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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), 3 E ( 3 d n ) STATE OF ;  MOLECULAR HYDROGEN  by Cary Way-Theng C h i e n  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OP - PHILOSOPHY i n t h e Department of PHYSICS  We a c c e p t t h i s t h e s i s as conforming to the r e q u i r e d  THE  standard  UNIVERSITY OF BRITISH COLUMBIA August 1975  In p r e s e n t i n g t h i s  thesis  an advanced degree at the L i b r a r y s h a l l I  f u r t h e r agree  in p a r t i a l  fulfilment of  the requirements f o r  the U n i v e r s i t y of B r i t i s h Columbia,  make it  freely available  that permission  for  I agree  r e f e r e n c e and  for e x t e n s i v e copying o f  this  that  study. thesis  f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s of  this  written  representatives. thesis  is understood that  f o r f i n a n c i a l gain s h a l l  permission.  Department of The U n i v e r s i t y of B r i t i s h 2075 Wesbrook P l a c e Vancouver, Canada V6T 1W5  Date  It  < \ Columbia  C  A  copying or p u b l i c a t i o n  not be allowed without my  ii  ABSTRACT  This thesis describes the h y p e r f i n e techniques: tion  s t r u c t u r e constant  The Hanle e f f e c t ,  the l i f e t i m e ,  the Lan.de g - f a c t o r  r e s u l t s from t h r e e major  the magnetic  and  indpendent  r e s o n a n c e , and t h e r e p o l a r i z a -  experiments. The Hanle e f f e c t ( Z e r o - f i e l d l e v e l c r o s s i n g )  measure the l i f e t i m e s o f the 3D excited)  ( 3 d ^ I T ) and Z (3*k d o u b l e  the 3 D,  (Paschen n o t a t i o n )  1  4 D, L  and 5 lD  states  s t a t e s o f a r g o n and neon.  s t a t e s were e x c i t e d by e l e c t r o n e x c i t a t i o n i n a 450  radio-frequency or S t a r k  1  s t a t e s of m o l e c u l a r hydrogen,  of h e l i u m , and the 2p The upper  ( 3 d ! ) , 3E  has been used t o  electric field.  Where f r e e of any c a s c a d i n g  e f f e c t , the l i f e t i m e measured were a c c u r a t e  The p r e s s u r e also reported  MHz effect  to w i t h i n  5%.  b r o a d e n i n g c r o s s - s e c t i o n s f o r the above s t a t e s have been i n this thesis.  By t h e r e p o l a r i z a t i o n experiment  some of t h e h f s  constants  of 3D and 3E s t a t e s of hydrogen have a l s o been measured t o w i t h i n In the c a l c u l a t i o n of l i f e t i m e s , some o f r e q u i r e d  Lande  g - f a c t o r s were measured by the magnetic resonance experiment and by t h e Zeeman e f f e c t i n a 27,000 gauss magnetic  field  10%.  some  i n this lab.  iii  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 E f f e c t  2  1.3  The E l e c t i o n E x c i t a t i o n  3  I.A  The Magnetic Resonance Experiment  3  1.5  The Magnetic Repolarization Experiment  4  Summary of the Results  ^  Notation of the Molecular Hydrogen  H  -1.6 1.7  .<Chapter Two  THEORY  I I .1  Introduction  11.2  Theory of the Hanle E f f e c t  1  4  ^ 1  4  II.2A  C l a s s i c a l Approach  II.2B  Quantum Mechanical Description  19  Theory of Magnetic Resonance Experiment  27  11.3  ^  II.3A  C l a s s i c a l Approach  ^7  II.3B  Quantum Mechanical Description  ^8  11.4  Theory of Repolarization Experiment  3  4  11.5  Summary  3  6  3  8  Chapter Three  THE APPARATUS  III.l  Experimental Arrangement  3  8  III..2  The Light Source and I t s Power Supply  4  0  III.3  The O p t i c a l System  ^  iv  III.4  Tha Vacuum System  45  III. 5  The M a g n e t i c F i e l d  47  III.6  Signal Processing  53  EXPERIMENTAL RESULTS  C h a p t e r Four  57  IV. 1  Introduction  IV.2  The Lifetime Measurements of 3'D, 4'D, and 5'D States i n Helium ...  IV.3  57 58  The Lifetime Measurements of 2P States i n Argon and Neon  IV.4  .  ..  65  The 3D(3dT), 3E(3d»n) andZ(3'K) State of Hz .  IV.4A  The Lifetime Measurements  69 .'.  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 i n 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  Chapter Five Appendix A  ,  - 94  DISCUSSION AND CONCLUSION  96  The Path of the Electron i n the Hanle Effect Experiment  «  Appendix B The Cascading Effect BIBLIOGRAPHY  «  101 103 105  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 i n the Repolarization Experiment  '•'vi  ILLUSTRATIONS AND  F i g u r e 1.1  The Arrangement  FIGURES  o f t h e Hanle  Experiment  1.2  The S i n g l e t  S t a t e s o f Helium  1.3  The 2P and 2S S t a t e s o f Argon  1.4  The 2P and 2S S t a t e s o f Neon  1.5  The S i n g l e t S t a t e s - o f -Molecular^H^drogen  2.1  The Damping R o s e t t e s  2.2  The T h e o r e t i c a l Hanle E f f e c t  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" L e v e l  2.5  The E u l e r A n g l e s  2.6  The C l a s s i c a l P i c t u r e o f t h e M a g n e t i c Resonance Experiment  2.7  The Quantum M e c h a n i c a l P i c t u r e o f the M a g n e t i c Resonance Experiment  Curves •  System  Curves  3.1  The Apparatus  3.2  The S t a t i c M a g n e t i c F i e l d  3.3  The D i s c h a r g e c e l l and i t s Power  3.4  The R o t a t i n g  3.5  The Vacuum  3.6  The Power Supply f o r t h e S t a t i c Magnetic  3.7  The Power Supply f o r t h e R.F. M a g n e t i c  318  The P h o t o m u l t i p l i e r W i r i n g Schematic  4.1  M a g n e t i c Resonance Experiment Curves i n Helium  4.2  Zeeman E f f e c t  4.3  The H a l f w i d t h v e r s u s the Power o f t h e R.F. e l e c t r o n i c  4.4  M a g n e t i c Resonance Experiment  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 L i n e  Coils Supply  Polaroid  System Fields  Field  States  i n the Presence of the S t a r k E f f e c t Field  on 6267A L i n e o f Neon  vii  F i g u r e 4.6  L e a s t Squares F i t t e d Curves f o r 3D0  2B0  RO  4.7  Hanle E f f e c t 3D0 S t a t e  Curve H a l f w i d t h as a F u n c t i o n of  Pressure  4.8  Hanle E f f e c t . 3D1 S t a t e  Curve H a l f w i d t h as a F u n c t i o n of  Pressure  4.9  Hanle E f f e c t Curve H a l f w i d t h as a F u n c t i o n o f P r e s s u r e 3D2 S t a t e  4.10  Hanle E f f e c t 3D3 S t a t e  4.11  Hanle E f f e c t Curve H a l f w i d t h as a F u n c t i o n of P r e s s u r e Z2 S t a t e  4.12  H a n l e E f f e c t Curve H a l f w i d t h as a F u n c t i o n o f 3E.0 S t a t e  Curve H a l f w i d t h as a F u n c t i o n of P r e s s u r e  Pressure  D  4.13  H a n l e E f f e c t Curve H a l f w i d t h as a F u n c t i o n o f P r e s s u r e 3E 0 S t a t e a  4.14  H a n l e E f f e c t Curve H a l f w i d t h as a F u n c t i o n o f P r e s s u r e 3E 1 S t a t e a  4.15  The M a g n e t i c R e p o l a r i z a t i o n Experiment C u r v e s  4.16  The P l o t s o f P(a)/P(a=0) v e r s u s  5.1  Zeeman E f f e c t  a/F  i n the Presence of Hyperfine  Splitting  viii  ACKNOWLEDGEMENT  I would l i k e  to take t h i s o p p o r t u n i t y to s i n c e r e l y  my r e s e a r c h s u p e r v i s o r , D r . F. W. Dalby encouragement, c l e v e r the c o u r s e o f t h i s I  f o r h i s continued  thank  guidance,  s u g g e s t i o n s , and h e l p f u l d i s c u s s i o n s  throughout  project.  would a l s o l i k e t o thank Dr. J . Van Der L i n d e f o r h i s  s u g g e s t i o n s and t h e s t i m u l a t i n g d i s c u s s i o n s a t t h e b e g i n n i n g o f t h i s project.  My thanks  his efficient  a r e a l s o extended  s o l u t i o n to i n t e r p r e t  t o P r o f e s s o r M.H.L. P r y c e f o r  some e x p e r i m e n t a l problems.  The  t e c h n i c a l . a s s i s t a n c e s of t h e machine shop,.Mr. J . L e e s and Mr. E . W i l l i a m s , a r e v e r y much a p p r e c i a t e d . I  would a l s o l i k e t o thank t h e members o f my committee,  D r s . A . J . B a r n a r d , J.W. B i c h a r d and,G. Jones f o r r e a d i n g my and  o f f e r i n g many v a l u a b l e s u g g e s t i o n s .  D r s . J.G. B u r n e t t and G. Copley.and  thesis  Thanks a r e a l s o extended t o  my w i f e f o r t h e i r h e l p t o complete  t h i s t h e s i s ; and a l s o t o Mrs. D i a n e Boyd f o r h e r t y p i n g . T h i s r e s e a r c h p r o j e c t was supported from t h e N a t i o n a l R e s e a r c h C o u n c i l .  by a r e s e a r c h g r a n t  -1-  Chapter One 1.1  INTRODUCTION  Introduction  The measurement of the radiative lifetimes and c o l l i s i o n 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  i s given by Stroke (S66). .^Whilea.;Variety»o£,-»techn;L,qu.es are available for the measureu  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 d i f f i c u l t i e s in the days before adequate photomultiplier tubes became commercially available.  The Hanle effect, which i s nothing  more than a special case of level-crossing (the levels referred to here are the Zeeman sublevels) at zero magnetic f i e l d , 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). i t i s particularly effective for lifetimes in the 10~  8  to I O  Secondly, -9  second  range where other techniques also independent of vapor pressure begin  -2-  to lose their accuracy.  1.2  The Hanle Effect In 1922,Rayleigh  H  (R22)  discovered that the 2537A* fluorescence line of mercury, excited by polarized resonance radiation, was polarized i f viewed at right angle  LAMP  to the exciting beam. Wood and POLARIZER  Ellet (WE23) investigated this effect further and found that at low pressures and i n the absence of magnetic fields, the emitted radiation was almost completely  Fig. 1.1  polarized, with i t s electric vector parallel to that of the exciting light.  Hanle (H24) performed a more  thorough investigation and found that the application of a magnetic f i e l d 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 i s given by the expression (sec. 2.1)  P(H) P(0)  =  1 1 + (gT yoH)  (1.1)  z  where H i s the applied magnetic f i e l d , x i s the mean lifetime of the excited state, yo g-value.  i s the Bohr magneton  O-^)  »  a n <  *  8 I  ^ ^  s fc  e  a t l  ^  e  -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 i s 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 i n order to measure the Lande'  g—factor, a magnetic resonance experiment was "also performed. The magnetic resonance experiment mentioned here i s equivalent to an optic double resonance experiment except that the f i r s t resonance i s by electron excitation. introduced into the P 3  1  The double resonance method was f i r s t  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 f i e l d (Fig. 2.7) was subjected to bombardment by a beam of electrons moving perpendicularly to the RF magnetic f i e l d . 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 i s 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 f i e l d .  Precise information  about g-values can be found by noting the magnetic f i e l d 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 i s  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 i s about 10 ev.  which i s 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 f i e l d curve whose width i s determined by the fine or hyperfine splitting and the lifetime.  Whereas in the  magnetic resonance and level crossing techniques, the fine or hyperfine splitting i s given by the magnetic f i e l d 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 f i e l d , unlike the transverse magnetic f i e l d used in the Hanle effect w i l l not cause the electric dipole of the excited state to precess but w i l l 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, i t s usage has been limited in the past. Recently a modified repolarization method has been used in a l k a l i atoms (GCH72) to measure hfs which i s much larger than the natural width, by f i t t i n g theoretical  -6-  and experimental curves in which J and I were decoupled through cascading from higher levels. the product a.r lifetime.  ;  The original repolarization technique only gives  Where a i s the hfs splitting constant and T i s the  Marechal and Lombard! employed this original technique  on t h e 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,  i n the 3D and v=0, 1, i n the 3E states of molecular hydrogen are given i n Tables  (4.3)  and  (4.4).  We w i l l 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 f i e l d than at higher longitudinal magnetic f i e l d , and the spin 1=0 states are not found to change polarization i n different magnetic fields.  At zero magnetic f i e l d I and J are coupled and  through this interaction, aI«J, the alignment of the electronic Zeeman sublevels i s partially transfered into an alignment of nuclear Zeeman sublevels (Fig. 2.7).  As the longitudinal magnetic f i e l d i s applied,  \t and J are decoupl8.d, no alignment transfer can occur and the polarization w i l l 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 w i l l be found in the next chapter and the results are given in chapter four. 1.6  Summary of the Results  Helium i s the simplest stable atom and most of the data i n helium have been measured with the highest precision.  The lifetimes  -of 3'D, 4'D>and 5'D i n helium, have been measured in the lab by using  FIGURE  1.2  The S i n g l e t S t a t e o f 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 i s given in Fig. 1.2 and the results of the measurements w i l l be found i n 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 i n section IV.2. Lifetime measurements of the excited states in argon and neon have surged because of interest i n shock tubes, high arcs and laser  temperatures  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 i s given in Figure 1.3 and of neon i s given i n 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 i s 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 i s given i n section IV.3.  Accurate measurements of the properties of H 2 are of importance because i t i s the simplest neutral molecule and so a detailed theoretical interprelation can be formulated to compare with the data.  For this  -9-  c Q)  •t 5o Q.  2P1 2P2  2P3 2P4 2P5 2P6 2P7 2P8 2P9 2P10  inf» f n H VO HN rtOO h  oo •  t~ •  tn i n fHO ^ Ol  co r ~ '  •  •  •  rf rH  rr n u ) T n IN H t-»0400 r H C O r ^ r IO <J rH O i n m CM r r  vo r -  co co co r - r ~ r » r »  I  f  FIGURE 1.3  I  i  l  co M  T  r - cr. r~ r »  r - i co r r  m  C N O V O O  i n r r (N i n co co co r—  l  The 2P and 2S S t a t e s od Argon  L-S J 0 1 2 1 0 2 1 2 3 1  L s  p p p p D D D D S  2S+1 • 1 3 3 3 1 1 3 3 3 3  -10-  L-S  *  I — — — — — — — — — —  m  in m  r»  o n t— cn CM o oo o  o  invovovovDvovovorvo vo vo vo  vo vo o m  r - l CM IT) •"3"  vo vo vo t * »  mcntnr-f-ioitNr-co  M l / H O k O t ^ O l O H O  mvovovovovo[~r~co  tt  OO O O  FIGURE 1 . 4 The TBe 2 P and 2 S S t a t e s o f NEON  2P1 2P2 2P3 2P4 2P5 2P6 2P7 2P8 2P9 2P10  J 0 1 2 1 0 2 1 2 3 1  L » S P P P P D D D D S  I 3 3 3  1 1 3 3 3 3  -11-  reason this thesis concerns i t s e l f primarily with the measurements in hydrogen. The Hanle effect has been used to determine the of 3D(3d'E), 3E(3d'n) and Z(3'K) states of H2.  lifetimes  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 i n Figure 1.5.  A l l the notations for the electronic states used in this  figure are from Dieke (C70) and summarized i n 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 i s 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 i s understood, i f i t i s 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  —  CM  sf- cvi  O H  > M  C  i  l  o  II  >  l  I  II  II  TJ  O  CVJ—  II >  i  O  II >  III  ro  —  OCM  O  II >  c  II >  III  "-a  I  XI'  ,——»  CVJ —  r  O  ^-rocvj  II  c  [ i  "a.  i  Q.  ro  ^J-  —  o  II i  r  Q. CVJ  O  CVJ  II  10  ^  M  i  A  CM  —  II  l  CJ.  ro O  <fr  l  1  .  •_  <o  i  o £ — u  FIGURE  1 1 -+—  II 1 1  :  CM  1 — —  —  1.5  II  T  The  1  1  CL  cvj O  CM  II  <s  O  CM  II  o —  r I—  cn  o  S i n g l e t S t a t e s o f M o l e c u l a r Hydrogen  1  1  -13-  a, b, c, d, e, f are used for the triplet states s E, p £, 3  3  p n, 3  d Z, d II, d A respectively. The letters T, U, V, W, X, Z are used 3  3  3  for doubly excited states and again i t i s 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 II.1  THEORY  Introduction  In this chapter, the classical and quantum mechanical theory of the Hanle effect w i l l 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 i s given in section 2.4.  A l l the equations which w i l l be needed i n the  calculation of the results are enclosed in boxes and a summary of the usage of these equations i s given in section II.5.  II.2 II.2A  Theory of the Hanle effect  Classical Approach: In order to explain the fact that when the radiation i s  observed in the direction of magnetic f i e l d (Z-direction), i t becomes depolarized with increasing f i e l d , i t i s sufficient to adopt the classical model of a damped oscillator.  If the oscillator i s excited  in the X direction i t w i l l start to vibrate parallel to the X-axis, but w i l l precess about the magnetic f i e l d , i t s amplitude of oscillation dying down with time due to damping.  The path described by the precessing  oscillator when viewed along the f i e l d w i l l take the form of a rosette. In a strong magnetic f i e l d , i f the precession period Is much less than the damping time, the rosette w i l l be symmetric as shown in Figure 2.1A. It Is clear that the  light from the oscillator w i l l show no linear  polarization i f observed along the magnetic f i e l d .  On the other hand,  i f the damping time i s of the same order of magnitude as the precession period, the motion of the oscillator w i l l be as i n Fig. 2.IB and Fig. 2.1C, in which case the rosette i s incomplete and shows asymmetry.  -15-  Thus the resulting resonance radiation w i l l be partially polarized. If the exciting radiation i s polarized with i t s electric vector i n the X-direction, the excited atom or molecule can be replaced by an electric dipole which possesses an angular momentum L perpendicular to the dipole axis and a magnetic moment y=yL, where y is the gyromagnetic ratio.  If, however, a magnetic field H = Hz K i s placed  along the z-axis the dipole precesses about the z-axis with angular velocity oi = y H , so that z  u  A  /H*  Ui  = 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 w i l l not remain in i t s 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  i (t)= x  i co5a((j40  <t>)  e" Vc t/r  ( 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 w i l l be the average value from 0 to T and T i s the time constant in the measuring equipment•.  Since T>>x  -17-  and both the I ( t ) and the I^(t) are exponiantial functions. The x  averaged signals are  I, = iU  r f f j l ^ t )  d t  - T C I I M  D  T  T —> CO  (2.2.3) The polarization P(<fvH) i s then defined as  9(4, H) - Ix -ly Jo e  (2.2.4)  When evaluated this gives  P  ^>  )  H  =  -  (Qos^-2KHlSln2<f>)  T  (2.2.5) For the special case of <J>=0 this reduces to  P(H)  =  P(0)  / I+(2XIHZ) X  (2.2.6) which i s just a Lorentzian line shape.  If  i s the magnetic f i e l d  required to reduce the polarization to half i t s maximum value, then  (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 casety= IT/4  P(H) P(0)  _ -2MHZ (2.2.8)  FIGURE  2.2  The T h e o r i c a l Hanle E f f e c t  Curves  -19-  the resulting curve i s 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 w i l l f i r s t be given ( H 7 2 , 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 •operator i s P = atomic state.  fjj-Tr(p).  Thus the polarization  p-^Tr(p) where N is the number of the sublevels i n the  The polarization operator i s always traceless; i t s  diagonal matrix elements are called population excesses and i t s offdiagonal components <u|p|v> are called coherences between the level u and  v.  -1  Case  Polarization  (£>  None  (b)  Dipole  —o  <£>  Quadrupole  -v—0  N.  u  A  • < • >  - •  O .»  0 f\  •1  0  f\ n V  Fig. 2.3  0  0  u 1  o  fi  KJ  u  u u n  vj  o  V  - 2 0 -  In terms of spherical basis operators, a multipole polarization can be represented by the tensor operator P" where k i s the rank of the tensor and q i s the component.  The f i r s t 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 i s an iso-  tropic distribution, there are two atoms in each one of the three ~ 1 » 0 > 1 > with no polarization.  states nip  =  The only non-zero character  i s t i c s of this state i s i t s population and i t s density matrix is a tensor of rank zero.  In case (b) there i s 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 i s 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 i s said ->-  to be oriented.  The orientation vector 0 ^ can be represented by i t s  elements0^ = |<i'|j |i>| where q = 1 , 0 , - 1 . In case (c), there i s 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 i s said to be aligned and the alignment tensor is a second rank spherical tensor which can be represented by the elements  A  =\<<l  3^-J /^//j(j /) J  +  •= |< VI ± J, 3j i J 3,1 i > l / j u o  A and  0  3  A i = l<^'l * Jx" + 2  +  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 , J^, J a  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> i s 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) i s (M61)  7 = - T $ - l < b i 2 t  -p/c>/ acLn (2.2.9)  e 1 ->where a - TT,—r^r = T^=T i s the fine structure constant and P = Zer. 4lle hC 137 i o 2  i s the electric diapole operator.  The total intensity from state  |b> to state |c> and with polarization vector  e%  ^  \\rr\y  iSl  is  (2.2.10)  -22-  where I = e o ) / 8 I I C o 2  2  2  3  and b b , mm  are the elements of density matrix  p describing the ensemble of excited atoms. b I t i s also convenient to introduce a measuring operator M which contains information about the p o l a r i z a t i o n of the spontaneous emission  M C e j ) =Z et - ?lJcM>< j n ) itc  r (2.2.11)  n  A f t e r summing over the excited atoms of the ensemble one f i n d s that the instantaneous fluorescent i n t e n s i t y i s  I  f  e  ) c f J 2 = l X ,<™'IJ>lt«x™lrf!>«'?clJl e  = I. T  r  { f hi} JJl (2.2.12)  I t i s convenient to expand the density matrix i n terms of i r r e d u c i b l e tensor operators which act only on state vectors i n the subspace spanned by  |j^m>  (K)  The operators T  , are normalized by requiring that the reduced matrix  element be given by  <T  B  il t\\\  l  and the components of 2  b  }  = (afttir  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 ' >  i s the modulus of the reduced matrix element k  of the dipole operator and <j>^ i s a tensor which specifies the polarization of exciting radiation  Where the eq are the components of 1 i n 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  Where  tf  Q  = (-j)  +J  +  /  I  I  I  */ (2.2.18)  In the presence of magnetic f i e l d H the density matrix of the excited state p satisfies Liouville's equation  ir=*[x,f]-rf*r f" M  )  (2.2.19)  -24-  Where the Hamiltonian  J\t  ~  J j ^ * 0  '{  J  r  describes the relaxation  process of excited atoms i n a gas owing to collisions with atoms in the ground state,  i s the pumping rate and  i s 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 f i e l d and also the direction of the incident electrons and the y'-axis the direction of observation, then the Hamiltonian i n eq. (2.2.19) can be written as  %  =Mo3j  HJ3>  =<0 Jy o  (2.2.20) Making use of the expansion i n equation (2.2.13), the orthogonality of T , and the commutation relation K  q  f  u  J»  7"^ 7  ,  g  =  £ ^  g.  -i  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 i s 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°O 0  • r\  i o  •T.O (2.2.23)  and  r*  - r *  r  4 0  ' * -  r"'  (2.2.24) In the Hanle effect experiment, the magnetic f i e l d was perpendicular to the direction of the incident electrons, so that a rotation of 90° about y' Is necessary.  R(0,n/2,0) i s the rotation  operator (E58). After the rotation we c a l l the axis of the magnetic f i e l d 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 ^ o ,10)  )  after rotation i s ox  2.  (2.2.26) From equations (2.2.22, 23, 24, 25, 26), that eq. (2.2.19) w i l l take the form  -26to)  (2.2.27) In (D65) the following values of 4^ are given  3o and  2< <^ (2.2.28)  Where the angles o and 4 are defined i n Figure (2.15).  A3  Fig. 2.15 As shown i n Fig. 2.15,  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 i s  If  i s the magnetic f i e l d required to reduce the polarization to  half i t s maximum value, then  %  ---TIT-  o r  r  ^ r  =  S^U.H*  which agrees with the classical result, eq. (2.2.7).  II.3 II-3A  Theory of Magnetic Resonance Experiment  Classical Approach If an atom having an angular momentum J, i s placed in a  magnetic f i e l d H , then the magnetic moment y = u J w i l l precess around q  H  q  with a Larmor angular frequency O) = y g j H q  magnetic field  o  Suppose that a weak  o<  i s applied at right angles to H , and rotates around q  \\  i t at an angular frequency  9  ,  as shown in Fig. 2.6. If the angular frequencies ui^ and u>  o  \&/  differ appreciably, then the effect  ^ ^1  of the rotating magnetic f i e l d  Fig. 2.6  w i l l be negligible.  However, i f  to = ui , due to the action of the f i e l d H. the angle of precession 1 o' 1 &  r  w i l l then be changed. If the magnetic f i e l d H at which the resonance occurs i s q  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, i s placed i n a magnetic f i e l d H , each energy level w i l l split into 2J+1 equally q  spaced sub-levels, (Figure 2.7a,b).  To a f i r s t order approximation  the energy separation, E , i s given by: m  - mMoJH  Em  0  -  m  u) -Pi 0  (2.3.2) where m i s the magnetic quantum number J>m>-J. The periodic magnetic f i e l d , H^cosw^t induces magnetic dipole transitions between adjacent energy levels (Am = ±1) provided this f i e l d i s perpendicular to H and i f the resonance condition i s satisfied (Fig. 2.7C). have  Q  Thus we  . . .  Bm  -  Ew .  / ~ LOo £ = u)i "fi (2.3.3)  This requirement i s identical with the classical condition equation (2.3.1).  In 1937, the transition probabilities for these induced  transitions were f i 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 m =  b MAGNETIC FIELD (H) HA  o C ^—  V  N fc!  < r^f  o  CL w  ,=«V=^ gjH 0  FIGURE  2.7  (  Magnetic Resonance Experiment  +2  -30-  0  r?fTMi=  ^  r  i  u ) , >  w  1  io, (r -KA), +4AiA)') a  aL  3  ( r +4 u), + 4 * w\) (r +u), * A io ) 1  a  3  1  a  (2.3.4) Where Au = u g_|oj ,-o> I and T i s the lifetime of this state from which o J 1 o 1  1  the radiation i s emitted.  As shown i n Fig. 2.8;R(J.H) represents the  bell-shaped curves. It i s 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 i s 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 f i e l d H can be expressed as  H *  ft  t  M,CoS cot  ^/SifliOt (2.3.6)  where H  Q  and HI are the amplitudes of the slowly sweeping magnetic  f i e l d and the periodic magnetic f i e l d , respectively. By substituting the equation 2.3.2 into eq. 2.3.1 the Hamiltonian  g = l.5  0  10  20 , MAGNETIC  FIGURE  2.8  30  40  FIELD (Gauss)  Magnetic Resonance Experiment Curves  50  -32-  %  -  L0 o  + 10, ( j " x C o s « A ) t +  -  u) ^ #  +  u) (e  I t t >  (  = u).3,+ u). ( e  Z^n\tit)  *3 +e-  f M } t  +  X a ) t  3  + +  e-  i)'  f u ) t  jj (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, l e t  (2.3.10) Equation 2.3.9 w i l l then take the form  -^Jiwjrt^o  l i + r » *  r *  -r}  ff].o (2.3.11)  -33-  This i s a set of time independent solutions.  When k = 0, t h i s describes  an i s o t r o p i c population d i s t r i b u t i o n of the magnetic sublevels and eq. (2.3.11) becomes  (2.3.12) When k = 1 the population d i s t r i b u t i o n i s oriented and eq. (2.3.11) becomes  < *>f ;> -  to*  (  t  r, (2.3.13) When k = 2 the population d i s t r i b u t i o n f o r the magnetic sublevels i s aligned and i n t h i s case equation 2.3.11 becomes a  :  33 1W,*(44Wr.»-W**r 0 , ^ ( 4 - ^ 4-10," + r 1 )x )  | "  - C l - R O ,  ~] r-(o)  j>i°)2  H ) J  ( 2  .3.  1 4 )  As we have shown i n (sec. 2.2.B) the p o l a r i z a t i o n of the resonance radiation  (2.3.15)  J  were A^ and A  2  are function of j ,  so that  A,r «>)<> 0,  o  L  A;r_ v f ,  r„  , a  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 l = : u H M  can be calculated from the equation g  0  , in agreement with the Q  classical explanation eq. (2.3.2).  II.4  Theory of Repolarization Experiment  At zero magnetic f i e l d , through the interaction Hamiltonian a*I.J, the alignment i s partially transfered from the electronic Zeeman levels to the nuclear Zeeman levels.  As the magnetic f i e l d  increases, I and J w i l l be decoupled, and the electronic Zeeman levels are repolarized.  From the change i n 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' f  o) to)  (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  FF  V| (2.4.2)  and in the basis of |j>|l>  -35-  r-i"'f{(^"rj). • (2.4.3.) The relation between  FF'  k  p and  T T'  k  p  i s (MJL72)  The intensity of dipole emission with polarization vector eq i s then (ML74)  O  K  =  (-0  C  U  *  +  I  )  U  F  +  O U F ' + I ) ]  j j j ,J 3  33e  37  (2.4.5) In the case of zero magnetic f i e l d the stationary solution of the Liouville equation i s  h  ,  "  l  -  •FF'  S I  P  F  >  -  \  rFtF+O-FfFVOj (2.4.6)  The polarization PCa) at zero f i e l d i s  POO(2.4;7) As shown i n Fig. 2.2.5 and sec. 2.2. B  -36-  Xj  F o r  9 - 0  ;  (2.4.8)  Ix  For  e *i * = 0  ,  t  ^ . . J -  (2.4.9)  From eq. (2.2.4, 5, 8, 9), we have  i  i ^ a = o,  Men,  tr.*+r,)tji  J1  F F  .  ;  o  '= 0  r bFfi)UF'+<) r F r ' $ 7 * (r»+r)*  PCa)  I 3 j 1 j (r.+r; +-T2 /  P ( ^ o ) £ , • v x +i  v  P  where  F F  Jlp * F  =. - | - f  FF  F(F+0  ~  (2.4.10)  F V F + O J  Once the ratio P(a)/P(a=0) i s 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^, i s 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  -37-  o f the Lande g-factor, g , can be deduced from equation (2.3.2) provided that the magnetic f i e l d 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 i n 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 i s the reciprocal of the lifetime, i s obtained from the Hanle effect experiment.  -38-  Chapter Three III.l  THE APPARATUS  Experimental Arrangement  A block diagram of the apparatus i s 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 i n Fig. 3.1, light emitted from the light source i s focused by a pair of lenses onto the entrance s l i t of the monochromator.  Light appearing at the exit s l i t of the monochromator  f a l l s on a photomultiplier  whose output i s fed into the signal channel  of a lock-in amplifier. Between the two lenses the light i s passed through a polaroid which has i t s plane perpendicular to the beam and i s rotated about the x-axis.  The polarized component of the light i s 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 i s 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 i s placed i n the beam of radiation, just before the entrance s l i t of the monochromator, to reduce polarization 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 f i e l d  in the longitudinal and transverse directions (Figure 3.2), the medium  V  plate  4  Rotating  Polaroid  ^  "  Mono  _ . Ecosi/t  chromator  >MA  Signal  Light Source  Reference Signal  Lock in Amp. t To Helmholtz Coils  Averager  X-Y  ^ 3 -  axis of observation  T H E  Recorder  Field Sweep  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 f i e l d .  III.2  The Light Source and Its Power Supply  The light source i s a discharge c e l l which i s made of a horizontally placed pyrex glass tube 1" i n diameter and 1 1/8" long. Both ends are sealed and the c e l l i s connected to the vacuum system by two 5 mm pyrex glass tubes as shown i n Fig. 3.2 and Fig. 3.3. Two circular copper disks of 2" diameter are placed one on each end of the glass c e l l , the plates lying parallel to the axis of observation. The output of a 450 MHz radio frequency transmitter i s coupled to these plates i n such a manner that the R.F. electric field i s perpendicular to the copper plates.and has i t s maximum i n 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 i s 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 i s essentially a Simac 4x150 G vacuum tube with a silver plated resonance cavity.  Through an RG 8/U cable the output of the amplifier i s  connected to an LC resonant circuit as shown inside the dotted square in Fig. 3.3. The inductor of the resonant circuit i s just a copper loop and the variable capacitor i s made of two concentric copper tubes,  FIGURE  3.3  The  Discharge C e l l and i t s 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. is coupled to a resonant circuit.  The LC 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 i t 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 where  X  2  = 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 i s 3.5 x 1 0  15  molecules per ml and the collision cross-  section for electron i s of the order of IO"" cm . 15  path i s found to be L = l/p*d w 3 mm.  2  The mean free  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.^ i s about  25 ev.  (K.E.) = Jgn max  That gives E  q  >  (eE /OJ) o  2  > 25 ev.  4.5 x 10 V/m, and the maximum amplitude of the 4  electrons i n the discharge i s :  X = eE /rm2 > 9.4 x max o  10~ k  m.  This is much less than the 30 mm dimension of the discharge c e l l 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 i t s focal length from the light source, and the other at i t s 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 i s focussed onto the entrance s l i t of the monochromator. Between the lenses a rotating polaroid i s placed.  As shown in Fig. 3.4, the polaroid i s glued to  a 2" I.D. brass pipe which i s 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 i s 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 i s 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 a i r , 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  F i g u r e 3.4  The  Rotating Polaroid  R A C E W A Y  -47-  the equilibrium pressure of the system: two P i r a n i 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 i a glass stopcocks.  The vacuum pump was a mechanical pump which was  capable of reducing the pressure i n the system to l e s s than 5 x 1 0 - l f mm Hg when a nitrogen cold trap (.to prevent backstreaming of pump o i l ) was i n place.  For low pressure measurement an o i l d i f f u s i o n pump was  used as shown i n F i g . 3 . 5 . This combination produced a vacuum down to .2 micron measured by the 0—130 micron McLeod gauge.  III.5  S t a t i c Magnetic F i e l d  Three sets of mutually perpendicular Helmholtz c o i l s centered at the discharge c e l l were used i n t h i s experiment for the purpose of producing homogeneous magnetic f i e l d s f o r the measurements and for n e u t r a l i z i n g the e a r t h ' s magnetic f i e l d . The s p e c i f i c a t i o n s are given i n the following subsections. The inhomogeneities near the center were on the order of (y/R)  4  y i s the displacement from the center and R i s the c o i l radius.  where For  our 3 cm discharge c e l l and f o r the smallest c o i l which has an average radius of 2 0 cm, (y/R) « k  III.5A  (1/6.5)  h  or better than 1 part per 1 0 0 0 .  E a r t h ' s Magnetic F i e l d N e u t r a l i z a t i o n  A pair of Helmholtz c o i l s was used to n e u t r a l i z e the v e r t i c a l component of e a r t h ' s magnetic f i e l d i n the discharge c e l l .  These c o 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 i n series i n t h i s configuration.  The  f i e l d produced at the center of the c o i l s was approximately 4 . 5 Gauss/amp.  FIGURE  3.5  The Vacuum S y s t e m  -49-  Th ere was no need to calibrate these coils as i t was only necessary to adjust the current u n t i l the vertical component of the earth's f i e l d was minimized.  This configuration was able to reduce the vertical  component of the earth's magnetic f i e l d to less than 0.03 Gauss, measured by a Bell "240" Incremental Hall probe gaussmeter.  III.5B  Slowly Sweeping Magnetic Field  A longitudinal f i e l d , applied along the same direction as the discharge-maintaining electric f i e l d , was produced by a pair of aluminum frame, water cooled Helmholtz c o i l s .  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 i n  series the f i e l d 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 f i e l d of 250 Gauss.  For smaller magnetic  fields a Kepco Bipolar Operational power supply was used. A transverse magnetic f i e l d , along the direction of observation, was used in the Hanle effect experiment.  In order to obtain high  accuracy this f i e l d 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 cell.  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 f i e l d 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 i n 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 d r i f t was less than 2°C during an hour of operation.  The electronic circuit diagram i s shown i n Fig. 3.6.  III.5C  Oscillating Magnetic Field  In the magnetic resonance experiment a high power radiofrequency magnetic f i e l d was required.  In order to obtain the high  power uniform f i e l d , single-loop water-cooled Helmholtz coils as shown i n Fig. 3.3 were employed.  These coils were made of \ inch  copper tubing and, when i n operation, water flowed constantly through the coils i n order to maintain constant temperature so that the tuning would not change due to thermal expansion.  The power supply for this  oscillating magnetic f i e l d was built i n 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 i n Fig. 3.7, the amplifier had two main stages.  In the f i r s t stage, an 829B high frequency power vacuum tube was used Cwith the two channels of this tube acting) i n 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 i n parallel so that the two power tubes acted in push-pull.  The power  FIGURE  3.7  Power supply f o r 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 c o i l was more than 100 watts and the reflected power was less than 0.5 watt.  This produced an RF magnetic  f i e l d of 6 gauss at 54 MHz.  III.6  Signal Processing  A block diagram of the electronics i s 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 10 *.  The  1  output was D.C. ±10 V at f u l l scale.  In the mode in which i t was used,  i t supplied i t s 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* i s quoted by the manufacturer to be approximately 23%. was operated with a cathode to anode potential of -1280 volts.  It The  dynode chain resistors were a l l 33 Kohms while the cathode to f i 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  Anode o  Cathode  i  Dynodes o o  92  01  I  -X  100K  33K  ft  *  K  33K  3.8  Photomultiplier  VVNA  33K  •1300 V  FIGURE  OUT PUT  Q11  93  W i r i n g Schematic  schematic i s shown i n 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 d i g i t a l 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 w i l l remain fixed, so that after N measurements the signal to noise ratio w i l l 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 i s 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 f i e l d and provided a linearity of 0.5% in the resulting f i e l d .  -56-  III.7 For x-y  the Hanle  recorder, Fig.  the h a l f - w i d t h  punched  Into computer  to  fit  effect  4.1,  extract  a function of  Data  were H^.  experiment  subjected Relative  cards the  Processing  by an  the graphs p l o t t e d  on  to numerical processing  values  of  the to  the p o l a r i z a t i o n  electronic digitizer  and  were  then  used  form  P - A, + A»x  7TT  +  i  A+TTF'  +  (3.6.1) H-H  with X =  ° a n d Aj^, A ,  A3, A ,  2  fitted  by a computer  fitted  curves  are  4  "least  The average pressure, pressure and  the  Hj^ was  half-width, slope  computed,  the in  for  that  squares"  w h i c h was  are discussed  At  routine  each gas  parameters  (U.B.C.L.Q.F.).  pressure  used,  i n d e p e n d e n t l y f i t t e d by the e q u a t i o n  "least  from which  fitting  4.2.  t h e n computed  by a l i n e a r  a n d H^ w e r e a d j u s t a b l e  q  square"  shown i n F i g .  8 g r a p h s were p r o d u c e d and  H  used  to  pressure  the next  pressure  fitting  and p l o t t e d  routine.  The  4  The to  (3.6.1). versus  zero-  calculate  the r a d i a t i v e  lifetime,  broadening  cross-section  were  chapter.  -57-  Chapter  Four  EXPERIMENTAL R E S U L T S  IV.1 The l i f e t i m e s measured PH65,  b y many w o r k e r s  KB63,  lifetimes  are given  the above  and  in Table  4.1  (10-80 m i c r o n s ) There i s  4'D  and  and by u s i n g  listed  states used  in  this  and a r e d i s c u s s e d of  2P  and h i g h  cading given  showed  from the higher in  section  measured  i n 3D,  are given Chapter  Lande  7  helium have techniques  states  of  (200-500  that  lab. in  levels.  of  the results  4.2.  and neon measured  microns)  pressures  between t h e s e  resonance  are  two  at  listed  important  g-factors  and  3E and Z s t a t e s  i n T a b l e 4.4  and 4.5  in  this  be due t o  thesis  the h y p e r f i n e s t r u c t u r e of  molecular  and d i s c u s s e d  hydrogen. in  the  cas-  are  is  the  constants The  s e c t i o n 4.4  results and  in  5. Possible  errors  are listed  and d i s c u s s e d  in  Table  performed.  A more d e t a i l e d d i s c u s s i o n  work r e p o r t e d  in  measurements.  e x p e r i m e n t was  the d i s c r e p a n c y might  energy  test  (D67,  remeasured  The remeasured  Sec.  argon  The  been  4.3.  The most lifetimes,  of  p r o v i d e d a good  an unexpected d i s c r e p a n c y  experiment  states  many d i f f e r e n t  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 This  5'D  OV67, MBBB70, BK67, D P B 6 1 ) .  the apparatus  The l i f e t i m e s  4.2.  3'D,  FHJC64, AJS69,  of  techniques  low  of  Introduction  Section  4.5.  -58-  IV.2 The helium  is  Several  special  that  4'D  The 3*0,  interest  the t h e o r e t i c a l  most  observations  of  of  these  decay  with In  seriously  to  5'D  the It  with  other  lifetimes was  the  found  instead  in  of  For 3'D,  4'D  1.  More at  2.  as  than  agreement  other of  possible  the l i f e t i m e s  otherwords,  this  at  of  for  available. cross-sections  in  of  at  3'D but  error,  5'D  lower  are  pressures  field, the  with  showed  (5  -  closer  lifetime  not  lifetimes As  theory  and  results, 100  microns).  agreement  showed a n  with  unexpected  broadened  pressures.  the magnetic  i n h e l i u m was the  lab  4.1).  been measured.  F o r more a c c u r a t e  and 4 ' D the  i n our  i n agreement  lower  fairly  (Table  the magnetic  helium have a l s o are  are  theory  of  direct  coincidence  t h e L o r e n t z i a n c u r v e had been  reason,  states  with  sources  experimental r e s u l t s .  phenomena w e r e f o u n d listed  in  were a l s o measured  and 5'D  are  are  (D67),  experimental results  our measurements  narrowed  crossing  t h e l i f e t i m e s measured  theoretical calculations  decrease,  the  and  states  shown i n T a b l e 4 . 1 , also  information  probabilities  level  the inhomogeneities  f i e l d and  and  All  prove  a f f e c t e d by  4'D  lifetime  h e l i u m l i f e t i m e and  experiments  each other  order  electric  3'D,  of  Helium  (FHJC64, BK67, AJS69), d e l a y e d  t e c h n i q u e s were a p p l i e d .  of  transition  of  b e e n made.  In  consistent  States  in radiative  experimental determinations  ihave a l r e a d y  R.F.  5'D  and  5'D  resonance  experiment on  the  p e r f o r m e d and more u n e x p e c t e d  states.  All  the unusual  phenomena  follows: one g - v a l u e  pressures  lower  appeared  than  lOu  in  Fig.  the magnetic  resonance  experiment  4.1.  The L o r e n t z i a n c u r v e s were broadened as  the pressure  decreased  L i f e t i m e s (n sec.)  Author  Techniques  Date  VD  VD  12(3)  41.5(5) 49(5)  Descoubes (D67)  Level Crossing  1967  16(2)  47(5)  79(6)  P e n d l e t o n & Hughes (PH65)  D i r e c t O b s e r v a t i o n Decay  1965  16(4)  30(5)  46(3)  Kindleman  Delayed  1963  18(5)  35(4)  5^  15.5(5) 38(5) ' 16(2)  & Bennett  (KB63)  Coincidence  Fowler e t . a t . (FHJC64)  D i r e c t O b s e r v a t i o n Decay  1969  Allen et.al.  D i r e c t O b s e r v a t i o n Decay  1968  Delayed  1968  (AJS69)  46(3)  Obsheovich  38(3)  66(4)  M a r t i s o n e t . a t . (MBBB70)  Beam F o i l  1969  39(5)  63(9)  B r i d g e t t & King  D e r e c t O b s e r v a t i o n Decay  1967  39(2)  49(2)  Descoubes e t . a l .  Magnetic  1960  SVerolaimen  (BK67) (DPB61)  20.3(2) 33.6(3) 74.4(5) Ours(100-300 microns) 17.6(3) 35.1(3)  Ours(1-70  1.5+10% 35+10% .72+10%  Wiese e t . a l . (WSG66)  Table  4-1  (OV67)  microns)  (CBD71)  Coincidence  Resonance  Hanle E f f e c t  1971  Hanle E f f e c t  1972  Theoretical  1965  The L i f e t i m e s i n Helium 3 D , 4 D, 5 D s t a t e s  -61-  below 12u. 3.  The r a t i o of  of  the amplitude of  the dispersion  the L o r e n t z i a n curve decreased at Since a l l  the  singlet  states  these  same l o w  assistance  effects.  After  further  t h e s e phenomena i n  amplitude  pressures.  cannot be  the  explained  experimental investigation,  and a d v i c e from P r o f e s s o r s  an e x p l a n a t i o n of  the  i n h e l i u m p o s s e s s g = 1,  a b o v e phenomena w h i c h h a d m o r e t h a n o n e g - v a l u e by c a s c a d i n g  curve to  M.L.H.  P r y c e and A . J .  terms of  the  Stark  with  Barnard,  Effect  was  developed. In source,  our  and t h e e l e c t r o n s  from a strong potential  free  path of  the pressure  the l e n g t h of  the  more towards  in  the discharge  electric field  the  started  effect  Where E  z  cell  used  is  shift  is  T h e 5'D  shift  obtained  about  due t o  |n> a n d  |n'>  the  (B65,  E(n)  cell  Stark  light  their  across  of  cathode  Pg93).  space  then  and atoms were  As path extended subject  pressures.  increased, the effect.  the  t h e mean  t h e mean f r e e  higher  energy  the  times  (L66,  The c a t h o d e d a r k cell  the  most  four  cell  lowered,  the discharge  g i v e n by  state  was  the discharge  the e l e c t r i c f i e l d ,  excited state  is  t h a n t h e y had b e e n a t  inside to  space  cell  as  a glow d i s c h a r g e  the discharge  increased.  the center of  the e l e c t r i c f i e l d  Stark  In  this  electrons in  t h e e l e c t r o n s was  sublevels  the discharge  was  a p p l i e d between c a t h o d e and anode a p p e a r s  s p a c e and  to higher  in  RF e l e c t r i c f i e l d .  dark  of  experiment a glow d i s c h a r g e  As  magnetic  The second  order  CS35)  and E ( n ' )  are  the  energies  of  respectively.  i n helium is  very  close  to  the 5'F  state  with  -63-  energy  separation  <n'|EjZi|n> comparable R.F.  is to  occur  high. the  magnetic  E(n')  -  At  field.  As  i n magnetic  resonancesare  A detailed  Effect  and  this  in  the r a t i o  the 4.2  shifts  of  the  (Fig.  4.1)  applied should  location the  then  of  the  unexpected  theory.  theory which includes field  experiments has  of  probability become  the resonance  and m a g n e t i c  resonance  strong  energy  agree w i t h the  quantum m e c h a n i c a l  •  in  electric fields  Hanle  been g i v e n  L o r e n t z i a n c u r v e and the dispersion  the  the  curve to  the  by Pryce  (P74).  decrease  that  (low p r e s s u r e s )  of  the  are  explained.  the  resonance  *  Because it  ments  t h e 4 5 0 MHz  of  is  the detecting u n i t  circuit,  very*difficult  from the c e n t r e of ment o f  electric the  5'D  field  is  that  axis  field state  is of  of  hand  side).  of is  field.  field a loop  stength  a reasonably  good  proportional  to  As is  also  broadened as  given  The v a r i a t i o n it  the  p r e d i c t e d by  the amplitude  of  measureof  the  square  of  the theory, the  this  decrease with  4.3  ratio the  the in  electric  the dispersion  in Figure of  measure-  p l a c e d a f e w cm  halfwidth  the h a l f w i d t h  The r a t i o  disturb  The measured  4.3.  w i t h the t h e o r e t i c a l p r e d i c t i o n that electric  gives  something  the L o r e n t z i a n curve  on t h e r i g h t  cell  in Figure  helium,  increased.  However  electric field.  given  strongly  t o make a b s o l u t e  the discharge  the r e l a t i v e  will  electric field.  L o r e n t z i a n c u r v e AH^ v e r s u s  to  and  the t r a n s i t i o n  the Stark  experiment  the amplitude of  Lorentzian curve at  and  1  By c o m p a r i n g w i t h t h e  resonance  the broadening  of  -  shown i n F i g u r e  the e l e c t r i c f i e l d  theory,  cm -  pressures  fields.  the magnetic  In  low gas  qualitatively  i n t e r a c t i o n of  = 1.7  zeeman s p l i t t i n g s  a t many d i f f e r e n t  resonance  E(n)  (the also  curve vertical  agrees  increasing  .FIGURE  4.3  .Halfwidth  as  function  of  R.  F.  E l e c t r i c  F i e l d  -65-  IV.3  The L i f e t i m e s o f  In  order  to reduce r a d i a t i v e  low p r e s s u r e  (100 m i c r o n o r  lifetimes  argon.  of  l i f e t i m e s measured  As in  In  measured. that  of  view of  this  neon pressures  are  study d i f f e r However,  low pressures  microns)  and  from higher  (50  -  excited states  but  the magnetic  also  neon i s  resonance  corresponding to  as  i n neon were  to  type of  of  (500  to  errors  in  1.30  is  (BB52).  identify  -  there are  for  (Fig.  this  presumed to  low  1000  cascading  the  effect of  o n l y measured At  at  by  lifetimes  low gas  of  argon the  pressures,  showed m o r e t h a n o n e g - v a l u e .  0.994  as  experiment  pressures  large  order  and g = 1.30  also  Using  clearly  two  resonances,  4.4).  The  Lande'g-factor  2P5 s t a t e be due t o  (P67).  This  cascading  from  some  levels.  A s we h a v e state  In  less  v e r y , much t h e same  These experiments not  g = 0.99  second resonance a t  cascaded  and h i g h e r  lead  these  is  the low p r e s s u r e measurements  an example,  a w e l l known v a l u e  energy  similar  curves  pressure  i n neon have been performed  performed a  might  2P  t h e l i f e t i m e measurements  the Lande g - f a c t o r s  t h e n e o n 2P5 l e v e l  low  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  and neon were p e r f o r m e d . lifetimes  the  effects,  the  b y m o r e t h a n 200% f r o m  others.  effect curves.  magnetic  some o f  with  in  and c o l l i s i o n a l  t h e 2P l i f e t i m e s  150 m i c r o n )  suggested that  deduced from Hanle cascading,  (C72)  Neon  the experimental e r r o r  in Table 4.2,  again disagree  Carrington  higher  i n T a b l e 4.2  these r e s u l t s  shown  and  m e a s u r e m e n t s w e r e made o f  a r g o n and l i f e t i m e measurements As  has  i n Argon trapping  The e l e c t r o n i c s t r u c t u r e of  many w o r k e r s .  at  less)  shown  obtained by other workers. t h a n 5%.  4P S t a t e s  is  shown  In  proportional  A p p e n d i x B, to  the d e n s i t y matrix  p of  the  -66-  ARGON  2P  2  P  Landman  Klose  L68  K67  26.0(1)  3  6  2P  0  A  B  C  46.0(2)  27:1(2)  29.0C1.7)  29.5(3)  31.6(1.6)  37.4(3)  32.4(2)  28.7(3)  91.0(5)  NEON  2  P  4  2P  2  P  6  2P  2 P  5  ?  8  2P  Q  Bennett BK66  Carrington C72  19.1(.3)  19.2(1.)  19.5(1.5)  19.9(.4)  18.6(1.3)  20.7(1.7)  26.1(.8)  19.7(.2)  18.2(.7)  19.1(1.9).  21.3(.6)  19.9(.4)  19.4(.9)  20.5(2.2)  37.0(.8)  19.8(.2)  19.6(1.)  21.1(2.1)  25.4(.7)  19.4(.6)  18.7(.7)  20.1(2.0)  33.7(.6)  A  B  C  20.9(.9)  19.0(1.6)  I A:  Higher P r e s s u r e Measurements  B:  LQF F i t t e d  C:  Measured by Hanle E f f e c t  TABLE 4 - 2 .  with Cascading  (200-500 M i c r o n ) .  Effect. a t Low P r e s s u r e  The L i f e t i m e Measurements o f a n d NEON.  (3-80  t h e 2P S t a t e s  u).  i n ARGON  - 6 8 -  f °C  °^ ^  ~ ^  Const.  X  ' . whereof is  ~  another  "  ^  parameter  to  it  was  found  the  results  of  that  parameters  the l i f e t i m e s  equation  An i n t e r e s t i n g ments.  As  the pressure  Lorentzian and as This  signal  interesting  after  detailed  result  of  in  investigation  and  t h e p o l a r i z a t i o n a x i s was  levels  at  and  the discharge  and t h e i n t e n s i t y  t h e two  rather  excitation arises  than  that  the complexity of  be f i t t e d ,  from l i g h t  in  increases  it  otherwords,  (Table  4.2).  200  i n v e r t e d and  this  the d i r e c t i o n of  levels.  In  was  focused  onto  our  the discharge  excitations e l e c t r o n beam.  the metastable  the extrance was  to  2s  optical  experiment, only slit  of  found b r i g h t e r  the c e n t r e column.  travelled parallel  a  pressures  were then p o p u l a t e d by  2s  of  of  (C72);  t h e low  by the e l e c t r o n  the  The  the  microns,  phenomenon i s At  of  stronger.  i n d e p e n d e n t l y by C a r r i n g t o n  the p o p u l a t i o n  experi-  the amplitude  pressure near  becomes  with the  t h e neon and a r g o n  zero at  program  agreed  in  aligned  of  states  noted  t h e 2p s t a t e s  monochromater sides  the  converge  then along  from the metastable  column of  t h e computer LQF  he s u g g e s t e d t h a t  pressures  were i n c r e a s e d and  excitations centre  were p o p u l a t e d  the higher  program.  the e x c i t a t i o n mechanism.  2p s t a t e s  const,  to  further  found  the  failed  goes t o  the  However,  due to  the discharge  increased  in  and  L  some o f  could not  e f f e c t was  e f f e c t was  t h e change  of  However  (3.6.1)  decreases,  the pressure  H  had been f i t t e d u s i n g  other workers.  in  '  be f i t t e d b y computer LQF  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 the  * i  f  Equation 4.3.1 and  (4.3.1)  the the at  optical  e l e c t r o n beam  and  -69-  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  e l e c t r o n beam l e a d i n g The at  higher  times of  t o a n 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  "optical  pressures  the axis  e x c i t a t i o n " Hanle  (200  to  500 m i c r o n s )  e f f e c t measurement was u s e d .  reported results  (Table  4.2).  with  t h e most  the  expected. obtained  The r a d i a t i o n  t h a t were deduced from the e x t r a p o l a t e d z e r o p r e s s u r e  the L o r e n t z i a n p r o f i l e s were i n agreement  of  life-  halfwidth reliable  - 7 0 -  IV.4  The 3D,  3E and  Molecular  IV.4A  state is  of  hydrogen as  shown i n F i g .  curves  is  curve  in  inches  4.6.  is  scale  excited  i n Tables  4.3  of  the  and  From t h e estimate assumed  of  compared t o collision  at  "x"  are  the  Lorentzian  at  3D,  and  g  were s c a l e d  computer.  halfmaximum, is  Hj^, o f  the f i t t e d  Lorentzian  the L a n d e ' g - f a c t o r .  zero pressure  and  3E and Z s t a t e s  of  The  the l i f e t i m e s hydrogen  are  of  different  tabulated  4.4. slope  of  the halfwidth versus  cross-section  t h e number d e n s i t y  of  t h e number d e n s i t y  cross-section  of  M  o  pressure  may, b e o b t a i n e d .  the excited molecules ground  state molecules  can be c a l c u l a t e d  - • * 3s  (j~  the crosses  and t h e p o l a r i z a t i o n s  p l o t t e d by t h e  the c o l l i s i o n  that  figure  (LQF)  to  arbitrary  halfwidths  state  this  fitted  field  is  the Bohr magneton  extrapolated  In  squares  magnetic  The  before being  Q  transverse  3D  e f f e c t experiment by an e l e c t r o n i c d i g i t i z e r .  The h a l f w i d t h s w h e r e \i  applied  excited  the p o l a r i z a t i o n , which were r e a d from the  the Hanle  polarization 9  of  emitted from the  The r e s p e c t i v e l e a s t  shown i n F i g .  r e l a t i v e values  Measurements  the l i g h t  a f u n c t i o n of  4.5.  of  Hydrogen  The L i f e t i m e  The p o l a r i z a t i o n of  Z States  from the  , d  T  graph  an  If  is  N  F  it is  small  N , then  equation  the  (V70)  i-k  ( 4 . 4 . 2 )  where N of  q  is  t h e gas  A v o g a d r o ' s number, in  K and  v is  T  q  equals  2 7 3 K,  T is  the r e l a t i v e v e l o c i t y of  the  temperature  colliding  molecules.  Magnetic Field -8.0  -6.0  FIG.  4.0  2.0  -4.0 4""5  Experimental  6.0  Hanle E f f e c t Curve f o r t h e  3D0 2B0 RO L i n e  4628  A  8.0 Gauss  Magnetic Field(Gauss) -8.0  -6.0  FI6. 4-6  -4.0  -20  2.0  40  L e a s t Squares F i t t e d Curve f o r the 3Do 2B0 RO L i n e  (4628 A)  6J0  8.0  -73-  In  t h e d e r i v a t i o n a B o l t z m a n n v e l o c i t y d i s t r i b u t i o n was  curves are plotted against shown i n F i g u r e s spectral  line  to 4.14.  lines,  or  Z(3'K)  belong  hydrogen,  reported  taken for  each one of  gas  pressures.  on the the  signal  spectral  in  upper  state  Each l i n e  to  electronic  in  this  thesis  the  spectral  averager,  level  states.  at  the average  depending  There are levels  on t h e  in  The  as  shows  i n one of  and t w e n t y H a n l e lines  cell  these figures  fifteen rotational  Each curve i s  the  one 3D  twenty-two  molecular  effect  curves  four  to  six  values  of  1 t o 32  signal-to-noise  were  different sweeps  ratio  of  line.  The v e r t i c a l halfwidths  i n the discharge  and one s p e c i f i c v i b r a t i o n a l  (3d'Z), 3E(3d'n) spectral  4.7  the pressure  assumed.  at  intercepts  zero pressure.  natural  in Fig.  4.7  These h a l f w i d t h s  lifetimes with  the aid  to  4.14  are  represent  the  converted to  the  of  \  (4.4.1) Calculated  cross-sections  are l i s t e d  i n T a b l e 4.3  and  4.4.  STATES  upper lower 3D 2B V'  J  1  X  (A)  g-VALUES OURS  OTHER'S  (n. sec.)  OURS  OTHER'S  CROSSr-SECTIONS OURS  hfs CONSTANTS  OTHER'S  OURS (MHz)  ±10%  ±5%  (1%)  v" J "  LIFETIMES  0 2 1 1 0 3 0 2  35.9 36.2  149 148  .2±(.3)  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  60.3  5.1  1 2 0 1  4199  40.7  0 1 0 0 0 2 0 1  B*21(l) G 15.8(8)  ±10%  D*.901 4628 +.886 B. 908(10) C. 889(10) 4631 +.572 D.571 4932 +.568 4632 +.440 D . 4 4 5  26.2  G23.8  153  60.6  D.275  44.2  63.0  4067  D.293  42.5  87.0  4206  D.407  38.9  173  4714  1 3 0 2  4205  2 1 1 0 3 3 2 2  TABLE 4-3.  G;ML74  .2±(.3) 40.6  1 2 2 1  D;DCB53 B;FM73  4.1  G 190 (20!  62.3  D.358  OTHER'S  The 3D(3d'£) State of Hydrogen Molecules (H„).  4.6  G 6.3(6)  OURS  UPPER  3E  3 E  Z  a  b  LIFETIMES  8-\ FALUE  LOWER  V»  N'  V  N  X  0  2  0  3  4576  0  3  0  4  4568  (A)  .412  (n  OURS  OTHER'S D53  CROSSSECTION  s e c . ) ±10%  hfs  CONSTANTS  (S ) 2  (MHz)  +.42(1)  33.7(3.)  347  +  37.9(3.)  389  4.2  +  39.4(3.)  388  4.1  -  97.0(0.)  230  1.7  66.5(6.)  135  3.0  117  . Ji/  0  3  1  4  4856  0  2  0  2  4580  .142  1  2  0  2  4937  .169  1  3  0  3  4175  2  1  4  0  4814  *M.495(8) Z.48(l)  49.2(5.)  132  2  1  5  0  5103  Z.48(l)  45.3(5.)  138  2  2  5  1  5107  Z.17C3)  106.6(9.)  2  3  5  2  5113  Z.23(2)  59.3(6.)  65 122  * M  magnetic resonance  Z  Zeeman E f f e c t  TABLE 4 - 4 .  The 3 E ( 3 d ' n )  and Z ( 3 ' K )  States of Hydrogen Molecules  1  THE 3D0 STRTE OF HYDROGEN MOLECULE  H a  c  ••3  tr  (D Ul D o  w  r+  U>  J=3  fD  4638 A  rt  I  O Hi  l  a  J=2 04631 A A4932 A  H 0  iQ ro 3  •s o  o 4628 A  J  ro o  c  ro  0.0  10.0  20.0  I  30.0  PRESSURE IN  i 40.0  MICRONS  50.0  60.0  70.0  80.0  =  1  H Ci G  THE 3D1 STATE OF HYDROGEN MOLECULE  •i. J=2 4714 A J=l  °5003 A °f4709 A 44196 A  40.0  30.0  PRESSURE  IN  MICRONS  •Nl  I  °0 o I  0 , 0  io~0  2oTu  3oTo  T o  PRESSURE IN MICRONS  50.0  60.0  70JD  ^50.0  THE 3E0 STATE OF HYDROGEN MOLECULE  -84-  IV.4B As at  The Measurement  shown p r e v i o u s l y ,  zero pressure  of t h e g - v a l u e  and t h e l i f e t i m e T.  However, of  the energy of  the magnetic  field,  high  A series magnetic  longitudinal  the r e c i p r o c a l In  the g-values  so  that  the  is  required.  In  curve  product lifetime 1953  Dieke  o f . 3D ( 3 d ' I ) , 4D (3d ' I) a n d . 3E(3d'II)  is  the g-values at  field.  not a l i n e a r  function  l o w e r f i e l d s may d i f f e r  fields. of magnetic  r e s o n a n c e e x p e r i m e n t s was  f i e l d b e t w e e n 40 a n d 2 0 0 G a u s s . s t a t i c magnetic  As  performed  shown i n F i g .  f i e l d was a p p l i e d a l o n g  2.7A,  a  the d i r e c t i o n  a n d a 54 MHz R F m a g n e t i c  field  was  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 . the energy separations  As the l o n g i t u d i n a l magnetic  b e t w e e n Zeeman s u b l e v e l s  the energy s e p a r a t i o n e q u a l l e d the energy of u)j = u g H , t h e a l i g n m e n t O J o  of  also  a R.F.  t h e Zeeman s u b l e v e l s  s t a t e was d e s t r o y e d a n d t h e c h a n g e o f (Fig.  of  o r d e r t o deduce t h e  t h e Zeeman s u b l e v e l s  of t h e pumping e l e c t r i c f i e l d , applied  a Hanle e f f e c t  t h e Zeeman e f f e c t i n a 3 5 , 0 0 0 g a u s s m a g n e t i c  from those at  at  Lande'g-factors  the Lande g - f a c t o r  (DCB53) m e a s u r e d some o f using  the  the h a l f w i d t h of  i n p r o p o r t i o n a l to  of t h e e x c i t e d s t a t e s  states  of  field  increased  increased.  When  photon 2.7B,  i.e.  of  p o l a r i z a t i o n was  the  excited  detected  2.7C) The g - v a l u e s r e s u l t s  hydrogen are a l s o  listed  for  the 3D,  i n T a b l e s 4.3  The l i f e t i m e s o f  the s t a t e s  3 E , and Z s t a t e s  and in  lifetimes  for  those  states  t h e RF m a g n e t i c  the t a b l e s were c a l c u l a t e d  which have v e r y f i e l d was n o t  molecular  4.4.  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 However,  of  resonance  small  experiment.  g-values or very  p o w e r f u l enough t o  induce  short  -85-  observable  transitions.  from D i e k e ' s Z  work  In  (DCB53).  those cases However,  s t a t e had never been measured.  ment,  similar  hydrogen gas  to  that  of D i e k e ' s  pressure of  In  the g - v a l u e s used were  g-values this  i n the doubly  1000 m i c r o n , was  excited  c a s e a Zeeman e f f e c t  (DCB53),but.at  27,000 gauss  performed i n  this  taken  experi-  arid lab.  XV.IC As  described  emitted from the nuclear field  spin  is  The Measurement  excited  1 = 1  applied,  .comes f r o m t h e  in  section states  increases but  of  the hfs  2.3,  of  hydrogen molecules  slightly  states  with  h  e  r  E  and where T i s For vanishes fields,  F  -E '  It  change  has  the  v e r y high magnetic  (Fig.  If  P(a  = 0)  excited  fields,  to  magnetic if  the  photon  been proven  r +  that  S2p >  a  F  F'(FV/))  state.  the coupling  represents  light  C2.4.10)  f (RF+/>-  =  F  the l i f e t i m e of  (a = 0 ) . then  not  the  corresponding  a longitudinal  )XFF'J  n ^ >  e  as  1 = 0 .  PCCX-o)  v  the p o l a r i z a t i o n of  the p o l a r i z a t i o n does  excited  Constant  b e t w e e n J and  the p o l a r i z a t i o n  at  I  high  4.11)  (4.4.4) w h e r e P^  is  experiment effect  the change and P  fitting  p(a)/p(a=0) T a b l e 4.5 .: i s  (4.5)  lifetime  as  (2.4.10)  by computer,  in  is  polarization  too  but  a f u n c t i o n of  and p l o t t e d  obtained,  Table  t h e change  observed  in  the  observed  repolarization in  the  Hanle  experiment. Equation  square  in polarization  using  (a/T)  in Fig.  Figure  (4.15).  from the Hanle  effect  is  (4.15).  the numerical v a l u e or  complicated  of  a/T  Again,  eq.  to  program  (2.4.10)  calculated  the  for  Once t h e r a t i o was  read o f f  by t a k i n g  experiment,  for  least  ratio,  J=l  J=5  in  p(a)/p(a=0) from  the value  the hyperfine  either of  the  structure  -87-  FIGURE  4.16  The P l o t o f P ( a ) / P ( a = 0 )  Vsv  a/p  J  o  B  B  l  B  2  B  3  1  .278 ,  .500  .222  2  .474  .234  .266  3  .704  4  .813  5  .873  .142  B  4.  B  5  B  6  B  7  B  8  B  9  B  10  B  l l  .026  .148  .092  .006 .094  .002  .064  .064  00 P(a)/P(a=0)  = YB ' ^ +(na/r) l—L " lI4.fr. neO  TABLE 4 . 5 A The C o e f f i c i e n t s o f B  n  i n The E x p r e s i o n p ( a ) / P ( a = 0 )  .002  -90P(a)/P(a=0)  a/r  J-2  o.o  • 01000  .,02000 ,03000  1.00.000 ,99960 ,99841 ,99t>42  —ro^rootr  -7-99-5 B T -  ,05000 ,06000 — -,07000,06000  ,99016 .98594 -J9810T,97543 .96922  09000  TtOTVOTr ,11000 ,12000 -113000" ,14000 .15000 TlKtroxr .17000 ,16000  ,9b244 ,95512 ,94730 "793903,93036 ,92133  .20000 ,21000  ,90237 .B9251 -;8B?47,87227 ,86195  ,22000 ,23000 .24000 -.'25000.26000 ,27000  .651S4 ,84107 .B3058 "782008,80960 .79917  -,I«JOOO-  ,28000 ,29000 ,30 000 T3100O,32000 ,33000  .78679,77850 ,76830 -T75B21,74824 ,73840 ,72871 .71916  .34000 .35000 .36000 T37000,38000 .39000  —7005-4,69148 ,68258  ,40000 ,41000 .42000 "743O00,44000 ,45000  ,67366 ,66532 ,65695 -76-afl75,64074 ,63290  ,460  ,70977  "T  99B60 99741 99545 99274  ,61774 ,61043 "7-60328.59631 ,58950  -7-5^*6-  99700 99661 99543 99350 9B753  98518  98353 -97908" 97409  ^8003" 97509 96920 96284 95604  96867 •9B?6-9-  94886 94134-  95051 90403 93744 93076  93355 92552 91731 90894 90046 89191"  95682  92407 91738  68331  91073 90416" 89768  87470  69132  66610  BB5I0  65753 84902  87903 B7311 86-73686176 85637 85114  8 4«1r983224 82400 8 I 588 60768 60002 T9?30" 78473 77732 77006 76296 75b03 7492574264  73619 72990 72377 71760  1,0010 1,0006 ,9994 ,9974  0 0 2 9  —r99Tt65-  98930  84609 64122 U 3 * 5 ^ 83199 82763  •6ZS1S 81940 61551  «-ti7«80820 80476 60145 79827  ,99160 ,98778 —J98348,97881 ,97382  —r9W62~ ,96326 ,95781  —.95234 ,94690 ,94152  —r»*<>-rr ,93108 ,92608 - . 9 2 1 2 3 ,91657 ,91209 r9«7T9" ,90368 ,89975 -T89601,89245 ,88906  —85-509-  70632 70081  73947 78676 7 8417  67077 b6b23 66183 65754  -T5500 0,56000 ,57000  ,57637 ,57005 "756388.55787 ,55200  653-38-  "T5BT)0"0-  T5T&-28-  7 6 6 6 9  ,65167 ,85032 , , , —  849 03 84761 84660 8 4 55-2-  ,64446  9056798132 97678 9721b 96753 96294 95844 95407 94986 94197 93831 93484 93157 92849 9 2 5 5 9 — 92286 92030 ,-9179 0 — 91565 91 J 5 4  90071 89951  S983689732 69631 8953 7  89407 89363 B-928389207 89136 89068 89003 88942  B15W4  ,6434a -.84247,84155 ,84066  86829 88777 68727 88679 86634  ,83900 ,83622  *B59T88550 8851 1  -r8-596-r  6 4 5 3 9  7 6 4 8 7" 7631 1 76142  V4157  7-5-979-  T«"3T4r  64933  989/7  90 199"  79522  67543  99*7^" 99349  ,86964 ,86740 .86528 -766 3 2 6 ,86134 .85952  79^29-  78167 77927 "77 6 9 V " 7 7 « 7 5 77261 77-OU676859  001 i 6 99939  91156 90970 90795 <>t)632 90478 90334  71T98-  69024 68516  00300 00259  .88584 ,68278 ,87987 "787711.87449 ,67200  T 8 5 7 7 9 ,85614 .85457  b954g-  00"  ,47000 ,48000 —,-490 0 0" ,50000 .51000 5 2 0 0TT ,53000 .54000  99900  TABLE 4.5B The Numerical Values o f P(a)/P(a=0)  •BT47-3-  !  -91-  splitting hfs  constant  splitting  is  constant  determined. are l i s t e d  The experimental v a l u e s i n Tables  4.3  and  4.4.  of  the  -92-  IV.5  Sources  IV.5A One o f experiment  t h e more s e r i o u s  In  - o s c i l l a t e along field.  Discharge  came f r o m t h e  the discharge.  As  effects  the absence  a straight  the transverse  electrons  line,  changes  f u n c t i o n of  -uhere B is  was  the Hanle  -.-minor a x i s  to major  in  (eq.  error  the f i r s t 3.6.1).  in  240"  of  for  Higher  of  over  the  have r e s u l t e d  magnetic  magnetic  applied  effect  field  field  t h e 4 5 0 MHz  on  electrons  electric  the path of  the  an e l l i p t i c a l o r b i t .  of minor  axis  to major  field ^  of  effects  '-  axis  is  (Appendix  transverse magnetic  a n d co  field  to  so  e x c i t e the  the r e s u l t i n g about  0.07.  a  A), is electrons.  t h e maximum m a g n e t i c  field  ratio In  of  the  the Lorentzian curve, has  been i n c l u d e d  could not  Field  in  this  the  term  c r e a t e more t h a n  2%  Inhomogeneity  f i e l d measurements  incremental Hall  the Hanle  lifetimes.  Magnetic  The c a l i b r a t i o n of  could  is  t h e e l l i p s e was  order  a Magnlon FFC-4 r o t a t i n g error  into  the h a l f w i d t h  the magnetic  inhomogeneity  3.5B).  field  to  e f f e c t measurement  the measurements  All  1.000  parallel  order approximation,  IV.5B  ""Bell  a transvers  the e l e c t r i c f i e l d used  axis  computer LQF program  A2X  the  in  the transverse  2 0 G a u s s a n d ut = 211 x 4 5 0 M H z ,  about  error,  of  frequency of  In  errors  the transverse magnetic  the amplitude  the angular  Stability  of  magnetic  then g r a d u a l l y  Error  possible  of  The. ratio linear  of  probe gaussmeter. entire discharge the H a l l  coil  Less cell  than  was  probe gaussmeter  magnetometer.  from f i e l d  h a v e b e e n made w i t h 2 parts  detected was  a in  (Sec.  checked  with  A n e s t i m a t e d maximum  inhomogeneity  and  calibration  2%  -93-  ;errors combined. expect  in  the magnetic  .known v a l u e resonance  This w i l l  resonance  can be used  to  in a l l  sharp  the magnetic  determination of section 3.4,  Both P i r a n i  Pressure  pressure  in  resonance of  field  at  the discharge  cell  b y two P i r a n i  and t h e o t h e r  gauges were c a l i b r a t e d w i t h a 0 the system  close  130 m i c r o n  of  the upper  the halfwidth  of  the Lorentzian p r o f i l e at  t h e r e l a t i v e p r e s s u r e was  the.pressure reading w i l l of  less  t h a n 1% a n d a n e r r o r o f  TV.5D In of  The S t a r k  the pressure  of  a L o r e n t z i a n p r o f i l e has  4.2). of  i n t r o d u c e an e r r o r  On t h e o t h e r h a n d  stark  strength broading  hydrogen.  of is  the  a strong  negligible  in  the  Furtherpropressure,  The i n a c c u r a c y  the l i f e t i m e  electric field,  (Fig.  Stark  t h e h e l i u m 5'D of  electric fields  electric field  zero  With  in  measuremeasurements.  Broadening  been found f o r  various  cell.  the c r o s s - s e c t i o n  the measured h a l f w i d t h  hydrogen molecules at  on the  Effect  5% i n  in  the  MacLeod  were i n v e r s e l y  important.  in  steam.  a c c u r a t e to w i t h i n ±5%. states  the  one i n  the discharge  lifetimes  only  in  the lower  more the n a t u r a l to  is  to  in  gauges,  pressure readings  ments  the  As mentioned  1:his arrangement  that  well  which  from i n a c c u r a t i e s  the d i s c h a r g e .  were measured  gauge w h i c h c o n n e c t e d to  so  measurements  Readings  error could arise  t h e gas  pressures  steam o f  portional  the  occurs.  Another major  r  error  i n which a  locate  TV.5C  upper  g i v e n a 2% o f  broadening  state  Lorentzian showed no  4.19).  This  l i f e t i m e measurements  (sec.  profiles  dependence  shows in  the  molecular  T94-  TV.5E -All  Data  data points  punched on computer c a r d s  Processing  obtained from the Hanle e f f e c t curves  were  by u s i n g  test  an e l e c t r o n i c d i g i t i z e r .  t t h e 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 independently for halfwidths  that  s e v e r a l of  •When l i g h t  in  states  the discharge collision  -molecular  IV.5G  error  (Sec. in  In  This  thesis,  the ground  Some o f  4.3,  by r a d i a t i v e  "narrower"  system has  t h e r e were  s t a t e nor were Furthermore, the  in  a  phenomenon d i d  because  of  there pressure  the helium  the levels  transitions  t h e l i f e t i m e s measurements to be s y s t e m a t i c a l l y  the l i f e t i m e s measured  the magnetic  be  and and  Effect  the alignment  C72, K66, OV67).  The reasons  will  thereby coherence narrowing  Cascading  interested, are affect  hydrogen. a)  signal  before  measurements.  r e f e r s to  A r g o n and Neon were f o u n d errors  to  this  was v e r y l o w ;  hydrogen l i f e t i m e  energy l e v e l s .  yielded  absorbed by another  e f f e c t s w e r e r e d u c e d t o a minimum  Cascading  they  obtained  0.5%.  i n t o which to decay.  cell  were  i n d i c a t e , because the composite  the works r e p o r t e d i n  any metastable  one i s  each case  the Hanle e f f e c t  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  also  In  l i f e t i m e than the i n d i v i d u a l molecule.  tnot occur  in  than  data points  To  Coherence Narrowing  cell,  the l i f e t i m e would  longer  of  e m i t t e d by one atom i s  cleaving the discharge -than  sets  the curves.  d i f f e r e d by l e s s  TV.5F  Error  a r e as  resonance  Cascading  i n the  in  from  which higher  i n 2P s t a t e s  too l a r g e d i d not  excited states  due to  of cascade  cause an  important  (3D,  Z)  3E,  of  follows: experiment the g-values  found agreed  to  -95-  w i t h i n 1% w i t h t h o s e m e a s u r e d b y D i e k e Lab  (FM73bi  different  MF71)  and by M a r e c h a l  g-value belonging  to  et  (ML74).  a higher  b) at  As  quite unlikely  concluded i n  lower pressures  3D,  3E, Z  states  sec.  4.3,  in  state  of  was  that  Bell.  Tel.  ever found.  possessed  effect  obtained at  is  lower  hydrogen agreed w i t h the higher  a Thus  identical  the case of molecular  the cascading  and t h e r e s u l t s  (DCB53),  A l s o , , no e v i d e n c e o f  -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 g-values, which i s  al  hydrogen,  strong  only  pressures pressure  in  measure-  ments.  IV.5H Simply by mentioned  in  this  summing  Conclusion  all  the p o s s i b l e  s e c t i o n and a l l o w i n g  clude  that  the l i f e t i m e measurements,  stark  e f f e c t s , are accurate to w i t h i n  e r r o r s which have  some r a n d o m e r r o r , we c a n if  f r e e from cascading  5%.  The measurement  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  pressure  i n a hynamic In  the magnetic  resonance  were found from the magnetic This  sharp  factors  resonance of  change  3  of  helium.  t h a n 1%  Thus  in polarization. a larger  of  a small Due t o  change  so  1.5  the Lande  from g-  error. constant  was  i n p o l a r i z a t i o n over a  the noise  relative error  dip.  calibration  t h e w e l l known g - v a l u e o f  state  10%.  g-factors  the resonance  the f i e l d  the r e p o l a r i z a t i o n experiment the h f s  from the r a t i o  change has 10%.  the 3 P  a r e b e l i e v e d to have l e s s In  culated  using  since  the  accurate to w i t h i n  the center of  can be d e t e r m i n e d v e r y p r e c i s e l y ,  cross-  of  experiment, the Lande  f i e l d at  can be a c c u r a t e l y e s t a b l i s h e d the  are only  con-  and  of  section,  flow discharge,  been  that  level is  the  small  callarge  polarization  only accurate  to  within  -96-  Many o f electronic should and  state  have had  the h f s  the spectral (Figure  to  s t u d i e d were from t h e  F i g u r e 4.10)  and  identical radiative lifetimes,  constants.  to a g r e e w i t h  4.3  lines  each other  so  theoretically  cross-sections,  E x p e r i m e n t a l l y t h e s e measurements to w i t h i n  same u p p e r  the accuracies  quoted  were above.  g-values found  -97-  Chapter  Five  The l i f e t i m e s  D I S C U S S I O N AND  of  t h e J = 1,  hydrogen m o l e c u l e were f i r s t  e x c i t e d by e l e c t r o n s III.2,  lifetime  = 39.3  of  (2.5)  the J=l  In curve  that  Marechal's  resonance  negligible of  in  the long  that  errors will  in  this  contribute  by Marechal  section  she  IV.2  stated  that  given  i n her  that  to  IV.5G,  experiment,  intensity  the J=l  changes  or  Hg.  it  is  other  the l i f e t i m e of  level  function.  the  of  my is  possible random  measured reported  lifetime. lifetimes  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  f u n c t i o n and o n l y v e r y w e a k l y  fact  Because  t h e 3D s t a t e  approximation,  t h e wave  the  measurements.  H^ were a l s o of  cascading  effect  of  the Born-Oppenheimer  of  Lorentzian  the r e s u l t s  the cascading  3E a n d Z s t a t e s  primarily  the  measurements.  Under  depends  (2.0)  experiment  explain  than our measured  state  Her  the  a g a i n f o u n d 20% l e s s  a  section  except  be narrowed by t h e  the d i f f e r e n c e i n  The l i f e t i m e of  in  M a r e c h a l measured  e l e c t r o n gun.  and  time of M a r e c h a l ' s  3D,  molecules  T(J=2) = 38.3  e f f e c t l i f e t i m e measurements  to  of  Dalby  e x p e r i m e n t a l method  appear  showed  the  state  described  was  of  t h e wave  of  as  (1.2),  b u t no r e a s o n was  fluctuations,  work.  (M73),  experiment  the Hanle  Lifetimes  same  experiment might  in  3D0  sec.  e f f e c t d i d not  averaging  pressure  n  thesis  As discussed magnetic  with the  energy l e v e l s ,  the cascading  = 26.1  Independently,  15.8(.8)  i n Van Der L i n d e ' s  from higher  T(J=1)  cell,  w e r e made b y a 30 e v .  y i e l d e d a l i f e t i m e of  of  on the Hanle E f f e c t w i t h  discharge  n sec.  level  the excitations  based  a R.F.  and y i e l d e d l i f e t i m e s  and T(J=3)  that  in  2 and 3 l e v e l s  measured b y Van D e r L i n d e and  T h e i r e x p e r i m e n t was  CVD69).  CONCLUSION  on the r o t a t i o n a l  parts  part  of  Van Der L i n d e t h a n 40% d i s c r e p a n c y and  that  found  of  in  t h e J=2  noticed that,  C V 7 0 )  and 3 s t a t e s .  t h e 3D0 a n d 3D1  the a n a l y s i s  the  e f f e c t of  of  in  our  the Hanle  hyperfine  the absence  -to J t o is  it  e f f e c t curves  in  the magnetic  angular  of  g-factors  the g-factors, g  are  For  J - l , g  For  J=2,  For  J=3  values  a » v „ ,  N  should  then the hfs the  F  5 MHz and  1=0,  g  state,  F  the case  of  of  g  a r e about  the  theory.  ignored  in  hfs  experiment,  the nuclear  low f i e l d  spin  I  magnetic  separately  couples field  about  the  the  high  to  field.  follows:  =  gj  g  for  11/12  T  states  the natural  the c a l c u l a t i o n In  g  the  case  g  is  constants  F=2,  and .95  3,  3/4  g  and 4  T  the  are average  g . T  l i n e width, of  lifetimes  of  the  30 n s e c w h i c h y i e l d s  intermediate  Van Der L i n d e .  far  When a l a r g e  , at very  these  N  be used  The s e c u l a r  so  repolarization  the g-factor  where v„ i s  t h e measured  was  hSj  =  c a n be n e g l e c t e d .  lifetimes  state  disagreement  re-examine  we h a v e  precess  c a l c u l a t e d as  g-factor If  to  field,  momentum F .  r e s p e c t i v e l y 4/3  g  necessary  t h e y become d e c o u p l e d and  The r e l a t i o n s  of  the J=l  more  experiment.  an e x t e r n a l magnetic  form a t o t a l  applied  field  of  T h e same k i n d  of  there i s  splittings.  A s we d i s c u s s e d in  t h e 3D0 s t a t e  appeared between the l i f e t i m e s  T h i s d i s c r e p a n c y makes In  in  about  the case  J=l,  above  and  if  a<<v  3D s t a t e s  of  H2  a natural  are also  then the  l i n e width  5 MHz.  This  of  is  coupling.  equations,  The s o l u t i o n ,  for  i n which the energy  were of  solved  t h e Zeeman  by sub-  ,  l e v e l s a r e expressed as Figure  a f u n c t i o n of magnetic  that  required for  the Lorentzian curve  the energy  equals  l i n e width. to the hfs  shown,  that  In  splitting  indicate  -then the s u p e r p o s i t i o n halfwidths  are given If  Lorentzian curves yB/a).  hyperfine Although  As  crossing  constant  there are  of  a.  six  is  shown i n F i g u r e 5 . 1 ,  it  the population of  t h e Zeeman s u b l e v e l s  thesis  was  in process.  5.1,  six  is  arrows fields  at  curve  is  whose  the halfwidth  likely  of  equal to  that  the  simple,  of  the 1  J=l.  the numerical  in  uB/vp  magnetic  the Hanle curve f o r is  also is  arrows.  calculations  the c a l c u l a t i o n  the excited state  from the e l e c t r o n to  Unfortunately,  already  the  may i n v o l v e d i f f i c u l t i e s  the alignment  coupling.  of  the  halfwidth  The o b s e r v e d H a n l e  b r o a d e n somewhat  It  of  Figure  negligible  the t h e o r e t i c a l e x p l a i n a t i o n  -transfer  this  magnetic  sublevels, to  i n d i v i d u a l Lorentzian curves  are complicated.  1,J  in  the  e f f e c t , equals  the Hanle e f f e c t experiment i s  effect will  equal to  d i f f e r e n t magnetic  fulfilled.  splitting  in  In  six  by the l o c a t i o n s  the hfs  is  o u r c a s e , w h i c h a = v^,  -which the above c o n d i t i o n i s  .(=1  shown  s e p a r a t i o n b e t w e e n t h e Zeeman  can i n t e r f e r e to produce l e v e l  natural  are  is  5.1. The h a l f w i d t h of  field  field,  and  t h e n u c l e u s due  t h e s e phenomena w e r e n o t The d e t a i l e d t h e o r y has  of the  to  found u n t i l not  yet  the ,  been  completed. The h f s first  splitting  measured,rto  measurement w i t h molecular 5.2(.5)  upper  of  be 6 . 3 ( . 6 )  the J=l MHz,  level  by Marechal  three different radiative state.  and 4. 8(.5)  of  3D0  state  (M73).  transitions  Those experiments y i e l d v a l u e s  MHz f o r  the hfs  splitting  constant.  of  H2was  We r e p e a t e d from the of  this  same  5.1(.5), The  average  -101value  is  20% l e s s  understood  were found  number J a n d v a r i e d  only  of  t h e 3D a n d  measured. with  to  the measured  in  with  of  3E e l e c t r o n i c s t a t e s lifetimes  has  is  state.  constant  the r o t a t i o n a l  quantum  quantum  number  thesis  of  molecular v-1  of  been proven n e g l i g i a b l e  in  and r o t a t i o n  hydrogen  3D s t a t e  t h o s e measured b y Van Der L i n d e and D a l b y .  cascading  this  splitting  many v i b r a t i o n a l  of  difference, of  the v i b r a t i o n a l  this  lifetimes  The measured  hfs  be independent of  slightly  the accomplishment The measured  This  i n h e r l i f e t i m e measurement  shown i n T a b l e 4 . 3 ,  t h e 3D s t a t e  Summary of  r e p o r t e d by M a r e c h a l .  from the e r r o r s As  of  than that  has  are  in  been agreement  The p o s s i b i l i t y  t h e measurements  levels  of  of  molecular  hydrogen. The m a g n e t i c  hfs  and  3E e l e c t r o n i c s t a t e s  the  states  has  states  found to  BK66).  was  found  (FHJC64, MBBB70). fields  in  to  of  3D,  that  with  the  3D  for  one  of  measured  3E and Z  i n agreement  t h e 2p s t a t e s with  here.  electronic  the high  magnetic  of  to be dominant 3'D,  4'D,  5'D  The i n t e r a c t i o n of of  5'D  neon and a r g o n were  measured  t h e most r e l i a b l e measurements  be i n agreement  t h e measurement  with  in  (DCB53).  found  The l i f e t i m e s and  of  found  levels  The p u b l i s h e d v a l u e  be i n agreement  and  be i n agreement  Cascading  measured  to  by Dieke  The l i f e t i m e s and  ten rotational  f i e l d Lande g - f a c t o r  were a l s o measured  f i e l d measurements  of  were measured.  been found  Low m a g n e t i c  splitting  state  with  states  electronic of  the R.F. at  excitation.'  h e l i u m were  w i t h many r e l i a b l e electric  low pressure  (C72,  also  measurements field  were  and  magnetic  studied.  -102-  ,Suggestions f o r  Further  Work  :The t h e o r e t i c a l c a l c u l a t i o n of  Hyperfine  splitting  The percentage  of  for  the J=l  broadening  of  of  the Hanle  l e v e l have  to  effect  in  the  be and w i l l  the Lorentzian p r o f i l e ,  be  then,  presence studied.  can  be  calculated. The t h e o r y -complex  (3d'E,H,A)  is  for  the  calculation  needed f o r  of  the hfs  constant  the i n t e r p r e t a t i o n of  of  the  3d  the  experimental  the  rediative  results. T h e method used lifetimes,  the Lande  be a p p l i c a b l e .state  t o many  involved  -the magnetic  has  hfs  in  this  g-factor, states  a gx  is  f o r measuring  the magnetic  splitting  constants  should  o f many a t o m s a n d m o l e c u l e s ,  providing  the  product  splitting  thesis  in  the range  larger  than 1  hfs  10  - 7  MHz.  sec  to  10  -  1  0  sec  or  -103-  Appendlx The d i s c h a r g e neutral In  is  assumed  A to  consist  atoms o r m o l e c u l e s and a much s m a l l e r  the absence of  collisions,  the motion of  of  a d i l u t e gas  number o f  free  the electrons  of electrons.  in a  radio-  A  frequency e l e c t r i c f i e l d field  H = H k, Q  is  i  E  governed  Q  ojt a n d  COS  small  perpendicular  magnetic  by  m* = e E o Cos cot - e H ^ (A.l)  (A. 2) Let  V  *  Equations  — (A.l)  and and  }X  ^  ( A . 2 ) now t a k e  the  form:  (A. 3 )  (A.4) Solving  equations  (A.3)  and  (A.4)  (A.5) When  X  =  7f  -  0  Implies  A|  - rtx ~  O  -104-.  so  that  (A.6) and  00"  -  V " CA.7)  Substituting  equation  (A.7)  back  into  eq.  CA.4)  (A.8) The s o l u t i o n  of  equation  CA.8)  is:  ( A . 9) When so  = * J  £  ^  ^ - 0  ^piies  that  (A.10) Equation  (A.5)  and  CA.10)  may b e c o m b i n e d  to  give  (A.11) Equation  (A.11)  miner axis  over  is  the equation of  the major  axis  is  an e l l i p s e -  where t h e r a t i o ^ °  of  -105-  Appendlx Let us as  consider  shown i n F i g u r e B . l .  a four  B  level  The atoms  are  system  |a>,  to  |b>.  a higher Through  excited  |c>  If  solution  of  then as  the d e n s i t y matrix  JiLet  shown  ^(-|  r  r  -  *  of  - A.  are  |c>  is  state  |b>  M  *  y  and  then  and  if  populated o n l y by  is  (2.2B), given  the  to  |d>.  excited to  continuously,  section  emission  intermediate  |b>  in  state  excited state  t h e atoms  |d>  state  spontaneous an  state  and  excited  they decay to  the lower  |b>,  |c>,  e x c i t e d from ground  |a>  decay from state  |b>,  state  state radiative  stationary  by  (2.2.22)  *  13 jtio b  Equation  (2.2.22)  now t a k e s  f  the  form:  =  A H u - X H  If  the d i r e c t i o n of  which given:  is  observation  proportional  to  is  the r e a l  fI  chosen a p p r o p r i a t e l y part  of  CB.D the  the d e n s i t y matrix  polarization, , p b  is  -106-  P(H) oC I + Xv H = -^g—  where curve  in  and  AH^ i s  the halfwidth  the Hanle  effect  experiment.  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