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The lifetime and the magnetic hyperfine structure constant measurement of 3D(3d¹∑), 3E(3d¹π) state of… Chien, Cary Way-Theng 1975

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THE LIFETIME AND THE MAGNETIC HYPERFINE STRUCTURE CONSTANT MEASUREMENT OF 3D (3d*2), 3E(3d ;n) STATE OF MOLECULAR HYDROGEN by Cary Way-Theng Chien A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OP - PHILOSOPHY i n the Department of PHYSICS We accept t h i s t h e s i s as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA August 1975 In presenting th i s thesis in par t i a l fu l f i lment of the requirements fo r an advanced degree at the Univers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make it f ree ly ava i lab le for reference and study. I fur ther agree that permission for extensive copying of th i s thesis for scho lar ly purposes may be granted by the Head of my Department or by his representat ives. It is understood that copying or pub l i ca t i on of th i s thes i s fo r f i n anc i a l gain sha l l not be allowed without my written permiss ion. Department of < \ CA The Univers i ty of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date i i ABSTRACT This t h e s i s describes the l i f e t i m e , the Lan.de g-fa c t o r and the hyperfine s t r u c t u r e constant r e s u l t s from three major indpendent techniques: The Hanle e f f e c t , the magnetic resonance, and the repolariza-t i o n experiments. The Hanle e f f e c t ( Z e r o - f i e l d l e v e l crossing) has been used to measure the l i f e t i m e s of the 3D (3 d 1 ! ) , 3E (3d^I T ) and Z (3*k double excited) s t a t e s of molecular hydrogen, the 3 1D, 4 LD, and 5 lD s t a t e s of helium, and the 2p (Paschen notation) states of argon and neon. The upper states were excited by electron e x c i t a t i o n i n a 450 MHz radio-frequency e l e c t r i c f i e l d . Where f r e e of any cascading e f f e c t or Stark e f f e c t , the l i f e t i m e measured were accurate to w i t h i n 5%. The pressure broadening cross-sections f or the above states have been also reported i n t h i s t h e s i s . By the r e p o l a r i z a t i o n experiment some of the h f s constants of 3D and 3E states of hydrogen have also been measured to w i t h i n 10%. In the c a l c u l a t i o n of l i f e t i m e s , some of required Lande g-factors were measured by the magnetic resonance experiment and some by the Zeeman e f f e c t i n a 27,000 gauss magnetic f i e l d i n t h i s l a b . i i i TABLE OF CONTENTS Abstract L i s t of Figures and Tables Acknowled g ement s Chapter One INTRODUCTION 1 1.1 Introduction 1 1.2 The Hanle Effect 2 1.3 The Election Excitation 3 I.A The Magnetic Resonance Experiment 3 1.5 The Magnetic Repolarization Experiment 4 -1.6 Summary of the Results ^ 1.7 Notation of the Molecular Hydrogen H .<Chapter Two THEORY 1 4 II .1 Introduction ^ 11.2 Theory of the Hanle Effect 1 4 II.2A Classical Approach ^ II.2B Quantum Mechanical Description 19 11.3 Theory of Magnetic Resonance Experiment 27 II.3A Classical Approach 7^ II.3B Quantum Mechanical Description 8^ 11.4 Theory of Repolarization Experiment 3 4 11.5 Summary 3 6 Chapter Three THE APPARATUS 3 8 I I I . l Experimental Arrangement 3 8 III..2 The Light Source and Its Power Supply 4 0 III.3 The Optical System ^ iv III.4 Tha Vacuum System 45 I I I . 5 The Magnetic F i e l d 47 III.6 Signal Processing 53 Chapter Four EXPERIMENTAL RESULTS 57 IV. 1 Introduction 57 IV.2 The Lifetime Measurements of 3'D, 4'D, and 5'D States in Helium ... . 58 IV.3 The Lifetime Measurements of 2P States in Argon and Neon .. 65 IV.4 The 3D(3dT), 3E(3d»n) andZ(3'K) State of Hz . 69 IV.4A The Lifetime Measurements .'. 69 •IV.4B The Measurement of the Lande g-factors 83 IV.4C The Measurement of the Hyperfine Structure Constant « 85 IV.5 Sources of Error 91 IV.5A Discharge Stability 91 IV.5B Magnetic Field in Homogeneity 91 IV.5C Pressure Readings , 92 IV.5D The Stark Effect Broadening 92 IV.5E Data Processing Error 93 IV.5F Coherence Narrowing 93 IV. 5G Cascading Effect 93 IV.5H Conclusion - 94 Chapter Five DISCUSSION AND CONCLUSION 96 Appendix A The Path of the Electron in the Hanle Effect Experiment « « 101 Appendix B The Cascading Effect 103 BIBLIOGRAPHY 105 LIST OF TABLES Table 4.1 The Lifetime of 3'D, 4'D and 5'D States in Helium 4.2 The Lifetime Measurements of the 2P States in Argon and Neon 4.3 The 3D(3d'I) State of Hydrogen Molecules 4.4 The 3E(3d'n) and Z(3'K) States of Hydrogen Molecules 4.5a The Coefficients B q in the Repolarization Experiment 4.5b The Numerical Value of P(a)/P(a=0) for J=l to J=5 in the Repolarization Experiment '•'vi ILLUSTRATIONS AND FIGURES Figure 1.1 The Arrangement of the Hanle Experiment 1.2 The Singlet States of Helium 1.3 The 2P and 2S States of Argon 1.4 The 2P and 2S States of Neon 1.5 The Si n g l e t States-of -Molecular^H^drogen 2.1 The Damping Rosettes 2.2 The T h e o r e t i c a l Hanle E f f e c t Curves 2.3 The M u l t i p o l e P o l a r i z a t i o n • 2.4 "Three" Level System 2.5 The Euler Angles 2.6 The C l a s s i c a l P i c t u r e of the Magnetic Resonance Experiment 2.7 The Quantum Mechanical P i c t u r e of the Magnetic Resonance Experiment Curves 3.1 The Apparatus 3.2 The S t a t i c Magnetic F i e l d C o i l s 3.3 The Discharge c e l l and i t s Power Supply 3.4 The Rotating Polaroid 3.5 The Vacuum System 3.6 The Power Supply f o r the S t a t i c Magnetic F i e l d s 3.7 The Power Supply f o r the R.F. Magnetic F i e l d 318 The Photomultiplier Wiring Schematic 4.1 Magnetic Resonance Experiment Curves i n Helium States 4.2 Zeeman E f f e c t i n the Presence of the Stark E f f e c t 4.3 The Halfwidth versus the Power of the R.F. e l e c t r o n i c F i e l d 4.4 Magnetic Resonance Experiment on 6267A Line of Neon 4.5 Experimental Hanle E f f e c t Curve f o r the 3D0 2B0 RO Line v i i Figure 4.6 Least Squares F i t t e d Curves f o r 3D0 2B0 RO 4.7 Hanle E f f e c t Curve Halfwidth as a Function of Pressure 3D0 State 4.8 Hanle E f f e c t Curve Halfwidth as a Function of Pressure . 3D1 State 4.9 Hanle E f f e c t Curve Halfwidth as a Function of Pressure 3D2 State 4.10 Hanle E f f e c t Curve Halfwidth as a Function of Pressure 3D3 State 4.11 Hanle E f f e c t Curve Halfwidth as a Function of Pressure Z2 State 4.12 Hanle E f f e c t Curve Halfwidth as a Function of Pressure 3E.0 State D 4.13 Hanle E f f e c t Curve Halfwidth as a Function of Pressure 3E 0 State a 4.14 Hanle E f f e c t Curve Halfwidth as a Function of Pressure 3E 1 State a 4.15 The Magnetic R e p o l a r i z a t i o n Experiment Curves 4.16 The P l o t s of P(a)/P(a=0) versus a/F 5.1 Zeeman E f f e c t i n the Presence of Hyperfine S p l i t t i n g v i i i ACKNOWLEDGEMENT I would l i k e to take t h i s opportunity to s i n c e r e l y thank my research supervisor, Dr. F. W. Dalby f o r h i s continued guidance, encouragement, clever suggestions, and h e l p f u l discussions throughout the course of t h i s p r o ject. I would also l i k e to thank Dr. J . Van Der Linde f o r h i s suggestions and the stimulating discussions at the beginning of t h i s p r o j e c t . My thanks are also extended to Professor M.H.L. Pryce f o r hi s e f f i c i e n t s o l u t i o n to i n t e r p r e t some experimental problems. The tec h n i c a l . a s s i s t a n c e s of the machine shop,.Mr. J . Lees and Mr. E. Williams, are very much appreciated. I would also l i k e to thank the members of my committee, Drs. A.J. Barnard, J.W. Bichard and,G. Jones f o r reading my t h e s i s and o f f e r i n g many valuable suggestions. Thanks are also extended to Drs. J.G. Burnett and G. Copley.and my wife f o r t h e i r help to complete t h i s t h e s i s ; and also to Mrs. Diane Boyd f o r her typing. This research project was supported by a research grant from the National Research Council. -1-Chapter One INTRODUCTION 1.1 Introduction The measurement of the radiative lifetimes and collision cross-sections of excited states of atoms and molecules provides basic data which are useful in the fields of astrophysics, plasma physics, and laser physics. A large- number of experimental methods have been developed for this purpose, but some of the most accurate measurements have been made by techniques using resonance fluorescence, namely optical double resonance (BB52, FM73b, MJ69, P59 a, b), level crossing (F61, OM68, HS67), and the Hanle effect (H24, SH66, VD72, CBD71, CC71, H72,.ML74). A brief review of lifetime measurements is given by Stroke (S66). .^While ua.;Variety»o£,-»techn;L,qu.es are available for the measure-ment of the lifetime of an excited state, few are as elegant as the technique discovered by Hanle in the 1920's (H24). Hanle's technique was largely forgotten until the last two decades, perhaps owing to observational difficulties in the days before adequate photomultiplier tubes became commercially available. The Hanle effect, which is nothing more than a special case of level-crossing (the levels referred to here are the Zeeman sublevels) at zero magnetic field, has been used in a number of lifetime measurements with good precision. The reasons for this are twofold: the Hanle effect technique does not require a direct knowledge of the vapor density of the gas whose excited state lifetimes are being measured, a requirement which has led to systematic errors in other techniques such as the "Hook Method" (MZ61). Secondly, i t is particularly effective for lifetimes in the 10~8 to IO - 9 second range where other techniques also independent of vapor pressure begin -2-to lose their accuracy. 1.2 The Hanle Effect LAMP H POLARIZER Fig. 1.1 In 1922,Rayleigh (R22) discovered that the 2537A* fluorescence line of mercury, excited by polarized resonance radiation, was polarized i f viewed at right angle to the exciting beam. Wood and Ellet (WE23) investigated this effect further and found that at low pressures and in the absence of magnetic fields, the emitted radiation was almost completely polarized, with its electric vector parallel to that of the exciting light. Hanle (H24) performed a more thorough investigation and found that the application of a magnetic field perpendicular to the direction of the exciting light and to the direction of observation not only decreased the polarization but also rotated the plane of polarization of the emitted light (Fig.1.1). Breit (B25) explained the effect in classical terms and showed that the degree of polarization, P is given by the expression (sec. 2.1) P(H) = 1 P(0) 1 + (gT yoH)z (1.1) where H is the applied magnetic field, x is the mean lifetime of the excited state, yo is the Bohr magneton O - ^ ) » a n < * 8 I s fc^e ^ a t l^ e g-value. - 3 -From the plot of P(H) versus H, we may easily obtain the product gx, from equation (1.1). An independent measurement of g then yields the radiative lifetime x. 1 . 3 The Electron Excitation Excitation by photons has one major limitation, namely that the energy levels to be studied are restricted to those that can be reached optically from the ground state, i.e. by strong electric dipole transitions. This restriction can be removed i f we use electrons instead of photons to excite the atoms or molecules. Frank and Hertz began their controlled electron spectroscopy in 1914. In 1927 Skinner and Appleyard (SA27) found most of the spectral lines emitted after electron impact were polarized with the maximum electric field vector parallel to the electron beam direction. This indicates that for electron excitation the selection rule is Am = o with the axis of quantization along the excitation axis. 1 . 4 Magnetic Resonance Experiment From the half width of the Lorentzian curve in the Hanle effect, only the products of the radiation lifetime x and the Lande' g-factor can be^  deduced. Therefore in order to measure the Lande' g—factor, a magnetic resonance experiment was "also performed. The magnetic resonance experiment mentioned here is equivalent to an optic double resonance experiment except that the f i r s t resonance is by electron excitation. The double resonance method was fir s t introduced into the 3P 1 state of mercury by Brossel and Bitter (BB52) -and since then has been used to study the excited state of many different kinds of atoms (L57, LM57, WL57, LS60, WL60, BE71, JL71, MF71, ML74). - 4 -This technique was recently introduced into molecular spectroscopy (FM73). In our experiment, a sample of ground state molecules located in an RF magnetic field (Fig. 2.7) was subjected to bombardment by a beam of electrons moving perpendicularly to the RF magnetic field. Excitation of molecules in the sample by the electrons produced unequal populations of the Zeeman sublevels of the excited state. If the population of a sublevel with magnetic quantum number m varies directly as |m|, the state is said to be aligned (sec. 2.2B). The emitted optical resonance radiation is therefore partially polarized. But the aligned molecular excited states can be quenched by magnetically tuning the Zeeman levels to resonance with a R.F. magnetic field. Precise information about g-values can be found by noting the magnetic field at which the change in polarization occurs. Consequently this experiment not only gives the accurate g-factors which are needed for the calculations of the lifetimes, but also leads to the confirmation of a significant cascading from higher energy levels (see sec. 4.4G) in the lifetime measurements for some of the excited states of neon and argon. Moreover, this experiment proved that the cascading effect can be neglected in the radiative lifetime measurements for molecular hydrogen. 1.5 The Magnetic Repolarization Experiment Fine structure and hyperfine structures (hfs) splittings have been measured by various techniques. The traditional optical spectroscopy methods, i.e. by grating spectrometer^ by interferometer, etc., are used for splittings that are greater than the Doppler width. Magnetic resonance (BB52) and level crossing (CFLS59) techniques can -5-be used for hfs. splittings that are between the Doppler width and natural line width. In the case of weak hfs, where the splitting is less than the natural line width the latter two methods begin to lose their accuracy. Moreover, they both require optical pumping from the ground state. In molecular hydrogen the energy required is about 10 ev. which is many times higher than the limitation of the optical pumping, and therefore the above techniques are not even feasible. In this case an old technique called the magnetic repolarization technique may be applied. This technique, known for a very long time (MZ61), gives a polarization versus magnetic field curve whose width is determined by the fine or hyperfine splitting and the lifetime. Whereas in the magnetic resonance and level crossing techniques, the fine or hyperfine splitting is given by the magnetic field at which the resonance occurs and the lifetime are determined from the width of the resonance. In the repolarization experiment a magnetic field has to be applied along the direction of the electron beam. This longitudinal magnetic field, unlike the transverse magnetic field used in the Hanle effect will not cause the electric dipole of the excited state to precess but will decouple the interaction of the total angular momentum J and the nuclear spin I. Because the magnetic repolarization technique does not give a sharp, natural width-limited resonance but only gives a very broad signal dependent on the product of the lifetime and the fine structure constant, its usage has been limited in the past. Recently a modified repolarization method has been used in alkali atoms (GCH72) to measure hfs which is much larger than the natural width, by fitting theoretical -6-and experimental curves in which J and I were decoupled through cascading from higher levels. The original repolarization technique only gives the product a.r ; Where a is the hfs splitting constant and T is the lifetime. Marechal and Lombard! employed this original technique on the vibrational state v = 1 of the 3D state in molecular hydrogen 01L74), after the determination of the lifetime (MJL72) of the same state. In this thesis the hfs splittings of vibrational states v =0, in the 3D and v=0, 1, in the 3E states of molecular hydrogen are given in Tables ( 4 . 3 ) and ( 4 . 4 ) . We will consider the specific case of hydrogen molecules in explaining this technique, tn hydrogen molecules the states corres-ponding to nuclear spin 1=1 are found to be less polarized at zero -magnetic field than at higher longitudinal magnetic field, and the spin 1=0 states are not found to change polarization in different magnetic fields. At zero magnetic field I and J are coupled and through this interaction, aI«J, the alignment of the electronic Zeeman sublevels is partially transfered into an alignment of nuclear Zeeman sublevels (Fig. 2.7). As the longitudinal magnetic field is applied, \t and J are decoupl8.d, no alignment transfer can occur and the polariza-tion will be restored. From the change in polarization, in addition to the lifetime measurement from the Hanle effect experiments, the hfs constant a, can be determined. This detailed theory for a l l above techniques will be found in the next chapter and the results are given in chapter four. 1.6 Summary of the Results Helium is the simplest stable atom and most of the data in helium have been measured with the highest precision. The lifetimes -of 3'D, 4'D>and 5'D in helium, have been measured in the lab by using FIGURE 1 . 2 The Singlet State of Helium - 8 -the Hanle effect. These measurements are used as a test of the technique and the apparatus used in this lab. An energy diagram of the singlet states of helium is given in Fig. 1.2 and the results of the measure-ments will be found in Table 4.1. While measuring the-lifetimes of the 5'D state at very low pressures (5 to 10 microns), the stark effect became so important that the Lorentzian curves were broadened. This effect was studied and discussed in section IV.2. Lifetime measurements of the excited states in argon and neon have surged because of interest in shock tubes, high temperatures arcs and laser physics. For this reason the lifetimes of some of the 2P states in argon and neon are measured at low pressures (1 to 100 micron) in this lab. The measurements were made at low pressures so that the radiation trapping and collison-effect were largely eliminated, allowing the natural lifetimes to be accurately measured. An energy diagram of a l l the 2P states of argon is given in Figure 1.3 and of neon is given in Figure 1.4. In these Figures a l l the transitions from 2P states to 2S states are shown and the measured ones are marked with arrows. The results of argon and neon are given in Table 4.2. There is a large discrepancy between some of the low pressure measurements and the higher pressure measurements of the lifetimes of 2p states in argon and neon. More information was obtained by using the magnetic resonance experiment and now understand i t might be due to the cascading from the higher energy levels. The detailed discussion is given in section IV.3. Accurate measurements of the properties of H 2 are of importance because i t is the simplest neutral molecule and so a detailed theoretical interprelation can be formulated to compare with the data. For this -9-c Q ) •5 L - S t o Q . J L 2S+1 2 P 1 0 s • 1 2 P 2 1 p 3 2 P 3 2 p 3 2 P 4 1 p 3 2 P 5 0 p 1 2 P 6 2 D 1 2 P 7 1 D 3 2 P 8 2 D 3 2 P 9 3 D 3 2 P 1 0 1 S 3 i n f » f n t n i n r - r r n u) H VO HN fHO f t-»0400 rtOO h ^ Ol rH IO <J rH O oo t~ co r ~ vo r - co co co • • ' • • • I I f i l l T n IN H co r - i co r r m r H C O r ^ r - M T C N O V O O i n m CM r r r - cr. i n r r (N i n r - r~ r » r » r~ r » co co co r— FIGURE 1.3 The 2P and 2S States od Argon -10-* L-S I J L » — 2 P 1 0 S I — 2 P 2 1 P 3 — 2 P 3 2 P 3 — 2P4 1 P 3 — 2 P 5 0 P 1 — 2 P 6 2 D 1 — 2 P 7 1 D 3 — 2 P 8 2 D 3 — 2 P 9 3 D 3 — 2 P 1 0 1 S 3 m in m vo vo vo vo r» o n t— cn CM o oo o o invovovovDvovovor- vo vo o m mcntnr-f-ioitNr-co r - l CM IT) •"3" M l / H O k O t ^ O l O H O vo vo vo t * » mvovovovovo[~r~co t t O OO O FIGURE 1 . 4 The TBe 2P and 2S States of NEON -11-reason this thesis concerns itself primarily with the measurements in hydrogen. The Hanle effect has been used to determine the lifetimes of 3D(3d'E), 3E(3d'n) and Z(3'K) states of H2. The Lande'g-factors, needed for the calculation of the lifetimes, were measured by the magnetic resonance experiment or by a Zeeman effect experiment. After the lifetimes were determined the magnetic hyperfine structure (hfs) constants "a" were measured by the magnetic repolarization experiment. The singlet states in molecular hydrogen are given in Figure 1.5. A l l the notations for the electronic states used in this figure are from Dieke (C70) and summarized in section 1.7. The quantum number v in the diagram labels different vibrational levels and the transitions discussed in this thesis are marked with arrows. The results of the lifetimes, g-factors and hfs constants are given in section IV.4 and are discussed in chapter V. 1.7 Notation's of the Molecular Hydrogen If only one of the electrons in molecular hydrogen is excited with electronic orbital quantum numbers £ and the component along the internuclear axis X, the state has the dominant electron configuration Clso)Cn£X) where n runs from 2 to °°. In common notation, the (lsa) configuration of the inner electron is understood, if i t is not written explicitly. Thus the notation for the H2 state consists of the spectro-scopic letter followed by the appropriate value for (n£), followed by the term symbol i.e. D(3d'Z), (3d'n) . The spectroscopic letters are used as follows: the capital letters A, B, C, D, E, F are used for the singlet states s'E, p'E, p'n, d'E, d'll and d'A; and the small letter C TJ c "-a c "a. CM — O sf- cvi o H II > > M i l l I II II O C V J — O II II > > III i r o O C M — O II II > > III I X I ' ,——» CVJ — O ^ - r o c v j — o II II [ i r i II i r Q. Q. r o CVJ ^J- CVJ O 10 ^ CM O II II M i l l 1 1 1 1 1 1 r A CJ. CL ro . cvj CM — O <fr CM O II II <s 1 1 T II 1 1 r • _ -+— : 1 I— <o i CM — o cn o £ — — — o — u FIGURE 1 . 5 The S i n g l e t States of Molecular Hydrogen -13-a, b, c, d, e, f are used for the triplet states s 3E, p 3£, p 3n, d3Z, d3II, d3A respectively. The letters T, U, V, W, X, Z are used for doubly excited states and again i t is understood that the capital letters are for singlet states and the small letters are for triplet states. The notation used in this thesis were taken from Dicke's (C70) notation, in which the principal quantum number n, followed by the spectroscopic letter, followed by the vibrational quantum number v. i.e. 3D0 (3d'I, v = 0), 3E2(3d'n, v = 2) and Z2(3'K, doubly excited states with v = 2). ; -14-Chapter Two THEORY II.1 Introduction In this chapter, the classical and quantum mechanical theory of the Hanle effect will be discussed f i r s t in section II.2, followed by the magnetic resonance experiment in section II.3. The quantum mechanical discription of the magnetic repolarization experiment is given in section 2.4. A l l the equations which will be needed in the calculation of the results are enclosed in boxes and a summary of the usage of these equations is given in section II.5. II.2 Theory of the Hanle effect II.2A Classical Approach: In order to explain the fact that when the radiation is observed in the direction of magnetic field (Z-direction), i t becomes depolarized with increasing field, i t is sufficient to adopt the classical model of a damped oscillator. If the oscillator is excited in the X direction i t will start to vibrate parallel to the X-axis, but will precess about the magnetic field, its amplitude of oscillation dying down with time due to damping. The path described by the precessing oscillator when viewed along the field will take the form of a rosette. In a strong magnetic field, i f the precession period Is much less than the damping time, the rosette will be symmetric as shown in Figure 2.1A. It Is clear that the light from the oscillator will show no linear polarization i f observed along the magnetic field. On the other hand, i f the damping time is of the same order of magnitude as the precession period, the motion of the oscillator will be as in Fig. 2.IB and Fig. 2.1C, in which case the rosette is incomplete and shows asymmetry. -15-Thus the resulting resonance radiation will be partially polarized. If the exciting radiation is polarized with its electric vector in the X-direction, the excited atom or molecule can be replaced by an electric dipole which possesses an angular momentum L perpen-dicular to the dipole axis and a magnetic moment y=yL, where y is the gyromagnetic ratio. If, however, a magnetic field H = Hz K is placed along the z-axis the dipole precesses about the z-axis with angular velocity oi = y H , so that u z A Ui/H* = h * 1 * A ( 2 - 2 with g^ being the electronic Lande g-factor for the excited state and po the Bohr magneton (e/2mc). Since the atom will not remain in its excited state forever, t/x a damping term, e~ , must be included, where x represents the mean l i f e of the excited state of the atom or molecule. The damped oscillator precessing about the field can be treated as follows: the components of intensity of the radiation Ix and Iy are ix(t)= i 0 c o 5 a ( ( j 4 - <t>) e"t/r Vc ( 2 . 2 in which the phase angle cj> indicates the angle between the analyzing polaroid in Fig. 3.1 and x-axis at zero time, and 01 is the natural frequency of the oscillator. The observed intensity will be the average value from 0 to T and T is the time constant in the measuring equipment•. Since T>>x -17-and both the I x(t) and the I^(t) are exponiantial functions. The averaged signals are I, = iU r f f j l ^ t ) d t - T C I I M D T T —> CO The polarization P(<fvH) is then defined as 9(4, H) - Ix -ly (2.2.3) When evaluated this gives (2.2.4) Jo e P ^ > H) = - T(Qos^-2KHlSln2<f>) For the special case of <J>=0 this reduces to P(H) = / P(0) I+(2XIHZ) X which is just a Lorentzian line shape. If is the magnetic field required to reduce the polarization to half its maximum value, then (2.2.5) (2.2.6) (2.2.7) Hence a simple measure of the width at half maximum serves to establish the mean l i f e T of the radiating state. (Fig. 2.2.A) For the case ty = IT/4 P(H) _ -2MHZ P ( 0 ) (2.2.8) FIGURE 2 . 2 The Theorical Hanle E f f e c t Curves -19-the resulting curve is shown in Fig. 2.2. This curve not only yields the lifetime but also the sign of the magnetic moment of the oscillator, i.e. the sign of Lande g-factor. II.2B Quantum Mechanical Description Before introducing the quantum mechanical theory of the Hanle effect, a summary of the multipole polarization will f i r s t be given (H72, H 6 9 ) . The polarization, P, of an ensemble of molecules or atoms is the difference between the actual density matrix p and the density matrix of an unpolarized ensemble fjj-Tr(p). Thus the polarization •operator is P = p-^Tr(p) where N is the number of the sublevels in the atomic state. The polarization operator is always traceless; its diagonal matrix elements are called population excesses and its off-diagonal components <u|p|v> are called coherences between the level u and v . Case Polarization N. - 1 0 • 1 (£> None u •<•> - • O 0 u u (b) Dipole . » -— o 0 0 1 o u u <£> Quadrupole A f\ f\ f i n o -v—0 V n KJ v j V Fig. 2.3 - 2 0 -In terms of spherical basis operators, a multipole polariza-tion can be represented by the tensor operator P" where k is the rank of the tensor and q is the component. The first three types of multi-pole polarizations are shown in Figure 2.3, using the three sublevels of an ensemble of six atoms with J=l. In case (a), and i t is an iso-tropic distribution, there are two atoms in each one of the three states nip = ~ 1 » 0 > 1 > with no polarization. The only non-zero character istics of this state is its population and its density matrix is a tensor of rank zero. In case (b) there is a dipole polarization. The atoms are pumped in one direction only with regard to the sign of m^,. The atoms can be concentrated in either the m^  = 1 level or the m^, = - 1 level, depending upon whether a + or a" excitation is utilized. The average value of the magnetic dipole moment is nonzero, but a l l the higher multipole moment are zero. In this case the state is said ->-to be oriented. The orientation vector 0 ^ can be represented by its elements0^ = |<i'|j |i>| where q = 1 , 0 , - 1 . In case (c), there is a quadrupole polarization. The atoms, in this case, are pumped into the highest and the lowest m^, levels simultaneously. This ensemble of atoms has a zero average magnetic moment but levels with I m ^ ] = F are more probable than those with = 0 . The state is said to be aligned and the alignment tensor is a second rank spherical tensor which can be represented by the elements A 0 =\<<l 3 ^ - J J / ^ / / j ( j + / ) A •= |< VI ± J, 3j i J 3 3,1 i> l/ju + o and A 2 i = l<^'l * Jx" + k > I/JCT+ 0 -21-Quantum theory We restrict ourselves to a consideration lb} =• l"3b,M) o f a three level system |a>, |b>, |c> as shown in Fig. 2.4 with total angular momenta J a , J^, J c and Zeeman sublevels u, m, n, respectively. Fig. 2.4 The atoms are excited from ground state ja> to an upper excited state |b> by electron excitation. Through spontaneous emission they decay to a lower excited state |c>, which could be the i n i t i a l state |a>. The spontaneous emission of light from state |b> to state |c> is assumed to be of the electric dipole type and the transition rate for the light into solid angle dn with a polarization vector e^ and frequency a) is (M61) 7 = - T $ - l < b i 2 t -p/c>/acLn (2.2.9) e 2 1 ->-where a - TT,—r^r = T^=T is the fine structure constant and P = Zer. 4lle hC 137 i o is the electric diapole operator. The total intensity from state |b> to state |c> and with polarization vector is e% ^ \\rr\y iSl (2.2.10) -22-where I = e 2o) 2/8II 2C 3 and b b , are the elements of density matrix o mm p describing the ensemble of excited atoms. b It i s also convenient to introduce a measuring operator M which contains information about the polarization of the spontaneous emission MCe j ) =Z et - ?lJcM>< j c n ) it- r n (2.2.11) After summing over the excited atoms of the ensemble one finds that the instantaneous fluorescent intensity i s I f e ) c f J 2 = l e X ,<™'IJ>lt«x™lrf!>«'?clJl = I. T r { f hi} JJl (2.2.12) It i s convenient to expand the density matrix in terms of irreducible tensor operators which act only on state vectors in the subspace spanned by |j^ m> ( K ) The operators T , are normalized by requiring that the reduced matrix element be given by <TB il t\\\ l b } = ( a f t t i r and the components of 2 multipole moment of the density matrix of the excited state 0 { U J (2.2.14) -23-The measuring operator M can also be decomposed into irreducible tensor operators (HS67, CC71) (2.2.15) where Ipj^l = | < T | | P | | J ' > is the modulus of the reduced matrix element k of the dipole operator and <j>^ is a tensor which specifies the polariza-tion of exciting radiation Where the eq are the components of 1 in spherical basis defined by e±, = ? 2 ~ ' W < e , ; , e„ = e 5 (2.2.17) The round and curly bracket at the end of (2.2.15, 16) are respectively 3-J and 6-J symbols which can be easily evaluated (E58). Equations (2.2.12, 13, 15, 16) give C 73 I I I Where tfQ = ( - j ) J + + / * / (2.2.18) In the presence of magnetic field H the density matrix of the excited state p satisfies Liouville's equation ir=*[x,f]-rf*rMf") (2.2.19) -24-Where the Hamiltonian J\t ~ J j ^ * 0 J ' { r describes the relaxation process of excited atoms in a gas owing to collisions with atoms in the ground state, is the pumping rate and is the time independent density matrix which represents the condition of the excited state |b> immediately after the excitation. If we take the z'-axis to be the direction of the magnetic field and also the direction of the incident electrons and the y'-axis the direction of observation, then the Hamiltonian in eq. (2.2.19) can be written as % =Mo3j HJ3> =<0 o Jy (2.2.20) Making use of the expansion in equation (2.2.13), the orthogonality of T K, and the commutation relation f J » 7"^ 7 = £ ^ q u , g - i g . equation (2.2.19) now takes the form (2.2.21) d k The stationary solution can be obtained by setting ^ ( P ^ ) = 0 (2.2.22) The symmetry property of the 6J symbols in equation (2.2.18) gives the selection rule 0<k<2 or k = 0, 1, 2. The axial symmetry of the system, which is invariant under rotation about the z'-axis, gives -25-q o 0 and restricts k to even numbers. Equation (2.2.13) takes the form f - f l r°0 • r\ T. O i o • O (2.2.23) and r * - r * r 4 0 ' * - r " ' (2.2.24) In the Hanle effect experiment, the magnetic field was perpendicular to the direction of the incident electrons, so that a rotation of 90° about y' Is necessary. R(0,n/2,0) is the rotation operator (E58). After the rotation we call the axis of the magnetic field the z-axis, and the axis of incident electron the x-axis. Equation (2.2.3) after rotation then becomes = f<O); T; H r v ) j f ^ -i n •£ T_\I (2.2.25) and the time independent density matrix (p ^  ) after rotation is o ox ,10) 2. (2.2.26) From equations (2.2.22, 23, 24, 25, 26), that eq. (2.2.19) will take the form -26-to) (2.2.27) In (D65) the following values of 4^ are given 3 o and 2< <^  Where the angles o and 4 are defined in Figure (2.15). A3 Fig. 2.15 As shown in Fig. 2.15, (2.2.28) for I , ty = 0°, 6 = 90° we have (2.2.29) for 1.4.= 90° and 6 = 90° we have y (2.2.30) -27-From equations (2.2.27, 29, 30) the linear polarization is If is the magnetic field required to reduce the polarization to half its maximum value, then % ---TIT-  o r r ^ r - = S ^U .H * which agrees with the classical result, eq. (2.2.7). II.3 Theory of Magnetic Resonance Experiment  II-3A Classical Approach If an atom having an angular momentum J, is placed in a magnetic field H q, then the magnetic moment y = u J will precess around H q with a Larmor angular frequency O)q = y ogjH o < Suppose that a weak magnetic field is applied at right angles to H q, and rotates around \\9 i t at an angular frequency , as shown in Fig. 2.6. If the angular frequencies ui^  and u>o \&/ differ appreciably, then the effect ^ ^1 of the rotating magnetic field Fig. 2.6 will be negligible. However, if to = ui , due to the action of the field H. the angle of precession 1 o' 1 & r will then be changed. If the magnetic field H q at which the resonance occurs is measured, then the Land£ g-value can be determined from -28-(2.3.1) II.3.B Quantum Mechanical Approach If an atom with a total angular momentum J, is placed in a magnetic field H q , each energy level will split into 2J+1 equally spaced sub-levels, (Figure 2.7a,b). To a fir s t order approximation the energy separation, E , is given by: m Em - mMoJH0 - m u)0-Pi (2.3.2) where m is the magnetic quantum number J>m>-J. The periodic magnetic field, H^cosw^t induces magnetic dipole transitions between adjacent energy levels (Am = ±1) provided this field is perpendicular to H Q and i f the resonance condition is satisfied (Fig. 2.7C). Thus we have . . . Bm - Ew. / ~ LOo £ = u)i "fi (2.3.3) This requirement is identical with the classical condition equation (2.3.1). In 1937, the transition probabilities for these induced transitions were fi r s t computed by Rabi (R37). In 1951, when Brossel and Bitter discovered the "Double resonance" method, they proved that the polarization of the resonance radiation should be proportional to the quantity R(J.H) where (BB52) PJ= =54.07 MHz f B| cos ai,t a b m = + 2 MAGNETIC FIELD (H) C fc! ^— r^f H A o N < o CL V w ,=«V=^ 0 gjH ( FIGURE 2.7 Magnetic Resonance Experiment 0 -30-r ? f T M i = ^ r u ) , > i w 1 io, a(r a L -KA), 3+4AiA)') ( r 1 +4 u),a + 4 * w\) (r3+u),1* A i o a ) (2.3.4) Where Au = u g_|oj ,-o> I and T is the lifetime of this state from which o J 1 1 o1 the radiation is emitted. As shown in Fig. 2.8;R(J.H) represents the bell-shaped curves. It is interesting to see that the complicated equation (2.3.4) can be derived rather easily by using the density matrices. As shown in the section (2.2.B) the intensity of the spontaneous emission is proportional to the trace of pM and the density matrix p satisfies the Liauville equation (2.3.5) where the Hamiltonian . In the magnetic resonance experiment the magnetic field H can be expressed as H * ft t M,CoS cot ^/Sifl iOt (2.3.6) where H Q and HI are the amplitudes of the slowly sweeping magnetic field and the periodic magnetic field, respectively. By substituting the equation 2.3.2 into eq. 2.3.1 the Hamiltonian g = l.5 0 10 20 , 30 40 50 MAGNETIC FIELD (Gauss) FIGURE 2.8 Magnetic Resonance Experiment Curves -32-% - L0o + 10, ( j " x C o s « A ) t + Z^n\tit) - u ) # ^ + u ) ( ( e I t t > * 3 + + e - f M } t i ) ' = u).3,+ u). ( e X a ) t 3 + + e - f u ) t j j (2.3.7) From (2.3.7), the commutator By decomposing the density matrix p into spherical tensor operators k k T^, by using the orthogonality of T , and equations (2.2.7)^(2.2.8), the Liouville equation takes the form (2.3.9) For a stationary solution in the rotating frame, let (2.3.10) Equation 2.3.9 will then take the form - ^ J i w j r t ^ o l i + r » * r * -r} ff].o (2.3.11) -33-This i s a set of time independent solutions. When k = 0, this describes an isotropic population distribution of the magnetic sublevels and eq. (2.3.11) becomes (2.3.12) When k = 1 the population distribution i s oriented and eq. (2.3.11) becomes <t*>f(;> - t o * r, (2.3.13) When k = 2 the population distribution for the magnetic sublevels i s aligned and in this case equation 2.3.11 becomes 3 W,*(44Wr . » -W**r x ) ~] r-(o) j > i ° ) 2 a : | " 3 1 0 , ^ ( 4 - ^ 4-10," + r 1 ) - C l - R O , H ) J ( 2 . 3 . 1 4 ) As we have shown i n (sec. 2.2.B) the polarization of the resonance radiation J (2.3.15) were A^ and A 2 are function of j , so that A,r0,o«>)<> A ; r _ f , v , a L r „ J (2.3. 16) -34-As mentioned in equation (2.3.4), R(J.H) represents the traditional double resonance curve centered at = 0 so that the Land^ g-function M l can be calculated from the equation g = : , in agreement with the u 0H Q classical explanation eq. (2.3.2). II.4 Theory of Repolarization Experiment At zero magnetic field, through the interaction Hamiltonian a*I.J, the alignment is partially transfered from the electronic Zeeman levels to the nuclear Zeeman levels. As the magnetic field increases, I and J will be decoupled, and the electronic Zeeman levels are repolarized. From the change in polarization the hfs constant a can be determined. Consider the density matrix of the excited state, p, which is the stationary solution of the Liouville equation lkf= A'0-CJ]-rf+r'o)fto) (2.4.1) In order to solve eq. (2.4.1) we again have to expand the density matrix in terms of irreducible tensor operators T^ (E58), (H72). If in the basis of |F> where M F F V | (2.4.2) and in the basis of |j>|l> -35-r - i " ' f { ( ^ " r j ) . • (2.4.3.) F F ' k T T ' k The relation between p and p is (MJL72) The intensity of dipole emission with polarization vector eq is then (ML74) O K = (-0 C U * + I ) U F + O U F ' + I ) ] j 3 33ej j 37 ,J (2.4.5) In the case of zero magnetic field the stationary solution of the Liouville equation is , h "  l -• F F ' S I P F > - \ r F t F + O - F f F V O j (2.4.6) The polarization PCa) at zero field is P O O -(2.4;7) As shown in Fig. 2.2.5 and sec. 2.2. B -36-F o r X j ; 9 - 0 For I x , e *i t * =0 ^ . . J -(2.4.8) (2.4.9) From eq. (2.2.4, 5, 8, 9), we have (2.4.10) i t r . * + r , ) t j i F F . ; o i ^ a = o, Men, J 1 F F ' = 0 PCa) r bFfi)UF'+<) r F r ' $ 7 * (r»+r)* P ( ^ o ) £ P , • v x + i I 3 j 1 j (r.+r;v+-T2FF/ where J l p F * =. - | - f F ( F + 0 ~ F V F + O J Once the ratio P(a)/P(a=0) is measured, the hyperfine structure constant, "a", can be determined either from tabulation of equation (2.4.10)or from a plot of equation (2.4.10)(P(a)/P(a=0) versus a/r). II.5 Summary In the Hanle experiment, once the halfwidth at half maximum, Hj^ , is obtained from the Lorentzian curve, the product of the l i f e -time, x, and the Lande g-factor g can be deduced from equation (2.2.7.) J In order to obtain the lifetimes, the Lande g can either be taken from the well known values measured by many different workers (DCB53), P67) or be measured using the magnetic resonance technique. In the magnetic resonance experiment, the absolute value - 3 7 -of the Lande g-factor, g , can be deduced from equation (2.3.2) provided that the magnetic field at which the resonance occurs can be measured. However, i f needed, the sign of the g-factor can be found from the dispersion curve in the Hanle effect experiment by equation (2.2.8). In the magnetic resonance experiment, the ratio of hfs constant over the relaxation rate can be obtained from equation (2.4.10). The relaxation rate, which is the reciprocal of the lifetime, is obtained from the Hanle effect experiment. -38-Chapter Three THE APPARATUS III.l Experimental Arrangement A block diagram of the apparatus is given in Figure 3.1. The polarization of the signal was measured using a rotating polaroid, a grating spectrometer, a photomultiplier, and a lock-in amplifier. When the signal-to-noise ratio was low, the output of the lock-in amplifier was averaged by a signal average. As shown in Fig. 3.1, light emitted from the light source is focused by a pair of lenses onto the entrance s l i t of the mono-chromator. Light appearing at the exit s l i t of the monochromator falls on a photomultiplier whose output is fed into the signal channel of a lock-in amplifier. Between the two lenses the light is passed through a polaroid which has its plane perpendicular to the beam and is rotated about the x-axis. The polarized component of the light is thus modulated at twice the rotational frequency. The combination of a small light source and photodiode placed at the rim of the polaroid, one on each side, provides a reference signal for the lock-in amplifier. The out-put of the lock-in amplifier is connected to the input of a signal averager whose memory can be viewed by an oscilloscope and/or recorded by an X-Y recorder. A quarter wave plate is placed in the beam of radiation, just before the entrance s l i t of the monochromator, to reduce polariza-tion effects produced by the monochromator grating. Four sets of Helmholtz coils centered about the light source were used. The largest two were used to produce the magnetic field in the longitudinal and transverse directions (Figure 3.2), the medium V4 plate Rotating Polaroid ^ " Light Source Mono chromator >MA Signal Averager _ . axis of E c o s i / t observation Reference Signal Lock in Amp. t To Helmholtz Coils X - Y Recorder Field Sweep ^ 3 - T H E A P P A R A T U S - 4 0 -size one was used to neutralize the vertical component of the earth's magnetic field (Fig. 3.2), and the smallest one (Fig. 3.3) was used to produce RF magnetic field. III.2 The Light Source and Its Power Supply The light source is a discharge cell which is made of a horizontally placed pyrex glass tube 1" in diameter and 1 1/8" long. Both ends are sealed and the cell is connected to the vacuum system by two 5 mm pyrex glass tubes as shown in Fig. 3.2 and Fig. 3.3. Two circular copper disks of 2" diameter are placed one on each end of the glass ce l l , the plates lying parallel to the axis of observation. The output of a 450 MHz radio frequency transmitter is coupled to these plates in such a manner that the R.F. electric field is per-pendicular to the copper plates.and has its maximum in the center. The transmitter consists of an R.C.A. MI-17436-1 transmitter and a Canadian Marconi Model 163-107 high frequency power amplifier with an output impedance of 50 and out put power of 15 watts. The MI-17436-1 transmitter frequency is normally controlled by a single crystal oscillator, providing a frequency stability of ± 0.0001% over the operating temperature range, with a fundamental between 12.50 and 13.05 MHz. To produce the output frequency, two tripler and two doubler stages multiply the crystal frequency by 36. The power amplifier is essentially a Simac 4x150 G vacuum tube with a silver plated resonance cavity. Through an RG 8/U cable the output of the amplifier is connected to an LC resonant circuit as shown inside the dotted square in Fig. 3.3. The inductor of the resonant circuit is just a copper loop and the variable capacitor is made of two concentric copper tubes, FIGURE 3 . 3 The Discharge C e l l and its Power Supply -43-insulated by a quartz tube (Fig. 3.3A). As shown in the figure, the inner copper tube is soldered to a screw and connected to the 3/4" cylinder, and the outer tube is connected to the one-turn inductance loop in order to form a Serier LC circuit. The LC resonant circuit is coupled to a resonant circuit. The resonant circuit is tuned to resonance by moving the ajustable bar up and down, as shown in Fig. 3.2. By adjusting the moveable bar and inner copper tubing of the variable capacitor, we can tune the whole circuit into resonance. By measuring the intensity of the discharge, we know, at resonance the maximum electric field is at the center of the discharge cell and oscillates perpendicular to the two copper plates. The discharge medium is presumed to consist of a dilute gas of neutral molecules and a much smaller number of free electrons. Subject to a radio-frequency electric field, the electrons oscillate back and forth in the direction of this field (call it the x direction). In the absence of collisions and trasevers magnetic fields, the kinetic energy of the electrons is given by K.E. = h m x 2 where X = e/m E coso>t o In order to maintain the discharge, three conditions must be satisfied: 1) The mean free path of an electron should considerably exceed the amplitude of its motion. 2) The dimensions of the discharge cell ought to considerably exceed the amplitude of the electron motion. 3) Electrons must be sufficiently energetic to ionize the -44-occasional molecule in order to make up for electrons lost by recombination and sustain the discharge. For 100 microns pressure at room temperature the density of the gas is 3.5 x 10 1 5 molecules per ml and the collision cross-section for electron is of the order of IO""15 cm2. The mean free path is found to be L = l/p*d w 3 mm. In order to satisfy the third condition, the maximum kinetic energy of the electrons must be greater than or equal to e^, the ionization potential. For Helium e.^  is about 25 ev. (K.E.) = Jgn (eE /OJ) 2 > 25 ev. max o That gives E q > 4.5 x 104 V/m, and the maximum amplitude of the electrons in the discharge i s : X = eE /rm2 > 9.4 x 10~ k m. max o This is much less than the 30 mm dimension of the discharge cell and the 3 mm mean free path. A l l the three conditions are satisfied for Helium at 100 micron. III.3 The Optical System As shown in Fig. 3.1, a pair of plane-convex lenses each of focal length F = 20 cm and aperture corresponding to F/6, are placed one at its focal length from the light source, and the other at its focal length from the entrance s l i t of the monochromator, so that the light originating at the center of the discharge traverses the -45-space between the lenses In a parallel beam and is focussed onto the entrance s l i t of the monochromator. Between the lenses a rotating polaroid is placed. As shown in Fig. 3.4, the polaroid is glued to a 2" I.D. brass pipe which is fitted inside a large ball-bearing. A sewing machine belt laid over the pipe and over the motor pulley rotates the polaroid. The monochromator used in these experiments is an F/8 Spex 1 m instrument which has a dispersion of lOA/mm in the f i r s t order • and 5A/mm in the second order. That gives a resolution of better than 0.1A* in the second order of operation. o A quarter wave plate at 5000 A is placed in front of the entrance s l i t of the monochromater. According to the theory of the Hanle effect, the polarization signal at high magnetic fields should be zero. By rotating the quarter wave plate about the axis of observation (Fig. 3.1), the polarization produced by the monochromater grating can be minimized and by rotating about the vertical axis makes the quarter wave plate become suitable for the spectral line at different wavelength. III.4 The Vacuum System . The sample gas input flow rate was controlled by two Edward's High Vacuum Ltd. type LB2B needle valves with a charcoal trap between them. Sample gas leaked through the f i r s t needle valve, entering the charcoal trap which was immersed in a liquid nitrogen bath. The charcoal trap was an effective pump for most impurities such as air, water vapor, etc. Beyond the charcoal trap, sample gas leaked into the system through the second needle valve, the leakage rate establishing -46-B E A R I N G R A C E W A Y Figure 3.4 The R o t a t i n g P o l a r o i d -47-the equilibrium pressure of the system: two Pirani gauges one on the upper stream of the discharge c e l l and the other one the lower stream and one 0 - 1 5 0 micron Hg McLeod gauge were connected to the system v ia glass stopcocks. The vacuum pump was a mechanical pump which was capable of reducing the pressure in the system to less than 5 x 1 0 - l f mm Hg when a nitrogen cold trap (.to prevent backstreaming of pump o i l ) was in place. For low pressure measurement an o i l d i f fus ion pump was used as shown in F ig . 3 . 5 . This combination produced a vacuum down to .2 micron measured by the 0—130 micron McLeod gauge. I I I . 5 Static Magnetic F ie ld Three sets of mutually perpendicular Helmholtz co i l s centered at the discharge c e l l were used in this experiment for the purpose of producing homogeneous magnetic f ie lds for the measurements and for neutralizing the earth's magnetic f i e l d . The specif ications are given in the following subsections. The inhomogeneities near the center were on the order of (y/R) 4 where y i s the displacement from the center and R i s the c o i l radius. For our 3 cm discharge c e l l and for the smallest c o i l which has an average radius of 2 0 cm, (y/R)k« ( 1 / 6 . 5 ) h or better than 1 part per 1 0 0 0 . I I I . 5 A Earth's Magnetic F ie ld Neutralization A pair of Helmholtz co i l s was used to neutralize the ver t i ca l component of earth's magnetic f i e l d in the discharge c e l l . These co i l s had a 3 5 cm mean diameter and were 1 8 cm apart; each had 1 0 0 turns of .#18 copper wire and were used in series in this configuration. The f i e l d produced at the center of the co i l s was approximately 4 . 5 Gauss/amp. FIGURE 3.5 The Vacuum System -49-Th ere was no need to calibrate these coils as i t was only necessary to adjust the current until the vertical component of the earth's field was minimized. This configuration was able to reduce the vertical component of the earth's magnetic field to less than 0.03 Gauss, measured by a Bell "240" Incremental Hall probe gaussmeter. III.5B Slowly Sweeping Magnetic Field A longitudinal field, applied along the same direction as the discharge-maintaining electric field, was produced by a pair of aluminum frame, water cooled Helmholtz coils. These coils had 35 cm mean diameter, were spaced 18 cm apart, and each had 407 turns of #10 poly-thermaleze copper wire with a total resistance of 1.5 ohms. The specifications are shown in Fig. 3.2B. When the two coils used in series the field produced at the center was approximately 20 Gauss/Amp. This longitudinal field was required in the magnetic resonance and the repolarization experiment. A Kepco JQE 36 volt-15 am programmable power supply was used to produce a maximum magnetic field of 250 Gauss. For smaller magnetic fields a Kepco Bipolar Operational power supply was used. A transverse magnetic field, along the direction of observation, was used in the Hanle effect experiment. In order to obtain high accuracy this field was produced by a large pair of Helmholtz coils (60 cm mean diameter and separated by 30 cm); each coil had 150 turns of #16 copper wire and a total resistance of 2.8 ohms. The magnetic variation, measured by a Bell "240" Incremental Hall probe gaussmeter, was found to be less than 1 part in 3000 change over the discharge c e l l . 100K i o I Kepco JQE 36-15 Power Supply * -51-The same Kepco JQE 36 volt-15 amp programmable power supply was used to give a maximum magnetic field of 65 Gauss. The magnetic f i e l d was determined from the voltage across a 20 milliohm sense resistor which was a 20 cm long nichrome wire immersed in a can which contained 1 quart of transformer o i l . The outer surface of this can was painted black for better thermal radiation. After 20 minutes warm-up, the temperature drift was less than 2°C during an hour of operation. The electronic circuit diagram is shown in Fig. 3.6. III.5C Oscillating Magnetic Field In the magnetic resonance experiment a high power radio-frequency magnetic field was required. In order to obtain the high power uniform field, single-loop water-cooled Helmholtz coils as shown in Fig. 3.3 were employed. These coils were made of \ inch copper tubing and, when in operation, water flowed constantly through the coils in order to maintain constant temperature so that the tuning would not change due to thermal expansion. The power supply for this oscillating magnetic field was built in the lab. It contained an oscillator, a frequency doubler, and (a two-stage) power amplifier. The oscillator was controlled by a 27.035 MHz crystal oscillator and after being frequency doubled and amplified, gave an output of 54.07 MHz and 0.2 watt. As shown in Fig. 3.7, the amplifier had two main stages. In the first stage, an 829B high frequency power vacuum tube was used Cwith the two channels of this tube acting) in push pull, giving an output on the order of 20 watts. In the last stage, which consisted of two 829B vacuum tubes, the two channels of both tubes were in parallel so that the two power tubes acted in push-pull. The power FIGURE 3.7 Power supply for the R. F. Magnetic F i e l d -53-supply of the last stage was a Kepco Model 500R which supplied a maximum of 600 volts and 300 mA. The output of the push-pull circuit was matched to a resonant LC circuit and when tuned to resonance, the imput power to the Helmholtz coil was more than 100 watts and the reflected power was less than 0.5 watt. This produced an RF magnetic field of 6 gauss at 54 MHz. III.6 Signal Processing A block diagram of the electronics is shown in Fig. 3.1. The functions of the various components are described in the following sections. III.6A Lock-In Amplifier The Lock-in Amplifier, Princeton Applied Research Model 120, consisted of a tuned pre-amplifier with a Q of about 10, and a phase sensitive detector. It had a linearity of 1% and a gain of 101*. The output was D.C. ±10 V at f u l l scale. In the mode in which i t was used, it supplied its own sinusoidal reference signal. In this experiment , a 1-3 sec. time constant was used. III.6B Photomultiplier The photomultiplier used for this experiment was an E.M.I. 955QB. It had an S-20 (NaKSbCs) surface. The Quantum Efficiency at 4900 A* is quoted by the manufacturer to be approximately 23%. It was operated with a cathode to anode potential of -1280 volts. The dynode chain resistors were a l l 33 Kohms while the cathode to fi r s t dynode potential was maintained at -150 V by a Zener diode. The anode was connected to ground through a 100K ohm resistor. The circuit Cathode o o 01 100K •1300 V Dynodes 92 93 33K 33K -X ft * K Anode o Q11 OUT PUT V V N A 33K i I FIGURE 3.8 Photomultiplier Wiring Schematic schematic is shown in Fig. 3.8. III.6C X-Y Recorder The X-Y recorder used was a Varian model F100 having a linearity of 1% and input impedance of 100K ohms into each channel. The Y channel was taken from the signal averager output which was proportional to the polarization. The X channel was the voltage across the sense resistor, as mentioned in Sec. 3.5.2. III.6D Signal Averager In order to reduce the noise level or increase the signal to noise ratio, a Fabri Tek Model 1010 digital signal averager was used between the Lock-in Amplifier and X-Y recorder. As i t was known that the noise component was random about zero, and as i t was assumed that the noise had a Gaussian amplitude distribution, the average of these errors after N measurements had a value within the range ± e / V'N where e was the i n i t i a l root mean square error magnitude, n n But the average of the true signal will remain fixed, so that after N measurements the signal to noise ratio will be improved to a factor of J/N. Due to a storage limitation of the segnal average, no more than 32 sweeps were used. The sweep output of this averager is 0 to 4.0 volts sawtooth waveform and the instantaneous voltage was proportional to the address number of the momery in the average. This sweep output was used to drive the programmable power supply for the magnetic field and provided a linearity of 0.5% in the resulting field. - 5 6 -III.7 D a t a P r o c e s s i n g F o r t h e H a n l e e f f e c t e x p e r i m e n t t h e g r a p h s p l o t t e d on t h e x - y r e c o r d e r , F i g . 4 . 1 , were s u b j e c t e d t o n u m e r i c a l p r o c e s s i n g t o e x t r a c t t h e h a l f - w i d t h H^. R e l a t i v e v a l u e s o f t h e p o l a r i z a t i o n were punched I n t o computer c a r d s by an e l e c t r o n i c d i g i t i z e r and t h e n u s e d t o f i t a f u n c t i o n o f t h e f o r m P - A, + A»x +7TTi + A + T T F ' ( 3 . 6 . 1 ) H-H w i t h X = ° and Aj^, A 2 , A 3 , A 4 , H q and H^ were a d j u s t a b l e p a r a m e t e r s f i t t e d by a computer " l e a s t s q u a r e " f i t t i n g r o u t i n e ( U . B . C . L . Q . F . ) . The f i t t e d c u r v e s a r e shown i n F i g . 4 . 2 . A t e a c h gas p r e s s u r e u s e d , 4 t o 8 g r a p h s were p r o d u c e d and i n d e p e n d e n t l y f i t t e d by t h e e q u a t i o n ( 3 . 6 . 1 ) . T h e a v e r a g e Hj^ was t h e n computed f o r t h a t p r e s s u r e and p l o t t e d v e r s u s p r e s s u r e , by a l i n e a r " l e a s t s q u a r e s " f i t t i n g r o u t i n e . The z e r o -p r e s s u r e h a l f - w i d t h , w h i c h was u s e d t o c a l c u l a t e t h e r a d i a t i v e l i f e t i m e , and t h e s l o p e f r om w h i c h the p r e s s u r e b r o a d e n i n g c r o s s - s e c t i o n were computed , a r e d i s c u s s e d i n t h e n e x t c h a p t e r . -57-C h a p t e r F o u r EXPERIMENTAL RESULTS IV.1 I n t r o d u c t i o n The l i f e t i m e s o f 3 ' D , 4 'D and 5'D s t a t e s o f h e l i u m have b e e n measured by many w o r k e r s and by u s i n g many d i f f e r e n t t e c h n i q u e s (D67, PH65, KB63, F H J C 6 4 , A J S 6 9 , OV67, MBBB70, BK67, DPB61) . T h e r e m e a s u r e d l i f e t i m e s o f t h e above l i s t e d s t a t e s p r o v i d e d a good t e s t o f t h e t e c h n i q u e s and t h e a p p a r a t u s u s e d i n t h i s l a b . The remeasu red r e s u l t s a r e g i v e n i n T a b l e 4.1 and a r e d i s c u s s e d i n S e c . 4 . 2 . The l i f e t i m e s o f 2P s t a t e s o f a r g o n and neon measured a t l o w (10-80 m i c r o n s ) and h i g h (200-500 m i c r o n s ) p r e s s u r e s a r e l i s t e d i n T a b l e 4 . 2 . T h e r e i s an u n e x p e c t e d d i s c r e p a n c y between t h e s e two measurement s . To p r o v i d e more i n f o r m a t i o n a m a g n e t i c r e s o n a n c e e x p e r i m e n t was p e r f o r m e d . T h i s e x p e r i m e n t showed t h a t t h e d i s c r e p a n c y m i gh t be due t o t h e c a s -c a d i n g f r o m t h e h i g h e r e n e r g y l e v e l s . A more d e t a i l e d d i s c u s s i o n i s g i v e n i n s e c t i o n 4 . 3 . The most i m p o r t a n t work r e p o r t e d i n t h i s t h e s i s a r e t h e l i f e t i m e s , Lande 7 g - f a c t o r s and t h e h y p e r f i n e s t r u c t u r e c o n s t a n t s measured i n 3D, 3E and Z s t a t e s o f m o l e c u l a r h y d r o g e n . The r e s u l t s a r e g i v e n i n T a b l e 4 .4 and 4 .5 and d i s c u s s e d i n s e c t i o n 4 .4 and i n C h a p t e r 5. P o s s i b l e e r r o r s a r e l i s t e d and d i s c u s s e d i n S e c t i o n 4.5. - 5 8 -IV .2 The 3 * 0 , 4 ' D and 5 ' D S t a t e s o f H e l i u m The s p e c i a l i n t e r e s t i n r a d i a t i v e l i f e t i m e i n f o r m a t i o n f o r h e l i u m i s t h a t t h e t h e o r e t i c a l t r a n s i t i o n p r o b a b i l i t i e s a r e a v a i l a b l e . S e v e r a l e x p e r i m e n t a l d e t e r m i n a t i o n s o f h e l i u m l i f e t i m e and c r o s s - s e c t i o n s ihave a l r e a d y been made. In most o f t h e s e e x p e r i m e n t s l e v e l c r o s s i n g (D67 ) , d i r e c t o b s e r v a t i o n s o f d e c a y (FHJC64, BK67, A J S 6 9 ) , d e l a y e d c o i n c i d e n c e t e c h n i q u e s were a p p l i e d . A l l t h e e x p e r i m e n t a l r e s u l t s a r e f a i r l y c o n s i s t e n t w i t h e a c h o t h e r and i n agreement w i t h t h e o r y ( T a b l e 4 . 1 ) . I n o r d e r t o p r o v e t h e l i f e t i m e s measured i n o u r l a b a r e n o t s e r i o u s l y a f f e c t e d by t h e i n h o m o g e n e i t i e s o f t h e m a g n e t i c f i e l d , R . F . e l e c t r i c f i e l d and o t h e r p o s s i b l e s o u r c e s o f e r r o r , t h e l i f e t i m e s o f 3 ' D , 4 'D and 5'D s t a t e s o f h e l i u m have a l s o been m e a s u r e d . As shown i n T a b l e 4 . 1 , o u r measurements a r e i n agreement w i t h t h e o r y and a l s o w i t h o t h e r e x p e r i m e n t a l r e s u l t s . F o r more a c c u r a t e r e s u l t s , t h e l i f e t i m e s were a l s o measured a t l o w e r p r e s s u r e s (5 - 100 m i c r o n s ) . I t was f ound t h e l i f e t i m e s o f 3 'D and 4 ' D showed c l o s e r agreement w i t h t h e t h e o r e t i c a l c a l c u l a t i o n s b u t t h e 5 ' D l i f e t i m e showed an u n e x p e c t e d d e c r e a s e , i n o t h e r w o r d s , t h e L o r e n t z i a n c u r v e had been b roadened i n s t e a d o f nar rowed a t l ower p r e s s u r e s . F o r t h i s r e a s o n , t h e m a g n e t i c r e s o n a n c e e x p e r i m e n t on t h e 3 ' D , 4 'D and 5 'D s t a t e s i n h e l i u m was p e r f o r m e d and more u n e x p e c t e d phenomena were f o u n d i n t he 5'D s t a t e s . A l l t h e u n u s u a l phenomena a r e l i s t e d a s f o l l o w s : 1. More t h a n one g - v a l u e a p p e a r e d i n t he m a g n e t i c r e s o n a n c e e x p e r i m e n t a t p r e s s u r e s l o w e r t h a n lOu F i g . 4 . 1 . 2. The L o r e n t z i a n c u r v e s were b r o a d e n e d a s t h e p r e s s u r e d e c r e a s e d L i f e t i m e s (n sec.) Author Techniques Date VD VD 5 ^ 12(3) 41.5(5) 49(5) Descoubes (D67) Le v e l Crossing 1967 16(2) 47(5) 79(6) Pendleton & Hughes (PH65) D i r e c t Observation Decay 1965 16(4) 30(5) 46(3) Kindleman & Bennett (KB63) Delayed Coincidence 1963 18(5) 35(4) Fowler e t . at. (FHJC64) D i r e c t Observation Decay 1969 15.5(5) 38(5) ' A l l e n e t . a l . (AJS69) D i r e c t Observation Decay 1968 16(2) 46(3) Obsheovich SVerolaimen (OV67) Delayed Coincidence 1968 38(3) 66(4) Martison e t . a t . (MBBB70) Beam F o i l 1969 39(5) 63(9) B r i d g e t t & King (BK67) Derect Observation Decay 1967 39(2) 49(2) Descoubes e t . a l . (DPB61) Magnetic Resonance 1960 20.3(2) 33.6(3) 74.4(5) Ours(100-300 microns) (CBD71) Hanle E f f e c t 1971 17.6(3) 35.1(3) Ours(1-70 microns) Hanle E f f e c t 1972 1.5+10% 35+10% .72+10% Wiese e t . a l . (WSG66) T h e o r e t i c a l 1965 Table 4-1 The L i f e t i m e s i n Helium 3 D , 4 D, 5 Dstates -61-b e l o w 1 2 u . 3. The r a t i o o f t h e a m p l i t u d e o f t h e d i s p e r s i o n c u r v e t o t h e a m p l i t u d e o f t he L o r e n t z i a n c u r v e d e c r e a s e d a t t h e s e same l ow p r e s s u r e s . S i n c e a l l t h e s i n g l e t s t a t e s i n h e l i u m p o s s e s s g = 1, t h e above phenomena w h i c h had more t h a n one g - v a l u e c a n n o t b e e x p l a i n e d by c a s c a d i n g e f f e c t s . A f t e r f u r t h e r e x p e r i m e n t a l i n v e s t i g a t i o n , w i t h a s s i s t a n c e and a d v i c e f r o m P r o f e s s o r s M . L . H . P r y c e and A . J . B a r n a r d , an e x p l a n a t i o n o f t h e s e phenomena i n te rms o f t h e S t a r k E f f e c t was d e v e l o p e d . s o u r c e , and t h e e l e c t r o n s i n t h e d i s c h a r g e c e l l o b t a i n e d t h e i r e n e r g y f r o m a s t r o n g RF e l e c t r i c f i e l d . In a g low d i s c h a r g e most o f t h e p o t e n t i a l a p p l i e d between c a t h o d e and anode a p p e a r s a c r o s s t h e c a t h o d e d a r k s p a c e and t h e l e n g t h o f t h i s s p a c e i s about f o u r t i m e s t h e mean f r e e p a t h o f t h e e l e c t r o n s i n t h e d i s c h a r g e c e l l ( L 6 6 , P g 9 3 ) . As t h e p r e s s u r e i n t h e d i s c h a r g e c e l l was l o w e r e d , t h e mean f r e e p a t h o f t h e e l e c t r o n s was i n c r e a s e d . The c a t h o d e d a r k space t h e n e x t e n d e d more towards t h e c e n t e r o f t h e d i s c h a r g e c e l l and atoms were s u b j e c t t o h i g h e r e l e c t r i c f i e l d t h a n t h e y had b e e n a t h i g h e r p r e s s u r e s . As t h e e l e c t r i c f i e l d i n s i d e t h e d i s c h a r g e c e l l i n c r e a s e d , t h e m a g n e t i c s u b l e v e l s s t a r t e d t o s h i f t due t o t h e S t a r k e f f e c t . The second o r d e r S t a r k e f f e c t s h i f t i s g i v e n by (B65, CS35) I n o u r e x p e r i m e n t a g low d i s c h a r g e was u sed as t h e l i g h t Where E i s t h e e l e c t r i c f i e l d , E (n ) and E ( n ' ) a r e t h e e n e r g i e s o f z t h e e x c i t e d s t a t e |n> and |n'> r e s p e c t i v e l y . The 5'D s t a t e i n h e l i u m i s v e r y c l o s e to t h e 5 ' F s t a t e w i t h - 6 3 -energy s e p a r a t i o n E ( n ' ) - E (n ) = 1.7 cm - - 1 and t h e t r a n s i t i o n p r o b a b i l i t y <n '|E jZ i|n> i s h i g h . A t l ow gas p r e s s u r e s t h e S t a r k s h i f t s become c o m p a r a b l e t o t h e zeeman s p l i t t i n g s and the e n e r g y o f t h e a p p l i e d R . F . m a g n e t i c f i e l d . As shown i n F i g u r e 4 .2 t h e r e s o n a n c e s h o u l d t h e n o c c u r a t many d i f f e r e n t f i e l d s . By c o m p a r i n g w i t h t h e l o c a t i o n o f t h e r e s o n a n c e i n m a g n e t i c r e s o n a n c e e x p e r i m e n t ( F i g . 4 .1 ) t h e u n e x p e c t e d r e s o n a n c e s a r e q u a l i t a t i v e l y a g r e e w i t h t h e t h e o r y . A d e t a i l e d quantum m e c h a n i c a l t h e o r y w h i c h i n c l u d e s t h e i n t e r a c t i o n o f t h e e l e c t r i c f i e l d and m a g n e t i c f i e l d i n t h e H a n l e E f f e c t and t h e m a g n e t i c r e s o n a n c e e x p e r i m e n t s has been g i v e n by P r y c e (P74 ) . I n t h i s t h e o r y , t h e b r o a d e n i n g o f L o r e n t z i a n c u r v e and t h e d e c r e a s e i n t h e r a t i o o f t h e a m p l i t u d e o f t h e d i s p e r s i o n c u r v e t o t h a t o f t h e L o r e n t z i a n c u r v e a t s t r o n g e l e c t r i c f i e l d s ( low p r e s s u r e s ) a r e e x p l a i n e d . • * Because t h e d e t e c t i n g u n i t w i l l s t r o n g l y d i s t u r b t h e r e s o n a n c e c i r c u i t , i t i s v e r y * d i f f i c u l t t o make a b s o l u t e f i e l d s t e n g t h m e a s u r e -ments o f t h e 450 MHz e l e c t r i c f i e l d . However a l o o p p l a c e d a few cm f r o m the c e n t r e o f t h e d i s c h a r g e c e l l g i v e s a r e a s o n a b l y good m e a s u r e -ment o f t h e r e l a t i v e e l e c t r i c f i e l d . The measured h a l f w i d t h o f t h e L o r e n t z i a n c u r v e AH^ v e r s u s s ometh ing p r o p o r t i o n a l to t h e s q u a r e o f t h e e l e c t r i c f i e l d i s g i v e n i n F i g u r e 4 . 3 . As p r e d i c t e d by t h e t h e o r y , i n t h e 5'D s t a t e o f h e l i u m , the h a l f w i d t h i s b roadened as t he e l e c t r i c f i e l d i s i n c r e a s e d . The r a t i o o f t h e a m p l i t u d e o f t h e d i s p e r s i o n c u r v e t o t h a t o f t h e L o r e n t z i a n c u r v e i s a l s o g i v e n i n F i g u r e 4.3 ( t h e v e r t i c a l a x i s on t h e r i g h t hand s i d e ) . The v a r i a t i o n o f t h i s r a t i o a l s o a g r e e s w i t h t h e t h e o r e t i c a l p r e d i c t i o n t h a t i t d e c r e a s e w i t h t h e i n c r e a s i n g e l e c t r i c f i e l d . . F I G U R E 4.3 . H a l f w i d t h a s f u n c t i o n o f R. F . E l e c t r i c F i e l d - 6 5 -I V . 3 The L i f e t i m e s o f 4P S t a t e s i n A r g o n and Neon In o r d e r t o r e d u c e r a d i a t i v e t r a p p i n g and c o l l i s i o n a l e f f e c t s , l ow p r e s s u r e (100 m i c r o n o r l e s s ) measurements were made o f t h e 2P l i f e t i m e s o f a r g o n . A s shown i n T a b l e 4 .2 some o f t h e low p r e s s u r e l i f e t i m e s measured i n t h i s s t u d y d i f f e r by more t h a n 200% f r o m t h e s e o b t a i n e d by o t h e r w o r k e r s . However, t h e e x p e r i m e n t a l e r r o r i s l e s s t h a n 5%. In v i e w o f t h e s e r e s u l t s t h e 2P l i f e t i m e s i n neon were a l s o m e a s u r e d . The e l e c t r o n i c s t r u c t u r e o f neon i s ve ry , much t h e same a s t h a t o f a r g o n and l i f e t i m e measurements i n neon have been p e r f o r m e d by many w o r k e r s . A s shown i n T a b l e 4 . 2 , t h e l i f e t i m e measurements a t l ow n e o n p r e s s u r e s a r e a g a i n d i s a g r e e w i t h o t h e r s . C a r r i n g t o n (C72) p e r f o r m e d a s i m i l a r t y p e o f e x p e r i m e n t a t l o w p r e s s u r e s (50 - 150 m i c r o n ) and h i g h e r p r e s s u r e s (500 - 1000 m i c r o n s ) and s u g g e s t e d t h a t i n t h e l o w p r e s s u r e measurements c a s c a d i n g f r o m h i g h e r e x c i t e d s t a t e s m i gh t l e a d t o l a r g e e r r o r s i n l i f e t i m e s deduced f r o m H a n l e e f f e c t c u r v e s . In o r d e r to i d e n t i f y t h e e f f e c t o f c a s c a d i n g , m a g n e t i c r e s o n a n c e e x p e r i m e n t s o n t h e 2P s t a t e s o f a r g o n and neon were p e r f o r m e d . These e x p e r i m e n t s n o t o n l y measured t h e l i f e t i m e s b u t a l s o t h e Lande g - f a c t o r s (BB52) . A t l o w gas p r e s s u r e s , t h e m a g n e t i c r e s o n a n c e c u r v e s showed more t h a n one g - v a l u e . U s i n g t h e neon 2P5 l e v e l a s an examp le , t h e r e a r e c l e a r l y two r e s o n a n c e s , c o r r e s p o n d i n g t o g = 0.99 and g = 1.30 ( F i g . 4 . 4 ) . The L a n d e ' g - f a c t o r ha s a w e l l known v a l u e o f 0.994 f o r t h i s 2P5 s t a t e (P67 ) . T h i s second r e s o n a n c e a t 1.30 i s presumed to be due t o c a s c a d i n g f r o m some h i g h e r e n e r g y l e v e l s . A s we have shown In A p p e n d i x B, t h e d e n s i t y m a t r i x p o f t h e c a s c a d e d s t a t e i s p r o p o r t i o n a l t o -66-ARGON Landman L68 K l o s e K67 A B C 2 P 3 26.0(1) 27:1(2) 46.0(2) 2 P 6 29.0C1.7) 2 9 . 5 ( 3 ) 2 8 . 7 ( 3 ) 3 2 . 4 ( 2 ) 2 P 0 31.6(1 .6 ) 3 7 . 4 ( 3 ) 91.0(5) -NEON B e n n e t t BK66 C a r r i n g t o n C72 A B C 2 P 4 1 9 . 1 ( . 3 ) 1 9 . 2 ( 1 . ) 1 9 . 5 ( 1 . 5 ) 1 9 . 0 ( 1 . 6 ) 2 0 . 9 ( . 9 ) 2 P 5 1 9 . 9 ( . 4 ) 1 8 . 6 ( 1 . 3 ) 2 0 . 7 ( 1 . 7 ) 2 6 . 1 ( . 8 ) 2 P 6 1 9 . 7 ( . 2 ) 1 8 . 2 ( . 7 ) 1 9 . 1 ( 1 . 9 ) . 2 1 . 3 ( . 6 ) 2 P ? 1 9 . 9 ( . 4 ) 1 9 . 4 ( . 9 ) 2 0 . 5 ( 2 . 2 ) 3 7 . 0 ( . 8 ) 2 P 8 1 9 . 8 ( . 2 ) 1 9 . 6 ( 1 . ) 2 1 . 1 ( 2 . 1 ) 2 5 . 4 ( . 7 ) 2 P Q 1 9 . 4 ( . 6 ) 1 8 . 7 ( . 7 ) 2 0 . 1 ( 2 . 0 ) 3 3 . 7 ( . 6 ) I A : H i g h e r P r e s s u r e Measurements (200-500 M i c r o n ) . B: LQF F i t t e d w i t h C a s c a d i n g E f f e c t . C : Measured by H a n l e E f f e c t a t Low P r e s s u r e (3 -80 u ) . TABLE 4 - 2 . The L i f e t i m e Measurements o f t h e 2P S t a t e s i n ARGON and NEON. - 6 8 -f °C °^  ^  ~ X ^ Const. ' . ( 4 . 3 . 1 ) w h e r e o f ~ " ^ f * i ' H L and t h e c o n s t , i s a n o t h e r p a r a m e t e r t o be f i t t e d by computer LQF p rog ram. E q u a t i o n 4 . 3 . 1 had been f i t t e d u s i n g t h e computer LQF program and i t was f o u n d t h a t t h e l i f e t i m e s o f some o f t h e s t a t e s a g r e e d w i t h the r e s u l t s o f o t h e r w o r k e r s . However due to t h e c o m p l e x i t y o f t h e e q u a t i o n most L o r e n t z i a n c u r v e s c o u l d n o t be f i t t e d , i n o t h e r w o r d s , the p a r a m e t e r s i n e q u a t i o n ( 3 . 6 . 1 ) f a i l e d t o c o n v e r g e ( T a b l e 4 . 2 ) . An i n t e r e s t i n g e f f e c t was n o t e d i n t h e neon and a r g o n e x p e r i -m e n t s . A s t h e p r e s s u r e i n t h e d i s c h a r g e i n c r e a s e s t h e a m p l i t u d e o f t h e L o r e n t z i a n s i g n a l d e c r e a s e s , goes t o z e r o a t p r e s s u r e n e a r 200 m i c r o n s , and a s t h e p r e s s u r e i n c r e a s e d f u r t h e r i t becomes i n v e r t e d and s t r o n g e r . T h i s i n t e r e s t i n g e f f e c t was f ound i n d e p e n d e n t l y by C a r r i n g t o n ( C 7 2 ) ; a f t e r d e t a i l e d i n v e s t i g a t i o n he s u g g e s t e d t h a t t h i s phenomenon i s a r e s u l t o f t h e change i n t h e e x c i t a t i o n mechan i sm. A t t h e low p r e s s u r e s the 2p s t a t e s were p o p u l a t e d and a l i g n e d by t h e e l e c t r o n e x c i t a t i o n s and t h e p o l a r i z a t i o n a x i s was t h e n a l o n g t h e d i r e c t i o n o f e l e c t r o n beam. However, a t t h e h i g h e r p r e s s u r e s t he p o p u l a t i o n o f t h e m e t a s t a b l e 2s l e v e l s were i n c r e a s e d and t h e 2p s t a t e s were t h e n p o p u l a t e d by o p t i c a l e x c i t a t i o n s f r o m t h e m e t a s t a b l e 2s l e v e l s . I n o u r e x p e r i m e n t , o n l y t h e c e n t r e co lumn o f t h e d i s c h a r g e was f o c u s e d o n t o t h e e x t r a n c e s l i t o f t h e monochromater and t h e i n t e n s i t y o f t h e d i s c h a r g e was f o u n d b r i g h t e r a t t h e two s i d e s r a t h e r t h a n t h a t o f t h e c e n t r e co l umn. The o p t i c a l e x c i t a t i o n a r i s e s f r o m l i g h t t r a v e l l e d p a r a l l e l t o t h e e l e c t r o n beam and - 6 9 -hence i t s p o l a r i z a t i o n a x i s would be p e r p e n d i c u l a r t o t h e a x i s o f t h e e l e c t r o n beam l e a d i n g t o an i n v e r t e d L o r e n t z i a n p r o f i l e was e x p e c t e d . The " o p t i c a l e x c i t a t i o n " H a n l e e f f e c t measurement o b t a i n e d a t h i g h e r p r e s s u r e s (200 t o 500 m i c r o n s ) was u s e d . The r a d i a t i o n l i f e -t i m e s t h a t were deduced f r o m t h e e x t r a p o l a t e d z e r o p r e s s u r e h a l f w i d t h o f t h e L o r e n t z i a n p r o f i l e s were i n agreement w i t h t h e most r e l i a b l e r e p o r t e d r e s u l t s ( T a b l e 4 . 2 ) . - 7 0 -IV.4 The 3D, 3E and Z S t a t e s o f  M o l e c u l a r Hydrogen IV.4A The L i f e t i m e Measurements The p o l a r i z a t i o n o f t h e l i g h t e m i t t e d f r o m t h e e x c i t e d 3D s t a t e o f h y d r o g e n a s a f u n c t i o n o f a p p l i e d t r a n s v e r s e m a g n e t i c f i e l d i s shown i n F i g . 4 . 5 . The r e s p e c t i v e l e a s t s q u a r e s f i t t e d (LQF) c u r v e s i s shown i n F i g . 4.6. In t h i s f i g u r e t h e c r o s s e s " x " a r e t h e r e l a t i v e v a l u e s o f t h e p o l a r i z a t i o n , w h i c h were r e a d f r o m t h e L o r e n t z i a n c u r v e i n t h e H a n l e e f f e c t e x p e r i m e n t by an e l e c t r o n i c d i g i t i z e r . The p o l a r i z a t i o n s c a l e i s a r b i t r a r y and t h e p o l a r i z a t i o n s were s c a l e d t o 9 i n c h e s b e f o r e b e i n g p l o t t e d by t h e c o m p u t e r . The h a l f w i d t h s a t ha l fmax imum, Hj^, o f t h e f i t t e d L o r e n t z i a n where \iQ i s t h e Bohr magneton and g i s t h e L a n d e ' g - f a c t o r . The e x t r a p o l a t e d h a l f w i d t h s a t z e r o p r e s s u r e and t h e l i f e t i m e s o f d i f f e r e n t e x c i t e d s t a t e o f t h e 3D, 3E and Z s t a t e s o f h y d r o g e n a r e t a b u l a t e d i n T a b l e s 4 .3 and 4 . 4 . From t h e s l o p e o f t h e h a l f w i d t h v e r s u s p r e s s u r e g r a p h an e s t i m a t e o f t h e c o l l i s i o n c r o s s - s e c t i o n may, be o b t a i n e d . I f i t i s assumed t h a t t h e number d e n s i t y o f t h e e x c i t e d m o l e c u l e s N F i s s m a l l compared t o t h e number d e n s i t y o f g round s t a t e m o l e c u l e s N , t h e n t h e c o l l i s i o n c r o s s - s e c t i o n c a n b e c a l c u l a t e d f r o m t h e e q u a t i o n ( V 7 0 ) (j~ - • * 3s M o T , d i-k ( 4 . 4 . 2 ) where N q i s A v o g a d r o ' s number, T q e q u a l s 2 7 3 K, T i s t h e t e m p e r a t u r e o f t h e gas i n K and v i s t h e r e l a t i v e v e l o c i t y o f c o l l i d i n g m o l e c u l e s . Magnetic Field -8.0 -6.0 -4.0 2.0 4.0 6.0 8.0 Gauss FIG. 4""5 E x p e r i m e n t a l Hanle E f f e c t Curve f o r the 3D0 2B0 RO Line 4 6 2 8 A Magnetic Field(Gauss) -8.0 -6.0 -4.0 -20 2.0 40 6J0 8.0 FI6. 4-6 Least Squares F i t t e d Curve for the 3Do 2B0 RO Line (4628 A) - 7 3 -I n t he d e r i v a t i o n a Bo l t zmann v e l o c i t y d i s t r i b u t i o n was a s sumed. The c u r v e s a r e p l o t t e d a g a i n s t t h e p r e s s u r e i n t h e d i s c h a r g e c e l l a s shown i n F i g u r e s 4 . 7 t o 4 . 1 4 . E a c h l i n e i n t h e s e f i g u r e s shows one s p e c t r a l l i n e and one s p e c i f i c v i b r a t i o n a l l e v e l i n one o f t h e 3D ( 3 d ' Z ) , 3 E ( 3 d ' n ) o r Z ( 3 ' K ) e l e c t r o n i c s t a t e s . T h e r e a r e t w e n t y - t w o s p e c t r a l l i n e s , b e l o n g t o f i f t e e n r o t a t i o n a l l e v e l s i n m o l e c u l a r h y d r o g e n , r e p o r t e d i n t h i s t h e s i s and t w e n t y H a n l e e f f e c t c u r v e s were t a k e n f o r e a c h one o f t h e s p e c t r a l l i n e s a t f o u r t o s i x d i f f e r e n t g a s p r e s s u r e s . E a c h c u r v e i s t h e a v e r a g e v a l u e s o f 1 t o 32 sweeps o n t h e s i g n a l a v e r a g e r , d e p e n d i n g on t h e s i g n a l - t o - n o i s e r a t i o o f t h e s p e c t r a l l i n e . The v e r t i c a l i n t e r c e p t s i n F i g . 4 .7 t o 4.14 r e p r e s e n t t h e h a l f w i d t h s a t z e r o p r e s s u r e . T h e s e h a l f w i d t h s a r e c o n v e r t e d t o t h e u p p e r s t a t e n a t u r a l l i f e t i m e s w i t h t h e a i d o f \ ( 4 . 4 . 1 ) C a l c u l a t e d c r o s s - s e c t i o n s a r e l i s t e d i n T a b l e 4 .3 and 4 . 4 . STATES X (A) g-VALUES LIFETIMES (n. sec.) CROSSr-SECTIONS hfs CONSTANTS upper 3D lower 2B OURS OTHER'S OURS OTHER'S OURS OTHER'S OURS (MHz) OTHER'S V' J 1 v " J " (1%) ±5% ±10% ±10% 0 1 0 0 4628 +.886 D*.901 B. 908(10) C. 889(10) 26.2 B*21(l) G 15.8(8) 153 G 190 (20! 4.1 0 2 0 2 0 1 1 1 4 6 3 1 4932 +.572 +.568 D.571 35.9 36.2 149 148 .2±(.3) 0 3 0 2 4632 +.440 D . 4 4 5 37.. 9 159 3.9 1 1 0 0 4196 +.620 27.8 54.7 4.8 1 1 2 0 4709 +.622 D.606 27.7 55.4 5.2 1 1 3 0 5003 +.614 28.2 G23.8 60.3 5.1 G 6.3(6) 1 2 0 1 4199 D.358 40.7 62.3 .2±(.3) 1 2 2 1 4714 40.6 60.6 1 3 0 2 4205 D.275 44.2 63.0 2 1 1 0 4067 D.293 42.5 87.0 3 3 2 2 4206 D.407 38.9 173 4.6 D;DCB53 B;FM73 G;ML74 TABLE 4-3. The 3D(3d '£) State of Hydrogen Molecules (H„). UPPER LOWER 8-\ OURS FALUE L IFETIMES CROSS-SECTION h f s CONSTANTS V» N ' V N X (A) OTHER'S D53 OURS (n s e c . ) ±10% (S2) (MHz) 3E a 0 2 0 3 4576 .412 +.42(1) 3 3 . 7 ( 3 . ) 347 0 3 0 4 4568 1 1 7 + 3 7 . 9 ( 3 . ) 389 4 .2 0 3 1 4 4856 . J i / + 3 9 . 4 ( 3 . ) 388 4.1 3 E b 0 2 0 2 4580 .142 - 9 7 . 0 ( 0 . ) 230 1.7 1 2 0 2 4937 .169 6 6 . 5 ( 6 . ) 135 3.0 1 3 0 3 4175 Z 2 1 4 0 4814 *M.495(8) Z . 4 8 ( l ) 4 9 . 2 ( 5 . ) 132 2 1 5 0 5103 Z . 4 8 ( l ) 4 5 . 3 ( 5 . ) 138 2 2 5 1 5107 Z.17C3) 1 0 6 . 6 ( 9 . ) 65 2 3 5 2 5113 Z .23(2) 5 9 . 3 ( 6 . ) 122 * M magnet i c r e s o n a n c e Z Zeeman E f f e c t TABLE 4 - 4 . The 3E (3d ' n ) and Z ( 3 ' K ) S t a t e s o f Hydrogen M o l e c u l e s 1 H a c THE 3D0 STRTE OF HYDROGEN MOLECULE ••3 tr (D Ul D o w r+ U> rt fD O Hi a H 0 iQ ro 3 • s o ro o c ro J=3 4638 A J=2 04631 A A4932 A J = 1 o 4628 A I l 0.0 10.0 20.0 I 30.0 PRESSURE IN i 40.0 MICRONS 50.0 60.0 70.0 80.0 H Ci G THE 3D1 STATE OF HYDROGEN MOLECULE J=2 4714 A J=l °5003 A °f4709 A 44196 A •i. •Nl I 30.0 PRESSURE I N 40.0 MICRONS ° 0 I o io~0 2oTu 3oTo T o 50.0 60.0 70JD ^50.0 0 , 0 PRESSURE IN MICRONS THE 3E0 STATE OF HYDROGEN MOLECULE - 8 4 -IV .4B The Measurement o f t h e L a n d e ' g - f a c t o r s A s shown p r e v i o u s l y , t h e h a l f w i d t h o f a H a n l e e f f e c t c u r v e at z e r o p r e s s u r e i n p r o p o r t i o n a l t o t h e r e c i p r o c a l o f t h e p r o d u c t of t h e g - v a l u e and t h e l i f e t i m e T . I n o r d e r t o deduce t h e l i f e t i m e of t h e e x c i t e d s t a t e s t h e Lande g - f a c t o r i s r e q u i r e d . In 1953 D i e k e (DCB53) measured some o f t h e g - v a l u e s o f . 3D ( 3 d ' I ) , 4D (3d ' I) a n d . 3E(3d'II) s t a t e s u s i n g t h e Zeeman e f f e c t i n a 3 5 , 0 0 0 gaus s m a g n e t i c f i e l d . However , t h e ene r gy o f t h e Zeeman s u b l e v e l s i s n o t a l i n e a r f u n c t i o n of t h e m a g n e t i c f i e l d , so t h a t t h e g - v a l u e s a t l o w e r f i e l d s may d i f f e r f r o m t h o s e a t h i g h f i e l d s . A s e r i e s o f m a g n e t i c r e s o n a n c e e x p e r i m e n t s was p e r f o r m e d at m a g n e t i c f i e l d between 40 and 200 G a u s s . A s shown i n F i g . 2 .7A, a l o n g i t u d i n a l s t a t i c m a g n e t i c f i e l d was a p p l i e d a l o n g t h e d i r e c t i o n of t h e pumping e l e c t r i c f i e l d , and a 54 MHz RF m a g n e t i c f i e l d was a p p l i e d p e r p e n d i c u l a r t o b o t h t h e l o n g i t u d i n a l f i e l d and d i r e c t i o n of t h e o b s e r v a t i o n a x i s . A s t h e l o n g i t u d i n a l m a g n e t i c f i e l d i n c r e a s e d t h e e n e r g y s e p a r a t i o n s between Zeeman s u b l e v e l s a l s o i n c r e a s e d . When t h e e n e r g y s e p a r a t i o n e q u a l l e d t h e e n e r g y o f a R . F . p h o t o n 2 .7B, i . e . u)j = u g H , t h e a l i g n m e n t o f t h e Zeeman s u b l e v e l s o f t h e e x c i t e d O J o s t a t e was d e s t r o y e d and t h e change o f p o l a r i z a t i o n was d e t e c t e d ( F i g . 2.7C) The g - v a l u e s r e s u l t s f o r t h e 3 D , 3 E , and Z s t a t e s o f m o l e c u l a r h y d r o g e n a r e a l s o l i s t e d i n T a b l e s 4 .3 and 4 . 4 . The l i f e t i m e s o f t h e s t a t e s i n t h e t a b l e s were c a l c u l a t e d w i t h t h e g - v a l u e s -measured by t h i s m a g n e t i c r e s o n a n c e e x p e r i m e n t . However, f o r t h o s e s t a t e s w h i c h have v e r y s m a l l g - v a l u e s o r v e r y s h o r t l i f e t i m e s t h e RF m a g n e t i c f i e l d was no t p o w e r f u l enough t o i n d u c e - 8 5 -o b s e r v a b l e t r a n s i t i o n s . In t h o s e c a s e s t h e g - v a l u e s u s e d were t a k e n f r o m D i e k e ' s work (DCB53). However, g - v a l u e s i n t h e d o u b l y e x c i t e d Z s t a t e had n e v e r been m e a s u r e d . In t h i s c a s e a Zeeman e f f e c t e x p e r i -men t , s i m i l a r t o t h a t o f D i e k e ' s ( D C B 5 3 ) , b u t . a t 27 ,000 gaus s arid h y d r o g e n gas p r e s s u r e o f 1000 m i c r o n , was p e r f o r m e d i n t h i s l a b . X V . I C The Measurement o f t h e h f s C o n s t a n t A s d e s c r i b e d i n s e c t i o n 2 . 3 , t h e p o l a r i z a t i o n o f t h e l i g h t e m i t t e d f r o m t h e e x c i t e d s t a t e s o f h y d r o g e n m o l e c u l e s c o r r e s p o n d i n g t o n u c l e a r s p i n 1 = 1 i n c r e a s e s s l i g h t l y a s a l o n g i t u d i n a l m a g n e t i c f i e l d i s a p p l i e d , b u t t h e p o l a r i z a t i o n does n o t change i f t h e p h o t o n .comes f r o m t h e e x c i t e d s t a t e s w i t h 1 = 0 . I t ha s been p r o v e n t h a t P C C X-o) ) X F F ' J r a + S2pF> C 2 .4 .10) v h e r e n ^ > E F - E F ' = f (RF+/>- F ' (FV/ ) ) and where T i s t h e l i f e t i m e o f t h e e x c i t e d s t a t e . F o r v e r y h i g h m a g n e t i c f i e l d s , t h e c o u p l i n g be tween J and I v a n i s h e s (a = 0 ) . I f P ( a = 0) r e p r e s e n t s t h e p o l a r i z a t i o n a t h i g h f i e l d s , t h e n ( F i g . 4 .11 ) ( 4 . 4 . 4 ) where P^ i s t h e change i n p o l a r i z a t i o n o b s e r v e d i n t h e r e p o l a r i z a t i o n e x p e r i m e n t and P t h e change i n p o l a r i z a t i o n o b s e r v e d i n t h e H a n l e e f f e c t e x p e r i m e n t . E q u a t i o n ( 2 . 4 . 1 0 ) i s t o o c o m p l i c a t e d t o p rogram f o r l e a s t s q u a r e f i t t i n g by c o m p u t e r , bu t u s i n g e q . ( 2 . 4 . 1 0 ) t h e r a t i o , p ( a ) / p ( a = 0 ) a s a f u n c t i o n o f ( a / T ) i s c a l c u l a t e d f o r J = l J=5 i n T a b l e 4 .5 and p l o t t e d i n F i g . ( 4 . 1 5 ) . Once t h e r a t i o p ( a ) / p ( a = 0 ) .: i s o b t a i n e d , t h e n u m e r i c a l v a l u e o f a/T was r e a d o f f f r o m e i t h e r T a b l e (4 .5 ) o r F i g u r e ( 4 . 1 5 ) . A g a i n , by t a k i n g t h e v a l u e o f t h e l i f e t i m e f r o m t h e H a n l e e f f e c t e x p e r i m e n t , t h e h y p e r f i n e s t r u c t u r e -87-FIGURE 4 . 1 6 The Plot of P(a)/P(a=0) Vsv a/p J Bo B l B 2 B 3 B 4 . B 5 B 6 B 7 B 8 B 9 B10 B l l 1 . 2 7 8 , . 5 0 0 . 2 2 2 2 . 4 7 4 . 2 3 4 . 2 6 6 . 0 2 6 3 . 7 0 4 . 1 4 2 . 1 4 8 .006 4 . 8 1 3 . 0 9 2 . 0 9 4 . 0 0 2 5 . 8 7 3 . 0 6 4 . 0 6 4 .002 00 P ( a ) / P ( a = 0 ) = YB ' ^ l—L " I4.fr. n e O l + ( n a / r ) TABLE 4 . 5 A The Coefficients of B n i n The Expresion p(a)/P(a= 0 ) -90-a/r P(a)/P(a=0) J - 2 o.o • 0 1 0 0 0 . , 0 2 0 0 0 , 0 3 0 0 0 —ro^rootr , 0 5 0 0 0 , 0 6 0 0 0 — - , 0 7 0 0 0 -, 0 6 0 0 0 0 9 0 0 0 TtOTVOTr ,11000 ,12000 -113000" ,14000 .15000 T l K t r o x r .17000 ,16000 - , I «JOOO-.20000 ,21000 , 2 2 0 0 0 , 2 3 0 0 0 . 2 4 0 0 0 - . ' 2 5 0 0 0 -. 2 6 0 0 0 , 2 7 0 0 0 1 . 0 0 . 0 0 0 , 9 9 9 6 0 , 9 9 8 4 1 , 9 9 t > 4 2 -7-99-5 B T -, 9 9 0 1 6 . 9 8 5 9 4 - J 9 8 1 0 T -, 9 7 5 4 3 . 9 6 9 2 2 , 9 b 2 4 4 , 9 5 5 1 2 , 9 4 7 3 0 " 7 9 3 9 0 3 -, 9 3 0 3 6 , 9 2 1 3 3 , 9 0 2 3 7 . B 9 2 5 1 - ; 8 B ? 4 7 -, 8 7 2 2 7 , 8 6 1 9 5 . 6 5 1 S 4 , 8 4 1 0 7 . B 3 0 5 8 " 7 8 2 0 0 8 -, 8 0 9 6 0 . 7 9 9 1 7 9 9 9 0 0 9 9 B 6 0 9 9 7 4 1 9 9 5 4 5 9 9 2 7 4 9 8 9 3 0 9 8 5 1 8 ^8003" 9 7 5 0 9 9 6 9 2 0 9 6 2 8 4 9 5 6 0 4 9 4 8 8 6 9 4 1 3 4 -9 3 3 5 5 9 2 5 5 2 9 1 7 3 1 9 0 8 9 4 9 0 0 4 6 8 9 1 9 1 " 6 8 3 3 1 8 7 4 7 0 6 6 6 1 0 6 5 7 5 3 8 4 9 0 2 8 4 « 1 r 9 -8 3 2 2 4 8 2 4 0 0 9 9 7 0 0 9 9 6 6 1 9 9 5 4 3 9 9 3 5 0 9 B 7 5 3 9 8 3 5 3 - 9 7 9 0 8 " 9 7 4 0 9 9 6 8 6 7 • 9 B ? 6 - 9 -9 5 6 8 2 9 5 0 5 1 9 0 4 0 3 9 3 7 4 4 9 3 0 7 6 9 2 4 0 7 9 1 7 3 8 9 1 0 7 3 9 0 4 1 6 " 8 9 7 6 8 6 9 1 3 2 B B 5 I 0 8 7 9 0 3 B 7 3 1 1 8 6 - 7 3 6 -8 6 1 7 6 8 5 6 3 7 1 , 0 0 1 0 0 1 , 0 0 0 6 0 , 9 9 9 4 2 , 9 9 7 4 9 —r99Tt65-, 9 9 1 6 0 , 9 8 7 7 8 — J 9 8 3 4 8 -, 9 7 8 8 1 , 9 7 3 8 2 —r9W62~ , 9 6 3 2 6 , 9 5 7 8 1 — . 9 5 2 3 4 , 9 4 6 9 0 , 9 4 1 5 2 —r»*<>-rr , 9 3 1 0 8 , 9 2 6 0 8 - . 9 2 1 2 3 , 9 1 6 5 7 , 9 1 2 0 9 r 9 « 7 T 9 " , 9 0 3 6 8 , 8 9 9 7 5 - T 8 9 6 0 1 -, 8 9 2 4 5 , 8 8 9 0 6 9 2 5 5 9 — 9 2 2 8 6 9 2 0 3 0 , - 9 1 7 9 0 — 9 1 5 6 5 9 1 J 5 4 0 0 3 0 0 0 0 2 5 9 0 0 1 i 6 9 9 9 3 9 9 9 * 7 ^ " 9 9 3 4 9 9 8 9 / 7 9 0 5 6 7 -9 8 1 3 2 9 7 6 7 8 9 7 2 1 b 9 6 7 5 3 9 6 2 9 4 9 5 8 4 4 9 5 4 0 7 9 4 9 8 6 9 4 1 9 7 9 3 8 3 1 9 3 4 8 4 9 3 1 5 7 9 2 8 4 9 ,28000 ,29000 ,30 000 T3100O-,32000 ,33000 . 7 8 6 7 9 -, 7 7 8 5 0 , 7 6 8 3 0 - T 7 5 B 2 1 -, 7 4 8 2 4 , 7 3 8 4 0 8 I 5 8 8 6 0 7 6 8 6 0 0 0 2 T 9 ? 3 0 " 7 8 4 7 3 7 7 7 3 2 8 5 1 1 4 8 4 6 0 9 6 4 1 2 2 U 3 * 5 ^ -8 3 1 9 9 8 2 7 6 3 . 8 8 5 8 4 , 6 8 2 7 8 , 8 7 9 8 7 " 7 8 7 7 1 1 -. 8 7 4 4 9 , 6 7 2 0 0 9 1 1 5 6 9 0 9 7 0 9 0 7 9 5 < > t ) 6 3 2 9 0 4 7 8 9 0 3 3 4 . 3 4 0 0 0 . 3 5 0 0 0 . 3 6 0 0 0 T 3 7 0 0 0 -, 3 8 0 0 0 . 3 9 0 0 0 , 7 2 8 7 1 . 7 1 9 1 6 ,70977 — 7 0 0 5 - 4 -, 6 9 1 4 8 , 6 8 2 5 8 7 7 0 0 6 7 6 2 9 6 7 5 b 0 3 7 4 9 2 5 -7 4 2 6 4 73619 •6ZS1S 8 1 9 4 0 6 1 5 5 1 «-ti7«-8 0 8 2 0 8 0 4 7 6 , 8 6 9 6 4 , 8 6 7 4 0 . 8 6 5 2 8 -766 3 2 6 -, 8 6 1 3 4 . 8 5 9 5 2 9 0 1 9 9 " 9 0 0 7 1 8 9 9 5 1 S9836-8 9 7 3 2 6 9 6 3 1 , 4 0 0 0 0 , 4 1 0 0 0 . 4 2 0 0 0 " 7 4 3 O 0 0 -, 4 4 0 0 0 , 4 5 0 0 0 , 6 7 3 6 6 , 6 6 5 3 2 , 6 5 6 9 5 - 7 6 - a f l 7 5 -, 6 4 0 7 4 , 6 3 2 9 0 7 2 9 9 0 7 2 3 7 7 7 1 7 6 0 71T98-7 0 6 3 2 7 0 0 8 1 6 0 1 4 5 7 9 8 2 7 7 9 5 2 2 79^29-7 3 9 4 7 7 8 6 7 6 T 8 5 7 7 9 , 8 5 6 1 4 . 8 5 4 5 7 —85-509-, 6 5 1 6 7 , 8 5 0 3 2 8 9 5 3 7 89407 8 9 3 6 3 B - 9 2 8 3 -8 9 2 0 7 8 9 1 3 6 , 4 6 0 00" , 4 7 0 0 0 , 4 8 0 0 0 —,-490 0 0" , 5 0 0 0 0 . 5 1 0 0 0 "T 5 2 0 0TT , 5 3 0 0 0 . 5 4 0 0 0 -T5500 0-,56000 ,57000 "T5BT)0"0-, 6 1 7 7 4 , 6 1 0 4 3 " 7 - 6 0 3 2 8 -. 5 9 6 3 1 , 5 8 9 5 0 b954g-6 9 0 2 4 6 8 5 1 6 6 7 5 4 3 6 7 0 7 7 7 8 4 1 7 7 8 1 6 7 7 7 9 2 7 "77 6 9 V " 7 7 « 7 5 7 7 2 6 1 7 7 - O U 6 -7 6 8 5 9 7 6 6 6 9 7 6 4 8 7 " 7 6 3 1 1 7 6 1 4 2 7-5-979-, 8 4 9 0 3 , 8 4 7 6 1 , 8 4 6 6 0 — 8 4 5 5 - 2 -,64446 , 6 4 3 4 a - . 8 4 2 4 7 -, 8 4 1 5 5 , 8 4 0 6 6 -r8 - 5 9 6-r , 8 3 9 0 0 , 8 3 6 2 2 8 9 0 6 8 8 9 0 0 3 8 8 9 4 2 B15W4 ! 8 6 8 2 9 8 8 7 7 7 -7-5^*6-, 5 7 6 3 7 , 5 7 0 0 5 " 7 5 6 3 8 8 -. 5 5 7 8 7 , 5 5 2 0 0 T5T&-28-b 6 b 2 3 6 6 1 8 3 6 5 7 5 4 6 5 3 - 3 8 -64933 6 4 5 3 9 V 4 1 5 7 T«"3T4r 6 8 7 2 7 8 8 6 7 9 8 6 6 3 4 * B 5 9 T -8 8 5 5 0 8 8 5 1 1 • B T 4 7 - 3 -TABLE 4.5B The Numerical Values of P(a)/P(a=0) - 9 1 -s p l i t t i n g c o n s t a n t i s d e t e r m i n e d . The e x p e r i m e n t a l v a l u e s o f t h e h f s s p l i t t i n g c o n s t a n t a r e l i s t e d i n T a b l e s 4 .3 and 4 . 4 . - 9 2 -IV .5 S o u r c e s o f E r r o r  I V .5A D i s c h a r g e S t a b i l i t y One o f t h e more s e r i o u s p o s s i b l e e r r o r s i n t h e H a n l e e f f e c t e x p e r i m e n t came f r o m t h e e f f e c t s o f t h e t r a n s v e r s e m a g n e t i c f i e l d o n t h e d i s c h a r g e . In t h e a b s e n c e o f a t r a n s v e r s m a g n e t i c f i e l d e l e c t r o n s - o s c i l l a t e a l o n g a s t r a i g h t l i n e , p a r a l l e l t o t h e 450 MHz e l e c t r i c f i e l d . As t h e t r a n s v e r s e m a g n e t i c f i e l d i s a p p l i e d t h e p a t h o f t h e e l e c t r o n s t h e n g r a d u a l l y changes i n t o an e l l i p t i c a l o r b i t . '-T h e . r a t i o o f m i n o r a x i s t o ma jo r a x i s i s a l i n e a r f u n c t i o n o f t h e t r a n s v e r s e m a g n e t i c f i e l d ^ (Append ix A ) , - u h e r e B i s t h e a m p l i t u d e o f t h e t r a n s v e r s e m a g n e t i c f i e l d and co i s t h e a n g u l a r f r e q u e n c y o f t h e e l e c t r i c f i e l d u s e d to e x c i t e t h e e l e c t r o n s . I n t h e H a n l e e f f e c t measurement t h e maximum m a g n e t i c f i e l d was about 20 Gauss and ut = 211 x 450 MHz, so t h e r e s u l t i n g r a t i o o f -.-minor a x i s t o ma jo r a x i s o f t h e e l l i p s e was about 0 . 0 7 . In t h e computer LQF program f o r t h e h a l f w i d t h o f t h e L o r e n t z i a n c u r v e , t h i s e r r o r , i n t he f i r s t o r d e r a p p r o x i m a t i o n , has been i n c l u d e d i n t h e te rm A 2 X ( e q . 3 . 6 . 1 ) . H i g h e r o r d e r e f f e c t s c o u l d n o t c r e a t e more t h a n 2% e r r o r i n t h e measurements o f l i f e t i m e s . IV .5B M a g n e t i c F i e l d I nhomogene i t y A l l t h e m a g n e t i c f i e l d measurements have b e e n made w i t h a " " B e l l 2 4 0 " i n c r e m e n t a l H a l l p r o b e g a u s s m e t e r . L e s s t h a n 2 p a r t s i n 1.000 i n h o m o g e n e i t y o v e r t h e e n t i r e d i s c h a r g e c e l l was d e t e c t e d ( Sec . 3 . 5 B ) . The c a l i b r a t i o n o f t h e H a l l p r o b e gaus smeter was c h e c k e d w i t h a Magn lon F F C - 4 r o t a t i n g c o i l magnetometer . An e s t i m a t e d maximum 2% e r r o r c o u l d have r e s u l t e d f r om f i e l d i n h o m o g e n e i t y and c a l i b r a t i o n - 9 3 -; e r r o r s comb ined . T h i s w i l l g i v e n a 2% o f e r r o r i n a l l t h e measurements e x p e c t i n t h e m a g n e t i c r e s o n a n c e i n w h i c h a s h a r p r e s o n a n c e o f w e l l .known v a l u e can be u s e d t o l o c a t e t h e m a g n e t i c f i e l d a t w h i c h t h e r e s o n a n c e o c c u r s . TV .5C P r e s s u r e R e a d i n g s A n o t h e r m a j o r e r r o r c o u l d a r i s e f r o m i n a c c u r a t i e s i n t h e d e t e r m i n a t i o n o f t h e gas p r e s s u r e i n t h e d i s c h a r g e . As m e n t i o n e d i n s e c t i o n 3 . 4 , p r e s s u r e s were measured by two P i r a n i g auges , one i n t h e u p p e r steam o f t h e d i s c h a r g e c e l l and t h e o t h e r i n t he l o w e r s team. B o t h P i r a n i gauges were c a l i b r a t e d w i t h a 0 - 130 m i c r o n MacLeod gauge w h i c h c o n n e c t e d t o t h e s y s tem c l o s e t o t h e d i s c h a r g e c e l l . W i t h r 1:his a r rangement p r e s s u r e r e a d i n g s i s a c c u r a t e t o w i t h i n ±5% . F u r t h e r -m o r e t h e n a t u r a l l i f e t i m e s o f t h e u p p e r s t a t e s were i n v e r s e l y p r o -p o r t i o n a l t o t h e h a l f w i d t h o f t h e L o r e n t z i a n p r o f i l e a t z e r o p r e s s u r e , so t h a t o n l y t he r e l a t i v e p r e s s u r e was i m p o r t a n t . The i n a c c u r a c y i n t h e . p r e s s u r e r e a d i n g w i l l i n t r o d u c e an e r r o r i n t he l i f e t i m e m e a s u r e -ments o f l e s s t h a n 1% and an e r r o r o f 5% i n t h e c r o s s - s e c t i o n measu rement s . TV.5D The S t a r k E f f e c t B r o a d e n i n g I n t h e p r e s s u r e o f a s t r o n g e l e c t r i c f i e l d , S t a r k b r o a d e n i n g o f a L o r e n t z i a n p r o f i l e has been f o u n d f o r t h e h e l i u m 5'D s t a t e ( s e c . 4 . 2 ) . On t h e o t h e r h a n d t h e measured h a l f w i d t h o f L o r e n t z i a n p r o f i l e s o f h y d r o g e n m o l e c u l e s a t v a r i o u s e l e c t r i c f i e l d s showed no dependence on t h e s t r e n g t h o f t h e e l e c t r i c f i e l d ( F i g . 4 . 1 9 ) . T h i s shows t h e s t a r k b r o a d i n g i s n e g l i g i b l e i n t h e l i f e t i m e measurements i n m o l e c u l a r h y d r o g e n . T94-T V . 5 E D a t a P r o c e s s i n g E r r o r - A l l d a t a p o i n t s o b t a i n e d f r o m t h e H a n l e e f f e c t c u r v e s were punched on computer c a r d s by u s i n g an e l e c t r o n i c d i g i t i z e r . To t e s t t t he d a t a a n a l y z a t i o n p r o c e d u r e , two s e t s o f d a t a p o i n t s were o b t a i n e d i n d e p e n d e n t l y f o r s e v e r a l o f t h e c u r v e s . In e a c h c a s e t h e y y i e l d e d h a l f w i d t h s t h a t d i f f e r e d b y l e s s t h a n 0 .5% . T V . 5 F C o h e r e n c e N a r r o w i n g •When l i g h t e m i t t e d by one atom i s a b s o r b e d by a n o t h e r b e f o r e c l e a v i n g t h e d i s c h a r g e c e l l , t h e H a n l e e f f e c t s i g n a l w i l l b e " n a r r o w e r " - t h a n t h e l i f e t i m e wou ld i n d i c a t e , b e c a u s e t h e c o m p o s i t e s y s tem has a l o n g e r l i f e t i m e t h a n t h e i n d i v i d u a l m o l e c u l e . T h i s phenomenon d i d t n o t o c c u r i n t h e works r e p o r t e d i n t h i s t h e s i s , b e c a u s e t h e r e were no e l e c t r i c d i p o l e t r a n s i t i o n s t o t h e g r o u n d s t a t e n o r were t h e r e any m e t a s t a b l e s t a t e s i n t o w h i c h t o d e c a y . F u r t h e r m o r e , t h e p r e s s u r e i n t h e d i s c h a r g e c e l l was v e r y l o w ; t h e r e b y c o h e r e n c e n a r r o w i n g and a l s o c o l l i s i o n e f f e c t s were r e d u c e d t o a minimum i n t h e h e l i u m and - m o l e c u l a r h y d r o g e n l i f e t i m e measurements . IV .5G C a s c a d i n g E f f e c t C a s c a d i n g r e f e r s t o t h e a l i g n m e n t o f t h e l e v e l s i n w h i c h one i s i n t e r e s t e d , a r e a f f e c t by r a d i a t i v e t r a n s i t i o n s f r o m h i g h e r e n e r g y l e v e l s . Some o f t h e l i f e t i m e s measurements i n 2P s t a t e s o f A r g o n and Neon were f o u n d t o be s y s t e m a t i c a l l y too l a r g e due to c a s c a d e e r r o r s ( S e c . 4 . 3 , C 7 2 , K 6 6 , OV67 ) . C a s c a d i n g d i d n o t c a u s e a n i m p o r t a n t e r r o r i n t h e l i f e t i m e s measured i n t h e e x c i t e d s t a t e s (3D, 3 E , Z) o f h y d r o g e n . The r e a s o n s a r e a s f o l l o w s : a ) In t h e m a g n e t i c r e s o n a n c e e x p e r i m e n t t h e g - v a l u e s f o u n d a g r e e d t o - 9 5 -w i t h i n 1% w i t h t h o s e measured b y D i e k e e t a l (DCB53), B e l l . T e l . L a b (FM73bi MF71) and b y M a r e c h a l (ML74). A l s o , , no e v i d e n c e o f a d i f f e r e n t g - v a l u e b e l o n g i n g t o a h i g h e r s t a t e was e v e r f o u n d . Thus -any c a s c a d i n g must h a v e a r i s e n f r o m s t a t e s t h a t p o s s e s s e d i d e n t i c a l g - v a l u e s , w h i c h i s q u i t e u n l i k e l y i n t h e c a s e o f m o l e c u l a r h y d r o g e n , b ) A s c o n c l u d e d i n s e c . 4 . 3 , t h e c a s c a d i n g e f f e c t i s s t r o n g o n l y a t l o w e r p r e s s u r e s and t h e r e s u l t s o b t a i n e d a t l o w e r p r e s s u r e s i n 3D, 3 E , Z s t a t e s o f h y d r o g e n a g r e e d w i t h t h e h i g h e r p r e s s u r e m e a s u r e -m e n t s . I V .5H C o n c l u s i o n S i m p l y b y summing a l l t he p o s s i b l e e r r o r s w h i c h have b e e n m e n t i o n e d i n t h i s s e c t i o n and a l l o w i n g some random e r r o r , we c a n c o n -c l u d e t h a t t h e l i f e t i m e measurement s , i f f r e e f r om c a s c a d i n g and s t a r k e f f e c t s , a r e a c c u r a t e t o w i t h i n 5%. The measurement o f c r o s s -s e c t i o n , w h i c h depend i n a d d i t i o n on t h e d i r e c t measurement o f t h e p r e s s u r e i n a hynamic f l o w d i s c h a r g e , a r e o n l y a c c u r a t e t o w i t h i n 10%. I n t h e m a g n e t i c r e s o n a n c e e x p e r i m e n t , t h e Lande g - f a c t o r s were f ound f r om t h e m a g n e t i c f i e l d a t t he c e n t e r o f t h e r e s o n a n c e d i p . T h i s c an be d e t e r m i n e d v e r y p r e c i s e l y , s i n c e t h e f i e l d c a l i b r a t i o n c a n b e a c c u r a t e l y e s t a b l i s h e d u s i n g t h e w e l l known g - v a l u e o f 1.5 f r o m t h e s h a r p r e s o n a n c e o f t he 3 3 P s t a t e o f h e l i u m . Thus t h e Lande g -f a c t o r s a r e b e l i e v e d t o have l e s s t h a n 1% e r r o r . I n t h e r e p o l a r i z a t i o n e x p e r i m e n t t h e h f s c o n s t a n t was c a l -c u l a t e d f r o m t h e r a t i o o f a s m a l l change i n p o l a r i z a t i o n o v e r a l a r g e change i n p o l a r i z a t i o n . Due t o t h e n o i s e l e v e l t h e s m a l l p o l a r i z a t i o n change ha s a l a r g e r r e l a t i v e e r r o r so t h a t i s o n l y a c c u r a t e t o w i t h i n 10%. - 9 6 -Many o f t h e s p e c t r a l l i n e s s t u d i e d were f r o m t h e same u p p e r e l e c t r o n i c s t a t e ( F i g u r e 4.3 t o F i g u r e 4 .10 ) and so t h e o r e t i c a l l y s h o u l d have had i d e n t i c a l r a d i a t i v e l i f e t i m e s , c r o s s - s e c t i o n s , g - v a l u e s and t h e h f s c o n s t a n t s . E x p e r i m e n t a l l y t h e s e measurements were f o u n d to a g r e e w i t h e a c h o t h e r t o w i t h i n t h e a c c u r a c i e s q u o t e d a b o v e . - 9 7 -C h a p t e r F i v e DISCUSSION AND CONCLUSION The l i f e t i m e s o f t h e J = 1, 2 and 3 l e v e l s o f 3D0 s t a t e o f h y d r o g e n m o l e c u l e were f i r s t measured by Van Der L i n d e and D a l b y CVD69). T h e i r e x p e r i m e n t was ba sed on t h e H a n l e E f f e c t w i t h m o l e c u l e s e x c i t e d by e l e c t r o n s i n a R .F . d i s c h a r g e c e l l , as d e s c r i b e d i n s e c t i o n I I I . 2 , and y i e l d e d l i f e t i m e s T(J=1) = 26 .1 ( 1 . 2 ) , T(J=2) = 38 .3 (2 .0 ) and T(J=3) = 3 9 . 3 (2 .5 ) n s e c . I n d e p e n d e n t l y , M a r e c h a l measured t h e l i f e t i m e o f t h e J= l l e v e l w i t h t h e same e x p e r i m e n t a l method e x c e p t t h a t t h e e x c i t a t i o n s were made by a 30 e v . e l e c t r o n gun. Her e x p e r i m e n t y i e l d e d a l i f e t i m e o f 1 5 . 8 ( . 8 ) n s e c . I n M a r e c h a l ' s t h e s i s (M73), she s t a t e d t h a t t h e L o r e n t z i a n c u r v e i n Van D e r L i n d e ' s e x p e r i m e n t m i g h t be nar rowed by t h e c a s c a d i n g f r o m h i g h e r e n e r g y l e v e l s , bu t no r e a s o n was g i v e n t o e x p l a i n t h e f a c t t h a t t h e c a s c a d i n g e f f e c t d i d n o t a p p e a r i n h e r measurement s . A s d i s c u s s e d i n s e c t i o n IV .2 and I V . 5 G , t h e r e s u l t s o f my m a g n e t i c r e s o n a n c e e x p e r i m e n t showed t h a t t h e c a s c a d i n g e f f e c t i s n e g l i g i b l e i n t h e H a n l e e f f e c t l i f e t i m e measurements o f Hg. Becau se o f t h e l o n g a v e r a g i n g t i m e o f M a r e c h a l ' s e x p e r i m e n t , i t i s p o s s i b l e t h a t p r e s s u r e f l u c t u a t i o n s , t h e i n t e n s i t y changes o r o t h e r random e r r o r s w i l l c o n t r i b u t e t o t h e d i f f e r e n c e i n t h e l i f e t i m e measurement s . L i f e t i m e s o f 3D, 3E and Z s t a t e s o f H^ were a l s o measured i n t h i s work. The l i f e t i m e o f t h e J= l l e v e l o f t h e 3D s t a t e r e p o r t e d by M a r e c h a l was a g a i n f o u n d 20% l e s s t h a n our measured l i f e t i m e . Under t h e Born -Oppenhe imer a p p r o x i m a t i o n , t h e l i f e t i m e s o f a s t a t e depends p r i m a r i l y on t h e e l e c t r o n i c and v i b r a t i o n a l p a r t s o f t h e wave f u n c t i o n and o n l y v e r y w e a k l y on t h e r o t a t i o n a l p a r t o f t h e wave f u n c t i o n . V a n D e r L i n d e C V 7 0 ) n o t i c e d t h a t , i n t h e 3D0 s t a t e t h e r e i s more t h a n 40% d i s c r e p a n c y a p p e a r e d between t h e l i f e t i m e s o f t h e J = l s t a t e and t h a t o f t h e J=2 and 3 s t a t e s . T h e same k i n d o f d i s a g r e e m e n t was f o u n d i n t h e 3D0 and 3D1 i n ou r e x p e r i m e n t . T h i s d i s c r e p a n c y makes i t n e c e s s a r y t o r e - e x a m i n e t h e t h e o r y . I n t h e a n a l y s i s o f t h e H a n l e e f f e c t c u r v e s we have so f a r i g n o r e d the e f f e c t o f h y p e r f i n e s p l i t t i n g s . A s we d i s c u s s e d i n t h e m a g n e t i c r e p o l a r i z a t i o n e x p e r i m e n t , i n t h e a b s e n c e o f an e x t e r n a l m a g n e t i c f i e l d , t h e n u c l e a r s p i n I c o u p l e s -to J t o f o r m a t o t a l a n g u l a r momentum F . When a l a r g e m a g n e t i c f i e l d i s a p p l i e d t h e y become d e c o u p l e d and p r e c e s s s e p a r a t e l y about t h e f i e l d . T h e r e l a t i o n s o f t h e g - f a c t o r s , g , a t v e r y l ow f i e l d t o t h e h i g h f i e l d g - f a c t o r s g a r e c a l c u l a t e d a s f o l l o w s : F o r J - l , g F = hSj F o r J=2, 1=0, g F = g j F o r J=3 s t a t e , t h e g - f a c t o r g f o r F=2, 3 , and 4 a r e r e s p e c t i v e l y 4 /3 g T 11 /12 g and 3/4 g T t h e a v e r a g e g - f a c t o r o f t h e s e s t a t e s i s .95 g T . I f a » v „ , where v„ i s t h e n a t u r a l l i n e w i d t h , t h e n t h e above N N g v a l u e s s h o u l d be u s e d i n t he c a l c u l a t i o n o f l i f e t i m e s and i f a<<v , t h e n t h e h f s c a n be n e g l e c t e d . I n t h e c a s e o f t h e 3D s t a t e s o f H2 t h e l i f e t i m e s a r e about 30 n sec w h i c h y i e l d s a n a t u r a l l i n e w i d t h o f 5 MHz and t h e measured h f s c o n s t a n t s a r e a l s o about 5 MHz. T h i s i s t h e c a s e o f i n t e r m e d i a t e c o u p l i n g . The s e c u l a r e q u a t i o n s , f o r t h e c a s e J = l , were s o l v e d by V a n Der L i n d e . The s o l u t i o n , i n w h i c h t h e e n e r g y o f t h e Zeeman s u b -l e v e l s a r e e x p r e s s e d a s a f u n c t i o n o f m a g n e t i c f i e l d , i s shown i n F i g u r e 5 . 1 . The h a l f w i d t h o f t h e L o r e n t z i a n c u r v e i s e q u a l t o t h e m a g n e t i c f i e l d r e q u i r e d f o r t h e e n e r g y s e p a r a t i o n between t h e Zeeman s u b l e v e l s , t h a t c an i n t e r f e r e t o p r o d u c e l e v e l c r o s s i n g e f f e c t , e q u a l s t o t h e n a t u r a l l i n e w i d t h . I n ou r c a s e , w h i c h a = v^, t h i s h a l f w i d t h a l s o i s e q u a l s t o t h e h f s s p l i t t i n g c o n s t a n t a . I n F i g u r e 5 . 1 , s i x a r r o w s a r e shown, t h a t i n d i c a t e t h e r e a r e s i x d i f f e r e n t m a g n e t i c f i e l d s a t - w h i c h t h e above c o n d i t i o n i s f u l f i l l e d . The o b s e r v e d H a n l e c u r v e i s - t h e n t h e s u p e r p o s i t i o n o f s i x i n d i v i d u a l L o r e n t z i a n c u r v e s whose h a l f w i d t h s a r e g i v e n by t h e l o c a t i o n s o f t h e a r r o w s . I f t h e h f s s p l i t t i n g i s n e g l i g i b l e t h e h a l f w i d t h o f t h e L o r e n t z i a n c u r v e s i n t h e H a n l e e f f e c t e x p e r i m e n t i s e q u a l t o 1 uB/vp .(=1 y B / a ) . A s shown i n F i g u r e 5 . 1 , i t i s l i k e l y t h a t t h e m a g n e t i c h y p e r f i n e e f f e c t w i l l b r o a d e n somewhat t h e H a n l e c u r v e f o r J = l . A l t h o u g h t h e t h e o r e t i c a l e x p l a i n a t i o n i s s i m p l e , t h e n u m e r i c a l c a l c u l a t i o n s a r e c o m p l i c a t e d . I t may i n v o l v e d i f f i c u l t i e s i n t h e c a l c u l a t i o n o f t h e p o p u l a t i o n o f t h e Zeeman s u b l e v e l s o f t h e e x c i t e d s t a t e and t h e - t r a n s f e r o f t h e a l i g n m e n t f r o m t h e e l e c t r o n t o t h e n u c l e u s due t o 1 , J c o u p l i n g . U n f o r t u n a t e l y , t h e s e phenomena were n o t f o u n d u n t i l t h e , t h e s i s was a l r e a d y i n p r o c e s s . The d e t a i l e d t h e o r y has n o t y e t b e e n c o m p l e t e d . The h f s s p l i t t i n g o f t h e J = l l e v e l o f 3D0 s t a t e o f H 2 w a s f i r s t measured,rto be 6 . 3 ( . 6 ) MHz, by M a r e c h a l (M73). We r e p e a t e d t h i s measurement w i t h t h r e e d i f f e r e n t r a d i a t i v e t r a n s i t i o n s f r o m t h e same m o l e c u l a r uppe r s t a t e . Those e x p e r i m e n t s y i e l d v a l u e s o f 5 . 1 ( . 5 ) , 5 . 2 ( . 5 ) and 4. 8( .5) MHz f o r t h e h f s s p l i t t i n g c o n s t a n t . The a v e r a g e - 1 0 1 -v a l u e i s 20% l e s s t h a n t h a t r e p o r t e d by M a r e c h a l . T h i s d i f f e r e n c e , i s u n d e r s t o o d f r o m t h e e r r o r s i n h e r l i f e t i m e measurement o f t h i s s t a t e . A s shown i n T a b l e 4 . 3 , t h e measured h f s s p l i t t i n g c o n s t a n t o f t h e 3D s t a t e were f ound t o be i n d e p e n d e n t o f t h e r o t a t i o n a l quantum number J and v a r i e d o n l y s l i g h t l y w i t h t h e v i b r a t i o n a l quantum number S u m m a r y o f t h e a c c o m p l i s h m e n t i n t h i s t h e s i s The measured l i f e t i m e s o f many v i b r a t i o n a l and r o t a t i o n l e v e l s o f t h e 3D and 3E e l e c t r o n i c s t a t e s o f m o l e c u l a r h y d r o g e n has b e e n m e a s u r e d . The measured l i f e t i m e s o f v - 1 o f 3D s t a t e a r e i n agreement w i t h t h o s e measured b y Van Der L i n d e and D a l b y . The p o s s i b i l i t y o f c a s c a d i n g has been p r o v e n n e g l i g i a b l e i n t h e measurements o f m o l e c u l a r h y d r o g e n . The m a g n e t i c h f s s p l i t t i n g o f t e n r o t a t i o n a l l e v e l s i n t h e 3D and 3E e l e c t r o n i c s t a t e s were m e a s u r e d . The p u b l i s h e d v a l u e f o r one o f t h e s t a t e s has been f o u n d t o be i n agreement w i t h t h a t measured h e r e . Low m a g n e t i c f i e l d Lande g - f a c t o r 3D, 3E and Z e l e c t r o n i c s t a t e s were a l s o measured and f o u n d i n agreement w i t h t h e h i g h m a g n e t i c f i e l d measurements b y D i e k e (DCB53). The l i f e t i m e s o f t h e 2p s t a t e s o f neon and a r g o n were measured and f o u n d t o be i n agreement w i t h t h e most r e l i a b l e measurements (C72, BK66) . C a s c a d i n g was f o u n d t o be dominant w i t h e l e c t r o n i c e x c i t a t i o n . ' The l i f e t i m e s o f 3 ' D , 4 ' D , 5 'D s t a t e s o f h e l i u m were a l s o measured and f o u n d t o be i n agreement w i t h many r e l i a b l e measurements (FHJC64, MBBB70). The i n t e r a c t i o n o f t h e R . F . e l e c t r i c f i e l d and m a g n e t i c f i e l d s i n t h e measurement o f 5 'D s t a t e a t l o w p r e s s u r e were s t u d i e d . - 1 0 2 -, S u g g e s t i o n s f o r F u r t h e r Work :The t h e o r e t i c a l c a l c u l a t i o n o f t h e H a n l e e f f e c t i n t h e p r e s e n c e o f H y p e r f i n e s p l i t t i n g f o r t h e J = l l e v e l have t o be and w i l l b e s t u d i e d . The p e r c e n t a g e o f b r o a d e n i n g o f t h e L o r e n t z i a n p r o f i l e , t h e n , c a n be c a l c u l a t e d . The t h e o r y f o r t h e c a l c u l a t i o n o f t h e h f s c o n s t a n t o f t h e 3d - c o m p l e x (3d 'E,H,A) i s needed f o r t h e i n t e r p r e t a t i o n o f t h e e x p e r i m e n t a l r e s u l t s . T h e method u s e d i n t h i s t h e s i s f o r m e a s u r i n g t h e r e d i a t i v e l i f e t i m e s , t h e L a n d e g - f a c t o r , t h e m a g n e t i c h f s s p l i t t i n g c o n s t a n t s s h o u l d b e a p p l i c a b l e t o many s t a t e s o f many atoms and m o l e c u l e s , p r o v i d i n g t h e . s t a t e i n v o l v e d has a gx p r o d u c t i n t h e r a n g e 1 0 - 7 s ec t o 1 0 - 1 0 s e c o r - the m a g n e t i c h f s s p l i t t i n g i s l a r g e r t h a n 1 MHz. - 1 0 3 -A p p e n d l x A The d i s c h a r g e i s assumed t o c o n s i s t o f a d i l u t e gas o f n e u t r a l atoms o r m o l e c u l e s and a much s m a l l e r number o f f r e e e l e c t r o n s . In t h e a b s e n c e o f c o l l i s i o n s , t h e m o t i o n o f t h e e l e c t r o n s i n a r a d i o -A f r e q u e n c y e l e c t r i c f i e l d i E Q COS ojt and s m a l l p e r p e n d i c u l a r m a g n e t i c f i e l d H = H Q k , i s g o v e r n e d by m* = eEo Cos cot - e H ^ L e t V * — and }X ^ E q u a t i o n s ( A . l ) and (A .2) now t a k e t h e f o r m : S o l v i n g e q u a t i o n s (A .3 ) and (A .4 ) When X = 7f - 0 I m p l i e s A | - rtx ~ O ( A . l ) (A. 2) (A. 3 ) (A .4 ) ( A . 5 ) -104-. so t h a t (A .6 ) and 0 0 " - V " CA.7) S u b s t i t u t i n g e q u a t i o n (A.7) back i n t o e q . CA.4) T h e s o l u t i o n o f e q u a t i o n CA.8) i s : When £ = * J ^ ^ - 0 ^ p i i e s so t h a t (A .8 ) (A. 9) (A .10) E q u a t i o n (A .5 ) and CA.10) may be combined t o g i v e (A.11) E q u a t i o n (A.11) i s t h e e q u a t i o n o f an e l l i p s e where t h e r a t i o o f m i n e r a x i s o v e r t h e ma jo r a x i s i s - ^ °  - 1 0 5 -A p p e n d l x B L e t u s c o n s i d e r a f o u r l e v e l s y s tem |a>, |b>, |c>, and |d> a s shown i n F i g u r e B . l . T h e atoms a r e e x c i t e d f r o m g round s t a t e |a> t o a h i g h e r e x c i t e d s t a t e |b>. T h r o u g h s p o n t a n e o u s e m i s s i o n t h e y d e c a y t o an i n t e r m e d i a t e e x c i t e d s t a t e |c> and t h e n t o t h e l o w e r e x c i t e d s t a t e |d>. I f t h e atoms a r e e x c i t e d t o s t a t e |b> c o n t i n u o u s l y , and i f s t a t e |c> i s p o p u l a t e d o n l y b y r a d i a t i v e d e c a y f r o m s t a t e |b>, t h e n a s shown i n s e c t i o n ( 2 . 2 B ) , t h e s t a t i o n a r y s o l u t i o n o f t h e d e n s i t y m a t r i x o f s t a t e |b> i s g i v e n by Ji- r * - A. M y * L e t ^ ( - | -r * 13bjtio E q u a t i o n ( 2 . 2 . 2 2 ) now t a k e s t h e f o r m : ( 2 . 2 . 2 2 ) f = A H u - X H f I CB.D I f t h e d i r e c t i o n o f o b s e r v a t i o n i s c h o s e n a p p r o p r i a t e l y t h e p o l a r i z a t i o n , w h i c h i s p r o p o r t i o n a l t o t he r e a l p a r t o f t h e d e n s i t y m a t r i x , p i s b g i v e n : - 1 0 6 -P(H) oC I + Xv H where = -^ g— and AH^ i s t h e h a l f w i d t h a t h a l f maximum o f t h e L o r e n t z i a n c u r v e i n t h e H a n l e e f f e c t e x p e r i m e n t . F o r t h e i n t e r m e d i a t e s t a t e |c> t h e r e a l p a r t o f . p i s D p r o p o r t i o n a l t o R where ( A t f e x * H i ) C A H l b + HO I f s t a t e |c> i s a l s o c o n t i n o u s l y e x c i t e d f r o m t h e g round s t a t e |a>, t h e n i n t h e H a n l e e f f e c t t h e o b s e r v e d p o l a r i z a t i o n o f t he f l u o r e s c e n c e r a d i a t i o n f r o m s t a t e |c> t o s t a t e |d> o b s e r v e d i s p r o p o r t i o n a l t o P(H)-C ^ " a x l + . 1 , * c W . - 1 0 7 -BIBLIOGRAPHY A 7 0 H . J . A n d r a , P h y s . Rev . L e t t . , 2 5 , 325 ( 1 9 7 0 ) . A J S 6 9 L . A l l e n , D.G.C. J o n e s , D .G. S c h o f i e l d , J . O p t . S c o . Am. 5 9 , 842 ( 1 9 6 9 ) . B25 G. B r e i t , J . O p t . S o c . Amer. 1 0 , 439 ( 1 9 2 5 ) . B33 G. B r e i t , Rev. Mod. P h y s . _5, 91 ( 1 9 3 3 ) . B59 J . P . B a r a t , J . P h y s . Rad ium 2 0 , 5 4 1 , 6 3 3 , 657 ( 1 9 5 9 ) . B65 O p t i c a l P u m p i n g , R.A. B e r n h e i m , W.A. B e n j a m i n I n c . , P u b l i s h e r s " B73 P. B a l t a y a n , P h y s . L e t t . 42A , 435 ( 1 9 7 3 ) . BB52 J . B r o s s e l and F . B i t t e r , P h y s . R e v . 8 6 , 308 ( 1 9 5 2 ) . BG61 J . P . B a r a t and C . C o h e n - T a n n o u d j i , J . P h y s . Rad ium 3 2 , 3 2 9 , 443 ( 1 9 6 1 ) . BE71 M. Baumann and A . E i b o f n e r , P h y s . L e t t e r s 34A, 421 ( 1 9 7 1 ) . BK66 B e n n e t t and K u d l m a n n , P h y s . R e v . 1 4 9 , 3 8 - 5 1 ( 1 9 6 6 ) . BK67 K.A. B r i d g e t t and T . A . K i n g , P r o c . P h y s . S o c . ( L o n d o n ) , A 9 2 , 75 ( 1 9 6 7 ) . • C 7 l The H 2 W a v e l e n g t h T a b l e s o f G . H . D i e k e b y H.M. C r o s s w h i t e , W i l e y - I n t e r -s c i e n c e , " J o h n ' " W i l e y & s o n . C72 C . G. C a r r i n g t o n , J . P h y s . B: Atom M o l e x . P h y s . 51572(1972) CBD71 C. W. T . C h i e n , R. E . B a r d s l e y , And F . W. D a l b y C a n . 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