntegratedoscillatorstrengthsfor016018and180.2intheenergyregion10.19-10.35eV.261347] data. Column two in table 9.1 gives the energy regions over whichintegration was performed in order to obtain the absolute oscillatorstrength for each diffuse peak. The absolute oscillator strength valuesreported by Ogawa and Ogawa [340] were obtained by integrating theirBeer—Lambert law photoabsorption data over the same energy regions. Itcan be seen from table 9. 1 that the present results are consistent withthe photoabsorption work of Ogawa and Ogawa [340], as expected (seeabove). The recent Beer—Lambert law photoabsorption work of Lewis etal. [349] for the second and third bands is also in good agreement withthe present work and with that of Ogawa and Ogawa [340]. For thelowest(E3-(v0)) band, the data reported by Lewis et al. [348] are onlyfor the energy region 9.95—9.98 eV compared with 9.75—10.17 eV forboth the present work and that of Ogawa and Ogawa [340]. Hence thedata of Lewis et al. [348] cannot be compared directly with the presentwork in this region. However, as demonstrated in the work of Lewis etaL. [348], their absolute cross sections in the limited energy region 9.95—9.98 eV are in excellent agreement with the measurements of Ogawa andOgawa [3401 and thus also with the present work. The electron impactbased oscillator strength data reported by Huebner et al. [3511 are ingeneral higher than the present results and the data of Ogawa and Ogawa[340]. It should be noted thatthe accuracy of the Bethe—Born factor usedby Huebner et al. [3511 was not known over a wide energy range. Inaddition they employed an impact energy of only 100 eV to measure theenergy loss spectrum and this is too low an impact energy to obtain adipole—only spectrum (i.e. the momentum transfer K is to large). Severalvibronic bands in the X3g - a’u and X3g—systems in theenergy region 9.8—10.6 eV, which are dipole—forbidden transitions, were262observed even in direct photoabsorption measurements [331 ,349]. Theintensities of these dipole—forbidden peaks would be expected to besignificantly higher in the electron energy loss spectrum of Huebner etal. [351], which would cause higher oscillator strength values for thoseenergy 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 beenused by three groups [345—347] to calculate the absolute oscillatOrstrengths for the vibrational levels v’=O, 1 and 2 of the mixed—valenceRydbergE3state. The theoretical calculations reported by Yoshimineet al. [345] and Buenker et al. [3461, which assigned the longest, secondand third bands as the vibrational levels v=0, 1 and 2 of the mixedvalence—Rydberg E3 state from the calculated energy levels, giveoscillator strength values for these three bands which are much higherthan the present and other experimental values. The recent work of Liet al. [347] shows better agreement with the present results for the v’= 1and 2 bands while the value reported by Li et al. [347] for v’=O is evenhigher than that reported by Yoshimine et al. [345] and Buenker et al.[346]. Buenker et al. [346] also assigned three other peaks at energies of10.90, 11.24 and 11.55 eV as the vibronic bands v’=O, 1 and 2 of themixed valence—Rydberg23flstate. The calculated [346] oscillatorstrengths for these three peaks are only slightly higher than the presentresults as seen in table 9.1. The electron impact data reported byLassettre et al. [131 give an oscillator strength of 0.020 for the energyregion 9.46—10.7 eV while the present estimate for the same energyrange is 0.0 185. The total oscillator strength sum up to the first263ionization potential (12.07 eV) was determined to be 0.198 in thepresent work, which Is exactly the same value as was reported byHuebner et al. [351]. However, it should be remembered that theoscillator strength sum below 9.46 eV reported by Huebner et al. [351] Isslightly lower than that In the present work, while in the energy region9.46—12.07 eV their reported value is slightly higher.In the energy region 12—17 eV most of the bands in thephotoabsorption spectrum of oxygen have not been classified, while from17—25 eV there are many Rydberg series converging on the variousionization limits shown on figure 9.3(b). The energy positions and theassignments of these Rydberg states can be found In the criticalcompilation published by Krupenle [3311. Table 9.2 shows the presentintegrated oscillator strength values over selected energy intervals in theenergy region 12.07—18.29 eV. The electron Impact study by Huebner etal. [3511 (which like the present work Is free of “line—saturation” effects)also reported integrated absolute oscillator strength values in the energyregion 12.10—14.04 eV. These values [351], also shown in table 9.2, arein general somewhat higher than the present results. The absoluteoscillator strength sum in the energy region 12.10—14.04 eV wasestimated to be 0.181 by Huebner et al. [351], while the present resultfor the same energy region is 0.151. The value reported by Huebner etal. [351] is —20% higher than the present result which Is consistent withthe 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], itwas pointed out that much of the Beer—Lambert photoabsorption crosssection data for oxygen [354—356] in the energy region 12.10—20.66 eV issubject to bandwidth errors (or “line—saturation” effects) and also264Table 9.2Integrated absolute optical oscillator strengths for thephotoabsorption of molecular oxygen over intervalsin the energyregIon 12.07-18.29 eV0.001760.003250.006110.01060.01340.01490.01470.01470.01170.009990.008610.007930.007750.009250.009410.007010.008520.008120.001820.003790.007250.011760.014830.017240.016410.015670.013900.011860.009870.010330.009520.011660.014240.01027Integrated absolute opticalEnergy range (eV) oscillator strengthsPresent work Huebner et al.[351112.070 — 12.24012.240 — 12.41212.412 — 12.53812.538 — 12.67312.673 — 12.79412.794 — 12.91512.915 — 13.02613.026 — 13.15213.152—13.26313.263 — 13.36913.369 — 13.47613.476 — 13.57713.577 — 13.68413.684—13.81413.814—13.95413.954 — 14.05614.056—14.18114.181 — 14.302265Table 9.2 (continued)14.302 —14.408 —14.488 —14.603 —14.728 —14.853 —14.978 —15.092 —15.2 17—15.332 —15.472 —15.58715.862 —16.006 —16.151 —16.351 —16.481 —16.581 —17.171 —17.514 —17.875 —14.40814.48814.60314.72814.85314.97815.09215.21715.33215.47215.58715.86216.00616.15116.35116.48116.58117.17117.51417.87518.2870.007360.005730.009480.01270.01600.01950.02140.02940.03400.04270.03100.06140.02820.02660.03450.02 160.01640.1470.08970.08820.0740Integrated absolute opticalEnergy range (eV) oscillator strengthsPresent work Huebner et al.[351]266systematic errors. Based on the photoabsorptiondata reported byMatsunaga and Watanabe [356], theabsolute Integrated oscillator strengthin the energy region 12.07—16.53 eVwas estimated to be 0.724 byBerkowitz [1431. However, we find thata reanalysis of the data ofMatsunaga and Watanabe [356] givesan Integrated absolute oscillatorstrength value of 0.587. This value wehave obtained by digitizingfigures1 and 2 of ref. [356]. Alternatively wehave obtained a value of 0.685fromthe reported [356] numerical oscillatorstrength values In table 1 of ref.[3561.The difference occurs since the tabulatednumerical valuesreported in the paper of Matsunagaand Watanabe [356] only includeonethird of their actual experimental data.Thus, Insufficient data are givento obtain an accurate integration of thespectral area. Therefore, It wouldseem that Berkowitz [143] made useof the limited tabulated numericalvalues reported by Matsunaga and Watanabe [356]in order to obtain theintegrated oscillator strength in theenergy region 12.07—16.53 eV. Thepresent dipole (e,e) work forthe same region gives an integratedoscillator strength of 0.578,which agrees well with the presentlyrevisedvalue of 0.587 obtained by digitizingthe data in figures 1 and 2 reportedby Matsunaga and Watanabe [356].Digitizing the figures of otherphotoabsorption work reported byHuffman et al. [354] for the energyregion 12.07—16.53 eV, an integratedoscillator strength of 0.685 wasobtained, which is —20% higher thanthe value determined in thepresent work. This is again consistentwith the work of Matsunaga andWatanabe [3561, in which they state thatthe data of Huffman et a!. [354]were 20—30% higher than theirmeasured values in this energyregion.2679.3 ConclusionsAbsolute optical oscillator strengths for molecular oxygen have beenmeasured by high resolution dipole (e,e) spectroscopy In the energyregion 5—30 eV, which are free of ‘line—saturation” (bandwidth) effects.Absolute optical oscillator strengths for the broad Schumann—Rungecontinuum region of oxygen determined in the present work are Inexcellent agreement with most previously reported experimental results.This gives considerable confidence in the accuracy of the previouslydetermined Bethe—Born conversion factor for the high resolution dipole(e,e) spectrometer used in the present work, when extrapolated down to7 eV. This in turn lends support to the accuracy of the absolute oscillatorstrengths previously reported for argon, krypton and xenon [39] (seechapter 6), hydrogen [40] (see chapter 7) and nitrogen[41] (see chapter8) from this laboratory. The electron impact data reported by Huebner etal. [351] for oxygen are in general higher than the present work for theelectronic transitions higher in energy than the Schumann—Rungecontinuum. This may be due to appreciable contributions from dipoleforbidden transitions due to the low impact energy of 100 eV, oralternatively to inaccuracies in the Bethe—Born conversion factoremployed 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 oscillatorstrengths are in good agreement with the photoabsorption measurementsof Ogawa and Ogawa [340]. The present work is also in good agreementwith the integrated oscillator strength value reported by Matsunaga andWatanabe [356] in the energy region 12.07—16.53 eV. “Line—saturation”268effects which have caused severe difficulties In some of the direct Beer—Lambert law photoabsorption measurements In the valence discreteexcitation regions of the electronic spectra of hydrogen [40] (see chapter7) and nitrogen [41] (see chapter 8) are not found for the transitionsstudied in the present work in molecular oxygen. This Is probably due tothe generally broader nature of the transition peaks In the oxygenspectrum, in contrast to the situation for hydrogen and nitrogen (seechapters 7 and 8). Such broadening is to be expected In oxygen above12.07 eV (the first ionization potential) due to the short lifetimes of therapidly autoionizing excited states associated with the higher ionizationlimits.269Chapter 10Absolute Optical Oscillator Strengths for the Discrete andContinuum Photoabsorption of Carbon Monoxide (7-200 eV) andTransition Moments for the X1 — AH System10.1 IntroductionCarbon monoxide is of great importance in astrophysics since it isthe second most abundant interstellar molecule after hydrogen. It hasbeen detected in interstellar clouds and also in comets and planetaryatmospheres. Quantitative spectroscopic data such as the absoluteoscillator strengths (cross sections) for the photoabsorption andphotodissociation of carbon monoxide provide valuable Information forthe understanding of the formation and properties of interstellar matter[357,3581. Since molecular hydrogen cannot be observed directly indense opaque regions such as in our galaxy, carbon monoxide has beenutilized as a tracer of molecular hydrogen [357,358]. Absolute opticaloscillator strengths for the photoabsorption of carbon monoxide in thevalence discrete region can also be used to determine molecularabundances in planetary and stellar atmospheres [232]. In electronimpact experiments, the excitation cross section at sufficiently highImpact energy is related to the optical oscillator strength. Therefore, thelatter quantities can be used to normalize relative experimental electronimpact excitation cross sections [359]. Moreover, the absolute electronimpact excitation cross sections can be used in combination with theemission cross sections to determine the predissociation yields for270carbon monoxide, which are useful quantities in constructingphotochemical models of molecular clouds [360]. However, the existingabsolute optical oscillator strength (cross section) data for thephotoabsorption of carbon monoxide In the valence discrete region showlarge differences in the magnitudes of the absolute oscillator strengthsbetween the various experimental and theoretical values. In contrast,there is generally better agreement between the various availablemeasurements in the higher energy smooth continuum regions[30].Absolute optical oscillator strengths for the valence shell discretetransitions of carbon monoxide have been calculated by several groups.Absolute optical oscillator strengths for the discrete transitions from theX’ ground state to the A1fl, C1Z and B1 excited states have beencalculated by Rose et al. [301] and Coughran et al. [361], using anequation—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 andoscillator strengths for the low—lying valence states of carbon monoxideby applying the multiconfigurational random phase approximation(MCRPA). Padial et al. [365], have constructed pseudospectra of discretetransition frequencies and calculated the oscillator strengths for thediscrete and continuum excitations from the occupied molecular orbitalsby employing the Stieltjes—Tchebycheff (S—T) technique and separated—channel, static—exchange calculations. Ab initio CI calculations have beenperformed by Cooper and Lânghoff [366], Kirby and Cooper [367] andChantranupong et al. [368]. In particular, calculations of the absoluteoptical oscillator strengths for the transitions to the individual vibronic271levels of the A1fl, C1 and B1 excitedstates have been reported byKirby and Cooper [367] and Chantranuponget al. [368] while Cooper andLanghoff [3661 have calculated the theoreticalradiative lifetimes for thosesame vibronic states.A large number of experimentalphotoabsorption studies of carbonmonoxide have been made and critical reviewsand compilations of theavailable spectroscopic data can be found in refs. 130,46,369—37 1].Photoabsorption methods [372—392] have beencommonly employed andquantitative measurements based on the Beer—Lambertlaw[376,379,380,385—388,39 1,392] have providedmuch of the existingabsolute optical oscillator strength data.However, as pointed out earlierby Hudson [46] and discussed in furtherdetail recently by Chan et al.[37,411 (seechapter 2) the Beer—Lambert law is only strictly validin thehypothetical situation of infinite experimental energyresolution (i.e. zerobandwidth). Thus in practice Beer—Lambertlaw photoabsorption data fordiscrete transitions will be subject to so—called‘line—saturation’ effects(i.e bandwidth—linewidth interactions) whichlead to errors in thederived oscillator strengths. These arisefrom the logarithmic transforminvolved in Beer—Lambert lawphotoabsorption methods and the resonantnature of photon induced excitation. Sincethe peaks in the vibronicspectra for production of the A1fl, B1 andC1 excited states of carbonmonoxide have extremelynarrow natural linewidths, the absoluteoscillator strengths measuredfor these bands using Beer—Lambert lawphotoabsorption techniques may be expectedto exhibit severe “line—saturation” effects. For instance, theoscillator strengths for thevibrational bands of the A1fl excited statemeasured by Lee and Guest[387] using the Beer—Lambertlaw are found to be an order of magnitude272higher than those reported byMyer and Samson [385]which weremeasured at a lower resolution.While Lee and Guest [387]correctlystated that the cross sections at thepeak maxima would beaffected bythe monochromator bandwidth,their claim that theintegrated crosssection over the molecular band(I.e. the Integrated oscillatorstrength)would be independent ofthe bandwidth Is Incorrect.This Isconvincingly demonstrated inrefs. [37,391], where it isshown that It Isnot only the peak maximum thatis affected by the incidentbandwidth,but also more importantlythe integrated cross section for thetransition,which will be smaller than the truevalue. These spuriouseffects arefurther illustrated by the fact thatthe photoabsorptionoscillator strengthvalue reported by Lee andGuest [387] for productionof the v’=O level ofthe A1fl state is foundto be only —50% of the valueobtained by Lassettreand Skerbele [69] using anelectron impact based method.In other morerecent photoabsorptionwork, Eidelsberg et al. [392]and Letzelter et al.[388] have reported discreteoscillator strengths for carbonmonoxideexcitation in the VUV energyregions 8.00—9.92 eV and10.78—14.01 eVrespectively. In order tominimize the “line saturation”effects involvedin using Beer—Lambert lawphotoabsorption, the integratedabsorptionwas measured in these studies[388,392] as a function ofpressure andthe integrated cross sectionwas determined at pressureslow enoughsuch that the integrated absorptionvaried linearly with pressure.Theseprocedures used by Eidelsberget al. [392] and Letzelteret al. [388] aresimilar to those involvedin measuring the integrated crosssection atseveral different pressuresand extrapolating to lowpressure in anattempt to obtain the trueIntegrated cross section.However, thesekinds of procedures putthe most weight on the leastaccurate data273determined at the lowest sample pressures [37,46] and as a result theintegrated cross sections measured by Eldelsberg et al. [3921 and byLetzelter et al. [3881 are most likely still subject to errors as was found Inthe case of nitrogen [37,41] (see chapter 8). Oscillator strengths for thevibrational levels of the A111 band have also been reported by Rich [393]using absorption measurements based on the shock tube technique andcurves of growth analyses.Lifetime measurements [202,251,394—408] have been extensivelyemployed for studying the valence shell discrete transitions of carbonmonoxide. However, large discrepancies exist between the variousreported experimental values. The lifetimes for the vibronic levels of theA1fl state have been measured by several groups [251,398—400,406,407].It has been found [407] that the decay rates for some of the vibroniclevels of the A1fl state are affected by perturbations from the nearbya’3+,e3—, d3z,j1-and D1A states. These kinds of perturbations cause themeasured lifetimes to differ by up to 20% from the true values. Field eta!. [4071 have derived deperturbed lifetimes for the vibronic levels of theA1fl state and reported a linear dipole moment function from their data.This function was used by Kirby and Cooper [3671 to calculate theabsolute oscillator strengths for photoabsorption from the ground state tothe vibronic bands of the A1fl state. Furthermore, in order to convert thelifetimes of the vibronic levels of the B12D andC1÷bands to oscillatorstrengths, it is necessary to know the branching ratios for the twosystems (B-X, B-A) and (C-X, C-A).Electron impact methods based on electron energy lossspectroscopy have also been applied to study the oscillator strengths forthe valence shell discrete [69,107,409] and continuum [87] transitions of274carbon monoxide. As pointed out In chapter 2, electron Impactexcitation is non—resonant even for discrete transitions, and becausenologarithmic transform is needed to obtain the cross section(In contrastto Beer—Lambert photoabsorption) no “line saturation”(I.e bandwidth)errors can occur. Lassettre and Skerbele[69] have measured generalizedoscillator strengths (GOS) for selected discrete transitions of carbonmonoxide as a function of momentum transfer using electron energy lossspectroscopy and varying the scattering angle.Absolute optical oscillatorstrengths for the four discrete electronic transitions of carbon monoxidewere reported [69] by extrapolating a series of GOS measurements foreach transition to zero momentum transfer and normalizing their relativedata on the absolute elastic electron cross sections measured byBromberg [4101. Wight et al. [87], using a 8 keV energy incidentelectron beam and zero—degree mean scattering angle in a low resolutiondipole (e,e) experiment, have determined the photoabsorption oscillatorstrengths of carbon monoxide in the energy region 7—70 eV. However,the data reported by Wight et al. [871 were made absolute bynormalization to previously published absolute photoionization datareported by Samson and Cairns [325] in the smooth continuum region at30 eV. Furthermore, since the resolution of the spectrum recorded byWight et al. [87] was only 0.5 eV FWHM, oscillator strengths for theindividual vibronic transitions could not be determined in the discreteregion of the spectrum. In addition, it appears, from recentinvestigations using the same apparatus, that Wight et al.[87] did notmake adequate corrections for background gases and non—spectralelectrons in their measurements.275In the present work,the high resolution dipole (e,e) methodasrecently used to measureabsolute photoabsorption oscillatorstrengthsfor the discrete transitionsof the noble gas atoms [37—39](see chapters4—6) and several small molecules [27,40—42,411](see chapters 7—9),Isnow applied to quantitativelystudy of the valence shell discretetransitions of carbon monoxide. Inaddition, new wide ranging(7—200eV) measurements of the photoabsorptionabsolute oscillator strengthsfor carbon monoxide have been made usinglow resolution dipole (e,e)spectroscopy. The absolute scaleof the present measurements isestablished independently ofany other measurements by usingTRK sum—rule considerations [30]. The accuracy ofthe high resolution and lowresolution dipole (e,e) methods hasbeen confirmed by studiescomparingmeasurements with ‘benchmark”theoretical calculations for helium [371(see chapter 4) and molecular hydrogen [40] (seechapter 7). Inaddition, results for molecular oxygen [42](see chapter 9) and nitrogen[411 (seechapter 8) have supported the accuracyof the energydependent Bethe—Born conversionfactor for the high resolutiondipole(e,e) spectrometer when extrapolateddown to lower equivalentphotonenergies than were used forits original determination usingmeasurements for helium [37] andneon [38].10.2 Results and DiscussionThe electronic transitions andphotoabsorption oscillator strengthsof carbon monoxide areconveniently discussed withreference to Itsground state molecular—orbital valenceshell independent particleconfiguration which may be writtenas276(3c)2(4a)(hr)4(5a)210.2.1 Low Resolution AbsolutePhotoabsorption Oscillator StrengthMeasurements for Carbon Monoxide(7—200 eV)A relative oscillator strengthspectrum was obtained byBethe—Bornconversion of the electronenergy loss spectrum measuredwith the lowresolution (—1 eV FWHM) dipole (e,e)spectrometer in the energyregion7—200 eV. The datawere least—squares fitted to the functionAE overthe energy region 90—200eV. The fit gave B=2.243and on this basis thefraction of the valence—shelloscillator strength above 200 eVwasestimated to be 6.7%. The totalarea was then TRK sum—rulenormalizedto a value of 10.3, whichincludes the total number of valenceelectrons(10) plus a small estimatedcorrection (0.3) for thePauli—excludedtransitions from the K shells to thealready occupied valenceshellorbitals [52,53]. Figures 10.1(a)and 10.1(b) show theresulting absoluteoptical oscillator strengthsfor carbon monoxide obtainedin the presentwork at low resolutionin the energy regions 5—50and 50—200 eVrespectively. Previouslyreported experimental data[87,292,325,328,329.4 12]are also shown for comparison.Numericalvalues of the presently determinedabsolute photoabsorption oscillatorstrengths for carbon monoxideobtained in the present workfrom 7—200eV are summarized in table10. 1.It can be seen infigures 10. 1(a) and 10. 1(b)that the presentresults are in extremelygood agreement with thephotoabsorption datareported by Samson andHaddad [292]. The datareported by Lee et al.Figure 10.1: Absolute oscillatorstrengths for the photoabsorptionof carbon monoxidemeasured using thelow resolution (FWHM=1eV) dipole (e,e) spectrometer(a) comparison with previouslyreported experimental data[87,292,325,328,329,412]in the energy region 5—SO eV.(b) comparisonwith previously reportedexperimental data [87,292,325,328,329]in theenergy region 50—200 eV.277(a)Ico!• Present LR Dipole(e,e)AWight et ol.[87] Dipole (e,e)oSamson & Haddad[292]Lee et al. [325]D Watson etal. [412]Ph.Abs.*Cole & Dexter[329]-4- De Reilhac& Dornany[328)A A AA.+C)C)U)C=C)Cl)0C)0.40.30.20.10.00.100.080.060.040.020.0040302010C)C)U)U)Cl)LII-C)0•1000.00Q.4I06420S 1525 3 45A(b)AIcolA4_______________+ ‘++++ ••••••..••• Present LR Dipole (e,e)A Wight et al. [ 87] Dipole (e,e)0 Samson & Haddad [292]Lee et al. [325)* Cole & Dexter[ 329]Ph.Abs.+ De Reilhac & Damony t 328]50 100 150Photon energy (eV)200278Table 10.1Absolute differential optical oscillator strengths for the photoabsorptionofcarbon 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(1O-2eV-l) (1O-2eV-1) (10-2eV-l)7.0 0.00 16.0 23.15 25.0 19.037.5 0.35 16.5 22.87 25.5 19.078.0 4.24 17.0 24.47 26.0 19.368.5 11.40 17.5 24.53 26.5 19.109.0 9.48 18.0 23.72 27.0 18.729.5 4.98 18.5 21.25 27.5 18.6010.0 2.14 19.0 20.72 28.0 18.1210.5 0.97 19.5 20.55 28.5 17.6711.0 6.25 20.0 19.97 29.0 16.9711.5 16.57 20.5 20.30 29.516.8012.0 13.43 21.0 20.18 30.0 16.2012.5 10.95 21.5 20.15 30.5 15.7613.0 26.97 22.0 20.22 31.0 15.4813.5 39.50 22.5 19.75 31.5 15.0914.0 40.19 23.0 19.80 32.0 14.5014.5 34.16 23.5 19.59 32.5 14.0315.0 25.82 24.0 19.48 33.0 13.5515.5 24.20 24.5 19.23 33.5 13.61279Table 10.1 (continued)Energy Oscillator Energy Oscillator EnergyOscillator(eV) Strength (eV) Strength (eV)Strength(102eV)(10-2eV-)(1O2eV-l)34.0 13.45 45.0 9.62 62.0 5.6934.5 13.28 45.5 9.82 63.05.5135.0 12.80 46.0 9.39 64.05.3635.5 12.80 46.5 9.31 65.05.1236.0 12.66 47.0 9.24 66.0 4.8736.5 12.47 47.5 9.01 67.0 4.7637.0 12.03 48.0 9.13 68.0 4.6337.5 11.84 48.5 8.94 69.04.5438.0 11.81 49.0 9.01 70.04.3538.5 11.33 49.5 8.84 71.0 4.2539.0 11.26 50.0 8.63 72.04.1039.5 11.05 51.0 8.42 73.0 4.0340.0 11.01 52.0 8.17 74.0 3.9040.5 10.91 53.0 7.75 75.0 3.8141.0 10.69 54.0 7.56 76.0 3.7141.5 10.64 55.0 7.32 77.0 3.6642.0 10.31 56.0 7.00 78.0 3.4642.5 10.11 57.0 6.85 79.0 3.3743.0 10.33 58.0 6.56 80.0 3.3443.5 9.88 59.0 6.40 81.0 3.2744.0 9.83 60.0 6.07 82.0 3.1344.5 9.88 61.0 5.88 83.0 3.05280Table 10.1 (continued)Energy Oscillator Energy Oscillator Energy Oscillator(eV) Strength (eV) Strength (eV) Strength(1O2eVl)(1O2eV’)(1O2eV’)84.0 3.03 118.0 1.40 162.0 0.69785.0 2.85 120.0 1.35 164.0 0.66786.0 2.82 122.0 1.30 166.0 0.65887.0 2.79 124.0 1.26 168.0 0.64288.0 2.75 126.0 1.20 170.0 0.61789.0 2.63 128.0 1.18 172.0 0.62590.0 2.58 130.0 1.12 174.0 0.58891.0 2.46 132.0 1.10 176.0 0.58292.0 2.51 134.0 1.05 178.0 0.57693.0 2.37 136.0 1.01 180.0 0.54694.0 2.35 138.0 0.991 182.0 0.53596.0 2.28 140.0 0.969 184.0 0.51598.0 2.15 142.0 0.909 186.0 0.509100.0 2.10 144.0 0.887 188.0 0.507102.0 1.98 146.0 0.868 190.0 0.502104.0 1.88 148.0 0.834 192.0 0.471106.0 1.77 150.0 0.820 194.0 0.473108.0 1.72 152.0 0.787 196.0 0.467110.0 1.65 154.0 0.781 198.0 0.451112.0 1.58 156.0 0.768 200.0 0.461114.0 1.51 158.0 0.716116.0 1.46 160.0 0.702a (Mb) = 1.0975 x 102-eV1281[325] are higher than the present data at energies above 30 eV while thedata reported by De Reilhac[3281 are —15% lower than the presentresults at 25 eV and also at energies above 60 eV. The data reportedbyCole and Dexter [329] are in general slightly lower than the presentwork. The earlier electron impact based dipole (e,e) data reportedbyWight et at. [87] are -10% higher than the present work. It should bepointed out that the data of Wight et at. [87] were normalizedIn thesmooth continuum at 30 eV on the earlier optical data of SamsonandCairns [3251 and in addition it appears that adequate backgroundsubtraction procedures were not employed. The present work is TRKsum—rule normalized and thus independent of any other measurements.The present low resolution data has been used to establish the absolutescale for the high resolution data as described in the followingsection.10.2.2 High Resolution Absolute Photoabsorption OscillatorStrength Measurements for Carbon Monoxide (12—22 eV)Figure 10.2 shows the absolute optical oscillator strength spectrumfor the photoabsorption of carbon monoxide in the energy region 7—21 eVobtained from the high resolution (0.048 eV FWHM) dipole (e,e)spectrometer. The presently determined low resolution dipole(e,e) dataand the photoabsorption data of Samson and Haddad [292] are also shownfor comparison. It can be seen in figure 10.2 that the present highresolution (HR) and low resolution (LR) data are in excellent agreementover the continuum energy region. Similarly, in the discrete region theHR and LR measurements are consistent when the large differences inenergy resolution (0.048 eV vs 1 eV FWHM) are taken into account.Thea)(I)02.01 .51 .00.50.02822000IRn 0IJ(I)Ci)U)0C)10001-40:°Absolute oscillatorstrengths for the photoabsorptionof carbon monoxidein the energy region7—21 eV measured usingthe high resolution dipole(e,e) spectrometer (FWHM=O.048eV).7 9 11 13 15 17 19 21Photon energy (eV)Figure 10.2:283present HR data in the continuum 17—21 eV are also in good quantitativeagreement with the photoabsorption data of Samson and Haddad [292].Figure 10.3 shows the absolute optica1 oscillator strength spectrumfor the vibronic bands of the A1fl state of carbon monoxide in the energyregion 7.5—10.5 eV. The energy positions have been taken from thedetailed spectroscopic studies reported In refs. [369,370,378]. A curve—fitting program using Voigt profiles has been employed to deconvolutethe spectrum and the resulting deconvoluted peaks are shown as thedashed lines in figure 10.3, while the total fit is shown as a solid line. Inthe present work, integration of each peak area gives directly theabsolute optical oscillator strength for the corresponding vibronictransition. Absolute vibronic optical oscillator strengths for v’=0—l2 ofthe A1fl state were thus obtained and the results are summarized in table10.2. Previously reported experimental [69,251,387,392,393,407] andtheoretical [367,368] values are also shown for comparison. Theuncertainties of the present results are estimated to be —5% for resolvedpeaks and —10% for unresolved peaks due to additional errors in thedeconvolution process. Lee and Guest [3871 obtained spectra for all thevibronic bands of the A1fl state using Beer—Lambert law photoabsorptionmethods. However, only the numerical oscillator strength value for thev’=O vibronic band was reported and that value is -40% lower than thepresent result. The photoabsorption data reported by Lee and Guest[386] are still subject to “line saturation” effects even though the authorsstate that their results were independent of the monochromatorbandwidth (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”284-4>a)a.)Cl)0=C.)Ci)0C.)‘-4C0.80.70.60.50.40.30.20.10.0897006050 ci040j30pI02010 00Absolute oscifiatorstrengths for thephotoabsorptionof carbon monoxidein the energy region7.5—10.5 eV at 0.048eV FWHM. The energypositionsare taken from references[369,370,3781. Deconvolutedpeaks are shownas dashed lines andthe solid line representsthe total fit to theexperimental data.7.5 8.08.5 9.09.5 10.0 10.5Photon energy (eV)Figure 10.3:Table10.2AbsoluteopticaloscillatorstrengthsforthevibronicbandsoftheX1E+—AmtransitionofcarbonmonoxideExperimentalresultsTheoryElectronimpactPhotoabsorptionCurvesofLifetimebasedwork(Beer—Lambertlaw)growthmeasurements(1)(II)v’PresentHRLassettre&EidelsbergLee&GuestRichFieldHesserChantranupangKirby&dipole(e,e)Skerbeleetal.(387][3931etal.[2511etal.Cooper(691(3921[4071#(36811367]00.01620.02000.01650.00960.01560.01110.01480.015510.03510.03800.03370.0270.03430.02260.03560.032420.04020.04290.04240.0330.04120.01620.04730.037330.03470.03600.03770.03610.01460.04620.031640.02420.02510.02580.03580.00740.03710.022050.01450.01550.01630.01610.00240.02620.013460.008050.008480.01040.00910.01680.007570.004140.004370.00590.00480.00100.003980.002020.002170.00290.00240.001990.000950.001080.00140.00110.0009100.000410.000500.000650.00050.0004110.000180.000250.00028120.000090.000100.00013asderivedbyKirbyandCooper13671usingthelineardipolemomentreportedbyFieldetat.[407J.286effects by determining the integrated cross sections at pressures lowenough that the integrated absorption varied linearly with pressure. Thephotoabsorption data reported by Eidelsberg et al. [392] are In muchbetter agreement with the present work than other optical work[385,387]. The photoabsorption values reported by Rich [393] for thev’= 1 and 2 levels of the A1fl state using a shock—tube experiment with acurves—of—growth analysis are —25% lower than the present work. Twosets of vibronic oscillator strength values for the A1fl state obtained fromlifetime measurements [251 ,407] have been reported. Hesser [251]converted lifetime data to optical oscillator strengths by using themeasured vibrational band emission intensities. However, the so—obtained oscillator strength values are much smaller than the presentlyreported results. In other lifetime work, Field et al. [4071 discussed thediscrepancies between different lifetime measurements and determinedthe deperturbed lifetimes for the vibronic bands of the A1fl state. Theyalso derived a linear dipole moment function from the deperturbedlifetimes. Kirby and Cooper [367] then used the linear dipole momentreported by Field et al. [4071 to derive oscillator strengths for the A1f1state vibronic bands which are found to be in good agreement with thepresent work. The only previously reported electron impact basedoscillator strength data for the A1fl bands of carbon monoxide are fromLassettre and Skerbele [691, who measured generalized oscillatorstrengths as a function of momentum transfer and obtained opticaloscillator strengths by extrapolating to zero momentum transfer. Theabsolute scale for these measurements [69] was obtained by normalizingon independent measurements of the absolute elastic scattering crosssection [410]. The data reported by Lassettre and Skerbele [69] are In287general -5—10% higher than the present values and thedifferences canbe largely attributed to the normalizationprocedures [69]. In theoreticalwork, two sets of oscillator strength calculations forthe vibronic bands ofthe A1fl state have been recently published. The theoreticalvaluesreported by Kirby and Cooper [367] are —5—10% lowerthan the presentexperimental values, while the theoretical resu1ts reportedbyChantranupong et al.[3681 show much greater discrepancies with thepresent work, in terms of both the absolute magnitudesof the oscillatorstrengths and also in the shape of the vibrational envelopeof the band.The absolute total oscillator strength for the A1fl state is obtainedby summing the oscillator strengths for all the vibronic bands.Table10.3 summarizes the present result, where ItIs compared withpreviously 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 thepresent work, are Inquite good agreement with each other, withvalues in the range 0.180 to0.195. In contrast, the theoretical values[301,361—365,367,368] varyfrom 0.11 to 0.342. The theoretical valuereported by Lynch et al. [364]is consistent with the present work while thatof Kirby and Cooper Is-9% lower.Figure 10.4 shows the presently measured absolute opticaloscillator strength spectrum for photoabsorption to the vibrationallevelsof the C1 and E1fl excited states of carbon monoxide intheenergy region 10.5—12 eV. The assignments and energy positionshavebeen taken from refs. [369,370,378]. The deconvoluted peaks resultingfrom a curve fit to the experimental data areshown as the dashed lines infigure 10.4, while the total fit is shown asthe solid line. Table 10.4288Table 10.3Absolute total optical oscillatorstrength for the X1 -. A111transition of carbon monoxideAbsolute optical oscillatorstrength for the A111 stateChantranupong et al.[368]Kirby and Cooper [367]Lynch etal. [364]Nielsen et al. [363]Padialetal. [365]Wood [362]Coughran et al. [3611Rose et al. [301]0.22500.16360.180.12080.3420.240.140.11Experiment:Present work0.1807Eidelsbergetal. [392]0. 1941Field etal. [4071 0.187Lassettre and Skerbele[69] 0.1945Theory:a)Sa.)1-1U)0C.)U)0C.)C0—* C’E0 1E1112.01 .51 .00.50.0IcolX1E — BEv= 01Ax32892000C.)150100:15QP000.410.51 2.0011.0 11.5Photon energy (eV)Figure 10.4: Absolute oscillator strengths for the photoabsorptionof carbon monoxidein the energy region 10.5—12 eV at 0.048 eV FWHM. The assignments andenergy positions are talcen from references [369,370,378. Deconvolutedpeaks are shown as dashed lines and the solid line representsthe total fitto the experimental data.Table10.4AbsoluteopticaloscillatorstrengthsforthevibronicbandsofthetransitionsfromtheX1groundstatetotheC1andE1flexcitedelectronicstatesofcarbonmonoxideAbsoluteopticaloscillatorstrengthB1E1flv’=Ov’=lv’=Ov=1v’=Ov’=lTheory:Chantranupongetal.[36810.005080.000520.06470.00490.02740.00329KirbyandCooperl3674l0.00210.00030.11810.00180.0490.0050Nlelsenetal.[363]0.002850.1327Padialetal.[365]0.004480.04950.0110Wood[362]0.0600.084Coughranetal.[361]0.003000.0400Roseetal.[301]0.004800.1200Experiment:Presentwork0.008030.001320.11770.003560.07060.00353Letzelteretal.[388]0.00450.00070.06190.00280.03650.0025LeeandGuest[387]0.00240.01270.0181LassettreandSkebele(69]0.01530.1630.094t’) (0 C291summarizes the presently measured absolute optical oscillator strengthsfor the vibronic bands of theC12+and E1fl excited states. wherethey are compared with previously reported experimental[69,387,3881and theoretical [301,361—363,365,367,3681 values. Experimentally,there are many reported lifetime measurements [202,251,394—397,40 1—406,408] for the B1 andC1+states. Large variations have been foundamong the reported lifetime values. Moreover, In order to convert thelifetime data to absolute oscillator strengths, the branching ratios for thetwo 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 ratiosmeasured by Dotchin and Chupp [402], have converted their lifetime datato absolute oscillator strength values. However, the branching ratiosreported 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 oflifetime data when using the different branching ratios. For example,from the lifetime data reported by Hesser [69], absolute oscillatorstrength values of 0.005 4 and 0.119 were obtained respectively for thev=0 band of the B12 andC1+states when using the branching ratiosreported by Dotchin and Chupp [402] while values of 0.0079 and 0.1350were obtained when using the branching ratios reported by Aarts and DeHeer [359]. For this reason, the data obtained from the lifetimemeasurements are not shown in table 10.4. A summary of the lifetimemeasurements and also the converted oscillator strengths using variousbranching ratios can be found in refs. [406,408]. It can be seen fromtable 10.4 that, unlike the situation for the A1fl state, large variations292exist among the reported experimental oscillator strength values for theB1D,C1+and E1fl states [69,387,3881. The photoabsorption datameasured by Lee and Guest [387] are much lower(<30%) than thepresent values, presumably due to serious “line saturation” effects asdiscussed above. The photoabsorption data of Letzelter et al. [388] arealso -25—50% lower than the present work. This difference is somewhatsurprising since the experimental procedures employed by Letzelter etal. [388] are the same as those used by Eidelsberg et al.[3921 for theirmeasurements on the vibronic bands of the A1fl state which are found tobe in good agreement with the present work (see table 10.2). In otherexperimental work, the electron impact based data of Lassettre andSkerbele [691 are found to be much higher than the present results.Turning to theory, absolute vibronic oscillator strengths for theBl+, C1+and E1fl states have been calculated by several groups[301,361—363,365]. Since the vibrational oscillator strengths for v’= 2and the higher bands of these states have been calculated to be muchsmaller(<1%) than the values for the v’=O and 1 bands [367], the datareported in refs. [301,361—363,365] should be almost equal to the sum ofthe oscillator strengths for the v’=O and 1 bands determined in thepresent experimental work. These values are shown in table 10.4. It canbe seen that large differences exist between the various theoreticalresults [301,361—363,365,367,368], and that no single set of theoreticaldata is consistent with the present work. Only the oscillator strength forthe v’=O level of the C1 state reported by Kirby and Cooper [367], andthe oscillator strength sum for theC1+state reported by Rose et al.[301], are in agreement with the present work.293The absolute optical oscillator strength spectrum determined inthe present work for the higher energy excited states In the energyregion 12—20 eV is shown in figure 10.5. The energy positions of theionization thresholds have been taken from refs. [369,4131. Detailedassignments of this energy region can be found In refs. [358,386].Integrated oscillator strengths determined from the present work oversmall energy ranges are summarised in table 10.5. The photoabsorptlondata reported by Stark et aL. [391] and Letzelter et a1. [388] wereobtained 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 beensummed and are compared with the present results. Also shown in table10.5, the photoabsorption data of Stark et al. [391] were obtained viadirect Beer—Lambert law photoabsorption measurements, using aresolution 20 times higher than in the work of Letzelter et al. [3881, andan attempt was made to monitor the “line—saturation effects bycomparing the photoabsorption values measured at a variety of pressures.Even under such experimental conditions, “line—saturation” effects werereported for some very sharp features [3911. As shown in table 10.5, thetwo sets of photoabsorption data [388,391] are found to be somewhatlower than the present work even though precautions were taken to tryto minimize “line—saturation” effects. The oscillator strength distributionof carbon monoxide has been reviewed by Berkowitz [143] using theexperimental data available before 1980. Berkowitz obtained an oscillatorstrength 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 of0.8 165 was obtained using the photoabsorption data of Cook et al. [3821.2940%,-a.)toa.)Cl)0=C)Ci)0C.,41 .21.00.80.60.40.20.010080120E0I.C)4)Cl)Cl)Cl)01C)040Cl).0006015 17Photon energy (cv)Figure 10.5:200Absolute oscillator strengthsfor the photoabsorptionof carbonmonoxidein the energy region12—20 eV at 0.048 eVFWHM. The assignmentsandenergy positions of theionization thresholdsare taken fromreferences[369.413].295Table 10.5Integrated absolute optical oscillatorstrengths for thephotoabsorption of carbon monoxideover energy intervals in theregion 12.13-16.98 eVIntegrated absolute opticaloscillator_strengthEnergy range (eV) Present Stark et al. Letzelterwork [391] etal. [388]0.02080.04380.01480.03010.05380.05940.025112.130 —12.463 —12.655 —12.896 —13.001 —13.115 —12.237 —13.364 —13.452 —13.614—13.780 —13.867 —14.016 —14.169—14.458 —14.743 —12.46312.65512.89613.00113.11513.23713.36413.45213.61413.78013.86714.01614.16914.45814.74314.9020.008020.01630.05790.01380.03240.04720.05690.02780.07190.07060.03270.01130.02700.08570.02020.03650.07210.07480.03370.09820.08200.03580.06780.05580.09000.06650.0334296Table 10.5 (continued)Integrated absolute opticaloscillator_strencthEnergy range (eV) Present Stark et al. Letzelterwork [3911 etal.[388]14.902 — 15.085 0.040215.085 — 15.296 0.044915.269 — 15.443 0.043015.443 — 15.621 0.040615.62 1 — 15.780 0.034715.780 — 15.939 0.034615.939— 16.107 0.035616.107— 16.286 0.038616.286 — 16.470 0.04 1716.470 — 16.658 0.044316.658 — 16.822 0.034316.822 — 16.978 0.0366297The present estimate for the same energy region is 0.640. Thephotoabsorption data reported by Huffman et al.[380] and Cook et al.[382] are -25% higher than the present result, which Is presumablydueto errors in the pressureand/or light Intensity measurements in thesedirect optical studies. On the other hand, It has been mentioned above(see table 10.5) that the recently reported high resolutionphotoabsorption data of Stark et al.[391] and Letzelter et al. [388] aresomewhat lower than the present work in the energy region —12.1—13.9eV. Hence, the data of Stark et al. [391] and Letzelter et al.[388] wouldbe much smaller than the data of Huffman et al. [380] and Cook et al.[382] over the same energy region. These large differences In oscillatorstrengths between different photoabsorption determinations reveal somefurther difficulties involved in absolute intensity measurementswhenusing the Beer—Lambert law, in addition to the ‘line saturation” effects.10.2.3 The Variation of Transition Moment with InternuclearDistance for the Vibronic Bands of the X1+ —‘ A1fl ElectronicTransitionThe vibronic band oscillator strength(f’”)for excitation to the A1flstate is related to the electronic transition momentIRe( r’”) throughequation 7.5 [40,367,368]. In the present work, the absolute opticaloscillator strengths(f’o)for the vibronic bands for excitation to the A111state have been measured directly (see table 10.2). The Franck—Condonfactorsqv’oand the centroidsrv’o can be taken from ref. [392], In whichthe values were calculated from the deperturbed RKR A111 potentialdetermined by Field [414] and revised molecular parameters for the298ground X1Z state[415]. The energies (E’—E’)have been taken fromrefs. [369,370,378]. 0Is the statistical weightingfactor which is equal to2 for a —‘Htransition. The electronictransition momentIRe( rv’v”)Cflthen be derivedfrom equation 7.5 for eachvibronic band. The resultingvalues of Re( r”) are plottedas a function of rv’o in figure10.6, whichshows the variation ofelectronic transition momentwith Internucleardistance in carbon monoxidefor the vibronic bandsof the A111 state.Previously reportedexperimental [392,407.4161and theoretical[367,3681values are also shown for comparison.From the measureddeperturbed lifetime data,Field et al. [407] havederived a lineardipolemoment function of theformIRe(rv’o)I7.48(1—0.683 r’o)(10.1)In other work involvinglaser induced fluorescencemeasurements tosample the electronic dipolemoment at large internucleardistance(1.35—1.80 A), combinedwith the data reported by Fieldet al. [407] atlower internuclear distance,Dc Leon [4161 has derivedan electronicdipole moment function ofthe formIRe(rvo)11.5741(1 — 1.17722 rv’o+0.35013 rv’02)(10.2)As shown in figure 10.6,the dipole moment functionsreported by Fieldet al. [407] (solid line) andDe Leon [416] (dashedline) are in goodagreement with the presentwork only for Internucleardistances (rv’o)above 1.1 A, and theirvalues become much higherthan the presentexperimental results at low rv’o.The photoabsorptionwork of Eidelsberg00E0I299Vibrational quantumnumber (v’)12 10 8 6 4 2 0o11 .31.10.90.70.50.3>A1F1x1+*0****• Present HR dipole (e,e)Exp*0 Eidelsberg et al.[ 392]Field et al. [ 407]De Leon [416]* Kirby & Cooper [ 367)*Chantranupong et al. [ 368]Theory0.9 1.0 1.11.2 1.3Internuclear distance rvo (A)Figure 10.6: The electronic transition moment IRe(r..o)I in atomic units (a.u.)as afunction of the internuclear distance rjO in Angstroms (A) forthevibronic bands of the X —, A1fl transition.300et 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 Kirbyand Cooper 1367] is in very good agreement with the present work overthe entire range of study, while the values calculated by Chantranupong e tal. [368] are much higher than the present results.10.3 ConclusionsAbsolute optical oscillator strengths for the photoabsorptlon ofcarbon monoxide have been measured in the energy region from 7—200eV. The data were TRK sum—rule normalized and thus are independentof any other measurements. Absolute optical oscillator strengths for thevibronic bands of the A1fl,C12+,B12 and E1fl states have been reported.Good agreement is found (see table 10.2) between the present and someof the previously published experimental [69,392,407] and theoretical[367] results for the vibronic bands of the A1fl state. Incontrast (seetable 10.4) considerable differences are seen for the vibronic bandoscillator strengths for the B1 and E1F1 states. It is noteworthythat severe “line saturation” effects due to incident photon bandwidth areobserved in some of the photoabsorption measurements (e.g. refs.[385,387,391]) for the discrete transitions In carbon monoxide.Theprocedures 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 ofprocedures place the most weight on the least accurate data obtained atlow pressure, which may be the reason for the discrepancies between thepresent work and the data reported by Letzelter et al. [388], even though301the data reported by Eidelsberg et al. [392]are consistent with thepresent work. For the lifetime measurements,accurate branching ratiosare necessary in order to obtainreliable absolute optical oscillatorstrengths. In contrast, the present dipole (e,e)method provides a directmeans for measuring the absoluteoptical oscillator strengths forthediscrete transitions of carbon monoxide, free of“line saturation’ effects.The variation of the electronic transitionmoment with the C—OInternuclear distance for the A1[1state derived from the presentmeasurements was found to be ingood agreement with the theoreticalresults of Kirby and Cooper [367].302Chapter 11Absolute Optical Oscillator Strengths for thePhotoabsorption of Nitric Oxide (5—30 eV)11.1 IntroductionAbsolute optical oscillator strengths for photoabsorptionby nitricoxide (NO) in the valence discrete region are of interest in areas such asatmospheric sciences [417,418] and the development of lasers[419].Nitric oxide is found in air at high temperatures and also occurs in theupper atmosphere. In addition, nitric oxide is a major atmosphericpollutant since it is a product of internal combustion engines andcombustion power plants. An accurate knowledge of the nitric oxideconcentration is essential for the understanding of atmosphericchemistry [4171. Oscillator strengths for they (A22—XI1) absorptionbands of nitric oxide have been used to estimate column densities in themesosphere [418]. They bands have also been considered as the basis ofan optically pumped laser involving bound electronic states withinherently narrow linewidths [419].Below 8 eV, the valence—shell excitation spectrum of nitric oxideconsists mainly of discrete transitions belonging to they (A2—Xfl),(B211—X11), ô(C2flX2fl)and £ (D2—Xfl)systems. Ory [420] hascalculated Franck—Condon factors for the ô and systems using Morseoscillator wavefunctions. In the same study [420], the total electronicoscillator strengths for they,ó and E systems have been derived byassuming a constant electronic transition moment and using published303experimental data for the oscillator strengths of a number of Individualvibronic levels. Cooper [421] has calculated the electronic transitionmoments for the and ô systems of nitric oxide using ab inltioconfiguration interaction methods. In other work, multireferenceconfiguration interaction (MRCI) methods have been used by de Vivie andPeyerimhoff [422] and Langhoffet al. [423,424] to calculate the lifetimes,Einstein coefficients (A) and transition moment functions for excitedstates of nitric oxide. Rydberg—vaience state Interactions occur betweenexcited bound levels of nitric oxide, and perturbations between thevibronic excited levels of2symmetry have been studied by Gallusser andDressier [425]. The absolute scale of the calculated (perturbed) oscillatorstrengths reported by Gallusser and Dressier [425] was adjusted byreferencing to previously reported experimental values [426]. Inaddition, the unperturbed oscillator strengths were also calculated [425].In experimental work, the energy levels of nitric oxide have beenstudied extensively using photoabsorption methods [427—436], butrelatively few studies have been made of the associated oscillatorstrengths. Critical reviews and compilations of the spectroscopic data upto 1976 can be found in refs. [46,330,437,438]. Beer—Lambert lawphotoabsorption measurements [46,326,330,439—445] have providedmuch of the existing absolute optical oscillator strength data for nitricoxide. However, as has been pointed out earlier [37,46] (see chapter 2)Beer—Lambert law photoabsorption data for discrete transitions aresubject to so—called “line—saturation’t(bandwidth) effects which result Inthe measured oscillator strengths being too small. These spurious effectsare more severe for transition with narrow linewidth and high crosssection as illustrated in recent studies of the electronic spectra of304nitrogen [41] (see chapter 8) andcarbon monoxide [43] (see chapter 10).Similar “line saturation” effectscan be seen In the photoabsorptionmeasurements of nitric oxide Inthe energy region 5.39—11.27eVreported by Marmo 1439]. Inthe latter work [4391, a decreaseIn theobserved photoabsorption crosssections was found for some ofthediscrete transitions of nitric oxide at highsample pressure, whilethisbehavior was not observed in the continuum.Improved determinationsof the absolute oscillator strengthsfor the valence discretetransitions ofnitric oxide using the Beer—Lambertlaw were subsequently reportedbyWeber and Penner [440], Bethke[426] and Hasson and Nicholls[441]. Inorder to minimize the “line saturation”effects in these studies[426,440,441],the nitric oxide sample was mixedwith a very highpressure of noble gas so that thelinewidths for the discretetransitions ofnitric oxide were collisionallybroadened and therefore much smallerthan the bandwidth of the spectrometer[426,440,441]. Othermeasurements of the absolutephotoabsorption oscillator strengthsforthe discrete transitions of nitricoxide have been reported by Mandelmanand Carrington [4461 using theresonance—line absorptionmethod, byCallear and Pilling [447) using thecurves—of—growth method, and byPery—Thorne and Banfield [4481 andFarmer et al. [449,450] using the“Hook”method (which measures the rateof change of the refractive Indexnearan absorption region).Shock tube emission and absorptionmeasurements were also carriedout by Keck et aL. [451] and DaiberandWilliams [452], respectively, to estimateelectronic oscillator strengthsfor some discrete transitions ofnitric oxide. In other work,Mandelmanet al. [453] have reported the oscillatorstrength for the ô (0,0) bandbymeasuring the absolute intensityof the recombination emission.305Lifetime measurements [251,394,417,454—467] have beenextensively employed for studying various discrete transitions of nitricoxide but differences exist In the measured values. Moreover, In order toconvert the lifetime values to oscillator strengths, the branching ratiosmust be known. The branching ratios can be obtained from relativeemission intensities and such measurements have been carried out byseveral groups [251,461,466—474]. However, the reported branchingratios also show large differences. For example, the branching ratio forthe y (0,0) band was measured by Callear et aL. [4691 and Hesser [251] as0.143 and 0.24 respectively.Electron impact methods based on electron energy lossspectroscopy have also been used to study the discrete and continuumregions of the excitation spectrum of nitric oxide. In early work,Lassettre et al. [4751 measured the electron energy loss spectrum ofnitric oxide in the energy region 5—9.5 eV at 50 eV impact energy andzero—degree scattering angle, but no absolute oscillator strengths for thediscrete transitions were reported. Later, quantitative low resolutiondipole (e,e) work by lida et al. [93] reported absolute oscillator strengthsfor the photoabsorption of nitric oxide In the energy region 6—190 eV. Inthis study [93], the absolute scale was established using TRK sum—rulenormalization. However, since the resolution of the spectrum recordedby lida et al. [93] was limited to 1 eV FWHM, the oscillator strengths forindividual discrete transitions could not be determined. The absoluteoscillator strength data reported by lida et al. [93] in the continuum havebeen compared with direct optical studies [326,445] in the datacompilation of Gallagher et al. [30].306In the present work, the high resolution dipole (e,e) method,which has recently been used to measure absolute oscillator strengths forthe 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 nowapplied to study the valence shell discrete transitions of nitric oxide.The absolute photoabsorption oscillator strengths obtained using thedipole (e,e) method are not subject to “line saturation” effects sincee1ectron impact excitation is non—resonant and because no logarithmictransform is required in order to convert the measured experimentalquantities to oscillator strengths, in contrast to Beer—Lambert lawphotoabsorption. The absolute scale of the present high resolution dipole(e,e) measurements is established by normalizing in the smoothphotoabsorption continuum at 25 eV to the photoabsorption oscillatorstrength reported by lida et al. [931. The high reliability of the highresolution dipole (e,e) method has been confirmed by a comparison ofthe results of the measurements for helium [37] (see chapter 4) andmolecular hydrogen [40] (see chapter 7) with highly accurate ab—initiocalculations. In addition, the results for molecular oxygen [421 (seechapter 9) are particular relevant to the present work, since they haveestablished the accuracy of the Bethe—Born factor of the high resolutiondipole (e,e) spectrometer when extrapolated down to equivalent photonenergies as low as 6 eV.307112 Results and DiscussionThe oscillator strength spectra of nitric oxide are convenientlydiscussed by reference to Its ground state molecular—orbital valenceshellindependent particle configuration which may bewritten as(3)2(4)2(13r)4(5a)2(2r)1Figure 11.1 (solid line) shows the absoluteoptical oscillatorstrength spectrum of nitric oxide in the energy region 5—30eV obtainedin the present work using the high resolution (0.048eV FWHM) dipole(e,e) spectrometer. The low resolution dipole (e,e)photoabsorption datapreviously determined by lida et al.[93], and the photoabsorption data ofLee et al. [326] and of Gardner et al. [445]are also shown forcomparison. It can be seen in figure 11. 1 that the presenthighresolution (HR) results and the low resolution (LR) datareported by lidaet al. [931 are in excellent agreement over thecontinuum region.Similarly in the discrete region the high and low resolutiondipole (e,e)measurements are highly consistent when thelarge differences in energyresolution (0.048 eV vs 1 eV FWHM) are takeninto account. Thepresently obtained HR data in the continuum21—30 eV are also in goodquantitative agreement with the photoabsorption dataof Gardner et al.[445], while the data of Lee et al. [326] are 10—15% lower than thepresent work.Figures 11.2—11.4 are expanded views of figure 11. 1 in the energyregions 5—8.2, 8—13 and 13—22 eV respectively. The assignmentsandenergy positions of the excited states and ionization thresholdshave beentaken from the detailed spectroscopic studies reported in refs.Figure 11.1: Absolute oscillator strengthsfor the photoabsorption of nitric oxideinthe energy region 5—30 eV measuredusing the high resolution dipole(e,e)spectrometer (FWHM=O.048 eV).1 .51.0C)0C.)C,)CC.)0.03081500-4C.)a.)U)10001C.)0-41.45000’5 9 1317 21 25 29Photon energy(eV)0.140.120.080.060.040.020.00Figure 11.2:309Expanded view of figure 11.1 in the energy region 5—8.2 eV. Theassignments are taken from references (425,437J. Deconvoluted peaks areshown as dashed lines and the solid line represents the total fit to theexperimental data.20s (B2u)I I I I I I I I I I5 7 9 11 13 15a (cfI)_________________‘2çDEjINOIt4-0.10I I0 1 2 3‘(A2E)0 1 2 312104-’C)a.)Cl)8 CjCl)0I-’C)604-4-’A 1.4-toI5 67 8Photon energy (eV)(a)310IN6X1 E543201 —C)Vr001-.C)0.060.050.040.03- 0.020.01I00.10.010 11 1213Photon energy (eV)Figure 11.3: Expandedview of figure 11.1. The Ionization limit for theX1 edge Istaken from reference [476].(a) in the energy region 8—10 eV. (b) in theenergy region 10—13 eV.030j0-..08.0 8.5 9.0 9.5 10.0(b)INQI201003111.61601.2• 1200.880—IC)‘— 0.440.-C)C)U)C)0). 0.00oU,o= 0.4C)0)40 0o Cl)— .0Ct Cto0.3030 Q0.2200.1•100.0018Photon energy (eV)Figure 11.4: Expanded view of figure 11.1.The Ionization limits are taken fromreference [476]. (a) in the energy region 13—16 eV.(b) in the energy region16—22 eV.(a)IN13 1415 16(b)w1Ah1EAflb’3EcE b3flc3nB3fl3w16 2022312[425,437,476]. Figure 11.2shows the discrete transitions below 8 eV. Acurve—fitting program was used to deconvolute the spectrum between6.25—7.5 eV and the resulting deconvoluted peaks are shown as dashedlines in figure 11.2. The total fit to the data Is shown as the solidline.In the present work, Integration of the peak areagives directly theabsolute optical oscillator strength for the correspondingvibronictransition. Absolute vibronic optical oscillator strengthsfor the discretetransitions in the energy region 5.48—7.44 eV determined in the presentwork are summarized in table 11. 1. The oscillator strength forthei(5,0) band was obtained by subtracting the leading edge of the tallof thecurve fitted to the y (3,0) band from the present experimentaldata In theenergy region 6.194—6.280 eV. The uncertainties inthe present resultsare estimated to be —5—10% for the strong, partiallyresolved peaks and- 10—20% for the remaining peaks due to the additional errors in thedeconvolution processes.Tables 11.2—1 1 .5 summarize the presently determined absolutevibrationally resolved oscillator strengths for the electronic transitions tothe y, 3, ô and states. Previously reported experimental andtheoreticaldata 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 theindividual transitions (shown in tables 11.3 and 11.4 respectively)wasestimated using the ratio of the oscillator strengths for thesebandscalculated by Gailusser and Dressier [4251 in conjunction with atotaloscillator strength for the bands determined from the presentlyreportedspectrum. The oscillator strength contributions of the otheroverlappingbands such as they (4,0), y (5,0), y (6,0), (8,0),I(10,0) and (13,0)are assumed to be negligible compared with thedominant ö and E peaks,313Table 11.1Absolute optical oscillator strengths for discrete transitions fromthe ground state of nitric oxide in the energy region 6.48—7.44 eV#5.4815.7716.0576.2566.3406.3746.4946.6086.7186.7826.8916.9397.0357.0637.1687.2597.3427.3967.438y(0,0)y(1,0)y (2,0)(3(5,0)y(3,0)(3(6,0)0) + b (0,0)13(8,0) + £ (0,0)13(9,0)(3(10,0) + ô (1,0)‘y(5,0) + s (1,0)(3(11,0)(3(12,0)o (2,0)(3(13,0) + £ (.2,0)13(14,0)o (3,0)(3(15,0)£ (3,0)0.0004200.0008240.0007300.0000290.0003560.0000370.002670.002750.0003140.006010.004610.0006480.002090.003080.003670.0003540.0009760.0008700.00179Energy (eV) Final state (v’,v”) Oscillator strength13(7•y(4,0) +y (6,0) +The assignments and energy positions have been taken from refs.[425,426,4371.Table11.2Absoluteopticaloscillatorstrengthsforthevibronicbandsofthey(X2fl—‘A2)transitioninnitricoxideAbsoluteoscillatorstrengthsforthey(v’,O)bandv’=Ov’=lv’=2v=3Theory:Langhoffetal.[42310.0003770.0007310.000620deVivieandPeyerlmhoff142210.001040.00247Experiment:Presentwork0.0004200.0008240.0007300.000356(HRdipole(e,e))PiperandCowles1473]0.000390.000820.00081(Branchingratios)McGeeetal.[47010.000323(Branchingratios)Mohlmannetal.(459]0.0004040.0008290.000750(Branchingratiosandlifetimes)Brzozowskietal.[45710.000345(Branching_ratios_and_lifetimes)Table11.2(continued)Absoluteoscillatorstrengthsforthey(v’,O)bandv’=Ov’=lv’=2v’=3Experiment:Farmeretal.[449]0.000400.0008090.0007000.000240(“Hook”method)Pery—ThorneandBanfleld[44810.000364(“Hook”method)Hesser[251]0.000250.000300.00171(Branchingratiosandlifetimes)Bethke[426]0.0003990.0007880.0006730.000360(Photoabsorptlon)WeberandPenner[440]0.000410.000880.00067(Photoabsorption)(‘3 01316Table 11.3Absolute optical oscillator strengthsfor the vibronic bands ofthe (X211 -B2fl) transition in nitricoxideAbso1ute oscillator strengths for theI(v’,O) bandExperimental Theoreticalv’ Present work Bethke[426] Gallusser and(HR Dipole (e,e)) (Photoabsorption) Dressier [425100102 0.0000015503 0.0000046104 0.0000138 0.000015 0.000029 0.0000264 0.000026 0.000037 0.0000462 0.000047 0.000375 0.000350 0.0003680.000129 0.000314 0.0003580.0003410 0.0000311 0.000648 0.000362 0.0003512 0.00209 0.0023 10.00245130.0000114 0.000354 0.0002010.0001515 0.0008700.00071Table11.4Absoluteopticaloscillatorstrengthsforthevibronicbandsoftheô(X2F1C2fl)transitioninnitricoxideAbsoluteoscillatorstrengthsfortheô(v,0)bandv=0v’=lv’=2v=3Theory:deVivieandPeyerimhoff[42210.00249GallusserandDressier[42510.002200.006100.002590.00098Experiment:Presentwork0.002290.006010.003080.000976(HRdipole(e,e))Brzozowskietal.(45710.00204(Lifetimes)MandelmannandCarrlngton[446]0.0022(Resonance—lineabsorption)Mandelmanetal.[45310.00213(RadiativerecombinationofN+O)CallearandPiling144710.00560(Curve—ofgrowth)Bethke[426]0.002140.005780.00274(Photoabsorptlon)cz•Thevaluewasobtainedbyassumingaconstantelectronictransitionmomentfortheöbands.Table11.5AbsoluteopticaloscillatorstrengthsforthevibronicbandsoftheE(X211—,D2)transitioninnitricoxideAbsoluteoscillatorstrenthsfortheE(v’,O)bandvOv’tlv’=2v’=3Theory:deVivieandPeyerlmhoff[422]0.001960.00245Experiment:Presentwork0.002630.004610.003670.00179(HRdipole(e,e))Hesser[251]0.00190.0040(Branchingratiosandlifetimes)Bethke[426]0.002420.004600.00332(Photoabsorptlon)319since they bands have small oscillator strength values even for the lowervibrational members. In this regardit should also be noted that thecalculations performed by Gallusserand Dressler [425] have also reportedvery small oscillator strength values for the1(8,0), (10,0) and (13,0)bands. Similar assumptions concerning contributionsfrom theoverlapping bands have also beenmade to the photoabsorption datareported by Bethke [426].It can be seen from table 11.2 that the various experimentalvaluesfor theybands are generally in reasonable agreement with each otherexcept for those reported by Hesser [251]. Hesser[251], Brzozowski etal. [457] and Mohlmann et al.[4591 have measured both branching ratiosand lifetimes while Piper and Cowles [473] and McGee et al. [471]haveonly measured the branching ratios, and the oscillator strength valuesreported by these authors[471,473] were obtained by using previouslypublished experimental lifetimes. The data reported by Mohlmann etal.[4591 for theybands are in excellent agreement with the present work,while the data reported by Piper and Cowles[473] for v’=O and 1 are alsoconsistent with the present work, but their value for v’=2 is slightlyhigher. In contrast, the values reported by Brzozowskiet aL.[4571andMcGee et al. [4711 for v’=O are —20% lower than the present result. The“Hook” method was employed by two groups [448,449]. The valueforv’=O reported by Pery—Thorne and Banfield[4481 is slightly lower thanthe present value. In the other work[4491, the values reported byFarmer et al. [449] show good agreement with the present workfor v’=O—2 while the value for v’=3 is -33% lower. The Beer—Lambert lawphotoabsorption measurements reported by Weber andPenner [440] andBethke [4261, which were obtained by collisionally broadening the natural320linewidths of the discrete transitionsof nitric oxide with noble gases,show very good agreement with thepresent work. However, the data[426,440] will still be subject to “line saturation” effects (whichhowevermay be smaller than other experimentaluncertainties in the presentcases) since it has been pointed out in ref.[37] (see chapter 2) that “linesaturation” effects will always occursince perfect resolution (i.e. zerobandwidth) cannot be obtained.Turning to theory, MRCI methods havebeen used by de Vivie and Peyerimhoff[4221 and by Langhoffet al. [423].The values calculated by Langhoffet al. [423] forthe y bands are -10—15% lower than the present work while those reportedby de Vivie andPeyerimhoff [422] are much higher than the presentresults.Table 11.3 shows the present and previouslypublished [425,426]oscillator strength results for the 3 bands ofnitric oxide anddemonstrates the irregularities in the oscillatorstrength distributionscaused by configuration interactions betweenthe valence and theRydberg states of 2fl symmetry. Note that the oscillator strengthscalculated by Gallusser and DressIer[4251 were obtained by adjusting theelectronic transition moments of the 3 and ô bandsby reference to thephotoabsorption data reported by Bethke[426]. Hence, the calculatedvalues of Gallusser and Dressier[425] are consistent with the datareported by Bethke [426]. The present resultsare in reasonableagreement with the data of Bethke[4261 except for the v’= 11 and 14bands for which the present values are somewhat higher.The largerdiscrepancies in the cases of these two bands may arise fromdeconvolution errors.The present and previously published[422,423,426,446,447,453,457] results for the ö bands are shownIn321table 11.4. It can be seen that the reported experimentaland theoreticaldata are in very good agreement with each other withthe exception thatthe 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 Ebands as shown In table 11.5, the present results are againIn goodagreement with the data of Bethke[4261. On the other hand, the lifetimedata of Hesser [251] and also the theoreticalvalues of de Vivie andPeyerimhoff [422] are considerably lower thanthan the present results.Absolute integrated oscillator strengths over selected ranges in theenergy 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 dataare not shown in table 11.6 since they are subject to the “line saturation”effects as discussed above. In contrast the present work provides aquantitative determination of oscillator strength below the first ionizationthreshold.Berkowitz [143] has performed a sum—rule analysis on allexperimental oscillator strength data for nitric oxide available before1980 and obtained an integrated oscillator strength valueof 14.17 fromthe lower limit of the data at 8.86 to infinity. As stated by Berkowitz[143], this analysis therefore implies that the integrated oscillatorstrength below 8.86 eV is 0.83 by difference (I.e. 15.00 minus14.17).In contrast, the presently measured integrated oscillator strength sum upto 8.86 eV gives a very different value of 0.0603. The present resulttherefore strongly suggests that the published data used by Berkowitz[143] misses appreciable oscillator strength at higher energies. In theenergy region 10—22 eV, the absorption spectrum of nitricoxide (figures11.3 and 11.4) consists of several unclassified bands and also numerous322Table 11.6Integrated absolute optical oscillator strengthsover the energyregion 7.52-9.43 eV in the photoabsorptionof nitric oxideEnergy range Integrated oscillator(eV) strength7.5 17 — 7.606 0.0006157.606 — 7.789 0.002357.789 — 7.907 0.00 1397.907 — 8.065 0.003358.065 — 8.199 0.002258.199 — 8.333 0.003898.333 — 8.442 0.002508.442 — 8.64 1 0.005988.64 1 — 8.747 0.002598.747 — 8.868 0.003758.868 — 8.94 1 0.00 1688.94 1 — 9.039 0.002559.039 — 9.148 0.002979.148—9.221 0.001449.221—9.323 0.002329.323 — 9.428 0.00251323transitions to the manyRydberg series convergingto the triplet andsinglet ionization limitscorresponding to theejection ofa 5a, 1t or 4oelectron. Details concerningthe assignmentsand energy positionsofthese Rydberg seriescan be foundIn refs. [430,432,433].Above the firstionization potentialthe discrete peaksare broadened by autolonizationand therefore Beer—Lambertlaw photoabsorptionstudies In this regionwould be expected tobe less affectedby “line saturation”effects. This Issupported by a comparisonof the present spectrum(figures 11.3 and11.4) and the photoabsorptiondata reported by Watanabeet aL.[443].Using the data of Watanabeet aL.[443], Berkowitz[143] reported anoscillator strength sumof 1.413 in theenergy region 8.86—18.44eVwhich Is in good agreementwith the present resultof 1.435.11.3 ConclusionsAbsolute opticaloscillator strengths forthe photoabsorptionofnitric oxidein the valence discrete region5—30 eV have been measured.Previously reportedlow resolution sum—rulenormalized dipole (e,e)data[931have been usedto establish the absolutescale for the presenthighresolution measurements.The presently determinedabsolute scale isthus completely independentof any direct opticaldata and the oscillatorstrengths are free of“line saturation”effects. Absolute optical oscillatorstrengths for the vibrationalbands of they, 3, ô and E states are reported.The results are in generallygood agreement withabsolutephotoabsorption data.This good agreementin the case of nitric oxidearises becausein general the oscillatorstrengths for discrete transitionsbelow the first ionizationpotential are not large.Furthermore, thepressure broadening techniques used in the Beer—Lambertphotoabsorption studies reported by Bethke [4261 enable the “linesaturation” effects to be considerably reduced.324325Chapter 12Concluding RemarksA new highresolution dipole (e,e)method has beendeveloped forthe measurements ofabsolute optical oscillatorstrengths for discreteandcontinuum transitionsthroughout the valenceshell electronicspectra ofgaseous atoms andmolecules. The presentwork has presentedabsoluteoptical oscillatorstrengths for thediscrete and continuumexcitations offive noble gases (He,Ne, Ar, Kr and Xe)and five diatomicgases (H2,N2,02,CO and NO).The new measurementshave considerablyextended therange of measuredabsolute oscillatorstrength data for theabove gases.The present resultsfor the discrete excitationtransitions (11S-÷nP,n=2—7) of heliumand for the Lymanand Werner bandsof hydrogen are inexcellent agreementwith high—level ab—initioquantum—mechanicalcalculations. Thesefindings confirm theviability of the highresolutiondipole (e,e) method andin particular the accuracyof the Bethe—Bornconversion factor determinedfor the high resolutiondipo1e (e,e)spectrometer. Thegood agreement of thepresent measurementsin theSchumann—Rungecontinuum region ofoxygen with mostpreviouslyreported experimentalresults furthersupport the accuracyof the highresolution Bethe—Bornconversion factor whenextrapolated down tolower energy (7 eV).The results alsoconfirm the validityof the Bethe—Born approximationfor high energyelectron scatteringand the suitabilityof the high resolutiondipole (e,e) methodusing TRK sumrulenormalizationfor general applicationto the measurementof optical326oscillator strengths for discrete electronicexcitations in atoms andmolecules at high resolution.The present work has also provideda detailed analysis of the “linesaturation” (bandwidth) effects that canoccur In quantitativephotoabsorption cross section measurements fordiscrete transitionswhen using Beer—Lambert law methods. 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