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Stark effect on emission spectra of diatomic molecules Phelps, Daniel Holdsworth 1966

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STARK  EFFECT OF  ON  EMISSION  DIATOMIC  SPECTRA  MOLECULES  by DANIEL HOLDSWORTH PHELPS B.A., M.A.,  Reed C o l l e g e ,  Dartmouth  A THESIS SUBMITTED  i960  College,  1962  IN PARTIAL FULFILMENT OF  THE REQUIREMENTS FOR  THE DEGREE OF  DOCTOR OF PHILOSOPHY in  t h e Department of PHYSICS  We  accept  required  this  t h e s i s as c o n f o r m i n g  t o the  standard  THE UNIVERSITY OF BRITISH COLUMBIA April,  19^6  In the  requirements  British  for  Columbia,  available mission  for  for  purposes his  presenting  I  agree  without  of  this  thesis  of  by  It for  May  12,  is  of  I  this  Head o f  understood  financial  Physics  1966  partial at  the L i b r a r y  permission.  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, Canada Date  the  in  degree  study.  copying  be g r a n t e d  my w r i t t e n  Department  that  r e f e r e n c e and  representatives.  cation  thesis  an a d v a n c e d  extensive  may  this  Columbia  fulfilment  of  the U n i v e r s i t y  of  shall  make  f u r t h e r agree thesis  for  that  gain  copying  shall  freely per-  scholarly  my D e p a r t m e n t that  it  not  or or  be  by publi-  allowed  The U n i v e r s i t y  of B r i t i s h  Columbia  FACULTY OF GRADUATE STUDIES  PROGRAMME OF THE FINAL ORAL EXAMINATION FOR THE  DEGREE OF  DOCTOR OF PHILOSOPHY  of  DANIEL H. PHELPS  B.A., Reed College., 1960 M„A„, Dartmouth College., 1962  THURSDAY, MAY 12, 1966, AT 2:30 P.M. IN ROOM 303, HENNINGS  COMMITTEE IN CHARGE Chairman:  D. H. C h i t t y  A. J , Barnard A. M. Crooker F. W. Dalby  R„ A. Nodwell E. A. O g r y z l o R„ D. R u s s e l l  E x t e r n a l Examiner: A. V. Jones U n i v e r s i t y of Saskatchewan . at Saskatoon Research S u p e r v i s o r :  F. W. Dalby  STARK EFFECT IN EMISSION SPECTRA OF DIATOMIC MOLECULES ABSTRACT The atomic  i n f u e n c e of an e x t e r n a l e l e c t r i c  or m o l e c u l a r  on the e l e c t r o n i c  to  the h i g h e l e c t r i c  The S t a r k  e m i s s i o n s p e c t r a of the OH  Stark s p l i t t i n g s  field  r e g i o n of a low p r e s s u r e glow f i e l d s were determined  i n hydrogen Balmer l i n e s . )  s e r v a t i o n s of t h e S t a r k e f f e c t  from  From ob-  on the m o l e c u l a r  d i p o l e moments were determined 2  up  The Stark s p e c t r a were produced i n  (The e l e c t r i c  the e l e c t r i c  and  was s t u d i e d f o r e x t e r n a l e l e c t r i c  68,000 v o l t s / c m .  discharge.  effect,  s h i f t s , broadenings  changes of i n t e n s i t y i n s p e c t r a l l i n e s .  and CH molecules  on  s p e c t r a , known as the S t a r k  t y p i c a l l y leads to s p l i t t i n g s ,  effect  field  spectra  f o r the OH  ~TT*  TT e l e c t r o n i c  molecule  i n the  molecule  i n both the  2  -  TT  arlc  j  2  s t a t e and f o r the  A  electronic  CH  states.  From t r a n s i t i o n s t o the f o l l o w i n g l e v e l s the v a l u e s of the d i p o l 2e moment were found t o be: OH 1 .73 " ^ l / 2 3 J = 1/2, v = 0 2  TT3/2,  =.  3/2, v = 0  =  1/2,  V  =  1  1 .69  J  =  1/2,  V  =  0  1 .46 +  J  =  7/2,  V  =  0  1 .13  J  •TTi/2. J 2  TTi/2>  CH  2  2  A 3  The  first  1 .63 •+ 0.03 7  T  2  t  0.04 0.06 15  ?°  r e p o r t e d o b s e r v a t i o n of r e s o l v e d  order Stark e f f e c t s on the e l e c t r o n i c d i a t o m i c molecule niques  t 0.02 Debye  2  developed  first  s p e c t r a of a  r e s u l t e d from t h i s work.  The t e c h -  i n t h i s i n v e s t i g a t i o n a r e well, s u i t e d  for  t h e study of s h o r t  l i v e d and c h e m i c a l l y  molecules i n both t h e i r ground  and e x c i t e d  reactive electronic  states.  GRADUATE STUDIES  Field  of Study; Elementary  M o l e c u l a r Spectroscopy Quantum  Mechanics  Waves  J.  Quantum Theory  of S o l i d s  Spectroscopy Molecular Advanced  W. Opechowski  Spectroscopy Spectroscopy  C o Savage R. B a r r i e  A. M„ Crooker F. W.  Dalby  A. J . Barnard  PUBLICATIONS R.W.  C h r i s t y and D.H. Phelps, " P r o d u c t i o n of V3 i n KCL by X Rays", P h y s i c a l Review 1_24, 1053  D.H. Phelps and F.W.  Dalby,  the S t a r k Effect, on OH",  (1961).  " O p t i c a l O b s e r v a t i o n s of Canadian J o u r n a l of  P h y s i c s 43, 144 (1965) . D.H. Phelps and F.W.  Dalby,  "Experimental  Determina-  t i o n of the E l e c t r i c D i p o l e Moment of the Ground Electronic  S t a t e of CH", P h y s i c a l Review L e t t e r s  16, 3 (1966)  ii ABSTRACT  The in  electronic  applied  These  electric  spectra  e m i s s i o n s p e c t r a o f t h e OH and CH fields  state  2  2 t t  CH  2  TT / , 1  2  2  Electric  3/2» 2  ^l/2> A  j  v - 0  electronic  1.73  " 3/2, v = 0  1.692 *  ™ i / ,  v - 0  1.^6  ,  J -  7/2, v - 0  f i e l d s were d e t e r m i n e d  Balmer l i n e s .  levels;  reactive states.  suited  o i +  1  15%  Stark s p l i t t i n g s  The S t a r k s p e c t r a were p r o d u c e d  f o r the study of s h o r t l i v e d  molecules  Debye  ± 0.06  1.13  from  °»  r e g i o n of a low p r e s s u r e glow d i s c h a r g e .  is well  i n both t h e i r  from  7  v = 1  2  electronic  1 . 6 3 ± 0.03  J = 1/2, J  moment o f  states  * 0.02  2  field-  dipole Z  on t r a n s i t i o n s - t o t h e f o l l o w i n g  T T ! / , J = 1/2,  and  f o r OH i n t h e Tf  2  2  broadenings  The e l e c t r i c  and CH i n b o t h 'the T T and 2/^  OH  field  lines.  has b e e n d e t e r m i n e d  Stark e f f e c t s  gen  68,000 v/cm h a v e been observed„  show S t a r k s p l i t t i n g s ,  induced, p a r i t y - f o r b i d d e n the m o l e c u l e s  up t o  molecules  ground  i n hydro-  i n the h i g h  This  technique  and c h e m i c a l l y  and e x c i t e d ,  electronic  ill  TABLE  CHAPTER I :  CHAPTER I I *  1  f o r Chapter  7  molecule  I n an e l e c t r i c  field  ...  elements o f the p e r t u r b a t i o n  model t r e a t m e n t  secular equation  Starlc e f f e c t  9  o f Hund s c o u p l i n g case 1  f o r lambda  spectrs.  doublet  . . . • . • . • . . • • . . • • • » « . « « . « © o « . . « . . .  treatment  Coupling  i n t e r m e d i a t e b e t w e e n Hund's c a s e  mixing  lambda  dOUbletS  Second  order Stark  ( a ) ...  levels  Rigorous  Parity  7 8  p e r t u r b a t i o n and p a r i t y  Vector The  5  I  THEORETICAL PRELUDE  Energy of a diatomic  The  CONTENTS  INTRODUCTION  Footnotes  Matrix  OF  of matrix  and t r a n s i t i o n s  e l e m e n t s .................  between  10 lk  15 19  (a)  perturbed  » . o » o f t » « o o o O 0 . o » e . » e o . » . o w 0 « a . 0 o . . o . o »  27 31  effects  Footnotes CHAPTER I I I : Electric  EXPERIMENTAL DETAILS discharge  Production Observing  tube  36.  o f OH and CH e l e c t r o n i c the S t a r k  Determination Footnotes  %  effect  spectra  ...........................  ^0 4-2  s t r e n g t h .........  43  I I I ............................  4-5  o f the e l e c t r i c  f o r Chapter  emission  field  iv  CHAPTER I V :  EXPERIMENTAL OBSERVATIONS  .  Stark  effect  on t h e OH, 2 Z ~ * T T hand  Stark  effect  on t h e CH,  Stark  splittings  Stark  effect  2  +  Z  2  ^~-* JJ Z  band  ................  i n . the a t o m i c hydrogen  on t h e CH, A~* 2  Experimental  ................  2  ..............  of Stark  .....  Footnotes CHAPTER V:  effect  spectra  69  o f e l e c t r i c d i p o l e moments o o . . « . . . . . . . . . . . . . . . .  ..............  . « . . © . © . . © . . * .  . » . . o . ©  f o r C h a p t e r IV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  CONCLUSION AND  Suggestions  62 62  Determination Summary  54  58  Measurements Analysis  46  Balmer  77" band  c o n d i t i o n s f o r spectrograms  46  SUGGESTION FOR FURTHER STUDY  f o r f u r t h e r work  ....  77  87 90 91 91  V  LIST  TABLE I :  TABLE I I :  TABLE I I I :  OF  TABLES  Experimental Conditions used i n F i g u r e s  f o r Spectrograms ,  O b s e r v e d S t a r k S p l i t t i n g s i n OH, £?-~ Band and i n h y d r o g e n B a l m e r H ^ « o » e « z  Observed induced,  2  63  77  64  « o o o  and C a l c u l a t e d P o s i t i o n s o f f i e l d p a r i t y - f o r b i d d e n l i n e s i n the ................  66  TABLE I V :  O b s e r v e d S t a r k S p l i t t i n g s i n CH, 2Z~^2TT Band and i n h y d r o g e n B a l m e r Hy .............  68  TABLE V:  Simultaneously Observed Stark S p l i t t i n g s i n CH and OH -> TT* Bands  70  TABLE V I :  E x p e r i m e n t a l C o n d i t i o n s f o r P l a t e s Used t o D e t e r m i n e OH and CH E l e c t r i c D i p o l e Moments .  71  TABLE V I I :  OH E l e c t r i c D i p o l e Moments D e r i v e d f r o m S'tfl.rk SpXi.*fc"tintrs O 0 o o » » » « e t > « o » 6 e o » » « . # o *  78  2  TABLE V I I I :  Z*~  >  2  7T,  Corrected Band 0 O O O  ( 0 , 0 ) , band  o f OH  Stark S p l i t t i n g s 6  0  O  C  6  t> 4» «  i n OH O  «  «  TABLE I X :  C o r r e c t e d Low D i s p e r s i o n S t a r k i n CH 2 £ - - . * 2 T T Band . . . . . . . .  TABLE X:  Corrected, Splittings  TABLE X I :  «  O  z  2?-> a  o a  e  2  6 * * « .  7T o  • o o ©o  Splittings  83  Simultaneous Observed S t a r k i n CH and OH £ " - » T T Bands ... 2  80  85  2  E l e c t r i c D i p o l e Moments f o r t h e OH and CH O O 4 O 0 O O O O * ) < I Molecules o o o o c o o e o o oo o « o  © • o o  89  vi  LIST  OF  FIGURES  Figure  2.1:  V e c t o r d i a g r a m o f a d i a t o m i c m o l e c u l e i n an e l e c t r i c f i e l d , Hund'a c a s e ( a ) o o o e o o o o i i  Figure  2.2;  Stark  Figure  2.3:  Z e r o f i e l d and f i e l d - i n d u c e d , p a r i t y f o r b i d d e n t r a n s i t i o n s a s s o c i a t e d w i t h 0^(4) and Q ( 4 ) l i n e s o f OH o o o o o o o o o o o o o o o o o o o o  effect  on OH, P i ( l ) 2  and P i ( l ) l i n e s  11  2.4;  18  e o  2 1  Figure  16  .  Z e r o f i e l d and f i e l d - i n d u c e d , p a r i t y f o r b i d d e n t r a n s i t i o n s between lambda d o u b l e t s . and Q  (3)  32  Figure  2.5'  Figure  3.1:  Modified  Fie-ure  4.1:  Allowed t r a n s i t i o n s t o lowest rotational 2 l e v e l s i n OH 2 y r and. rT 3 / s t a t e s . . . . . . . . . . . .  Stark  effect  on CH, Q  Stark  Figure 4 . 3 :  Stark, e f f e c t  on OH . o  Figure 4 . 4 :  Stark  effect  on OH,  4.5?  Stark  effect  on CH,  Figure 4 . 6 :  (3)  Lo Surdo d i s c h a r g e  Figure 4 . 2 :  Figure  l c  effect  on OH,  2  2  2  tube  j r - » T T , +  37  00  48  .  52  ( 1 , 1 ) band ...  53  £~-* TT.  ( 0 , 0 ) band . . .  55  2  2  S t a r k e f f e c t on CH, 5 T ~ - T T , ( 0 , 0 ) b a n d for three values of e l e c t r i c f i e l d 2  > 2  on h y d r o g e n B a i m e r  Figure 4 . 8 :  Stark  effect  on CH, A~* Z  2  TT  b  a  n  H d  y  0  0  0  D  0  0  57 Q  4  0  0  59  0  60  e « o e » o o o o e o  Corrected Stark s p l i t t i n g , A V ' , v s . e l e c t r i c f i e l d s t r e n g t h , E, f o r OH, R ( l ) , ( 0 , 0 ) l i n e  79  2  Figure 4 . 1 0 :  47  ]T% IT,  effect  4.9:  e o e e o o e o o o  o o o o o o e o o e u o o o o o o o w e f r  Stark  Figure  lines  ( 0 , 0 ) band  2  4.7:  Figure  l d  29  F i r s t - o r d e r S t a r k s p l i t t i n g o f CH, P ( l ) l i n e v s . f i r s t - o r d e r Stark s p l i t t i n g of OH, R ( l ) l i n e D O O O O O o o o o o t - o o e o o o o o e c o o 0 0 0 1 2  2  0  0  0  0  86  vi ACKNOWLEDGEMENTS  I tor,  wish  t o thank  for his helpful  Professor  F . W. D a l b y , ray r e s e a r c h  direc-  assistance  and c r i t i c i s m t h r o u g h o u t  this  work. This of  Canada.  work was s u p p o r t e d by t h e N a t i o n a l  Research  Council  CHAPTER I • INTRODUCTION The  i n f l u e n c e o f an e x t e r n a l e l e c t r i c f i e l d on a t o m i c o r  molecular  s p e c t r a , known as t h e S t a r k e f f e c t , t y p i c a l l y  pro-  duces s p l i t t i n g s , s h i f t s , b r o a d e n i n g s and changes i n i n t e n s i t y in spectral l i n e s .  T h i s study w i l l be concerned w i t h t h e  S t a r k e f f e c t on t h e e l e c t r o n i c e m i s s i o n s p e c t r a o f d i a t o m i c molecules.  Observations  o f t h e S t a r k e f f e c t on such  s p e c t r a p r o v i d e a means o f d e t e r m i n i n g  molecular  t h e e l e c t r i c d i p o l e mo-'  ment o f a molecule. The  S t a r k e f f e c t on an atomic spectrum was f i r s t  f o r hydrogen. LoSurdo  2  I t was observed i n d e p e n d e n t l y  i n 1913.  by S t a r k  observed 1 a  n d by  The S t a r k e f f e c t on t h e hydrogen Balmer  l i n e s p r o v i d e d a s u c c e s s f u l t e s t f o r t h e Bohr theory o f t h e hydrogen atom. ^  The S t a r k e f f e c t on v a r i o u s atomic, s p e c t r a was  s t u d i e d e x t e n s i v e l y u n t i l t h e mid-1930'e. V e r l e g e r p r o v i d e s many r e f e r e n c e s on t h i s  (A review a r t i c l e by subject.^)  S e v e r a l t h e o r e t i c a l s t u d i e s o f t h e S t a r k e f f e c t on molecu l a r band s p e c t r a were r e p o r t e d d u r i n g t h e 1920'a. ^ I n 1931» i  W. G. Penny p u b l i s h e d a t h e o r e t i c a l paper c o v e r i n g t h e S t a r k e f f e c t on both symmetric t o p and asymmetric t o p molecules.-' I n h i s i n t r o d u c t i o n he s a i d t h a t w i t h the I n c r e a s i n g Importance of t h e s u b j e c t o f band s p e c t r a h i s s t u d y had been u n d e r t a k e n .  i n ' t h e hope t h a t t h e e x p e r i m e n t a l  d i f f i c u l t i e s involved  i n t e s t i n g t h e r e s u l t s would soon be overcome."-' Penny ically  stated i n h i s conclusion that f o r a diatomic  specif-  molecule  2 In  an e l e c t r o n i c s t a t e w i t h a component o f a n g u l a r momentum,  a l o n g t h e I n t e r n u c l e a r a x i s ( i . e . a TT, A  f  e t c . s t a t e ) and  w i t h a n o n - v a n i s h i n g e l e c t r i c d i p o l e moment " . . . t h e r e  will  be a s p l i t t i n g , q u a d r a t i c a t f i r s t and l i n e a r as soon as the energy s h i f t s become l a r g e compared w i t h t h e n a t u r a l b l i n g I n t e r v a l s . "5  Penny a l s o s p e c i f i c a l l y  \-&  stated that  lar  from  s t a t e s ( f o r w h i c h t h e r e i s no component o f angu-  momentum a l o n g the I n t e r n u c l e a r  axis).  !  *:-r:. --.;• r  Contemporary t o P e n n y ' s w o r k , numerous e x p e r i m e n t a l ies  ~-  there  would be no a p p r e c i a b l e c o n t r i b u t i o n t o t h e S t a r k e f f e c t electronic X  o u  were made o f t h e S t a r k e f f e c t  YIIJ^..^..:.:..^...  stud-  on t h e band s p e c t r a o f t h e  6-11 hydrogen m o l e c u l e .  The observed s h i f t s  i n frequency  a quadratic r e l a t i o n s h i p to the applied e l e c t r i c f i e l d .  obeyed (The  observed t r a n s i t i o n s d i d i n v o l v e an e l e c t r o n i c TT s t a t e b u t s i n c e from symmetry t h e  m o l e c u l e can have no permanent  t r i c d i p o l e moment o n l y a second order S t a r k e f f e c t served.)  The  2  X - £ (0,0) 2  elec-  was o b -  band a t 39l4# and (0,1) band a t  4278$ were observed i n e l e c t r i c f i e l d s up t o 280 kV? no e p l i t t i n g s were o b s e r v e d . permanent  ( N o t i c e t h a t the N m o l e c u l e can have no 2  e l e c t r i c d i p o l e moment.  t h a t no a p p r e c i a b l e  Stark e f f e c t  which c o u l d have shown a f i r s t  Thus i t i s not s u r p r i s i n g was o b s e r v e d . )  order Stark effect  Experiments were made oh  the CO^ comet t a i l band® w i t h e l e c t r i c f i e l d s up t o 280 kV/cm and on the CO b a n d s  1 2  at 4835, 4511,  t r i c f i e l d s o f 115 k V / c m .  4393, and 4123$ w i t h e l e c -  B o t h o f these experiments  n e i t h e r displacements nor s p l i t t i n g s .  These n e g a t i v e  c o u l d be due t o t h e r a t h e r l o w d i s p e r s i o n u s e d .  showed results  (The g r e a t e s t  3 d i s p e r s i o n r e p o r t e d was k&/aua used i n the study of the S t a r k f e c t on CO.)  Also,  f o r the CO molecule i t  i s now known from  microwave measurements t h a t the d i p o l e moment i s o n l y Debye?-3 i n the ground  0.112  state.  Herzberg ^ i n d i s c u s s i n g the f i r s t order Stark e f f e c t  used  1  the example of a J = 1,  7T l e v e l ;  an e l e c t r i c d i p o l e moment of ,  1  1 Debye; and an e l e c t r i c f i e l d an o v e r a l l s p l i t t i n g o f 0.168  o f 10 kV/em w h i c h corresponds cm" . 1  He s a i d :  of o r d i n a r y s p e c t r o s c o p i c  reach  methods."  The r e s u l t s r e p o r t e d here i n c l u d e the f i r s t r e p o r t e d  tronic spectra. ^ 1  to  "No such s p l i t -  t i n g s have yet been observed even though they are w i t h i n  s e r v a t i o n s of f i r s t  ef-  ob-  order Stark s p l i t t i n g s i n molecular e l e c T h i s work p r o v i d e d the o n l y p u b l i s h e d  exper-  i m e n t a l v a l u e o f the e l e c t r i c d i p o l e moment o f the CH m o l e cule. ^ 1  Also  9  at i t s time o f p u b l i c a t i o n the v a l u e o f the  elec-  t r i c d i p o l e moment o f the OH m o l e c u l e determined from t h i s work ''' was more a c c u r a t e 1  microwave  than e a r l i e r v a l u e s determined u s i n g  techniques.  Knowledge of the e l e c t r i c d i p o l e moment o f a molecule i s i m p o r t a n t because o f fundamental  I n t e r e s t and a l s o as a t e s t  t h e o r e t i c a l l y computed wave f u n c t i o n s .  for  R e c e n t l y , knowledge o f  the e l e c t r i c d i p o l e moment o f molecules has a l s o become i m p o r ;  tant to radio astronomers.  F o r example, t o determine  the  densi-  t y o f OH molecules from observed microwave a b s o r p t i o n ^ i n the 1  Interstellar  medium the e l e c t r i c d i p o l e moment must be known.  The d i p o l e i moment o f the CH m o l e c u l e i s a l s o c u r r e n t l y o f importance i n e s t i m a t i n g the s t r e n g t h "of the lambda doublet  transl-  :  i. tion  f o r t h e J « 1/2  Douglas 3,400  level  and E l l i o t t ?  h  1  a  V  of the T7  determined t h i s  e  Stark e f f e c t  in a modified LoSurdo particularly of short  useful  lived  and  f o r studying  chemically reactive  electronically  moments have b e e n d e t e r m i n e d  c o n s t a n t , from  Stark  effect  tional  resonance  in their electronic  n i q u e has  addition  dipole states:  2  moment o f the NH 0  A  3TT,  i s b e i n g used  the H C l  successfully  molecule. C A  a  X  and  t o study the  dielec-  o f the s e c o n d from  order  m o l e c u l a r beam  However, t h e s e  applicable  only  conven-  to s t a b l e  mole-  state.  applied  molecule  A , and  their  Molecular e l e c t r i c  t o the work r e p o r t e d h e r e  a l s o been  spectra  from measurements o f  techniques.  ground  on t h e  :  states.  produced  technique i s  s p e c i e s i n both  microwave•observations  techniques are generally  In  nique  excited  on lambda d o u b l e t l e v e l s  experiments using  This  the S t a r k e f f e c t  dipole  ed  lambda d o u b l i n g t o be  type d i s c h a r g e tube.  2  and  tric  state.  on t h e s p e c t r a . r e p o r t e d h e r e was  ground  cules  ground  Mc/sec„ The  tric  electronic  2  c -^TTo  the LoSurdo  to determine  tech-  the  i n three electronic Presently  Stark e f f e c t  this  elecexcit-  tech-  on t h e s p e c t r a  of  5 Footnotes f o r Chapter I 1. J . S t a r k , Ann. P h y s i k j£,, 965 (1914). 2. A . Lb- Surdo, A l t - t i i . A c c a d . L l n c e l 22, 665 (1913). 3. See f o r example, E. U . Condon and G . H . S h o r t l e y , The Theory o f Atomic S p e c t r a (Cambridge U n i v e r s i t y P r e s s , Cambridge, E n g l a n d , 1935), p . 397. 4. H . V e r l e g e r , E r g i b . e x k t . a  N a t u r w i s s . 1 8 , 99 (193'9) .  5. W. G . Penny, P h i l . Mag. 11, 602 (1931).  •?  6. J . K . L . . M c D o n a l d , P r o c . Roy. S o c . (London) 123, 103 (1929). 7.  , P r o c . Roy. S o c . (London) 131, 146 (193D.  8. W. Rave, Z. P h y s i k ^ , 72 (1935). 9. H . S n e l l , T r a n s . Roy. S o c . (London) 234, 115 (1935). 10. H . Hasunuma, P r o c . P h y s . - M a t h . S o c . Japan 1 8 , 469 (1936). 1 1 . J . S. F o s t e r , 1029 (1935).  D . C . J o n e s , and S. M. Neamtam, P h y s . Rev. 51,  12.  B . Svenson, Z . P h y s i k 107., 485 (1937).  13.  C . A . B u r r u s , J . Chem. P h y s . 28, 427 (1958).  14. G . H e r z b e r g , M o l e c u l a r S p e c t r a and M o l e c u l a r S t r u c t u r e . I . S p e c t r a o f D i a t o m i c M o l e c u l e s (D. Van Nostrand C o . , New Y o r k , 1950), Second e d i t i o n , p . 308. 15.  D. H . Phelps and. F . W. D a l b y , paper p r e s e n t e d a t t h e Symposium on M o l e c u l a r S t r u c t u r e and S p e c t r o s c o p y , The Ohio S t a t e U n i v e r s i t y , Columbus, O h i o , June, 1963-  16.  D. H . Phelps and F . W. D a l b y , Phys. Rev. L e t t e r s (1966).  17.  D. H . Phelps and F . W. D a l b y , Can. J . P h y s . 4^, 144 (1965).  18.  S. Weinreb, A . H . B a r r e t t , Nature 200, 829 (1963).  M. L . Meeks, and J . C. H e n r y ,  19. A . E . Douglas and G . A . E l l i o t t , (1965). 1  16, 3  Can. J . Phys. 4^, 496  T. A. R. I r w i n  (1965).  and F. W . D a l b y , Can. J . P h y s . 43,  1766  Mr. S . Y. Wong i s c o m p l e t i n g h i s M. S c . t h e s i s a t U.B.C. on t h i s t o p i c u n d e r t h e d i r e c t i o n o f Dr. F. W. D a l b y .  CHAPTER I I THEORETICAL PRELUDE One  observes t h a t the S t a r k e f f e c t  a l t e r s b o t h the  quency and i n t e n s i t y of e l e c t r o n i c e m i s s i o n s p e c t r a l we w i l l  see,  t h i s i s the consequence  fre-  lines.As  of a p e r t u r b a t i o n o f  the  r o t a t i o n a l energy l e v e l s due to the i n t e r a c t i o n of the a p p l i e d electric field  and the average v a l u e o f the e l e c t r i c d i p o l e mo-  ment i n the d i r e c t i o n o f the e l e c t r i c f i e l d .  A l l the  observed  f e a t u r e s o f the S t a r k e f f e c t on the s p e c t r a o f a d i a t o m i c molec u l e can be p r e d i c t e d and the m a t h e m a t i c a l r e l a t i o n s h i p s  needed  to determine e l e c t r i c d i p o l e moments w i l l be o b t a i n e d by answering  the  following questions:  1) How does one d e s c r i b e the i n -  t e r a c t i o n o f the a p p l i e d e l e c t r i c f i e l d and the charge d i s t r i b u t i o n o f the molecule?  2) T r e a t i n g t h i s i n t e r a c t i o n as a p e r t u r -  b a t i o n u s i n g quantum mechanics, when does t h i s i n t e r a c t i o n have a nonzero m a t r i x element?  3) How does the p e r t u r b a t i o n  the energy of the m o l e c u l e ?  alter  4) How does t h e p e r t u r b a t i o n  effect  the c h a r a c t e r of the m o l e c u l a r energy l e v e l s ?  Energy o f a d i a t o m i c molecule i n an e l e c t r i c The  field  energy a s s o c i a t e d w i t h a d i s t r i b u t i o n o f e l e c t r o n s i n -  t e r a c t i n g w i t h an e x t e r n a l e l e c t r i c f i e l d ming the c o n t r i b u t i o n due to each c h a r g e .  can be found b y sumF o r the d i a t o m i c  molecule l e t us t a k e the c o - o r d i n a t e o r i g i n at the c e n t e r of p o s i t i v e charge.  The p e r t u r b a t i o n energy w i l l be o f the V =  erj/1? ,  form: (2.1)  8 r\  where e I s t h e e l e c t r o n i c c h a r g e , electron, will  and E i s t h e e l e c t r i c  since  the molecule i s a x i a l l y  nent o f the p o s i t i o n v e c t o r  the  contribute  along  to expression  strength.  Equation dipole  symmetric,  only  moment. t h e compo-  see t h a t  ming o v e r e r ^ , constant, equation  equation  since  and t h e n  (2.1) c o u l d be e v a l u a t e d field  the dot p r o d u c t  (2.1) w i l l  vector  e  f^n°E  s  Second,  by f i r s t  sum-  may be t a k e n as a  c o u l d be t a k e n .  Therefore,  be w r i t t e n :  Vsee t h i s  the i n t e r n u c l e a r a x i s .  the e l e c t r i c  ^ ,  Thus, t h e c o n t r i b u t i o n t o  e n e r g y f r o m an i n d i v i d u a l e l e c t r o n may be w r i t t e n :  we a l s o  (2.1)  the i n t e r n u c l e a r a x i s ,  (2.1).  where n i s a u n i t v e c t o r a l o n g  We  field  now be r e x i r r i t t e n i n terms o f t h e e l e c t r i c  First,  will  i s the p o s i t i o n of the i t h  = -p-E  (-e^^)n-E  expression  i s c o n s i s t e n t with  .  (2.2)  a d e s c r i p t i o n o f the —>  interaction (e^L^)  Matrix  e n e r g y w h i c h u s e s a d i p o l e moment, J d , o f m a g n i t u d e  d i r e c t e d along  elements o f t h e p e r t u r b a t i o n The  function,  perturbation  will  energy.  levels  studied  be I m p o r t a n t  here the matrix  energy l e v e l s  Thus we c o n c l u d e  i s comparable  the matrix  For  elements o f the  o n l y when t h e s e p a r a t i o n  between two l e v e l s w i l l  belong  c a n be  f a c t o r s , one a n e l e c t r o n i c e i g e n - •  t o v i b r a t i o n and one t o r o t a t i o n .  problem  otherwise appropriate  turbation  o f three  one r e l a t i n g  experimental  bation  energy  t o t a l wave f u n c t i o n d e s c r i b i n g a n e n e r g y l e v e l  taken as the p r o d u c t  the  the i n t e r n u c l e a r a x i s .  o f two  to the pertur-  elements o f the per-  o n l y be i m p o r t a n t  i f . t h e two .  t o t h e same e l e c t r o n i c and v i b r a t i o n a l l e v e l .  They then have the V  form:  1 2 - (feYv  fr \ ±  (-eli)S.E/  f  j  Taking the d i r e c t i o n o f the e l e c t r i c f i e l d  ^  ) .  (2.3)  as the z - a x i s o f a  c o - o r d i n a t e system f i x e d i n space we can r e p l a c e the dot p r o d u c t , n * E , by n E , where n i s the p r o j e c t i o n o f the u n i t •» ->  vector  n a l o n g the d i r e c t i o n o f E , the e l e c t r i c f i e l d ,  the  z  z  magnitude o f the e l e c t r i c f i e l d .  and E i s  N o t i n g t h a t the e l e c t r o n i c and  v i b r a t i o n a l wave f u n c t i o n s are the same i n t h e i n i t i a l and  final  s t a t e e q u a t i o n (2.3) becomes: V  1 2  = <«v|  (-el)\)  n E { %) z  z  ,  (2.4)  where the °< and the v c h a r a c t e r i z e the e l e c t r o n i c and v i b r a t i o n al  state.  The f i r s t  f a c t o r i n e x p r e s s i o n (2.4) Is the  quantum  m e c h a n i c a l e x p r e s s i o n f o r the e l e c t r i c d i p o l e moment i n the t i c u l a r e l e c t r o n i c and v i b r a t i o n a l s t a t e .  par-  We w i l l be s t u d y i n g  d i a t o m i c molecules f o r which t h e r e i s a net d i p o l e moment.  For  t h i s s i t u a t i o n e q u a t i o n (2.4) i n d i c a t e s t h a t the b e h a v i o r of the second f a c t o r , w h i c h I n v o l v e s t h e quantum m e c h a n i c a l average o f the z-component of a v e c t o r , w i l l  determine whether a S t a r k  ef-  f e c t w i l l be o b s e r v e d .  The p e r t u r b a t i o n  and p a r i t y  The i n i t i a l and f i n a l r o t a t i o n a l l e v e l s i n d i c a t e d above must have o p p o s i t e p a r i t y f o r the m a t r i x element o f the b a t i o n energy to be n o n z e r o . m a t r i x element  pertur-  F o r t h i s argument we can w r i t e  as: Vl2 = ^  (tit  ™* ©I Vz) ,  ( -5) 2  the  10  where © i s t h e a n g l e moment l y i n g reflection  along  between t h e e l e c t r i c  the i n t e r n u c l e a r axis.  through  the o r i g i n ,  parity.  For the value  for  a reflection.  have o p p o s i t e p a r i t y . the g r e a t e s t e f f e c t  of V  on r o t a t i o n a l  ring  f o r e l e c t r o n i c TT, A ,  a  i s , cos © has n e g a t i v e i t must n o t change  that  and ^  must  The p e r t u r b a t i o n d i s c u s s e d h e r e  respect to p a r i t y .  will  have  l e v e l s which a r e degenerate  Lambda d o u b l e t  rotational  etc. states closely  levels  occur-  approximate  such  situation.  V e c t o r model t r e a t m e n t Figure  o f Hund's c o u p l i n g c a s e ( a )  2 . 1 shows t h e v e c t o r model f o r Hund's c o u p l i n g  (a) f o r w h i c h t h e e l e c t r o n i c internuclear  axis.  shown i n e q u a t i o n doublet  level.  effect found  Using  motion  this  i s s t r o n g l y coupled  v e c t o r model  ( 2 . 4 ) c a n be f o u n d  the matrix  classically  This discussion i s presented  lows us t o e a s i l y  anticipate  the e s s e n t i a l  here  w i l l be d e r i v e d r i g o r o u s l y  o f N, t h e r o t a t i o n a l  angular  case  t o the elements  f o r a lambda  here  since i t a l -  features o f the Stark  on t h e s p e c t r a o f a d i a t o m i c m o l e c u l e .  I n F i g u r e 2 . 1 , "T, t h e t o t a l sum  That  Thus we c o n c l u d e  with  a  I f . w e now p e r f o r m  t o be n o n z e r o  1 2  and t h e d i p o l e  x becomes - x , y becomes - y , z b e -  comes - z , and c o s © becomes - c o s © .  such  field  (The r e s u l t s  later.)  angular  momentum i s t h e v e c t o r  momentum o f t h e n u c l e i  and o f  —»  jT,  the angular  nuclear tronic  axis.  momentum o f t h e e l e c t r o n s t a k e n  J\. i s composed o f if,  spin angular  electronic  orbital  the p r o j e c t i o n  momentum a n d o f A , angular  along  o f the e l e c -  the projection  momentum, each t a k e n  the i n t e r -  along  o f the the i n t e r -  11  F i g u r e 2.1. Vector diagram of a diatomic i n an e l e c t r i c f i e l d , Hund's c a s e (a).  molecule  12 nuclear axis. for  (This X  an e l e c t r o n i c  n o t be c o n f u s e d  s t a t e i n which the o r b i t a l  zero which corresponds gram a l s o  should  shows y-  t o an a t o m i c  , the e l e c t r i c  The v e c t o r d i a -  d i p o l e moment, E , t h e e l e c t r i c -*  - *  s t r e n g t h , and M, t h e component o f J i n t h e d i r e c t i o n Using  found  t h i s v e c t o r model t h e p e r t u r b a t i o n e n e r g y  as f o l l o w s .  discussion turbation field  (This treatment  o f t h e Zeeman e f f e c t energy  i s the product  s t r e n g t h , E,  dipole erage  a n g u l a r momentum i s  S state.)  —>  field  w i t h t h e symbol  and.offy,  4  of the e l e c t r i c  a l o n g ~J s i n c e Si of J .  then  the d i r e c t i o n  along  (a).)  The p e r -  of the e l e c t r i c field.  by f i r s t  (and}*) p r e c e s s  T h i s average v a l u e o f E.  rapidly  along J , ^ j , i s  Thus we w r i t e :  7 j=^co8(j?,J)^_^_  (2.6)  /V£  ( 2  CG8(  we now use e q u a t i o n  tion  ( 2 . 7 ) we  T h i s av-  finding the  i  If  1  o f the magnitude o f t h e e l e c t r i c  about t h e d i r e c t i o n averaged  1  i n Hund's c a s e  o f t h e d i p o l e moment i s found  average v a l u e o f j  w i l l be  t o Herzberg s  the average v a l u e  moment i n t h e d i r e c t i o n value  i s similar  of E.  "'^ITTT  (2.6) t o r e p l a c e t h e f a c t o r ^  -7)  i n equa-  find: 'T^fz  r  J ( J * I )  s i n c e t h e m a g n i t u d e o f t h e v e c t o r J c a n be r e p l a c e d b y (J(J+1))"2, the  total  write  ( i n u n i t s o f h/2n) J b e i n g t h e quantum number f o r a n g u l a r momentum.  Using  equation  (2.8) we c a n now  t h e p e r t u r b a t i o n energy a s : Vi2 =  =  '  (2.9)  13 Thus t h e p e r t u r b a t i o n e n e r g y tudes  o f the e l e c t r i c  strength;  c a n be f o u n d  d i p o l e moment and o f t h e e l e c t r i c  and t h e quantum numbers f o r t h e t o t a l  and  i t s p r o j e c t i o n s along  and  along  (2.9)  momentum field  we c a n c o n c l u d e  the f o l l o w i n g :  The  increase with increasing angular  ( T h i s i s due t o t h e f a c t o r M w h i c h w i l l . a s s u m e  J - l , . . ., - J . )  The s e p a r a t i o n between a d j a c e n t  p o n e n t s o f an e n e r g y J(J>1)  angular  the d i r e c t i o n o f the . e l e c t r i c  number o f S t a r k components w i l l  J,  field  the i n t e r n u c l e a r a x i s .  From e q u a t i o n  momentum.  i n t e r m s o f t h e magni-  level will  decrease  i n the denominator of equation  values  S t a r k com-  due t o t h e f a c t o r o f  (2.9).  Thus t h e S t a r k  s p l i t t i n g s w i l l be r e s o l v e d o n l y  f o r lower  also  s t a t e h a v i n g no component o f  conclude  electronic  t h a t an e l e c t r o n i c  angular  contribute nothing  momentum a l o n g t o the f i r s t t o fi=  s i t u a t i o n , corresponds  values of J .  the I n t e r n u c l e a r a x i s -will  order Stark  0.  We c a n  effect  F o r example,  since  this  i n an e l e c t r o n i c  2<r-  2.  state  the o r b i t a l  a n g u l a r momentum i s z e r o and t h e s p i n  a n g u l a r momentum i s c o u p l e d sulting  i n _Tl-=  0.  to the axis of nuclear rotation r e -  One c o u l d a l s o  would n o t c o n t r i b u t e t o a f i r s t the r o t a t i o n a l  state  There w i l l els  are  here  and t h u s  cannot  so w i d e l y  separated  ina  doubled  rotational levels  i n energy  t h a t they  2T  electronic  p e r t u r b each  However f o r t h e h y d r i d e  the adjacent  s i n c e each o f  parity.  "be p e r t u r b a t i o n s b e t w e e n s p i n  o f opposite p a r i t y .  studied  effect  the spin doublet l e v e l s  h a v e t h e same p a r i t y  state  2  order Stark  l e v e l s has d e f i n i t e  More p r e c i s e l y  t h a t a ]T  conclude  other.  rotational  lev-  molecules  of opposite  parity  contribute only a  14 very  s m a l l second  o r d e r term.  This i s also  true f o r the p e r t u r j 2/±  rotational  states  F u r t h e r d i s c u s s i o n o f the i n t e r a c t i o n  investigated  between ic  adjacent  section  here.  rotational  given due  energy  using  eigen-values  the m a t r i x  be a b l e  splittings  blet  found  field.  field-induced,  o f J , 2)  ~ v 22  =  ^ '  t  h  e  energy order  eigen-values Stark and  o f p e r t u r b e d , lambda  dou-  the f o l l o w i n g equation:  1  0  (2.10)  .  2  2  are g i v e n  i n equation  a r e the e n e r g i e s o f t h e two  unperturbed  I f we  8  0  l  u  -  t  V  take  tween t h e two u n p e r t u r b e d l l  these  dipole  "22 ~ £  lambda d o u b l e t s .  V  be  12  The o f f d i a g o n a l e l e m e n t s , and V  now  electric  Stark broadenlngs,  =  21  1 1  specif-  parity-forbidden lines.  det  V  (  f o r a perturbation  resolved f i r s t  a r e g i v e n by t h e r o o t s o f 6  V,  doublet w i l l  molecular  f o r the e n e r g y  V  (2.9).  n  reserved f o r a  above  Using  1)  values  eigen-values  levels  a  levels  f o r a lambda  o f a permanent  to p r e d i c t :  f o r lower  eleotric The  be  doublet  elements  an a p p l i e d e l e c t r i c  we w i l l  3)  f o r lambda  to the i n t e r a c t i o n  with  levels will  2  below.  The s e c u l a r e q u a t i o n The  levels  i n t h e 77  b a t i o n between n e i g h b o r i n g  l  o  = V  1 2  the zero of energy  levels n  t  o  2 1 >  and w r i t e  equation  their  as midway b e separation  (2.10) may be w r i t t e n  as:  £l = ± J ( V 2 ) 2 + From  this  solution  we  (V )2" .  (2.11)  1 2  see t h a t b o t h  levels  o f t h e lambda  doublet  will We  split  may  i n t o as  relate  many components as  this  the  appearance of  the  matrix  a factor of  the  of M  that  f o r a. s y s t e m w i t h a h a l f  spin  of  els  must be  p a r t i c l e s i n an doubly  studied  o f 1/2,  the  arbitrary  of  extent  f o r the  mixed p a r i t y on A  we  the  the  can  tive  parity  and  which are in  the  vice  resulting  which are 2.2  sum  of  the  a l l lev-  r e m a i n even  molespin  for  induced  figure  rule  are  by  w i l l be that  an  versa. f r o m the  the  f o r the  The  be be-  have  Stark  transitions  only with states  parity  m i x i n g due  absence o f parity  will the  m o l e c u l e and  The  to  lead  of  the to  is  negaper-  transi-  electric  forbidden  electric field. OH  levels  of t h e  e l e c t r i c dipole  electric field  of  in detail  perturbed feature  to  molecule.  combine  i n the  examples  the  levels  energy l e v e l s  discussed  essential  for  parity  forbidden  shows two  the  lambda d o u b l e t  perturbed  a diatomic  selection  of p o s i t i v e  the  knowing  of  states  Figure  M  states  total electronic  i n M would  mixing  predict  that  tions  cause  present  spectra  strict  turbation  having  to  This  S i n c e a l l the  1 , 2  to  spectra  mixed.  effect  . . . .  the  -M  due  squared.  of  |M|.  field.  will  but  of M and  electric field,  p e r t u r b a t i o n between a s s o c i a t e d  The  of  square root  value  arbitrary  Kramers' degeneracy  of o p p o s i t e p a r i t y  low,  Integral  degenerate  electric  values  Kramers' theorem which  h e r e were i n s t a t e s  Stark e f f e c t The  u n d e r the  2  perturbation being  degeneracy i s a consequence of  cules  are  energy degeneracy f o r v a l u e s  element  the  there  field.  transitions  transitions  corresponding  shown  lines  16  I,  K = 0,  J= '/  2  T F> (l)  F[ (I)  2  E=0  E=60kv/  cm  n »/2 J =/ 3  2  E=0  E = 60 kv/  F i g u r e 2.2. S t a r k e f f e c t on OH, P i 2 ( D and P i ( l ) l i n e s . Broken l i n e s i n d i c a t e f o r b i d d e n t r a n s i t i o n s . Lambda d o u b l i n g and S t a r k s p l i t t i n g s a r e drawn t o t h e same scale f o r both r o t a t i o n a l l e v e l s .  cm  show r e s o l v e d f i r s t first tion  o r d e r i n the energy  lambda  order Stark  applied electric  i s s e v e r a l times  doublet  splittings.  levels.  field  larger  than  Transitions  The  splittings  because the  the  perturba-  s e p a r a t i o n of  to r o t a t i o n a l  levels  of J d i d not  show r e s o l v e d S t a r k s p l i t t i n g s  the  reasons:  J i n c r e a s e s the  the number o f S t a r k tion  of the  Stark  Stark e f f e c t to the  components  rotational levels. than  components w i l l  be  well  lines  of  0^(4)  and  from  the  Q 1^) 2  The  lines  was  2  In  field 2  c o n c l u s i o n we  see  by  t h a t the  parity-forbidden lines  the  initial  to p a r i t y .  resulting  which b o t h matrix  2  the  except  those be-  doublet  2.3  and  shows an  transitions (0,0)  ex-,  f o r the  band o f t h e  the allowed  rota-  OH  associated  component  of  line.  induced,  tra  +  obscured  splittings,  respect  J,  Thus f o r h i g h e r  Figure  ZT -^ TT,  resolved  either  separa-  appear q u i t e narrow  induced  and  lambda d o u b l i n g  field-Induced, parity-forbidden line  the Q, ^(4) l i n e  the 0^(4)  will  allowed l i n e .  of the  the  increasing  a l l transitions  of mixed p a r i t y .  and  Since  p e r t u r b a t i o n , the lambda  forbidden line  the z e r o f i e l d  molecule. with  the  separated  ample  still  the  with  When t h e  for  lambda d o u b l i n g  increase.  g e n e r a l l y broaden  comes somewhat l a r g e r  tional  also  components d e c r e a s e s  will  lowest  As  the  with  larger values following  are  from  broadenings,  or f i n a l Before  and  clearly  i s degenerate  d i s c u s s i n g the  levels  will  e.g.  elements f o r the p e r t u r b a t i o n i n v o l v i n g  field-  i n energy  Stark effect  degenerate,  in  transitions i f  between e l e c t r o n i c  are  result  separated  for electronic  level  transitions  rotational  Stark e f f e c t  the  on  with spec-  states for 2  A - » »  2  TT  electric  , the  F i g u r e 2.3. transitions  2"s:-* 2jr +  sitions.  (  Z e r o f i e l d and - f i e l d - i n d u c e d } . p a r i t y - f o r b i d d e n a s s o c i a t e d w i t h Q]_(4) and Q 2 i(4) l i n e s o f OH, band. Broken l i n e s i n d i c a t e f i e l d induced t r a n -  field  and t h e e l e c t r i c  These r i g o r o u s l v a l u e s  dipole will  moment w i l l  confirm  be f o u n d  rigorously*  the correctness  o f the v e c t o r  model r e s u l t f o r t h e m a t r i x e l e m e n t s .  From t h e f o l l o w i n g  t i o n we w i l l  a r e t o be made when a r o -  also  tational level  s e e what  does n o t b e l o n g t o p u r e Hund's c a s e  Rigorous treatment In the  V  of matrix  the i n i t i a l  perturbation  dipole  corrections  a 1 2  We r e c a l l  (a) c o u p l i n g .  elements  discussion  o f the matrix  elements f o r  e n e r g y o f a m o l e c u l e w i t h a permanent  moment i n an a p p l i e d  electric  electric  f i e l d were g i v e n b y :  < « v | ( - e l i)|*v><4£fn Ej  (2.4)  z  that  the f i r s t  sec-  f a c t o r represents  the e l e c t r i c  dipole  moment f o r a p a r t i c u l a r e l e c t r o n i c a n d v i b r a t i o n a l s t a t e a c t e r i z e d b y <X and v . is  parallel  space. and  n  z  to the z-axis  i s t h e component  tion  causing  i n the introduction  of the e l e c t r i c  dipole  moment  ;  o f a co-ordinate  system  t o t h i s chapter,  and t h e a v e r a g e v a l u e  i n the d i r e c t i o n of the e l e c t r i c  o f the e l e c t r i c  field.  The d e -  on t h i s  c a n be e m p h a s i z e d b y w r i t i n g :  •i2  -/<Vi* K E  We have a l r e a d y  shown t h a t  eigen-functions  must have  remaining  the p e r t u r -  t o the i n t e r a c -  pendence o f the matlrx elements o f t h e p e r t u r b a t i o n averaging  axis  (field direction).  e f f e c t does c o r r e s p o n d  field  f i x e d In  to the internuclear  along the z-axis  the Stark  h a s magnitude'; * E , a n d  field  The u n i t v e c t o r "n i s p a r a l l e l  T h u s , as s t a t e d bation  The e l e c t r i c  char-  conditions  J  t >-  the i n i t i a l opposite  on t h e s e  < ' > 2  2  and f i n a l  parity.  rotational  We w i l l  eigen-functions  1 2  nowffind the  f o r nonzero  matrix  20 elements.  E s s e n t i a l l y we w i s h  c h a n i c a l average nonzero values  t o determine  when t h e quantum me-  o f t h e z-component o f a v e c t o r i s n o n z e r o .  o f f n ) f o r Hund's  c o u p l i n g case  (a) w i l l  The  now he  Li  discussed. I n Hund's c o u p l i n g c a s e strongly numbers  coupled  with  c o u p l i n g case  o f -A..  the exception orbital  i s the t o t a l  component  a r e ; ex , Ji, J , • M.  A corresponds  the e l e c t r o n i c  f i e l d . °C h a s been a b s o r b e d  electric  d i p o l e moment d i s p l a y e d i n e q u a t i o n  will  separated  t o t h e same e l e c t r o n i c  A  n o t be i n d i c a t e d  will  The  matrix  the m a t r i x the  z-a&is.  elements Hence  the a d d i t i o n a l  appropriate  selection  electric  case  explicitly  for electric  i n equation  (2.4).  (2.12)  rules  Matrix  ele-  of A  (which  reason  and f i n a l state  the  s t a t e s bea n d <X and  i n the f o l l o w i n g d i s c u s s i o n . (2.12)  are i d e n t i c a l  dipole radiation restrictions  a r e seen  for electric  (a) c o u p l i n g .  values  For this  and v i b r a t i o n a l  elements i n equation  ments g i v e n  f o r Hund's  effect.  be d i s c u s s e d f o r i n i t i a l  longing  o f the  compared t o t h e p e r t u r b a t i o n )  not c o n t r i b u t e t o the S t a r k  perturbation w i l l  axis.  i n t h e e x p r e s s i o n f o r the  states with d i f f e r e n t  i n energy  o f the  and M d e n o t e s t h e  a n g u l a r momentum i n t h e d i r e c t i o n  external  are w i d e l y  term  the i n t e r n u c l e a r  a n g u l a r momentum quantum number  ments b e t w e e n e l e c t r o n i c  <X d e n o t e s t h e  t o t h e component  a n g u l a r momentum a l o n g  o f the t o t a l  motion i s  The g o o d quantum  o f quantum numbers a s s o c i a t e d w i t h  electronic J  t o the I n t e r n u c l e a r a x i s .  f o r this  assembly  (a) the e l e c t r o n i c  from  with  polarized  on t h e m a t r i x  along ele-  a d i s c u s s i o n o f the  dipole transitions  and  The f o l l o w i n g g e n e r a l r u l e s f o r  dipole transitions are relevant:^  21 For  the t o t a l  except  a n g u l a r momentum quantum number, J , A J = * 1, 0 t h a t J = 0 does n o t combine w i t h J = G.  S t a t e s o f o d d p a r i t y combine o n l y w i t h even p a r i t y and v i c e v e r s a . The  other general  nuclei  o f equal  charge  have a permanent no ply  first  selection  t o b o t h Hund s 1  coupling  case  internuclear  nuclei  molecules  and f o r would not  d i p o l e moment and t h e r e f o r e w o u l d  effect.  The f o l l o w i n g s e l e c t i o n  c o u p l i n g case  (a) a n d c a s e  (b) t h e e l e c t r o n i c axis.  for identical  do n o t a p p l y a s s u c h  electric  order Stark  rules  states of  spin  (Hund's c a s e  (b).  show  r u l e s ap-  F o r Hund's  i s weakly coupled  t o the  (b) w i l l b e d i s c u s s e d i n d e t a i l  below.) F o r A , t h e component o f t h e e l e c t r o n i c a n g u l a r momentum: d A = ± 1,0 For the t o t a l  electronic  s p i n quantum number, S,  AS  The  remaining  selection  rules  of t h e p e r t u r b a t i o n matrix  orbital  0  =  needed t o complete  elements  the d i s c u s s i o n  i n Hund's c a s e  (a) a p p l y  when b o t h s t a t e s b e l o n g t o c a s e ( a ) : ^ The component o f t h e e l e c t r o n i c s p i n a l o n g t h e i n t e r n u c l e a r a x i s does n o t a l t e r , i . e . :  41=  0  F o r t h e component o f t h e t o t a l along the i n t e r n u c l e a r a x i s :  4/1=  ± 1, 0  As we h a v e r e s t r i c t e d  our i n t e r e s t  having  o f A. , o n l y  Jl  t h e same v a l u e  may combine  matrix  - A -=  since  the n e c e s s a r y  nonzero matrix  to Initial states with  a n d A X = 0.  e l e m e n t s o f n , A M = 0. z  a n g u l a r momentum  Using  elements  these  and f i n a l  states  t h e same v a l u e o f Specifically for f a c t s we f i n d  f o r the average  that  of a vec-  22 t o r i n the d i r e c t i o n  of the e l e c t r i c f i e l d  i n Hund's c a s e (a)  are:^ <JlJ  M| n  z  | J1J  M > = (/1J J n  (SI J M I n | y i J - l z  (ilJ-1  M| n  z  | i l J  M)  z  | 71 J> M  = (71 JI n |  J - l ) y/(j2 _  z  M2)  n | /I j) v/(J -  M) = ( / i J - l |  2  z  M ) 2  (2.13) Although  the p a r i t y  the i n i t i a l first  o f t h e s t a t e s i s n o t shown h e r e  and f i n a l  s t a t e must have o p p o s i t e p a r i t y .  r e l a t i o n s h i p w i l l be u s e d  e r two w i l l  be u s e d  i n finding  neighboring rotational  levels.  w h i c h depend o n l y on J and Si  (fLJ N  1  (Jlj\  |n | 2 1  z  J\ J> = /  J(J+1)  second  order  The f a c t o r s  effects  due t o  i n equation  (2.13)  are given by:^  .  n I Si J-l) =  t u r b a t i o n matrix tion  (2.9)  sult  i s obtained  agreement w i t h  f o r the per-  e l e m e n t s b e t w e e n lambda d o u b l e t s g i v e n  i s correct.  ship i n equation  from  The c o r r e s p o n d i n g equation  (2.13)  (2.12)  i n equa-  quantum m e c h a n i c a l r e -  using the f i r s t  relation-  and (2.14) and one o b t a i n s :  t h e v e c t o r model  I n Hund's c o u p l i n g c a s e momentum i s w e a k l y c o u p l e d the m a t r i x  The  f o r lambda d o u b l e t s a n d t h e o t h -  We can s e e f o r example t h a t t h e v e c t o r model r e s u l t  in  explicitly,  result.  (b) the e l e c t r o n i c  spin  t o the i n t e r n u c l e a r a x i s .  angular To f i n d  e l e m e n t s o f t h e p e r t u r b a t i o n f o r Hund's case  need t o know w h i c h quantum numbers a r e good and w h i c h  (b) we  selection  23 rules apply specifically. K, S, J , M, and parity.  The good quantum numbers are o( , A . As above; <* denotes the assembly of  quantum numbers describing the electronic term with the exception of A which corresponds to the projection of the electronic angular momentum on the internuclear axis; J is the total angular momentum quantum number; and M corresponds to the projection of the total angular momentum along the direction of the applied electric field.  The quantum number K denotes the total angular  momentum apart from spin.  K is composed of electron orbital  angular momentum along the internuclear axis and angular momentum due to rotation of the nuclei.  The total electron spin an-  gular momentum is denoted by S. The selection rules given above for the general situation of electric dipole transitions and for both Hund's case (a) and case (b) can be immediately applied.  Since we are only interest-  ed: in the interaction of neighboring rotational levels which both correspond to case (b) coupling we only need the appropriate selection rule for K, except for 2 -2 is forbidden.  i.e.:3 4 K  = ±1, 0  transitions for which  - 0  In complete detail the desired matrix element of n  2  for case (b)  coupling would be written: <VA K S J M| n l « ' A K S J'MJ). z  One may  summarize the discussion above and greatly simplify the matrix element by saying: <X = <*', AV./1'-, 5 = 8 and the parity although not shown explicitly must be opposite in the i n i t i a l and final states.  Let us drop the quantum numbers which are not needed  explicitly and use the selection rule for n , i . e . 2  AM - 0 . The  2k desired  matrix  element (A  These m a t r i x then u s i n g  K  S J M|  elements w i l l  n  formulas  J M> . neglecting  forfinding  to the addition of;angular  and K t h e n o n z e r o m a t r i x  the matrix  momenta.  elements  s p i n and ele-  Considering  are:^  A  n | A R> =  (AKJ  A KS  z  he f o u n d b y f i r s t  the appropriate  ments r e l a t i n g o n l y TV  thus s i m p l i f i e s t o :  z  K(K+l)  n \J\ K - l > - (A K - l l n  (AKl  z  1AK> =  z  (K - A ) (K +A ) (2K - 1) (2K + 1) ' We w i l l  be i n t e r e s t e d s p e c i f i c a l l y  w h i c h a l w a y s obey c a s e £-Z  transition i n (2.l6)  sion tor  given  above.  A. = 0 a n d t h e r e m a i n i n g <K|  n  z  |K-l)  2  (b) c o u p l i n g .  i s automatically  model r e s u l t  i n £ " electronic  = 0 i s forbidden  AK  (2.16)  As n o t e d  above f o r s u c h a  and thus  the f i r s t  zero.  This  i n (2.l6)  = <K-1| n ; | K> =  the are:  has been dropped.  nonzero matrix  the vec-  reduces t o : (2.17)  - 1)'  L e t u s now i n t r o d u c e  elements  expres-  state,  1  z  UM<where y\_  agrees with  F o r an e l e c t r o n i c X"  expression  states  s p i n and f i n d  i n t e r m s o f M , J , S, and K.  These  6  (K  S J  =  M|  n  z  M> =^ K - l S  |K-l S J  S J  M|  n | K S J z  M)=  M / ( J - S + K ) (J+S+K+l) ( S + K - J ) ( J * S - K > 1 ) ' 2 J ( J + 1 ) \{kYL*  (K  J  M|  n  |K-lS J - l  z  = ft J - M ) " 2  2  - 1)'  M >=  {K-l S J - lM  |  n  z  )K S J  M)=  j(J-S+K) ( J + S + K + l ) ( J - S + K - l ) ( J * S + K ) "  2J\|(4J  2  - 1)'  <I(4K - 1 ) 2  (2.18) I  25 I t i s understood opposite  t h a t t h e i n i t i a l and f i n a l s t a t e s must be o f  parity.  C o u p l i n g I n t e r m e d i a t e between Hund's oase (a) and case (b) As an example, i n t e r m e d i a t e c o u p l i n g I n the 77 e l e c t r o n i c 2  s t a t e w i l l be d i s c u s s e d .  Intermediate  coupling i n this  situa-  t i o n can be d e s c r i b e d as a m i x i n g o f TTi/x and TTfa r o t a t i o n a l 2  2  s t a t e s h a v i n g the same v a l u e o f J . C o r r e c t i o n s f o r i n t e r m e d i a t e c o u p l i n g were made s p e c i f i c a l l y i n a n a l y s i n g the S t a r k e f f e c t on t h e P ^ l ) t r a n s i t i o n t o t h e J - 3/2, Tfi/x l e v e l i n t h e 2  OH m o l e c u l e . ten  The g e n e r a l r e s u l t f o r t h i s m i x i n g can be w r i t -  5?  <¥int>l'-  2  /X  ,  " bWzfr,^, t  <fint>2  WTT}i)  *PTT, )  and  2  *Y( TT ) 2  Vx  af(27f )  7T3/ ) a r e pure'Hund's case (a) wave f u n c t i o n s . a  The upper s i g n s i n e q u a t i o n s  ( 2 . 1 9 ) a r e f o r r e g u l a r d o u b l e t s and  the l o w e r s i g n s a r e f o r i n v e r t e d d o u b l e t s . and b,  (2.19)  %  i n equations  The c o e f f i c i e n t s , a  (2.19) a r e g i v e n by:?  (2.20)  where  X -  +  + £ ) + (A/BXA/B-4) " . z  A i s t h e s p i n c o u p l i n g constant stant.  (2.21)  and B i s t h e r o t a t i o n a l con-  F o r r e g u l a r d o u b l e t s A / B i s p o s i t i v e and f o r i n v e r t e d  doublets A / B i s negative.  Hund's case (a) c o u p l i n g  t o t h e r a t i o A / B becoming l a r g e .  corresponds  S p e c i f i c a l l y , as A/B-+ 0 0 ,  a -# 1 and b - * 0 and we eee t h a t ! ^int)l^^ TT.A)  and ( V ^ t ^ ^ T T ^ ) ;  2  as A/B-* - q o a - * 0 and b - * 1 and t h i s c o r r e s p o n d s t o . f  ^lnt)l^T^( TT^) I t was convenient Intermediate  Y^™/,.). 2  ^ d ( f i n t ^  2  t o use Hund's case (a) wave f u n c t i o n s t o t r e a t  o o u p l i n g as t h e a p p r o p r i a t e m a t r i x elements a r e a l -  ready a v a i l a b l e .  The d e s c r i p t i o n g i v e n here may a l s o be used t o  t r e a t case (b) c o u p l i n g by s e t t i n g the c o e f f i c i e n t s g i v e n i n equation  (2.20):  a - b - l/lTT.  As a s p e c i f i c example, t h e ex-  p r e s s i o n s a v a i l a b l e here w i l l be a p p l i e d t o an i n v e r t e d ^ ' e l e c tronic  s t a t e t o e v a l u a t e the p e r t u r b a t i o n m a t r i x elements f o r  a lambda d o u b l e t r o t a t i o n a l l e v e l i n t h e T T 3 /  state.  2  p r o p r i a t e wave f u n c t i o n from e q u a t i o n ( T^lnth - a ^ H j / x ) + ^ V Z  i / x  4  The ap-  (2.19) i s s (2.22)  )  (2.12)  and t h e p e r t u r b a t i o n m a t r i x element g i v e n i n e q u a t i o n become! V 1 2 - -yz(*$i Tr^  ) + *f?< T7  z  The  J/A  )/  n  * | ^  2  7 T v  ) * ^< TT>AJ> (2.23) 2  A  s u b s c r i p t ± i n d i c a t e s t h e p a r i t y o f t h e I n i t i a l and f i n a l  state. •  2  As we have noted above, t h e c o m b i n a t i o n s A £ - 0.  (2.23) must obey t h e s e l e o t i o n r u l e ,  i n equation  Thus e q u a t i o n  (2.23) reduces tos V  1 2  - -f f f a  2  ^  2  ^  ^ ^ T f ^ i  )l  n 1 T^< T7y )> 2  z  a  ^1^(2%))].  (2.24)  T h i s e x p r e s s i o n can be e v a l u a t e d f o r a s p e c i f i c r o t a t i o n a l using expressions  (2.1$) and ( 2 . 2 0 ) .  level  27 There effect  are  two t o p i c s r e m a i n i n g  on s p e c t r a r e s u l t i n g  l e v e l s which are b o t h specific mixing topic the  o f lambda d o u b l e t  mixing In  let  be s e c o n d  o f neighboring  and  will  transitions  the l o w e r  unperturbed  e i g e n - f u n c t i o n s as ^  rotational  be r e v i e w e d .  and ^ .  the  due t o  levels.  lambda d o u b l e t  label  the  The f i n a l  order Stark e f f e c t s  corresponding  The p e r t u r b e d  doublets  o f mixed  "1" (one)  level  the  tothis  between p e r t u r b e d lambda  unperturbed  "2" and  level  Leading  rotational  d e s c r i b i n g a perturbed  us c a l l  between  The.Stark  be d i s c u s s e d , u s i n g  2  levels  for discussion will  Parity  will  CH /\ - TT band. 2  chapter.  transitions  degenerate  example o f t h e  interaction  from  in this  parity  and the  upper  unperturbed  levels will  be d e -  a  scribed  b y the  fupp "  eigen-functions:°  bJi -  < 2  '  2 5 )  O  where t h e  coefficients  a and b a r e g i v e n  by:°  a =  2 J(A/2)Z + ( V ) 2 '  .; i 2  * = Ii — 2  | 12| V  \ i s the V  1 2  will  f 1 - (X/2) |  2  .  27(A/2)  2  i  matrix  (2.26)  (V )21 2  s e p a r a t i o n o f the u n p e r t u r b e d  i s the The  1 2  lambda d o u b l e t  element f o r the p e r t u r b a t i o n  l e v e l s and  energy.  s i g n o f the p e r t u r b a t i o n a p p e a r i n g .in e q u a t i o n  a l l o w us t o determine  p o l e moment o f t h e  the  CH m o l e c u l e  relative  sign  i n the i n i t i a l  o f the  (2.26)  electric d i -  and f i n a l  state  28 from  observations  perturbation is  fixed  contains  relative  relative  o f the S t a r k  on t h e A  effect  the e l e c t r i c  - T T band.  d i p o l e moment whose  direction  o f t h e d i p o l e moment w i l l  determine  s i g n o f the p e r t u r b a t i o n which i n t u r n w i l l  er  the c o e f f i c i e n t s relative  • • • i. b a r e  splittings  upper and lower  .. p o s i t i v e  o f the Stark  h a s - t h e same o r o p p o s i t e  state.  wheth-  or negative.  components l e v e l s  s t a t e a r e known, t h e o b s e r v e d  The  the r e l a -  determine  Stark  If  i n the  spectra a l -  -,: i b o f one  lows one t o deduce w h e t h e r t h e "* .., c o e f f i c i e n t ' ; . state  direction  t o the i n t e r n u c l e a r a x i s o f the m o l e c u l e .  tive  the  The  2  2  s i g n as that'•'•>• i n t h e o t h e r  Thus we a r e a b l e t o d e d u c e  the r e l a t i v e  sign of the d i -  p o l e moments i n t h e two s t a t e s . The  transitions  shown i n F i g u r e 2.4 of the is  an e l e c t r i c  general  f o r zero  field  d i p o l e moment  between  i n Figure  strong  to h i g h e r quency assumes  2.4 a r e l a b e l l e d  frequency  allowed  the  lower  the  relative  and i n the presence relative  state.  (This  signs of example  levels.)  The a l l o w e d  I and I I .  o f the f i e l d  The p r i m e s  indicate  tranon t h e  forbidden  I f t h e d i p o l e moments have t h e same r e l a t i v e  component  there  l e v e l s are  i n d i s c u s s i n g the p e r t u r b a -  rotational  i n the presence  transitions.  field  i n the upper and lower  enough t o be u s e d l a t e r  transitions  the  electric  f o r t h e same and o p p o s i t e  t i o n between n e i g h b o r i n g sitions  two lambda d o u b l e t  line  o f the l o w e r  allowed  and the s t r o n g  component  moves t o l o w e r  frequency.  are g r e a t e r Stark  s t a t e which signs  frequency  i s correct  shifts  line  sign  moves  of the h i g h e r  fre-  (This conclusion  i n the upper s t a t e  f o r the GHJ/molecule.)  o f t h e d i p o l e moment a r e o p p o s i t e  than •  If'''  i n t h e up-  29  r A .  +  T  t  B Dipole  Moments  Parallel  Electric Field Zero  Electric  Dipole  Moments  Antiparallel  Field  Applied  F i g u r e 2.4. Z e r o f i e l d and f i e l d - i n d u c e d , parityf o r b i d d e n t r a n s i t l o n e b e t w e e n lambda d o u b l e t s . Broken l i n e s i n d i c a t e t r a n s i t i o n s w i t h lower i n t e n s i t y .  30 per  and l o w e r s t a t e s The  intensities  2.4 c a n be g i v e n tions.  the strong  Stark  of the Stark  components move  apart.  t r a n s i t i o n s shown i n F i g u r e  i n d e t a i l by f i n d i n g the p e r t u r b e d  wave f u n c - .  I f t h e s t a t e s have p a r i t y as shown i n t h e f i g u r e and  the  relative  dipole  and  B t h e wave  moments a r e t h e same i n t h e l e v e l s marked A  f u n c t i o n s are:  flow  =«AV4 +  fupp  = *AW  -  +  (2.27)  •h  The  I, I', II,  transitions labelled  ties  I:  (a a  i':  (a b  Ii': We e x p e c t tively.  A  A  +  B  b b ) A  will  have  intensl-  —  f i  b a ) A  B  A  (-a b -f A  that  A  2  B  b a )  B  a  (2.2%)  2  B  (a a +b b ) A  2  B  A  2  B  and b  A  will  be c o m p a r a b l e  t o a and b B  respec-  B  Thus, we s e e when the d i p o l e moments i n t h e two  have  t h e same r e l a t i v e  will  be s t r o n g  signs  II'  proportional to:  II:  weak.  and  sign  states  the t r a n s i t i o n s l a b e l l e d I and I I  and t h e f o r b i d d e n  transitions 1  1  and I I  1  will  be  A s i m i l a r argument c a n b e made a s s u m i n g t h e r e l a t i v e o f the dipole  opposite. efficient  This  moments i n t h e i n i t i a l  i s equivalent  to reversing  and f i n a l  state are  t h e s i g n o f t h e ' b -co-  • i n t h e d e s c r i p t i o n o f one o f t h e s t a t e s and r e s u l t s  in  the r e v e r s i n g  if  the r e l a t i v e  o f the primes signs  shown i n e q u a t i o n  o f the d i p o l e  moment  (2.28).  Thus  i n t h e two s t a t e s a r e  31 opposite  the strong  Q (3)  lines  showed  the l i n e s  (Only were  2  computed  2  moving t o g e t h e r  using  a value  s t a t e and 1.46  a  66kV/cm f o r t h e e l e c t r i c the  Z  s t a t e was t a k e n  the  final  m  This the  E  zero?  V  m  n  section will  |VM  The f i g u r e  component.  d i s c u s s c o n t r i b u t i o n s t o second  due t o t h e i n t e r a c t i o n  :'  i n energy,  of neighboring  rota-  g i v e n by.  2  E  ( - 9) 2  f o r the l e v e l  f o r m = n i s t o be o m i t t e d values  i s the matrix  equation  nonzero  shows t h a t r e l a t i v e t o  n " m  tween t h e l e v e l s this  and t h e lambda d o u b l i n g i n  The d i s c u s s i o n i s b a s e d on t h e e x p r e s s i o n f o r  are unperturbed and  The lambda d o u b l i n g i n  effects  i s the correction term  f o r t h e d i p o l e moment  strength.  order correction  *I ,  The s p l i t t i n g s  f o r example, t h e g r e a t e s t i n c r e a s e i n f r e q u e n c y  Stark effects  second  i n the f i g u r e .  field  order Stark  levels.  effect  X  Second  tional  Debye  Stark  f o r t h e TT s t a t e and a v a l u e o f  f o r t h e H = 7/2-»M = 5/2  order  as i n d i c a t e d  o f 1.0  occurs  This  The o b s e r v e d  are indicated.)  a s 0.38 c m ~ l .  line,  f o r t h e Q, (3) and  Debye  A state i s effectively  t h e Q-x c (3)  transitions  i n t h e CH £ - T 7 b a n d .  the strong t r a n s i t i o n s  o f t h e ZI  move a p a r t .  2.5 shows t h e S t a r k  Figure l d  components  "n" and "m".  are those  o n l y between  "n". The p r i m e i n d i c a t e s f r o m t h e sum.  f o r the energies element  given  2  E  n  and E  of the perturbing  m  levels  f o r the p e r t u r b a t i o n energy beThe m a t r i x  elements  above and we r e c a l l  states of opposite p a r i t y  t o be u s e d i n that  they are  and f o r  2  A , K=3, J=/2  Qic  (  3  )  Q, (3) d  :  n,  K=3, J=  \  AM  =0  Figure 2.5. Stark effect Only s t r o n g  Stark  AM =± I on CH, Q ( 3 ) ' a n d Q ( 3 ) l c  t r a n s i t i o n s a r e shown.  l d  lines,  33 A j = t i  f  o .  Because o f these  restrictions  ments we n e e d c o n s i d e r o n l y t h e e f f e c t s al  levels.  To e v a l u a t e s u c h  e l e m e n t s f o r Hund's c a s e tions  (2.17)  and  effects  on t h e m a t r i x  o f neighboring  i n the  state  (b) c o u p l i n g w h i c h a r e g i v e n  ele-  rotationthe matrix i n equa-  can b e a p p l i e d I m m e d i a t e l y t o e q u a t i o n  (.2.18)  (2.29). For  2  f T states,  the d i s c u s s i o n o f p a r i t y  doublets  and t r a n s i t i o n s b e t w e e n  simplify  t h e e v a l u a t i o n o f second  equation  (2.29)•  Consider  ic  and v i b r a t i o n a l  ciently  accurate  state  i n lambda  them may b e a p p l i e d t o g r e a t l y o r d e r c o r r e c t i o n s g i v e n by  the s i t u a t i o n  where t h e lambda d o u b l e t l e v e l s  mixing  shown i n F i g u r e  now b e l o n g  t o t h e same  and d i f f e r b y one i n J .  2.4,  electron-  Iti s suffi-  f o r our purpose t o take  t h e s e p a r a t i o n between  a lambda d o u b l e t  level  state  da d o u b l e t  o f the other  level  the r o t a t i o n a l the  same r o t a t i o n a l  (2.26).  Since  between parity |Mj  levels.  The p a r i t y  level  lamb-  as t h e mean s e p a r a t i o n o f mixing  o f lambda d o u b l e t s f o r  i s given by equations  w i t h t h e same v a l u e  (2.25)  and  levels  occurs  o f M one n e e d f i n d t h e  i n t h e two lambda d o u b l e t s  f o r o n l y one v a l u e o f  a t a time. The s e c o n d  vels w i l l One  state  and e i t h e r  t h e p e r t u r b a t i o n between r o t a t i o n a l  components mixing  o f one r o t a t i o n a l  order effect  move b o t h  due t o n e i g h b o r i n g r o t a t i o n a l l e -  lambda d o u b l e t  can see that t h e y  move t o g e t h e r from  (2.28).  A mixed lambda d o u b l e t  vel w i l l  be p e r t u r b e d  level.  The e n e r g y  levels  by b o t h  difference  component  b y t h e same amount. equations  (2.29)  and  o f one r o t a t i o n a l l e -  m i x e d lambda d o u b l e t s  of the other  In the numerator o f equation  (2.29)  (2.29)  tion The  is essentially we  a  (as  I I and  do  pressions  factor.  II').  the m a t r i x elements  expressions labelled The  factor  of opposite p a r i t y .  rotational  l e v e l push e a c h  If  l e v e l by  the r o t a t i o n a l  b e t w e e n Hund's c a s e  (2.24) can be a p p l i e d . an e q u a l m i x t u r e  squared.  matrix elements  I and  I ' sum  parity  j o i n t l y , both lambda d o u b l e t  and  to  to  one  f o r the  ex-  o f t h e m a t r i x element  l e v e l o f one Thus  From equa-  are  of proportionality  i n (2.28) i s the s q u a r e  other r o t a t i o n a l  ate  The  between a r o t a t i o n a l  z  level one  see t h a t  e x p r e s s i o n s i n (2.28) show t h e s e s q u a r e d  within  ^En  also  t h e same f o r the t r a n s i t i o n s .  for  the a d j a c e n t  lambda d o u b l e t s o f component  of  the  the same amount.  levels (a) and Pure  correspond case  (b) e q u a t i o n s  Hund's c a s e  o f pure Hund's c a s e  to coupling i n t e r m e d i -  (b)  (a) wave  can be  (2.20)  and  treated  functions.  as  35 Footnotes  f o r Chapter I I  1.  G-. H e r z b e r g , M o l e c u l a r S p e c t r a and M o l e c u l a r I S t r u c t lire.. -I. S p e c t r a o f D i a t o m i c M o l e c u l e s . ( D . Van N o s t r a n d Co., NewY o r k , 1950), S e c o n d E d i t i o n , p. 300.  2.  L . D. Landau and E. M. L i f s c h l t z , Quantum M e c h a n i c s — N o n - r e l a t i v l s t i c T h e o r y ( A d d i s o n - W e s l e y P u b l i s h i n g Co., R e a d i n g , M a s s a c h u s e t t s , 1958), p . 203.  3.  H e r z b e r g , p.  240-244.  4. L a n d a u and L i f s c h i t z ,  p.  294-298.  5.  p.  295.  Landau  and L i f s c h i t z ,  6. L a n d a u and L i f s c h i t z , p . 294-298 and p. 104-105. 7.  G-. C. Dousmanis,  100, 1735  8.  Landau  9.  A.  E.  (1955).  T. M.  and L i f s c h i t z , Douglas  (1965).  Saunders  p.  and  C. H.  Townes, P h y s .  139*  and.G. A. E l l i o t t ,  Can.  J . P h y s . 4^,  496  Rev.  CHAPTER I I I  EXPERIMENTAL DETAILS  The diatomic  Stark e f f e c t  tube p r o d u c e s  to that  sulting  large  provided  electronic  The  but a l s o  supplied  state.  e x p e r i m e n t a l equipment  the e l e c t r i c The  observation  the e l e c t r i c  Electric  study.  window and quartz. sealed the  and  The  a l s o be  Stark  moleeffect  chapter w i l l  t e c h n i q u e s used to  the e l e c t r o n i c a l l y  will  excited  dis-  produce  molecules.  the d e t e r m i n a t i o n of  discussed.  J.l  shows a d i a g r a m  The  t u b e was  capillary  The window was  blown from pyrex g l a s s .  sealed  i n the q u a r t z c a p i l l a r y  " Q " compound.  o f the d i s c h a r g e t u b e u s e d i n  tube i n s u l a t i n g  r u b b e r s t o p p e r was  Aplezon  and  only  the d e s i r e d  resulting This  o f t h e S t a r k s p e c t r a and  field  ions which pro-  d i s c h a r g e tube  Figure this  field  space  d i s c h a r g e tube n o t  s p e c t r a were o b s e r v e d p h o t o g r a p h i c a l l y . cuss the  de&k  i n a s m a l l d i s t a n c e w i t h the r e -  1  excited  electric  pressure discharge  moving p o s i t i v e  field. ) field  of  electric  The  ( I n the c a t h o d e  of slow  drop i n p o t e n t i a l  the e l e c t r i c  i n an  o f s u c h a low  the S t a r k e f f e c t .  electric  i n an  u s e d by L o S u r d o .  dark space  i s a high density  duce a l a r g e  cule  similar  i n the cathode  there  emission spectra  m o l e c u l e s r e p o r t e d h e r e W&B p r o d u c e d  d i s c h a r g e tube field  on t h e e l e c t r o n i c  the c a t h o d e were  t o t h e tube  and  plane both  the cathode  u s i n g d e K h o t i n s k y cement.  s e a l e d u s i n g an The  The  outlet  "0" r i n g  formed  was Often  from  o f the d i s c h a r g e tube was  con-  3?  To Pump  Needle Valve H 0 Vapor 2  5 cm  [ L J  To  V  *  Spectrograph  •Quartz Window  Rubber Stopper Quartz Tube d e Khotinsky Cement ^Aluminum Wire v  (drawn to Figure  3.1.  fit  M o d i f i e d Lo Surdo d i s c h a r g e  snug) tube.  38 nected  t o a m e c h a n i c a l pump v i a a l i q u i d  pressure  the d i r e c t i o n  produce  (The g a s i n l e t  f o r another a p p l i c a t i o n  way  when m e t h y l a l c o h o l v a p o u r  The  direction  molecules  When u s i n g  a l i n e r was p l a c e d  way  t h e tube w a l l s  ual  observation  was  a pyrex glass  ing  trap.  was u s e d  and r e m a i n e d  t o produce  the o p e r a t i o n  c a r b o n compounds t o p r o d u c e inside  the d i s c h a r g e tube. and e a s i l y  cylinder  fitting  o f the l i n e r  easily  i n front  that  CH m o l e c u l e s . )  CH In this  c l e a n e d when  o f t h e d i s c h a r g e became d i f f i c u l t . inside  vis-  The l i n e r  the d i s c h a r g e  o f the side  tube  lead-  current  glow.  t o t h e q u a r t z window was removed. d i s c h a r g e tube was o p e r a t e d as a d i r e c t  Under t h e s e c o n d i t i o n s the  cathode  For  representative  charge about duced.  most o f t h e p o t e n t i a l  operating  t u b e and 1 mm Hg t o t a l 1 mm  and an e l e c t r i c  The d i s c  conditions  space.  o f 4 k'V/ a c r o s s t h e d i s -  p r e s s u r e t h e d a r k s p a c e w o u l d be  field  o f about  40 kV/cm w o u l d  1 mm d i a m e t e r aluminum.  a q u a r t z tube s o t h a t The u p p e r  between  be p r o -  anode was made o f aluminum a n d t h e e l e c t r i c a l  a wire, usually  tube.  difference  and anode a p p e a r s a c r o s s t h e c a t h o d e d a r k  c o n n e c t i o n was v i a a t u n g s t e n w i r e - g l a s s b e a d  in  indi-  and pump c o n n e c t i o n s were  o f t h e tube  c o u l d be q u i c k l y  The p o r t i o n  The  was  The d i a g r a m  o f gas flow d i d not a p p a r e n t l y a l t e r  the d i s c h a r g e .  tube.  The  i n w h i c h g a s f l o w e d w h i l e u s i n g HgO v a p o u r t o  OH m o l e c u l e s .  reversed  of  trap.  i n t h e t u b e was measured w i t h a McLeod guage l o c a t e d b e -  tween t h e d i s c h a r g e tube and t h e c o l d cates  nitrogen  only  seal.  The c a t h o d e  The w i r e was  t h e end was e x p o s e d  inside the  end o f t h e c a t h o d e was u s u a l l y g r o u n d  f l u s h w i t h t h e end o f t h e q u a r t z t u b e .  sealed  f l a t and  (A more d e t a i l e d  discus-  39 s i o n  o f  a n o d e  c a t h o d e  ( a n d  p o s i t i v e  O t h e r w i s e , A  t h e  b a l l a s t  t u b e  B p . s i c t h e  t o  c a t h o d e . c a t h o d e  t o  o f  o f  c a t h o d e  was  t h e  ode  s u r f a c e  S i n c e  t h e  o p a q u e v i e w  i n s i d e  a f t e r  c u r r e n t s  a  t h e  d i a t e l y . f o r  r u n  i n c r e a s e d  some  c h o s e n  v a l u e  t u b e  w h o l e  i n s u r e f i r s t  s t a b l e b e c a m e  v o l t a g e  a n d  t h e  b r i g h t  p o s i t i v e  t h e  i n c r e a s e d .  a  w e r e v i a  The  g r o u n d e d .  t h e  s e r i e s  p u m p .  w i t h  b y  t h e  w o u l d The  w h i c h i n t o  t u b e  f i e l d  f a c t o r s  l i f e t i m e  b y  p o w e r  r e g i o n )  a t p i t  t h e  o f  u s e f u l  t h e  o f  t h e  t h e l i f e t i m e  t h e  q u a r t z  c o v e r e d  r e g i o n  t h e  a b i l i t y  l o w e r e d  w e r e  a f f e c -  d e s t r o y  c a t h t u b e .  w i t h  d i s a p p e a r e d  r e l a t i v e l y  l o w  was  i n  c o n e  w o u l d  p r e s s u r e s a f e  b u r n e d  i n  c o l u m n  a p p l i e d  g e n e r a l l y  o p e r a t i o n „ ) s t a b l e  c o n e  m a x i m u m  was  u s e f u l  s p u t t e r i n g  s m a l l  t h e  i n  b e l o w . )  f r o m  m o s t .  b r i g h t  v o l t a g e s  i n  t h e  A  t h e  t h e  t o  b y  s t a r t e d a  p l a c e d  i m m e d i a t e l y .  h i g h  u n t i l  c o r r e s p o n d e d  m u c h  t h e  was  g r o u n d  t o  l i m i t e d  m a t e r i a l  i n t o  When  was  f i e l d  a t  go  t h e  q u a r t z  s u r f a c e .  p i t  a n d  t h e  h o u r s  s u p p l y )  d e t e r m i n e d  o f  d i s c h a r g e  c a t h o d e  f r o m  l i m i t e d h i g h  p o w e r  was  w a s  T o o  c a t h o d e  w a l l s  few  a n d  p r o c e d u r e  t h e  a p p e a r s  c u r r e n t .  h e a t .  t h e  s p u t t e r e d  The  t h e  ( a n d  a l s o  s t a b i l i t y  d i s s i p a t e  p o r t i o n  t h e  s i z e s  t h e  ohms  s t a b i l i t y  t e r m  u s e f u l  o f  w o u l d  l i m i t  t e r m  S h o r t  v a r i o u s  50,000  o f  o p e r a t i n g  s h o r t  i n  t e r m i n a l  d i s c h a r g e  r e s i s t o r  d i s c h a r g e  t i n g  m a t e r i a l s  t h e  d i s c h a r g e  r e m a i n  s t a b l e  a n d  i n c r e a s e d  p o w e r . l i m i t e d  be  u n t i l  ( T h e t o  be  p o w e r  a b o u t  20  w h e n  t h e  c h o s e n  a n d  o f  e x t e n d i n g  a l m o s t  c o u l d  a n d  c e n t e r  a p p e a r  v o l t a g e  c o u l d  t h e  w o u l d  A l t e r n a t i v e l y ,  p r e s s u r e  v o l t a g e s  i m m e -  n a r r o w  r a i s e d t h e  t o  c u r r e n t  d i s s i p a t e d w a t t s  t o  d i s c h a r g e t h e n  t h e  Production  o f OH a n d CH e l e c t r o n i c  Relatively  The v a p o u r was s u p p l i e d H0  discharge tube  Justing  The p r e s s u r e o f H 0 2  0.5  from  t o 4.0mm Hg.  the flow rate  pressure  through  until  an e q u i l i b r i u m Experiments  0.5  mm I n d i a m e t e r  ter. ing  The l a r g e s t on t h e c a t h o d e  tral  the  often  q u a r t z tube  The p r e s s u r e was s e t b y a d -  the needle v a l v e .  temperature  Variations i n  of the l i q u i d  were done w i t h aluminum c a t h o d e s 2 . 0 ,  c a t h o d e s were d i f f i c u l t surface  evaporate from  the cathode.  The 1.0  the  easiest  to use and produced  The  largest  electric  field  was even  more d i f f i c u l t  t h e cathode  to  completely.  t o u s e as l o c a l  heat-  o f t e n became e x c e s s i v e and t h e c e n -  Tungsten  insulating  t o use  surface and coat  The e v a p o r a t e d  coating  the c h a r a c t e r o f the d i s c h a r g e  mm d i a m e t e r aluminum c a t h o d e was electric  fields  up t o 60  kV/cm.  i n t h e s t u d y o f t h e OH m o l e c u l e ,  63 kV/cm, v/as p r o d u c e d u s i n g  t h e 0.5  mm d i a m e t e r a l u m i n u m  ode.  However, t h e s e s m a l l c a t h o d e s were d i f f i c u l t  often  m e l t e d when t h e d i s c h a r g e was f i r s t  t h e OH m o l e c u l e  1.0,/and  and w i t h a t u n g s t e n c a t h o d e 1.0 ram i n diame-  and c a u s e d  of  H2O  was r e a c h e d .  conducted e l e c t r i c a l l y change  I n the d i s c h a r g e  a w a t e r b a t h o r b y pumping on t h e l i q u i d  p i t was d e s t r o y e d .  as i t w o u l d  c a r e f u l l y de-  flowed through the  vapour  due t o c h a n g e s i n t h e t e m p e r a t u r e  were r e d u c e d b y u s i n g  spectra  t o t h e d i s c h a r g e tube v i a a  The v a p o u r was c o n t i n u o u s l y  tube.  ranged  from a t r a p c o n t a i n i n g  and connected  2  OH e m i s s i o n  v a p o u r was u s e d .In t h e d i s c h a r g e t u b e .  2  needle valve.  spectra  s t r o n g and p u r e u l t r a v i o l e t  were o b s e r v e d when H 0  gassed l i q u i d  emission  the voltage  started.  a c r o s s and c u r r e n t  cath-<  t o u s e and In t h e study through the  41 discharge  tube r a n g e d  from about  6.5 kV a n d 4.2 ma f o r 1 mm c a t h o d e s a n d  eter:  cathodes t o about  about  3 kV and 2.4 ma f o r 0.5 mm Electronic  3-6 kV and 12 ma f o r 2 mm diam-  cathodes.  emission spectra  f r o m t h e CH m o l e c u l e were p r o -  duced  i n t h e d i s c h a r g e tube u s i n g  or H  was sometimes u s e d as a c a r r i e r g a s .  2  was CH^OH v a p o u r  2  i t sometimes  Balmer  lines  problem For  which  the preliminary  vapour  the intensity  were u s e d  t o determine  The r e s u l t i n g  H  2  and s t u d y i n g  tensity  a chosen  CH m o l e c u l a r l i n e . the c a r r i e r gas  contained i n a trap.  h o w e v e r , was t o i n t r o d u c e  The most the alcohol  gas through s e p a r a t e n e e d l e v a l v e s .  When CH^OH v a p o u r  and He were u s e d  o f the atomic hydrogen  Balmer  line  a t \66?8& was o b s e r v e d v i s u a l l y .  made  through the side  and v e r y much a i d e d fore  field  In t h i s and i n d e -  the r e l a t i v e i n -  l i n e , Hy and t h e h e l i u m These  o b s e r v a t i o n s were  o f the d i s c h a r g e with a prism spectroscope  the adjustment  of discharge c o n d i t i o n s be-  o b s e r v i n g the molecular s p e c t r a .  observations  field  complicated the  way t h e p r e s s u r e o f t h e two g a s s e s c o u l d be s e t e a s i l y pendently.  even  hydrogen  the e l e c t r i c  s t u d y o f CH e m i s s i o n s p e c t r a  arrangement,  and c a r r i e r  o f atomic  molecular l i n e s  flowed over a l c o h o l  satisfactory  combination  g a s was n o t v e r y s a t i s f a c t o r y  enhanced  of identifying  when u s e d  The b e s t  Helium  and a t o t a l p r e s s u r e o f 1 t o 3 mm Hg.  as a c a r r i e r  though  strength.  a l c o h o l vapour.  a n d He g a s w i t h a p a r t i a l p r e s s u r e o f 0.2 t o  0.4 mm Hg f o r t h e v a p o u r The u s e o f H  methyl  i t was p o s s i b l e  In f a c t ,  from s u c h  visual  to roughly estimate the e l e c t r i c  strength. The  use o f a hydrocarbon  s u c h as methane, p r o p a n e ,  benzene  or  cyclohexane  CH  emission spectra  a carrier dition  d i d n o t prove  f a c e xirhich q u i c k l y  molecule, Applied  in  1 mm d i a m e t e r  above tra  electric  cular  field  spectra,  combined  focal  t h e power d i s s i p a t e d :ln or less.  dark  space.  s u r f a c e and a l m o s t surface.)  ontn t h e s l i t  the spectra.  study  of a stigmatlc  (The h i g h  The e l e c t r i c  field  o f CH m o l e c u l a r s p e c t r a , a combined  of quartz-water  l e n g t h o f about  from  electric i s zero  ze.ro a g a i n a m i l l i m e t e r o r two  F o r the simultaneous a pair  the l i g h t  F o r t h e s t u d y o f OH m o l e c u l a r  convex q u a r t z l e n s h a v i n g  15 cm was u s e d .  and He g a s was u s e d  was o b s e r v e d by f o c u s i n g  and. t h e p r e l i m i n a r y  piano  on t h e OH  effect  i s i n the cathode  the cathode  that  a t 15 w a t t s  and p h o t o g r a p h i n g  the cathode  used.  and t h e e x p e r i m e n t a l c o n d i t i o n s were e s -  Stark e f f e c t  spectrograph  were g e n e r a l l y  3»0 t o 5.0 kV a n d c u r r e n t s r a n g e d  from  was k e p t  the Stark  sur-  on t h e s p e c t r a o f t h e CH  cathodes  as d e s c r i b e d above e x c e p t  the r e g i o n of h i g h  field  aluminum  tube  o f the discharge.  s i m u l t a n e o u s l y CH^OH v a p o u r  the d i s c h a r g e t u b e  The  i n the d i s c h a r g e  When s t u d y i n g t h e S t a r k e f f e c t  t h e d i s c h a r g e tube  the ad-  c o n d u c t i n g d e p o s i t on t h e c a t h o d e  studying the Stark e f f e c t  CH m o l e c u l e s  Observing  Such s u b s t a n c e s  destroyed the s t a b i l i t y  v o l t a g e s ranged  sentially  at  gas,  3-0 t o 6.7 ma.  from and  e i t h e r when u s e d a l o n e , w i t h t h e a d d i t i o n o f  an e l e c t r i c a l l y  For  f o r the production of  gas or'when mixed w i t h a l c o h o l w i t h o r w i t h o u t  of a carrier  produced  satisfactory  study  focal  spec-  a pair, o f  l e n g t h o f about  o f OH and CH mole-  achromatic  18 cm was used..  lens with a The m o l e c u l a r  Stark  s p e c t r a were p h o t o g r a p h e d , w i t h  graph equipped was dispersion  o f 4.2  the  the  sure times  molecule  from the  must know t h e  electric  The CH \ 4 3 0 o X  band was p h o t o -  o f the  Stark  s p e c t r a the  OH S t a r k  on a t o m i c  tings  atomic  of  the - 1  on e i t h e r  effect  splittings field  2  strength.  For t h e o f CH  s t r e n g t h was d e t e r m i n e d  i n frequency,  f r o m the  The S t a r k  were c h o s e n typically  s i d e o f the u n d i s p l a c e d l i n e .  i n hydrogen has been  d i p o l e moment o f a  i n t h e s p e c t r a one  hydrogen Balmer l i n e s .  shifts  developed  p r e l i m i n a r y study  hydrogen Balmer l i n e s  l a r g e observed  Expo-  strength  electric  field  1  P l a t e s were  Company.  s p e c t r a and t h e  electric  Stark effect o f the  field  (0.51  cm""/mm  f o r a l l photographs.  two h o u r s .  Stark  corresponding  study  i n f o u r t h o r d e r and  t o determine t h e e l e c t r i c  observed  simulta-  a plate disper-  recommended b y the...Eastman Kodak  In o r d e r  A3900$ was  order with  p l a t e s were u s e d  o f the  plate  a d i s p e r s i o n o f 7.4 cm~l/mm  a d i s p e r s i o n o f 2.8  were u s u a l l y a b o u t  Determination  cm  X/ram).  order with  $/mm). Kodak 103a-0  a resulting  OH and CH bands were o b s e r v e d  cnrVmm ( 0 . 6 l  i nthird  spectro-  The OH band  The CH b a n d  OH band was a g a i n p h o t o g r a p h e d  o f 4.0  graphed  as  order with  CH b a n d was p h o t o g r a p h e d i n t h i r d  sion  inch g r a t i n g .  S/mm).  1  When t h e s e  per  i n fourth order with  cm" /mm (0.39  i n second  2/mm).  neously  a 30,000 l i n e  photographed  photographed (0.83  with  a 3»4 meter E b e r t  split-  because 40 t o 60  A l s o the  Stark  s t u d i e d e x t e n s i v e l y and r e s u l t s  obtained  experimentally  and t h e o r e t i c a l l y  relation  between the a p p l i e d e l e c t r i c  agree v e r y w e l l .  field  The  and t h e o b s e r v e d  Stark  splittings  applied  a r e known t o terms  field.  (See f o r example,  Theory o f Atomic The  Spectra,  hydrogen  graph.  In t h i s  way  Stark  molecular  Stark  same way.  (During  t i n g s were  trograph.  splittings  splittings,  o f OH  and p h o t o g r a p h e d w i t h  through  f o r the e l e c t r i c  isons  i n other experiments  prism  and g r a t i n g p h o t o g r a p h s a g r e e d  observed observe reason  in third  order  OH  Stark  i t necessary by t h i s  showed t h a t f i e l d s  u s i n g one  molecule.  dis-  spec-  t o u s e a.  means.  determined  Comparfrom  ^3900$ band was  not p o s s i b l e t o  spectrograph  split-  to within ! % . ) •  s p e c t r a o f t h e CH  s p e c t r a and CH S t a r k  moment o f t h e CH m o l e c u l e OH  was  determined  i t was  i n the  quartz  simultaneously  t h e Sta.rk s p l i t t i n g o f a h y d r o g e n B a l m e r l i n e .  simultaneously  the  and i n t h e  the w a l l o f the  a H i l g e r medium  value  When t h e S t a r k  field  s p e c t r a , hydrogen Stark  i n o n l y one c a s e field  Stark,  t h e same s p e c t r o -  i f p r e s e n t , were a v e r a g e d  the study  However,  and m o l e c u l a r  i n the e l e c t r i c  sometimes a l s o o b s e r v e d  charge tube  Condon and S h o r t l e y , The  simultaneously with  drifts,  power o f t h e  397.)^  p.  s p e c t r a were p h o t o g r a p h e d  i n the t h i r d  s p e c t r a were  relative  this  observed  and t h e e l e c t r i c  was d e t e r m i n e d  For  dipole  to that of  45 Footnotes f o r Chapter I I I 1.  F o r a d i s c u s s i o n o f l o w p r e s s u r e g l o w d i s c h a r g e s see f o r example: F . A. M a x w e l l and R. R. B e n e d i c t , T h e o r y o f G a s eous C o n d u c t i o n and E l e c t r o n i c s (McGraw H i l l Book Co., New Y o r k , 1941), pp. 311-325; o r J . D. C o b i n e , G a s e o u s Conduct o r s , ( D o v e r P u b l i c a t i o n s , New Y o r k , 1958), pp. 212-216.  2. D e v e l o p i n g p r o c e d u r e u s e d i s g i v e n i n : Kodak P l a t e s and F i l m s f o r S c i e n c e and I n d u s t r y , Data Book P-9 (Eastman Kodak Co., R o c h e s t e r , New Y o r k , I 9 6 2 ) . 3.  E. U. Condon and G. H. S h o r t l e y , t r a (Cambridge U n i v e r s i t y P r e s s , P. 397. '  The T h e o r y o f A t o m i c Cambridge, E n g l a n d ,  Spec1935)  46 CHAPTER IV  EXPERIMENTAL OBSERVATIONS  The OH  and  CH  range: (0,0) 2  A - ^  2  Stark e f f e c t molecules  35  kV/cm t o  electronic  65  kV/cm.  Specifically,  h a n d , t h e CH,  T T ,  (o,o)  b a n d were s t u d i e d .  and  the e l e c t r i c a low  sion  s p e c t r a the  TT,  ground  state,  and To  these  o f the  i n the  emission  -  (The  direct  the  on  i n the CH,  lines  and  lines  observed  and  4)  the p o s i t i o n s o f OH  the  i n the  effect To  on  these  and  the  introduce  2  TT  f  lowed t r a n s i t i o n s  tube.)  i n the  ground  emisOH,  electronic  state. Stark  on  be p r e s e n t e d  In  d i s c u s s i o n o f them, splittings  i n OH  :  and  CH  field-induced, parity-forbidden  b a n d , 3) an  a n a l y s i s of these  values  f o r the  data,  electric di-  CH.  0H.. S*-» TT 2  the  were  electronic  found  CH,  including representative  Stark  experimentally determined  p o l e moment o f OH  Stark  (0,0)  the  emission  c o m p a r i s o n o f the  observations  of the observed  2 77"^  +  band and  s p e c r t r a the s i m i l a r a s p e c t s w i l l  measured v a l u e s  2 ^  Stark e f f e c t  d i p o l e moment was  s p e c t r o g r a m s f o l l o w e d by a q u a l i t a t i v e 2)  2  the  the  current glow d i s c h a r g e  d i s c u s s i o n and  1)  in  electronic  , excited electronic  2  following order:  spectra of  the OH,  (0,0)  2  causing  state,  CH, A  facilitate  2 -> TT,  Stark e f f e c t  electric  electronic  2  field  pressure  From o b s e r v a t i o n s  emission  studied f o r e l e c t r i c ^fields  (1,1)  p r o d u c e d by  the  was  the  and  spectra  2  on  OH  2  band  spectrograms,  t o the lowest  F i g u r e 4.1  rotational  level  of  shows t h e a l the  (K)  J  (2)  , 2  (I) (0)  u  ^  R,(l)  Q (D 9  Q, (l) 2  F| (I) J = '/>  Q,(l)  R,(l) R (I) 2I  J = /P 3  :  n /2 3  Figure 4 . 1 . i n OH 7 T i / 2  A  Allowed and TTy 2  x  transitions states.  to lowest  rotational  level  I  +  32 314.2 cm  -i  F i g u r e 4.2. f i e l d region  32 5 4 2 . 0 cm - I  S t a r k e f f e c t on OH, X - » (63 kV/cm) l a n e a r b o t t o m 2  +  2  T T , (0,0) b a n d . of print.  Maximum  49 and  2  TTv  electronic  a  s t a t e s o f t h e OH m o l e c u l e .  cludes the relevant r o t a t i o n a l state  levels  from which the t r a n s i t i o n s the A-type  gerates  b l i n g ' i n the  doubling  state.)  2  X  2  originate.  i n the  With  i n the  The f i g u r e i n +  electronic  (The d i a g r a m  T T s t a t e and t h e s p i n d o u -  t h i s d i a g r a m i n mind l e t u s now  t u r n t o F i g u r e 4 . 2 w h i c h i s an e n l a r g e d p o r t i o n o f a 21 ~*  p h i c p l a t e and shows a p o r t i o n o f the OH, A3064A. high  Wave number f r e q u e n c y  field  electric The tions  i s 63  simplest  tions are P tional  1 2  (l),  l e v e l there  lambda d o u b l e t  2  %  2  one p o s s i b l e v a l u e  and t h e S t a r k e f f e c t i n Chapter  P  1 2  (l)  and  blet l e v e l bidden field  R 2  level  o f the J = l / 2 , TTy 2  a  components o f t h e P ] _ ( l )  allowed  components o f t h e P  frequency Gv (l) 12  sitions  (to the r i g h t ) .  i n the high f i e l d  transitions  1 2  transi-  II.)  o f (M| f o r e a c h produce  doublets.  The e x p e c t e d  dou-  i n Figure 4.1,  a t t h e u p p e r lambda  s t a t e and as a r e s u l t and R ( l ) a p p e a r i n g 2  r e g i o n a r e on t h e h i g h f r e q u e n c y lines  will  diagram  ( l ) t r a n s i t i o n s terminate  allowed  These  region f o r each o f the a p p r o p r i a t e  the energy  2  for transi-  For a J = l / 2 rota-  2  blets a p p e a r i n the h i g h f i e l d As seen f r o m  and t h e  The maximum  occur  state.  ( l ) and R ( l ) .  ( T h i s was shown i n F i g u r e 2 . 2  lines..  splittings  o f t h e TTjj L  level  is. only  level  band,  kV/cm.  Q (l), 2  (0,0)  i n c r e a s e s to the r i g h t  pattern of Stark  t o t h e J = 1/2  photogra-  *1,  r e g i o n i s a t the b o t t o m o f t h e l i n e s .  field  exag-  side  the  dou-  the for-  i n the high  of t h e r e s p e c t i v e  We a l s o s e e i n t h e p l a t e t h a t the ( l ) and R ( l ) l i n e s  region.  2  Since  the allowed  go t o t h e l o w e r lambda d o u b l e t  o f the f o r b i d d e n and a l l o w e d  shift  t o lower Q- (l) and  level,  components f o r t h e s e  2  the potwo  50 lines  w i l l be r e v e r s e d , r e l a t i v e  lines,  (The s l i g h t  t o those  s e p a r a t i o n o f the Q ( l )  cm" The  TT-i/z  2  H i(1) * 2  doublet nents two  1  ^  t o t h e J - 3/2  (the lowest)  state are P (1) , % ( ! ) » Q x  splitting +  level  on t h e l e f t .  The 0^(1)  midway b e t w e e n t h a t o f t h e o t h e r ( b e c a u s e  a r e more s e p a r a t e d  a greater spin (X, Z  1  K = 2,  quency S t a r k lower  splitting, J = 5/2,  o f the R  1  2 1  ( l ) line  (The l o w e s t  i s blended  fail  splitR^(l) due t o  fre-  on t h e t h r e e  and t h e S t a r k  frequency  Stark  and t h e h i g h e s t  faint  line  the three h i g h e r  components o f t h e R | ( l ) l i n e resolved.  separa-  i n t h e upper s t a t e  As a r e s u l t  component o f t h e R-^(l) was v e r y trograph^  cm" ,^  (1)  The R ^ ( l ) a n d 2  2  frequency  of spin  t h e % ( l ) arid Q ^ ( l ) l i n e s  0*47  7/2)*  line.  components o f t h e R ^ ( l ) l i n e  ponents are c l e a r l y ponent  than  broad  fhe  and  However, f o r t h i s p l a t e t h e S t a r k p a t t e r n o f one  lines  compo-  are v i s i b l e be-  tion.  only a Very  lambda  (See a g a i n F i g u r e 2*2)  e a c h have S t a r k components w i t h t h e same r e l a t i v e  t i n g ) and one s e e s  and  each  lines  falls  of the  %(1)  two S t a r k  components o f t h e P ^ ( l ) l i n e  side t h e broad aluminum l i n e  lines in  jr .)  2  (l) ,  2 1  level will yield  and a q u a r t e t w i l l r e s u l t *  low frequency  2  can be l / 2 a n d 3/2  S i n c e t h e v a l u e s o f |M| o f t h e J = 3/2  ( l ) and R ( l )  i s due t o t h e s p i n l e v e l , K - 1,  electronic  1 2  0,^(1)  i n upper r o t a t i o n a l  transitions  level  and  2  the a b s e n c e o f t h e e l e c t r i c f i e l d o f 0.32  o f the P  comcom-  frequency  even on t h e o r i g i n a l  spec-  plate.  F i g u r e 4*2 bldden  lines  line *  One a l s o  clearly  completely sees  shows s e v e r a l separated  the decrease  from  field*induced parity-forv  the a s s o c i a t e d a l l o w e d  i n Stark broadening  with i n -  creasing values of J . ing  number o f S t a r k  the c o r r e s p o n d i n g p o n e n t s and  decrease  lambda d o u b l e t s .  duction in  the  i n Stark broadening  doubling tional  levels  and  lines  then  However, i n t h i s  stand  out  their  1  right  t h a t are  and Q i ( 5 ) >  line  R (l)  than  more c l e a r l y  F i g u r e 4.4  The  resolved ing,  lines, The  two  the N  2  taken  the  forlambda  rotaof J .  from  seen  on  left  to right.  P (U 12  the l i n e lines  molecule,  marked  The  The  1  the  broad-  also  Q]^ ^'  2  for-  s i d e of  print  » Q (D,  but  the P ^ d )  a  shows n  d  2  X -* TT, +  2  still  (1,1)  previous  clearly  l i n e , Stark  show  broaden-  field-Induced, parity-forbidden  "F"  on the  t h a t bend t o l o w e r (The  either  1  (The  lines with  s i m u l t a n e o u s l y w i t h the  the P]_(2) l i n e , and  broad  seen  the  few  two  s p e c t r a are g e n e r a l l y f a i n t e r  e.g.  first  re-  above.  S t a r k s p l i t t i n g s , e.g.  e.g.  example  The  shows a p o r t i o n o f the OH,  T h i s p l a t e was  two.  A  higher values  i s very apparent. f o r the  band.  f o r . the  i s 63 kV/cm.)  t h e f o r b i d d e n components lines  line.)  s e p a r a t e l y because  increases for s t i l l  field  ening o f the P ( 2 )  2  component a s s o c i a t e d  i n c r e a s i n g J can a l s o be  state decreases  a  a r e Qa(4)  line  2  on  the  shows an e n l a r g e d p o r t i o n o f F i g u r e 4.2.  maximum e l e c t r i c bidden  not  2  F i g u r e 4.3  R (l)  2  In t h e T T y  com-  o f t h e p e r t u r b a t i o n on  by the a l l o w e d  with  "to R ( 4 ) .  components do  and  l i n e s Q-^(l) t o 0,-^(5) show t h e s e f e a t u r e s .  i s overlapped  2  of J  s e p a r a t i o n of the S t a r k  f o r b i d d e n i l i n e s appear the  lines, R (l)  bidden  i n the  i n the e f f e c t  The  with the Qgi l i n e  to t h e i n c r e a s -  components w i t h I n c r e a s i n g v a l u e s  decrease  (When d i s t i n c t  These f e a t u r e s a r e r e l a t e d  cathode  left  o f the P-j_(2) l i n e .  f r e q u e n c i e s a r e due  s u r f a c e was  tilted  to  slightly to-  32314.2 CM-'  F i g u r e p r i n t .  4-3( T h i s  32415.5 CM-'  S t a r k i s  a n  e f f e c t  o n  O H .  e n l a r g e m e n t  M a x i m u m o f  F i g u r e  f i e l d  4.2,  r e g i o n l e f t  i s  half.)  n e a r  b o t t o m  o f  31  7 3 3 . 7 C M - I  F i g u r e 4.4. f i e l d region  3I893.0CM-I  S t a r k e f f e c t on OH, X ' - * T T (1,1) (63kV/cm) i s n e a r b o t t o m o f p r i n t . 2  t  2  )  band.  Maximum  54 ward t h e s l i t tric  field  and  moved t h e  Stark e f f e c t  on  2  Z  electric kV/cm. er  _ J  The  band,  In the r e g i o n  >3900$  of a spectrogram  taken  o f the l i n e s ;  t h e unmarked l i n e s  Stark e f f e c t  on  clearly  this  CH  molecule w i l l  the p l a t e  state  tions  originates  molecule  is a  2  example  observed  t h e OH,  to the N  portion  molecule.  + 2  due  t o the  energy l e v e l s  are taken  from which  2  spin  spectra in  the observed  splitting  and  i n the  CH  position for  be r e v e r s e d  t h e CH, 2  The  transi-  s p e c t r a d i s c u s s e d above.  i n F i g u r e 4.3  of  into account:  S t a r k component w i l l  i n t h e OH  The  i n the lower  £ " s t a t e hence the r e l a t i v e  R (l) line  i n F i g u r e 4.5.  rath-  Pecular discharge  which-shows t h e  an a l l o w e d and f o r b i d d e n CH from t h a t  of the  a i d t h e u n d e r s t a n d i n g o f t h e CH  i n t h e CH  52  band.  i f the f o l l o w i n g p o i n t s  upper  The  i s about  shows t h e numerous f e a t u r e s  A r e v i e w o f F i g u r e 4.1 t h e OH  a r e due  of  order.  are b r o a d because  t h e change o f i n t e n s i t y  so t h e p l a t e  in third  o f maximum s p l i t t i n g  i n F i g u r e 4.5  CH l i n e s  caused  elec-  2  h i g h p r e s s u r e i n the d i s c h a r g e tube.  conditions  Even  (0,0)  2  the  Z~-» Hband  2  shows an e n l a r g e d p o r t i o n  > TT,  field  r e s u l t e d because  molecule.)  t h e CH,  F i g u r e 4.5 t h e CH,  the Doppler s h i f t  See f o r R (l)  line  2  £ *" e l e c t r o n i c  •,(2) state Alsq  i s very small, the  CH T T 2  (b) c o u p l i n g  electronic  f o r which  other d i f f e r e n c e does n o t  less  alter  t h a n 0.3 state  even when K =  x  belongs n e a r l y  the s a t e l l i t e  between t h e CH  the  cm~  lines  and OH  t o Hund's  a r e v e r y weak.  5. case The  molecule, although i t  observed S t a r k e f f e c t ,  i s that  the  2  TT  state  25617 cm"  H  I  I  4  2  3  7  25807 cm"  1  6  5  4  e  Ip  3 I 21  TTT  1  T  2  P  Q,  Q  l  1 Q  2 ^ I  13  1 12  13 F i g u r e 4.5. f i e l d region  e f f e c t on CH, T~-^ TT, (52 kV/cm) i s n e a r b o t t o m of  Stark  2  Z  (0,0) band. print.  12  11 3 10 1  Maximum  211  3 10 4  56  in CH is regular while that in OH is inverted. Figure 4.5 shows that the CH P ( l ) ,  a  n  2^  d n  2  resulting from transitions to the J = 1/2 level of the state, are doublets in the high field region.  l l n e e  Tf>/x  z  The R^(l) line  shows a splitting into four Stark components as expected for a transition to the J = 3/2 level of the 7Tj/  state.  2  JJ  For this  particular plate the P ( 2 ) Une showed four Stark components due 2  to a transition to the J = 3/2 level of the TT'/a_ state.  Also  2  this plate shows very clearly the reduction in broadening and increase in separation of allowed and forbidden Stark components with Increasing values of J .  See for example the lines: P ^ ( l )  to P-L(3), P ( D to P ( 3 ) , R ^ D to 2  2  %(4),  and R (l) to 2  R (4). 2  The relative location of the allowed and forbidden Stark components can be easily seen by comparing the lines.  P^(3),  Q^(3), and  R^(3)  Relative to the allowed line, the forbidden component is  at lower frequencies for the P-j_ and R-j^ lines and at higher frequencies for the §1 line.  The ^ ( l ) and Q ( l ) lines obscured by 2  the Helium line, \3888.65$, appear in the center of Figure 4.6 (b). Figure 4.6 provides an opportunity to observe the Stark effect on the CH r ~ - » T 7 band for three different values of 2  2  the electric field strength.  The electric f i e l d increases going  down the figure from (a) to (c). . The electric fields are: (a) 34 kV/cm, (b) 47 kV/cm, and (c) 68 kV/cm.  The increase in  splitting with electric field shows most clearly for the fy^ ) 1  line.  These prints cover about the left three quarters of the  previous plate (Figure 4.5) plus, from left to right, the 0,^8)  25 575 c m  He  - 1  P (2) 2  P,(l)  P (l) 2  25756 cm"  Q (l) 2  F i g u r e 4.6. S t a r k e f f e c t on CH 2 x - - * 7 T (c,0) band f o r t h r e e v a l u e s o f e l e c t r i c field. ( a ) 34 kV/cm, ( b ) 4 ? kV/cm, ( c ) 68 kV/cm. Maximum f i e l d r e g i o n i s n e a r bottom o f p r i n t . 2  R,(l)  53 and Q, (8) l i n e s a t the l e f t edge of the p r i n t s . 2  This s e r i e s of  p l a t e s a l s o shows t h a t the f e a t u r e s r e l a t e d t o the S t a r k become more pronounced as t h e e l e c t r i c f i e l d  effect  Increases.  S t a r k s p l i t t i n g s i n t h e atomic hydrogen Balmer l i n e Hy F i g u r e 4.7 shows the S t a r k e f f e c t on the atomic hydrogen l i n e Hy, A4340.47$.  The maximum e l e c t r i c f i e l d i s about  36 kV/cm and the s p l i t t i n g between the two 18rr about 83  cm" . -1  components i s  The photograph was taken i n second o r d e r .  d i s c h a r g e tube c o n t a i n e d methyl a l c o h o l v a p o u r thus CH m o l e c u l a r l i n e s .  (The CH l i n e s appearing 2  2  producing  on t h i s p r i n t  to the P branches o f the A-+ TT , (0,0) band.)  (The  belong  The (b) p a r t o f  F i g u r e 4.7 shows t h e l o c a t i o n o f the S t a r k components o f t h e Hy line.  The l o c a t i o n s a r e drawn f o r an e l e c t r i c f i e l d o f 36 kV/cm  which corresponds  t o t h e maximum e l e c t r i c f i e l d on the p r i n t .  The numbers 2,3,5, e t c . i n the drawing g i v e t h e d i s p l a c e m e n t  of  a g i v e n component i n u n i t s o f 0.0642 E cm" , where E i s the mag1  n i t u d e o f t h e e l e c t r i c f i e l d s t r e n g t h i n kV/cm.  (The r e l a t i v e  i n t e n s i t i e s i n d i c a t e d i n t h e d r a w i n g a r e from Condon and S h o r t ley,  The Theory of Atomic S p e c t r a , page 4 0 1 . ) ^  The S t a r k  split-  t i n g s o f the Balmer Hy l i n e were used t o determine the e l e c t r i c f i e l d s t r e n g t h i n t h e s t u d y o f t h e S t a r k e f f e c t on OH  emission  s p e c t r a end i n the p r e l i m i n a r y study o f t h e S t a r k e f f e c t on the CH e m i s s i o n s p e c t r a .  S t a r k e f f e c t on the CH  2  A •* T T band 2  F i g u r e 4.8, the f i n a l s p e c t r o g r a m , shows the S t a r k e f f e c t 0  7T  (b)  18 15 12  Fieure 4 . 7 . S t a r k e f f e c t on h y d r o g e n B a l m e r H . (a) O b s e r v e d H Stark s p l i t t i n g s Maximum e l e c t r i c f i e l d I s 36 kV/cm. ( M o l e c u l a r l i n e s a r e f r o m CH J7T band.) (b) T h e o r e t i c a l s p l i t t i n g s and i n t e n s i t i e s . S p l i t t i n g s a r e drawn f o r 36 kV/cm (maximum f i e l d on p l a t e ) . Y  y  Q,(2)  Q,(3)  R,(l) 23329 cm-I  II R,(3) F i g u r e 4.8. S t a r k e f f e c t on CH A b o t t o m o f p l a t e ) i s a b o u t 66 kV/cm. 2  2  R (3) 2  R,(4)  R (4) 2  T T b a n d . Maximum e l e c t r i c f i e l d (near ( P a r t ( b ) .loins on t h e l e f t o f ( a ) . ) ON  on a p o r t i o n o f the CH A"*" n , (0,0). band, \bJ00&. 2  appearing  (The  t o t h e Q,^, Q , R^, and R  i n the enlargements b e l o n g  branches and extend  The l i n e s  2  2  2  from t h e 0^(2) l i n e s t o t h e R ( 0 l i n e s . i  2  (b) p o r t i o n o f t h e f i g u r e extends t o t h e r i g h t ( h i g h e r f r e -  q u e n c i e s ) from the r i g h t end o f t h e (a) p o r t i o n o f the f i g u r e . ) The r e g i o n o f maximum e l e c t r i c f i e l d i s a t t h e bottom o f t h e l i n e s on the p r i n t .  The maximum f i e l d i s about 66 kV/cm.  ;The  observed l i n e s r e s u l t from t r a n s i t i o n s from a lambda d o u b l e t > s t a t e t o one i n the T 7  r o t a t i o n a l l e v e l i n the A e l e c t r o n i c 2  electronic  state.  2  The lambda d o u b l i n g i n t h e /\ s t a t e i s neg2  l i g i b l e ^ w h i l e t h a t i n the T T s t a t e produces r e s o l v e d 2  i n t h e absence o f an e l e c t r i c f i e l d .  doublets  Compare f o r example t h e  l i n e s marked Q (2) and 0^(3). 1  F o r t h e CH A ~ * T T band t h e lambda d o u b l e t s i n b o t h t h e 2  2  upper and lower s t a t e w i l l be p e r t u r b e d by t h e e l e c t r i c and a l a r g e number o f S t a r k components w i l l  field  r e s u l t even f o r a  t r a n s i t i o n between l e v e l s w i t h l o w v a l u e s o f J .  ( F i g u r e 2.5 i n  Chapter I I shows t h e s t r o n g S t a r k t r a n s i t i o n s f o r the CH Q-i (3) c  and Q- (3) l i n e s . ) ld  As we see from the p r i n t i n F i g u r e 4.8 the  S t a r k e f f e c t on t h e CH A * TT 2  2  fc  and  d  o  e  e  C  a  U  s  e  lines to shift  and broaden but because o f t h e l a r g e number o f c l o s e l y  spaced  S t a r k components, no i n d i v i d u a l s p l i t t i n g s c o u l d be r e s o l v e d . We a l s o see from t h i s p r i n t t h a t t h e Q]_ (3) and Q i ( 3 ) ° l i n e s c  d  move t o g e t h e r i n t h e h i g h f i e l d r e g i o n as has been p r e d i c t e d . T h i s i s because the h i g h e r f r e q u e n c y frequency  S t a r k component o f t h e low  l i n e , 0, (3), and t h e lower frequency  of the h i g h frequency  S t a r k component  l i n e , Q]_ (3), a r e the s t r o n g ones. d  Thus  62 these will  two see  lines  below t h a t  CH Q i ( 3 )  and  c  tive  c r o s s i n the r e g i o n of high the  Q. (3) l i n e s ld  the  excited  To included  electric  is sufficient  CH  JT  lists  the  essential  i n F i g u r e s 4.2  following Information:  the  original  p h o t o g r a p h and  (in kilovolts)  i n the  t o the  relato  in i t s  nearest the  o r OH  tenth  Stark  y  Stark  splittings  4.8.  The  discharge  the d i s c h a r g e ( i n mm  the The  entry.  tube.  Hg)  and  The  I is The  the  gas  electric  fields  f o r t h e OH  other  ex-  or  cathode diameter  splittings f o r the  table  tube.  o f an h o u r i s t .  s p e c t r a and  I is  c o n d i t i o n s f o r the  t h e d a t a book  tube i s p  i t are a l s o g i v e n .  from Balmer H  on  Table  e x p o s u r e number i s t h a t  a c r o s s the  discharge  to produce  through The  ( i n mllliamperes) through  forming  determined  the  state.  experimental  gases used  the  molecule  the  time  on  s t a t e s and  and  pressure  f r o m CH  Z  the s p e c t r o g r a m s ,  current  material  and  d i s c u s s i o n of  V i s the v o l t a g e  posure  A  c l o s e the  marked on  total  to determine  We  c o n d i t i o n s f o r spectrograms  photographs appearing provides  2  field.  Stark e f f e c t  d i p o l e moment o f t h e  electronic  Experimental  the  o b s e r v a t i o n o f the  s i g n o f t h e d i p o l e moments i n t h e  determine  electric  and  were  plates  exposures used  and as  illustrations.  Measurements  order the  Table  II l i s t s  Stark  splittings  corresponding  the m e a s u r e d v a l u e s  Stark  observed  f o r the  i n the OH,  splittings  f o r the  2  X" -* f  atomic  resolved 2  H  band  first and  hydrogen B a l -  TABLE I E x p e r i m e n t a l C o n d i t i o n s f o r Spectrograms Figure  4.2  Exposure Number* F  - 10  V (kV)  I (ma)  3-0  3.4  0.9  P (mm Hg)  t (hrs)  +  1.5  used i n  Figures  Cathode  gas  Electric F (kV/cm)  0.5mm A l  H 0 2  . 63  4.3  it  n  II  II  II  it  n  it  it  4.4  n  n  ti  n  II  it  it  11  it  4.5  9/26/63 1  2.8  2.5  7.5  3.8  CH3OH,  He  0.5mm A l  52  4.6a  6/19/65 1  2.6  3.5  1.9  2.0  CH3OH,  He  1.0mm A l  3k  4.6b  8/25/63 1  3.6  3.0  0.5  2.6  CH 0H  1.0mm A l  47  4.6c  6/26/65 1  3.0  2.0  2.0  CH^OH, He  0.5mm A l  68  4.7  1/20/65 1  3-5  3.0  1.9  3-8  CH^OH, C H  1.0mm A l  36  4.8  6/28/65 u  3.6  1.9  2.8  1.3  CH3OH,  0.5mm A l  66  * u = upper, +  p i s total  Electric of  1 2  ,  He  He  pressure i n discharge tube  field  i n millimeters  f o r CH  CH Q ( l ) l i n e ; 2  splitting  6  1 = lower  * diameter o f cathode x  3  o f OH P  2  field 1 2  (l)  £  2  and m e t a l  7 T plates  f o r CH A~* 2  line.  2  used  Is determined from S t a r k  T T plate  i s determined  splitting  from S t a r k  I  TABLE I I Observed  R?.(D ,(o,o)  Exposure No.  1  E-27  AX(mm)  A~v(cm  )  S t a r k S p l i t t i n g s i n OH 2" ~* TT and i n h y d r o g e n B a l m e r Hy l i n e 2  Pl?(l),(l,l) ^VCcn,"1) -ax'(mm)  +  2  Band  AX (mm)  4X(mm)  E(kV/cm)  0.149*0.005 0.67^*0.02 0.176^0.012 0.72/0.05 0.135*0.007 0.63/0.03 0 . 8 4 / 0 . 0 2 34.9*0.8 0.230*0.003 1.04 *0.01 0.242*0.003 1.00/0.01 0.201-0.009 0.91/0.04 1.19*0.06 49,2*2.4  E-22  3  6/23/63 0.232*0.006 1.04*0.02 E-27  u  0.213*0.007 0.97^0.03  .. t  52.9*0.5  0.241*0.003 1.09/0.01 0.251*0.003 1.04*0.01 0.201*0.007 0.91/0.03 1.32/0.01 54.8*0.5  6/25/63 0.255*0.003 1.15/0.01 0.276*0.003 1.09/0.01 0.217 0.004 0 . 9 8 / 0 . 0 2 1.45/0.03 '59.9*1.3 i  F-10  X  0.265*0.003 1.20/0.01 0.285*0.003 1.18, to. 01 0.228*0.004 1 . 0 3 / 0 . 0 2 1.53*0.02 63.1*1.0  *" T h i s l i n e take f  Field  care  was v e r y  of possible  value  spectrogram. *Usss  only  weak.  The e r r o r has been i n c r e a s e d b y a f a c t o r o f 5 t o  systematic  f r o m maximum S t a r k  errors  i n measurement.  s p l i t t i n g of H  O b s e r v e d s p l i t t i n g xfas H « 2 ~ 2  h i g h f r e q u e n c y components.  order Stark effects  y  as measured on a p r i s m 1*0 cm  Corrections  and changes i n d i s p e r s i o n w i t h  -1  a r e made f o r s e c o n d frequency.  ON  mer  l i n e Hg.  P (l)> 1 2  s p l i t t i n g s f o r the 1*2(1), (0,0) l i n e and  The  (1»1)  l i n e are between the  s p l i t t i n g s l i s t e d f o r the P i ( l ) ,  the  |M| = 1/2 components. The  (0,0) l i n e are between the  d i s p l a c e d l i n e and t h e low f r e q u e n c y  = 3/2 component.  /MJ  s p l i t t i n g s are g i v e n i n terms of the d i s t a n c e on the  unThese  spectrogra-  p h i c p l a t e measured i n m i l l i m e t e r s and a l s o i n terms o f wave number u n i t s .  The  s p l i t t i n g s are the average of e i g h t measure-  ments on each l i n e . observers.  Four measurements were made by each o f  The R ( l ) , 2  (0,0) l i n e and the P ] ^ ) 1  sen because they were f r e e of o v e r l a p p i n g . the o n l y l i n e a r i s i n g  l i n e  two  were cho-  The P ( l ) , 1  (0,0)  from the l o w e s t r o t a t i o n a l l e v e l of  was  2  e l e c t r o n i c s t a t e t h a t had S t a r k components f r e e of o v e r l a p p i n g . The q u a n t i t y  l i s t e d f o r the Balmer H  y  l i n e and quoted i n  m i l l i m e t e r s c o r r e s p o n d s t o a u n i t s p l i t t i n g of 0.0642 E  cm , -1  where E i s the magnitude of the e l e c t r i c f i e l d s t r e n g t h i n kV/cm.  T h i s u n i t s p l i t t i n g i s d e r i v e d from measurements on  or more u s u a l l y t e n S t a r k components of Hy. components were t a k e n line.  I n t h i s way  the s m a l l l i n e a r nored.  i n corresponding  The  t e n Hy  five  Stark  p a i r s about the c e n t r a l  second o r d e r S t a r k e f f e c t s c a n c e l l e d out  and  change i n wave number d i s p e r s i o n c o u l d be i g -  When o n l y h a l f of the S t a r k p a t t e r n was  observed, cor-  r e c t i o n s were made f o r second o r d e r S t a r k e f f e c t s and f o r changing  dispersion.  The  u n i t s p l i t t i n g was  bers u s i n g a d i s p e r s i o n a t Hy o f 2.65  converted  to wave num-  cm"Vmm.  T a b l e I I I g i v e s the observed and c a l c u l a t e d p o s i t i o n s o f f i e l d induced-parity forbidden l i n e s 2  Z " - * T T , (0,0) band. V  2  observed i n the OH  The measurements were made on a photo-  TABLE I I I Observed  and c a l c u l a t e d p o s i t i o n s o f f i e l d - i n d u c e d p a r i t y , f o r b i d d e n - l i n e s i n t h e 2%+^ T T , ( 0 , 0 ) , band o f OH* 2  Pl(K) Calculated (cm  - 1  Ql(K)  Observed  Calc.-obs.  Calculated  Observed  C a l c . -obs..  (cm-1)  (cm- )  (cm-1)  (cm-1)  (cm )  )  1  3^0.22  32 340.15  4  288.34  288.19  +0.15  5  234.68  234.72  -0.04  6  179.11  179.03  7  121.13  8  060.75  3  32  +  - 1  0.07 32 424.61  -0.20  404.75  404.77  -0.02  + 0.08  382.71  382.77  -0.06  121.07  + 0.06  358.29  358.11  + 0.18  06O.4.3  + 0.32  331.05  331.39  -0.34  9  301.14  301.46  -0.32  10  268.00  11  232.01  231.97  + 0.04  ""These Q-^K). due  forbidden  lines  are associated  32 424.41.  with the allowed l i n e s :  The c a l c u l a t e d p o s i t i o n s have n o t b e e n  t o the Stark  1  for shifts  and In energy  effect.  "'"Measurements f r o m e x p o s u r e number F-10 63.I kV/cm  corrected  P (£)  a t maximum.  which  corresponds t o a n ' e l e c t r i c f i e l d o f  graphic  p l a t e f o r w h i c h the maximum e l e c t r i c  (63.1  1»0') kV/cm.  and  -  Q,-|_ a l l o w e d  using 2  lines.  the rotational  TT}/x s t a t e .  due  These f o r b i d d e n l i n e s  correspond  The c a l c u l a t e d p o s i t i o n s were  The c a l c u l a t i o n  ignores  f o r the  ( F o r example,  line  the Stark  between c a l c u l a t e d  and observed  t h e Pi(3)  than  and l e s s  Table 2  IV l i s t s  (0.0)  X~-^ TT> 2  splittings  nents  o f t h e ?2^)  fect  0.01  cm  slightly  shift values - 1  a n d makes t h e  higher  •  than ob-  t o be about 0.2  cm  - 1  for  0^(1).)  f o r the  A 3900$.  i n energy  would cause t h e d e v i a t i o n  the Stark s p l i t t i n g s band,  for  1  observed  i n the  These r e s o l v e d f i r s t  order  were measured between t h e two )M| = l / 2 compo-  Stark  photographed  determined  the s m a l l s h i f t  t o t h e p e r t u r b a t i o n o f t h e lambda d o u b l e t s  served.  t o t h e P.^  l e v e l s g i v e n by D i e k e a n d C r o s s w h i t e  calculated position  CH  f i e l d waa  a  n  d  i n second  ^2^ ^  lines.  1  These  S t a r k s p e c t r a were  order simultaneously  on t h e h y d r o g e n B a l m e r l i n e  with  the Stark  ef-  Hy from w h i c h t h e e l e c t r i c  field  was d e t e r m i n e d .  terms  o f t h e d i s t a n c e i n m i l l i m e t e r s m e a s u r e d on t h e s p e c t r o s c o -  pic is  The CH S t a r k  p l a t e and i n t e r m s t h e average v a l u e  o f wave number u n i t s .  for a unit  where E i s t h e m a g n i t u d e o f t h e kV/cm.  splitting electric  1  quently  Since  t h e CH S t a r k  provided  a value  0.0642  field  s p l i t t i n g s were  p o n e n t s were measured t w i c e data l i s t e d  four times  each  p a i r - w i s e about  - 1  ,  strength i n  was  y  E cm  (5.54 - 0.005)  small  (and  subse-  f o r t h e d i p o l e moment t o o n l y "t  CH l i n e s were measured  From t h e  are g i v e n i n  The q u a n t i t y AX  of  On t h i s p l a t e t h e d i s p e r s i o n f o r H  cm" /mm.  the  splittings  15$)  and t h e Hy S t a r k the central  i n T a b l e V a more a c c u r a t e  com-  line.  value o f  TABLE IV O b s e r v e d S t a r k S p l i t t i n g s i n CH -*^V Band and i n h y d r o g e n B a l m e r Hy. ( O b s e r v e d i n S e c o n d O r d e r . )  CH S t a r k S p l i t t i n g s  P  Y  Splittings  (1)  2 (1)  4x(mm)  E x p o s u r e No.  :H  AX(mm)  .  ZV(cm-l)  ^X(mm)  E(kV/cm)  2/16/65 u  0.06^*0.01  0.51*0.08  0.050*0.01  0.44^0.08  0.32 *0.01  27. *1.0  2/13/65  0.06 *0 0l  0.44±0.06  0.062*0.01  . 0.46*0,06  0.354*0.03  30 -*-3<o  0.071*0.01  • 0.54*0.09  0.434*0.01  37.4*0-9  0.12 0.01  0.90*0.08  0.446*0.01  38.3^1.0  0.457*0.005  39-3*0.5  o.47 -o.oi  40.^0.8  u  0  t  1/ 3/65 m 12/31/64 ra  O.lOo^/oi  0.74*0.0?  1/20/65 1  0.084*0.01  0.62*0,05  1/ 3/65 u  u = upper m = middle 1 = lower  t  2  o.09 o.oi t  3  0.69^0.08  6  0  7  the CH  electric  d i p o l e moment was  t i n g s l i s t e d here listed  the OH  listed  R (l),  i n Table  (0,0)  2  line  i n second  V f o r the  CH  measured f o u r t i m e s  v e r s and  of  an a v e r a g e  the  lists  the  f o r w h i c h measured S t a r k  table  i s In t h r e e p a r t s and  Stark  splittings  fourth  order,  (b)  CH  1 2  z  (l),  Stark  (0,0)  line  two  separate taken.  provides 2  information for:  third  T T ,  o r d e r w i t h OH  in  f o u r t h order.  i n the  to  measure t h e  s t a t e were  CH  electric  2  A-*  2  2.  '-*>  2  77 ,  (c) C H Stark  2  TT,  i n the  (0,0)  (0,0)  illustration  c o n d i t i o n s f o r that  Z  splittings  2L*-* TT,  in  (0,0)  Z  band S t a r k s p e c t r a used  d i p o l e moment o f t h e  shown a b o v e as an  experimental  and  Stark s p l i t t i n g s  The  OH  , (0,0) b a n d p h o t o g r a p h e d i n  77  splittings order,  The  (a)  (o,0) band p h o t o g r a p h e d s i m u l t a n e o u s l y  2  OH  exper-  are g i v e n above.  in  £ - - *  Each  The  c o n d i t i o n s f o r each  i n second  2  and  obser-  band p h o t o g r a p h e d the  those  simultaneously.  by  splittings  ^[?~~*  Stark  The  split-  i n fourth order.  experimental  iment  i n the  P  Stark  order while  e i g h t measurements was  s p e c t r a were p h o t o g r a p h e d T a b l e VI  CH  order.)  were p h o t o g r a p h e d  S t a r k s p l i t t i n g was  Stark  (The  were p h o t o g r a p h e d i n t h i r d  above were p h o t o g r a p h e d  splittings  derived.  CH  Z  A  electronic  i n F i g u r e 4.7.  experiment  are l i s t e d  The in  Table  I.  Analysis In shift  Chapter  effect  lines  Stark  spectra  II detailed  i n frequency  emission served  of Stark  e x p r e s s i o n s were g i v e n  o f a Stark, e f f e c t  component  of a diatomic molecule.  splittings  and  shifts  In t h i s  for  the  in electronic s e c t i o n the  i n e n e r g y w h i c h we  have  objust  TABLE V Simultaneously (CH  Observed  Stark Splittings  a n d OH b a n d s were o b s e r v e d  CH, •ft E x p o s u r e No.  P  4 X (mm')  1 2  i n3  i n CH and OH J £ "* 2  and 4^  r d  (D  2  T T Bands  orders respectively.)  OH, R ( l ) 2  4V ( c n r ) 1  AX (mm)  A V(cm-1)  6/19/65 1  0.142^0.010  0.57 *0.04  0.167*0.010*  0.70 *0.04  6/22/65 1  0.153-0.007  0.6l ±0.03  0.167*0.012  0.71^*0.05  6/17/65 u  0.162-^0.005  0.65 0.02  0.174*0.007  0.745*0.03  6/23/65 u  0.190-0.005  0.767*0.02  1 0.220-0.009  u = upper, 1 = lower.  2  7  t  1  OH, P  1 ?  (l)  J  2  0.94 ±0.04 0  71 TABLE V I Experimental Conditions for Plates Used to Determine OH and CH Electric Dipole Moments (a)  OH >3064^ band (4 -order), Hydrogen Balmer H ( 3  E-27 1 E-22 6/23/63 E-27 u 6/25/63 F-10  V (kV)  (ma)  3.6 3.7 6.3 4.7 6.5 3.0  11.5 4.5 3.2 12.0 4.1. 2.4  I  t P (mm Hg) (hrs) +  CH A3900A band ( 2 5  2/l6/65u 2/l3/65u 1/ 3/65m 12/3l/64m 1/20/6^1  3.5  T7T  I* 6.0 3.1 3.0 5  I'.O  5.0 3.5  1 / 3/65u 4.0 (c)  r d  Y  Exposure"* Number  (b)  order) Electric * Field cathode (icV/om)  th  5.0  CH >3900A band ( 3 >  6/19/651 2.6 6/22/6^. 3.0 6/17/65u 3.0 6/23/65u 4.1  3.1 3.5 3.4 3.5  0.5 4.5 0.8 0.5 0.9 0.9 nd  0.1 0.7 1.8 0.2 2.3 1.5  gas  2.0ram A l 1.0 w 1.0 Al II 2.0 II 1.0 II 0.5  H0 3  34.9 49.2 52.9 54.8 59.9 63.1  order), Hydrogen Balmer H (2nd order) y  3.1 3.5 0.55 0.12 1  «9.  0.40 r d  5.0 2.5 3.0 4.0 3.8  CHoOH,  He 1.0mm  "  CH3OH CH3OH CH3OH,  • » "  » • "  "  "  C6H12, CH3OH  1.5  \ He)  order), OH > 3064$ band ( 4  1.9 1.5 2.1 1.5  Al  CH^OH, He "  t h  ?  40.7  order)  CH 0H, He 1.0mm Al  2.1 1.0 2.3 1.7  27.7 30 37.4 38.3 39.3  «  ti  11  11  11  11  11  11  11  11  11  u  "* u = upper, m = middle, 1 = lower  1  * total pressure in discharge tube * Cathode diameter in millimeters and material used  34.  7  36.1  37.6 ^7. x  72 seen w i l l be r e l a t e d  t o the a p p r o p r i a t e mathematical  The  main p u r p o s e o f t h e s e c t i o n w i l l be t o p r o v i d e  for  the e l e c t r i c  ectronic shift,  d i p o l e moment  of a molecule  s t a t e i n terms o f t h e observed  the derived value  quantum numbers o f t h e r o t a t i o n a l  s p l i t t i n g or  field  levels  an e x p r e s s i o n  in a particular e l -  Stark  of the e l e c t r i c  expression.  s t r e n g t h , and the  i n v o l v e d i n the  transi-  tion. For  t h e OH  2  2  2  and  f o r t h e CH Z - * T 7 ,  the  Stark  _  2  I I that  tive  (0,0)  2  splittings  components h a v i n g ter  (0,0)  TT, R ( l ) ,  lines:  correspond  1 2  o f |M| .  o f a lambda d o u b l e t  to the center o f the unperturbed  £l = t  P  /(A/2)2+  (  V l 2  (l),  element  splitting tive  R  d  E .  of  2^  »  i n Chap-  doublet  1  rela-  i s g i v e n by:  )2 ,  corresponds  values  n  lines  S t a r k component  (2.11) doublet  f o r the p e r t u r b a t i o n energy.  of i n t e r e s t  and n e g a t i v e  a  We have s e e n  where X i s t h e s e p a r a t i o n o f t h e u n p e r t u r b e d the m a t r i x  (1,1)  t o t h e s e p a r a t i o n o f two S t a r k  t h e same v a l u e  the e n e r g y  and P i 2 ( l ) ,  and V  is  1 2  The S t a r k  t o the d i f f e r e n c e of t h e p o s i That  i s the observed  splitting  can be w r i t t e n :  = All  J(X/2) + 2  2  (V  ) '  2  q u a n t i t i e s a r e i n wave number u n i t s . 2 V  For a  2  1  2  =  2  > J  TT/  J(AV) =  1/2  2|»E ( M - V ( J ( J t 1))  2 V  i  r  2  - x  (4.D  ,  2  1  Solving f o rV  gives:  1 2  .  2  level,  (^-) 2  M = 1/2  and A  = 1/2  and. 2 V  1  =  2  becomes:  2/3fE=  w h i c h w i l l be r e f e r r e d  J(AV)2 - )2  s  t o as the c o r r e c t e d s p l i t t i n g .  (  4  #  3  )  Since the  73 J = l / 2 l e v e l of the case  (a)  coupling there  It  i s convenient  splitting CH  v = 0  s t a t e always b e l o n g s  a  i s no  and  here  to note  above.  w a s taken  lambda d o u b l i n g  f o r intermediate  cou-  T1^,  as  cm  the  f o r the  J = 1/2 f o r OH  - 1  level  lambda f o r t h e  determined  CH  The  1  was  OH the  i n both  \ - 0.1135 cm" .  f o r CH  lambda  f o r t h e J = 1/2  2  0.157  state;  \fas t a k e n  (4.3)  t h e OH  \=  as  chosen  the v a l u e s  equation For  v - l vibrational v - 0 level  correction  t o p u r e Hund's  (4.3).  evaluate  listed  doubling  - 1/2,  the  needed t o  lines  lambda  J  TTy  needed f o r e x p r e s s i o n  pling  and  2  by  2  the  TTi/  ;L  value  Douglas  , of  and  4 Elliott  from h i g h band.  dispersion  The  value  c a l c u l a t e d using data  optical  chosen  obtained  measurements o f t h e  f o r the OH  by  white bling ent  had  1  puted  from  cm  was  mad.e even  small values  made by  of the  blet).  In  is  the  lambda s p l i t t i n g .  of  X °  0.15  value  -  o f the For  Stark  the  was  the  effects  the  limit  0.03  of zero  cm  - 1  electric  w a s obtained  caused  by  analysis given  fields  and  lambda  dou-  independ-  t o be  com-  correct.  Stark s p l i t t i n g  (at the  field  From o b s e r v e d  lambda d o u b l i n g electric  measuring the field  Cross-  lambda d o u b l i n g thought  the  Stark thus  top of Stark  the  for dou-  splitting  splittings the  was  Townes^  and  s p e c t r u m an  though the  electric  Dieke  f o r t h e OH  - 1  the m i c r o w a v e measurements was  determination  very  ter  o f 0.31  Since  f r o m measurements o f t h e u l t r a v i o l e t determination  The  a value  obtained  lambda d o u b l i n g  Dousmanls, S a n d e r s and  f r o m microwave a b s o r p t i o n measurements.  CH  a  value  microwave  w a s chosen. used i n t h i s  neighboring  study  rotational  above f o r s p l i t t i n g s  second  levels  order  do  between S t a r k  not a l compo-  74 nents h a v i n g the shifted ond and  t h e same amount.  order effects a very  nents the  by  same v a l u e o f  o f the r o t a t i o n a l  X  state  t h e K = 2,  no  J = 3/2  preciable  calculated  ( £ 2  ground  state  2  Similarly  , K =» 1)  state But  finds  level.  level  shift  nents  o f t h e lambda d o u b l e t and o f t h e J = 3/2  the m i x i n g than  1.4$.  effects  do  moment  from  not  termine  Thus we effect  second  o f t h e OH  state  i s always  still  can  do  be  2  TTy  JL  level  amount t o o n l y 0.013  2^r only  is  2  that  second  cm .) -1  will  rota-  compowhile  - 1  always  order Stark  the e l e c t r i c Rgd)  be  negligi-  cm  o f t h e TT'/x. s t a t e  conclude  dipole  t o the are  of  f o r the  same f o r b o t h S t a r k  order Stark effects  the e l e c t r i c d i p o l e  found  due  ap-  (These  t h a n 0.03  less  spin  mixing  moment i n t h e  s p l i t t i n g o f t h e OH  doublet  of  assume t h e  to that  dipole  line. not a l t e r  s p l i t t i n g s w h i c h xvere used moment f r o m t r a n s i t i o n s  - 1  from  t h a n 1%.  less  order effects  i s the  level  since  in cm  o f the  in transitions  the d e t e r m i n a t i o n o f  the d o u b l e t  Similarly separation  in frequency  0.007  o f two t h e m i x i n g w o u l d  would  The  compo-  line, effects  other half  ground  i s comparable  ble.  less  The  l e v e l a d j a c e n t t o t h e J = 1/2,  tional  and M = 3/2  order effects  second  shift  2  even i f t h e d i p o l e  that  a slight  R ( l ) line arises  does n o t r e s u l t  the b r o a d e n i n g  one  The  t o the J = 1/2  2T  state.  and  cause  be  molecule sec-  d o u b l e t component by  at a l l .  were g r e a t e r by a f a c t o r  doubled  will  F o r t h e R2(l)  each  v a l u e s f o r second  moment o f t h e OH TT  5/2)  J -  lower  state  rotational  components w i l l  example, i n t h e OH  levels.  shift  intensity  the n e x t  £  2  would broaden  (K - 2,  doublet  For  since both  s e p a r a t i o n o f t h e M = 1/2  slight  with e s s e n t i a l l y  2  i n the  |M|  to  to the  the de-  75 J = 1/2, Tlfa 2  level.  The CH P j ( l ) l i n e 2  more a c c u r a t e d e t e r m i n a t i o n be  by J  of the e l e c t r i c  d i s c u s s e d as an example.  a single  level  0.016  only = 1/2)  K - 0,  ( £, 2  w h i c h c o u l d be i g n o r e d Mixing  The o b s e r v e d J = 1/2)  c m ~ l and t e r m i n a t e s  which i s s h i f t e d  o f adjacent  that  second  electric  in  frequency,  sis  must  line  JM/ = 3/2,  i n c l u d e second  f o r zero  field  from  for tric  the lower field  component  Since  The  £2  i n zero  order terms.  i n t h e 25L  2  TT3^  observed  the s p l i t t i n g  electric  field  was  and t h e  the analyof the P ^ d )  The f r e q u e n c y = F (o)  -  1  f^(l),  s t a t e a n d f ^ ( l ) i s t h e term In the presence  levels  o f an e l e c -  f o r the observed  Stark  i(\/2)  -  arises are: term:  s t a t e term:  and £  the l o w e r  i n the  f o r b i d d e n S t a r k component  t h e u p p e r and l o w e r  conclude  the a n a l y s i s o f  forthis line  lambda d o u b l e t l e v e l .  upper state lower  levels  Stark s p l i t t i n g s  c a n be w r i t t e n as P - ^ l )  where F-j_(0) i s t h e t e r m  shifts  Thus we  o f t h e OH m o l e c u l e  measured between t h e a l l o w e d l i n e low  2  here.  d i p o l e moment  (0,0) l i n e .  down  ( TT&, »  The  t h e J = 1/2  with  Stark doublets.  s t a t e was d e t e r m i n e d  the P - j ^ l ) ,  be s h i f t e d  from  are e f f e c t i v e l y c a n c e l l e d .  levels  observed  will  arises  a t t h e lambda d o u b l e t  o r d e r S t a r k e f f e c t s do n o t e f f e c t  CH S t a r k d o u b l e t s  electronic  which w i l l  individually  n o t broaden the observed  The  transition  1  rotational  f o r the  d i p o l e moment  down b y o n l y 0.014 cm" .  will  the  w h i c h was u s e d  z  state  ^(0) f - ^ l ) + A/2  a r e t h e second term  +  Z  order s h i f t s .  i s the perturbed  energy  1  (V  1 2  )  2  The s q u a r e o f the upper  62 ^ root i n lambda  76 d o u b l e t l e v e l ( t e r m i n a t i o n o f f o r b i d d e n t r a n s i t i o n ) measured lambda d o u b l e t ; f ^ ( l ) * A/2  from t h e c e n t e r o f t h e u n p e r t u r b e d  then i s t h e c e n t e r o f the u n p e r t u r b e d transition  w i l l have a frequency  doublet.  The f o r b i d d e n  found by the d i f f e r e n c e o f t h e  two p e r t u r b e d terms, i . e . :  - ( ^ ( 1 ) + A/2 + (|(A/2) + ( V  Fl<0) -8/ The observed  )  2  1 2  - £ * ) .  s p l i t t i n g i s the d i f f e r e n c e between t h i s  and t h a t g i v i n g the frequency  expression  o f the zero f i e l d P ^ l ) l i n e . Thus  we f i n d the s p l i t t i n g i s g i v e n by: J V t P i d ) ) = A/2 + |(A/2)2  +  (v )2 12  +  £ 2 . £2 ^  The v a l u e f o r the lambda d o u b l i n g i n the J = 3/2, X= 0.0 555  cm" as determined 1  wave experiments. the observed  S i n c e the lambda d o u b l i n g i s much l e s s  s p l i t t i n g t h e square r o o t i n e q u a t i o n (4.4)  The s m a l l c o r r e c t i o n t o V^  2  to give V  than was ex-  + (A /8V )» 2  1 2  12  was e v a l u a t e d u s i n g the observed  r a t h e r than the c o r r e c t e d s p l i t t i n g .  ting:  state i s  by E h r e n s t e i n ^ e t . a l . from m i c r o -  panded u s i n g the b i n o m i a l expansion  •was found  ^*/x  2  from e q u a t i o n (4.4)  The e l e c t r i c d i p o l e moment  by f i n d i n g the c o r r e c t e d s p l i t -  ^ V ( P ( l ) ) - (corrections) = V i . 1  2  The m a t r i x element, V  1 2  was e v a l u a t e d f o r i n t e r m e d i a t e c o u p l i n g and. t h e e x p r e s s i o n y i e l d ing  .the e l e c t r i c d i p o l e moment was: Corrected s p l i t t i n g , 4 V ' = V  1 2  = j  1  ' ^ ^ (3/5)  The e l e c t r i c d i p o l e moment o f the CH molecule e l e c t r o n i c s t a t e was determined high frequency displaced l i n e .  i n the A 2  from t h e maximum s h i f t I n the  component o f the Q.]_ (3) l i n e r e l a t i v e c  The observed  (4.5)  JAE  t o t h e un-  S t s r k e f f e c t on t h i s l i n e can o n l y  77 be  explained  and  by assuming that  t h e d i p o l e moments i n t h e u p p e r -  l o w e r s t a t e s h a v e t h e same r e l a t i v e s i g n and t h a t  mum s p l i t t i n g i n t h e u p p e r s t a t e lower s t a t e . 2.5) the  (This  4V(Q (3)) l c  matrix  with  line  component r e l a t i v e t o  i s given by:  = CV ) 12  A  - J(A/2)2  +  (V )2' 1 2  + A/2.  (4,6)  e l e m e n t s f o r t h e u p p e r and l o w e r l e v e l s a r e l a b e l l e d  s u b s c r i p t s and \ i s the lambda d o u b l e t s e p a r a t i o n  TT s t a t e .  (The l a m b d a d o u b l i n g  z e r o ^ and t h e r e f o r e  The Stark  against  In the A Z  s p l i t t i n g and the c o r r e c t e d electric field.  i s proportional  the d e t e r m i n e d v a l u e . corrected the  The s l o p e was f o u n d through the o r i g i n .  F o r example, Figure  This  field  4.9. shows a . p l o t o f  f o r t h e OH R ( l ) ?  , (0,0) band... I n t h e f i g u r e t h e l i n e a r  ship between the c o r r e c t e d field  using  t o t h e e l e c t r i c d i p o l e moment a n d p r o v i d e s  splitting vs. electric  Y-'-**~TT  t o the appropri-  s p l i t t i n g was p l o t t e d  a l e a s t squares f i t to a s t r a i g h t l i n e slope  (4.6).  moments  c o r r e c t i o n s g i v e n a b o v e were a p p l i e d  the applied  i n the  state i s e s s e n t i a l l y  does n o t a p p e a r i n e q u a t i o n  Determination of e l e c t r i c dipole  ate  than i n the  s i t u a t i o n was shown i n t h e d i a g r a m i n F i g u r e  The s h i f t i n f r e q u e n c y o f a S t a r k zero f i e l d  The  i s s l i g h t l y greater  t h e maxi-  s p l i t t i n g and t h e applied,  I s o b s e r v e d as e x p e c t e d .  The s l o p e  o f the l i n e  line i n relation-  electric I s (2/3J-0  i n u n i t s o f ( l / k V ) a n d i s c o n v e r t e d t o a d i p o l e moment i n Debyes by  m u l t i p l y i n g b y 3/2 and d i v i d i n g b y 0.01679 ( k V / D e b y e ) . Table V I I I l i s t s  t h e o b s e r v e d and c o r r e c t e d  t i n g e and corresponding e l e c t r i c  Stark  fields for the R (l), 2  split(0,0);  78 P  1 2  (1,1)  (l),  From t h e s e  j a n d P ^ l ) , (0,0)  data  lines  i n t h e OH,  the f o l l o w i n g values  ment o f t h e OH m o l e c u l e  were  2  2  of the e l e c t r i c  T T band.  d i p o l e mo-  obtained: TABLE V I I  OH E l e c t r i c  D i p o l e Moments D e r i v e d  Line  State  R (l),  (0,0)  P-LM),  (0,0)  2  2  TT,  V,  Dipole  1.732  1  v =0  I.637  ±  x  Z  1 2  , v -  A  e r r o r s quoted  ard  d e v i a t i o n s determined  Is  (0,0)  The o b s e r v e d  c l o s e t o a broad splitting  slightly  too small.  line  taken  P]_(l) l i n e  is  P^gd),  no a p p a r e n t  tings  observed The  that  by a s y s t e m a t i c e r (0,0)  line  w h i c h might make t h e  source  2  mo-  on t h e v a l u e electro-  s t a t e d i p o l e moment h a d been the value  derived  from the  Debye h i g h e r , j The R ( l ) , 2  are completely  of systematic  f o r these  dipole  2  o f the £  lines  of the e l e c t r i c  depends s l i g h t l y  2  electric  one w o u l d e x p e c t  o f t h e OH P ] _ ( l ) ,  that o f the T T s t a t e ,  (1,1)  o.o4  d i p o l e moment o f OH i n t h e ] ~  P - ^ l ) l i n e w o u l d b e a b o u t 0.02 and  0 2  °*°3  ±  w o u l d be e f f e c t e d  A l s o the v a l u e  I f a value  as h a l f  (Debye)  t o o s m a l l and hence t h e d e r i v e d d i p o l e moment  f o r the e l e c t r i c  state.  °»  2  aluminum i m p u r i t y l i n e  ment d e r i v e d f r o m t h i s assumed  Moment  from t h e f i t o f t h e p o i n t s t o the  S t a r k component  measured  nic  l.69  On t h e b a s i s o f t h e o b s e r v a t i o n s  only the P - ^ l ) , ror.  1  Splittings  on t h e d i p o l e moments i n T a b l e V I I a r e s t a n d -  The  line.  Stark  , v = 0  y ,  Z l T  P (l),(1,1)  /a  from  free  of blending  e r r o r i n the Stark  (0,0) so there split-  lines.  d i p o l e moment o f t h e OH m o l e c u l e  has been de-  79  Electric  Field, E  (KV/ ) c m  Figure 4 . 9 . C o r r e c t e d S t a r k s p l i t t i n g , >Ji v', v s . f i e l d s t r e n g t h , E, f o r OH, B 2 ( D , (0,0) line.  electric  TABLE V I I I Corrected  (0,0/  R (D , 2  Exposure  No.  AV ( c m  - 1  Stark S p l i t t i n g s  P (l), 1 2  )  AV(cm- ) 1  27 1  0.67<  22  i.o4  3  6/23/63  i.05  2  E - 27 u  1.093  1.08  6/25/63  1.156  I.145  1.20  1.19i  E E -  F -  10  2  1.03i 1.04  * Experimental uncertainties  i n OH  (l,l)  2  T  I.OO3  0.99i  and  f o r second  i n each  state  E(kV/cm)  cm ) - 1  0,57  34,9  3  9*??i  0,914  52,9  1.02g  .9>?l6  0,857  54,8  1.094  I.O83  0.980  ?.?2  59.9  1.18!  I.17i  1.03o  0.97e  1.04  0  5  63.I  a r e t h e same as g i v e n i n T a b l e I I .  doubling i n  order effects i s 1.7  AV(  49,2  2  f o r X-type  - 1  (0,0)*  O.863  * C o r r e c t e d f o r X-type d o u b l i n g i n T T ^ , J = l / 2 l e v e l *Corrected  AV> ( c m ) O.6I5  2  0  2  P (D, 1  1  0.71  T T Band*  f  Al/fcnr )  0.72q  2  TTy^ , J = 3/2  2  level  i n 2 " and 7 T ^ s t a t e s 2  2  using using  \  = 0.157  cm~}-  X = 0.0555  assuming d i p o l e  cm  -  moment  Debye.  co o  termined sion by  from  m i c r o w a v e measurements.  F o r purposes  of discus-  t h e most a c c u r a t e v a l u e o f (1.660 - 0.010) Debye  Powell  and L i d e ^ w i l l  the J = 7/2 l e v e l  o f the  r a t e microwave v a l u e s stein^  also  TTj/^ s t a t e .  XI  found  a t t h e end o f t h i s  and v i b r a t i o n a l  They o b t a i n e d a v a l u e  1 0  less  ternuclear distance.  Using  computed  Cade a n d Huo have  d i p o l e moment w i t h i n -  computed v a l u e s , t h e d i p o l e  t o i n c r e a s e by 0.02 Debye  in internuclear distance i n going  Ehren-  chapter.)  has been  o f 1.780 Debye.  their  accu-  g r o u n d s t a t e b y Cade and.  computed t h e change i n t h e e l e c t r i c  moment I s f o u n d  i s measured f o r  (The e a r l i e r ,  d i p o l e moment o f t h e OH m o l e c u l e  for the electronic Huo.  2  Their value  o b t a i n e d b y Meyer and Myers® and b y  appear i n Table  The e l e c t r i c  be u s e d .  obtained  f o r t h e 1.7$ i n c r e a s e  f r o m v = 0 t o v = 1. The  change i n I n t e r n u c l e a r d i s t a n c e was f o u n d b y u s i n g t h e f o r m u l a g i v e n by Ramsey:  11  (4.7) where  r i s t h e i n t e r n u c l e a r d i s t a n c e and r  rium,  <*  the  e  i s the v i b r a t i o n a l  equilibrium vibrational We may now compare  moment  g i v e n In T a b l e VII  and b y Cade and Huo.  correction  i s that at e q u i l i b -  e  at equilibrium  the v a l u e s with  those  o f t h e OH e l e c t r i c found  by Powell  that the value  pole  the Stark s p l i t t i n g  (0,0) values  line  i s t o o l a r g e by a t l e a s t  obtained from  is  the P.(1),  dipole  and L i d e  on t h e b a s i s o f  Cade a n d Huo's c a l c u l a t i o n , from  e  constant.  We c a n s a y i m m e d i a t e l y  moment . d e t e r m i n e d  and ^  o f the e l e c t r i c d i of the P ^ ) » 1  0.03 Debye, and t h a t t h e  (0,0) l i n e  and P _ ( l ) , n  (1,1) ap-  82 pear  i n the correct r a t i o .  gests  t h a t t h e computed v a l u e  0.1 Debye  too l a r g e .  splitting  measured  standard measure  The m i c r o w a v e v a l u e  i n the R ( l ) ,  o f the f i t o f t h e Stark  i f t h e microwave v a l u e  i s systematically high.  found  from the R ( l ) l i n e 2  tric  fields  line.  The microwave  found  (1,1) l i n e  the P ] _ ( l ) l i n e The electronic  are s l i g h t l y  electric  lines  2  2  splittings  fields  a r e given i n Table  was f o u n d . the  electric  1  values  and the  (The s p l i t t i n g s i n  o f t h e CH m o l e c u l e  of the P  T 7 band o b s e r v e d  through  i n that  i n the  2  Tf  experi-  o f t h e d i p o l e moment was f o u n d by  and c o r r e c t e d s p l i t t i n g s  of a line  splittings  elec-  low as a n t i c i p a t e d • a b o v e . )  served  slope  t h e d i p o l e moment  s t a t e was found, by two i n d e p e n d e n t  the Stark  o f the X  2  o f the P ( l ) , ( 0 , 0 ) l i n e  d i p o l e moment  ground  i n the R ( l ) ,  used to determine  a r e i n good a g r e e m e n t .  ments. The p r e l i m i n a r y v a l u e measuring  However,  conclude  o f t h e d i p o l e moment and t h o s e  from the S t a r k s p l i t t i n g s  (l),  line.  one must  splitting  The  realistic  2  f r o m measured v a l u e s o f S t a r k value  is a  f o rR (l),(0,0)  c o u l d be s a f e l y  that the  i s too l a r g e .  i s correct,  d i p o l e moment found, from t h e S t a r k line  1 2  effect  sug-  i s about  a l s o suggests  (0,0) l i n e  2  (0,0)  P  o f t h e OH d i p o l e moment  d e v i a t i o n i n t h e d i p o l e moment g i v e n  Therefore, the  In t u r n the s p e c t r o s c o p i c data  IX.  1 2  (l),  and Q ( l ) » (°»C) 2  i n second order.  The o b -  and. t h e c o r r e s p o n d i n g The d a t a were  the o r i g i n  (The s l o p e was 2/3/*.)  giving  electric  plotted  a least  The v a l u e  d i p o l e moment o f t h e CH m o l e c u l e  thus  and t h e  squares f i t obtained f o r  i n the T T ^ s t a t e 2  was 1.45 Debye ± 15#. A more a c c u r a t e  value of the e l e c t r i c  d i p o l e moment o f t h e  TABLE IX  Corrected  Low D i s p e r s i o n S t a r k S p l i t t i n g s  P (D  ^V(cm-l)) AV^cm- )  1  2/15/65 u  0.51  0.49  2/13/65 u  0.44  0.42  0,44  c  0.46  8  12/31/64 m  0.74  0.73  2  1/20/65 1  0.62  0.6l  4  0.90  = upper,  2  0.44g  30,0  2  0.69  f o r A-type  ?  38.3  O.89.3  0.68;  40.7  a r e t h e same a s g i v e n i n T a b l e I V  doubling  m = middle,  37 4  39-3  1/ 3 / 6 5 u  uncertainties  ?<?  <M 6  0.54  Experimental  Band  E(kV/cm)  1  1 / 3/65 m  *u  2-TT  Qp(l)  A V ( c m - 1 ) | hv\cm- )  Corrected  2  t  12  E x p o s u r e No?  i n CH ]  using  1 = lower  X= 0.1135  cm  - 1  84 CH m o l e c u l e was o b t a i n e d from measurements o f S t a r k of the 2 . ( l ) l i n e observed P  2  was determined  i n t h i r d order.  plates with sufficient  x  a  n  d  0 H  these l i n e s  >  R  T  h  e  i s 2/3j-<E.  p a i r s o f S t a r k l i n e s (CH,  c o r r e c t e d s p l i t t i n g f o r each o f A p l o t o f the CH c o r r e c t e d s p l i t t i n g v s .  OH c o r r e c t e d s p l i t t i n g appears i n F i g u r e 4.10. Table X p r e c e d i n g t h e f i g u r e . )  (The d a t a a r e I n  The slope o f t h e l i n e  shown  g i v e s t h e r a t i o o f t h e d i p o l e moment o f t h e CH molecule d i p o l e moment o f t h e OH molecule on the R ? ( l ) l i n e .  inate line.  inten-  The d i p o l e moment was found by u s i n g t h e c o r r e c t e d s p l i t -  12( )  fect  field  2  t i n g s o f s i m u l t a n e o u s l y observed p  The e l e c t r i c  from t h e OH, R ( l ) l i n e s i n c e no hydrogen Balmer  l i n e appeared on t h e p h o t o g r a p h i c sity.  splittings  determined  T h i s treatment  t o the  from the S t a r k e f -  should e f f e c t i v e l y  elim-  the small systematic e r r o r In the s p l i t t i n g of the R ( l ) 2  The s l o p e o f t h e l i n e i n F i g u r e 4.10, found from a l e a s t  square f i t , i s (0.84^ ± 0 . 0 3 ) .  Using t h e v a l u e o f the OH e l e c -  2  t r i c d i p o l e moment (determined  from the R ( l ) l i n e ) o f  (1.73 - 0.02) Debye t h e r e s u l t i n g moment o f CH i n t h e " 'A 2  (1.46 - 0.06) Debye. resulting  rT  2  value f o r t h e e l e c t r i c d i p o l e  e l e c t r o n i c ground s t a t e i s found t o be  The e r r o r quoted i s a s t a n d a r d d e v i a t i o n  from the f i t t o t h e l i n e and from t h e u n c e r t a i n t y i n  the d e r i v e d v a l u e o f t h e OH d i p o l e moment. used h e r e were s l i g h t l y blended  The CH s p l i t t i n g s  i n two cases and t h i s might r e -  s u l t i n a v a l u e o f t h e CH e l e c t r i c d i p o l e moment which was s y s t e m a t i c h i g h by 1%'  The v a l u e o f the CH e l e c t r i c d i p o l e moment  here can be compared w i t h a v a l u e o f 1.57 Debye computed by Cade and H u o .  1 0  Again t h e computed v a l u e i s h i g h e r than t h a t  found  TABLE X  Corrected,  Simultaneous Observed CH a n d OH J - * TT 2  CH, P Exposure  Mo!!  1 2  Z  (l)  Stark S p l i t t i n g s i n Bands*"  OH, R ( D *  +  2  4 V (cm" )  dVfcnr ) 1  1  Al/ (c-m- ) /  1  O.684  6/19/65 1  0.57  2  Oo56  6/22/65 1  o.6l  7  0.60g  O.7I4  0.69  6/17/65 u  0.65!  0.64-L  0.74  5  0.72g  6/23/65  0.76  0.75  0.94  0  0.92  u  *Experimental in  7  uncertainties  0 . 7 0  0  o  2  7  7  a r e t h e same as g i v e n  T a b l e V.  Corrected  f o r A-type doubling  using  A= 0.1135 cm  *Corrected  f o r A-type d o u b l i n g  using  A= 0.157 crn  f  * u - upper,  1 = loxirer  -  86  F i g u r e 4.10. F i r s t - o r d e r S t a r k s p l i t t i n g o f CH I W ) l i n e v s . f i r s t - o r d e r S t a r k : - s p l i t t i n g o f OH B ^ d ) l i n e . S p l i t t i n g s are c o r r e c t e d f o r lambda-type d o u b l i n g . 1  by  experiment.  dipole  No o t h e r e x p e r i m e n t a l  moment e x i s t  v a l u e s o f t h e CH e l e c t r i c  f o r comparison w i t h the v a l u e  determined  here. The  electric  electronic shift  d i p o l e moment  s t a t e was d e t e r m i n e d  field  o f 66 kV/cm.  (which  i s also  T h i s v a l u e was used v a l u e o f 0.38  earlier  the Q  (3) l i n e  lc  from  state;  5/2,  M -  field, o f  1  66 kV/cm;  Q (3)  )M| =  i nthe  2  i nthe value  1  A electronic  5/2  i n the upper  i n the lower  o f the e l e c t r i c  shift  s t a t e was  a n d a maximum s h i f t o f  value  The u n c e r t a i n t y i n t h i s  certainty  M = 7/2  a n d )\- 0.373 cm"  t o the  The maximum  t o t h e |M| = 7/2-*  u s i n g J = 7/2,  The r e s u l t i n g  t h e CH m o l e c u l e  15$.  2  2  7/2,  cm" .  i npreference  1  (4.6)  This  cm~l b y Douglas and E l l l -  f o rcalculation  corresponds  cor-  o f t h e lambda doub-  cm" o b t a i n e d b y G-ero.  equation  electric  0.06) of  J -  0.373  h  i n an  i nfrequency  The d i p o l e moment o f CH i n t h e A  S t a r k component.  an  t o be  z  Stark  a n d %^(3) l i n e s .  the r e q u i r e d value  l i n g ) h a s been d e t e r m i n e d  found  The maximum s h i f t c  separation  in  the maximum o b s e r v e d  t o the s e p a r a t i o n o f t h e Qi (3)  respond  ott.  from  i n the  components o f t h e Q-]_c(3) l i n e  o f the high frequency  electric  o f t h e CH m o l e c u l e  state;  (0.373 *  d i p o l e moment  s t a t e i s 1.13 Debye *  v a l u e i s p r i m a r i l y due t o t h e u n -  o f t h e maximum s h i f t  i nfrequency  o f the  line.  l c  Summary In  summary, t h e v a l u e s  determined tronic  from  emission  f o r the e l e c t r i c  d i p o l e moments  observations o f the Stark e f f e c t s p e c t r a o f t h e OH m o l e c u l e  (^1  on t h e e l e c -  -* -TT) a n d on  88 that In  Table XI.  ment ed. . and  o f t h e CH m o l e c u l e  (  2  I ~-* TT  F o r comparison  o f OH as d e t e r m i n e d  2  and  2  A -+ V) 2  are g i v e n below  v a l u e s of the e l e c t r i c  dipole  f r o m microwave measurements a r e  Computed v a l u e s o f t h e e l e c t r i c CH m o l e c u l e s a r e a l s o g i v e n .  dipole  mo-  includ-  moment o f t h e OH  89 TABLE X I  Electric Molecule OH  D i p o l e Moments f o r t h e OH and CH State  1  TF^.  2  J-9/2,  l x.' ? f^ Reference r -•(De-bye)(Debye) i v-0 1 . 6 5 * 0 . 2 5 Meyer and Myers ( 1 9 6 1 ) ® e  1.60 ± 0.12  Ehrenstein T h i s Work  J=l/2,  v=o  1.73a  J-3/2,  v-0  1.63,  TTv*>  J-l/2,  v=l  1.69^  o.o4  TTvi>  J = 7 / 2 , v=0  1.660*  0.010 Powell  2  2  CH  M o  e  J = 7 / 2 , v=0  2  2  2  2  n,  v =0  Fva'  J - l / 2 , v=0  TT, v =0  A  Molecules  . J = 7 / 2 , v=0  1  0.02  0.03  ±  11  11  ti  11  (1963)*  and L i d e  1.780 (computed)  Cade and Huo  1.46  T h i s work  * 0.06  1.57 (computed) 1.13  1  15$  Cade and Huo T h i s work  (1965)  (1965)  1 0  (1965)  1 0  7  90 F o o t n o t e s f o r Chapter IV 1.  G. H. D i e k e and H. M. C r o s s w h i t e , Bumblebee R e p o r t No. 8? ( J o h n H o p k i n s U n i v e r s i t y , 1948) .  2.  L . Gero,  3.  E . U. Condon and G. H. S h o r t l e y , t r a (Cambridge U n i v e r s i t y P r e s s , p. 4 0 1 .  Z. P h y s i k 118, 27  (19^1).  4. A. E . D o u g l a s and G. A. E l l i o t t ,  (1965).  5.  The T h e o r y o f A t o m i c S p e c Cambridge, E n g l a n d , 1935) C a n . J . P h y s . 43, 496,  G.C..Dousmanis, T. M. S a n d e r s , a n d C. H. Townes, Phys. R e v .  100, 1732 (1955).  6.  G. E h r e n s t e i n , L e t t e r s 2 , 40  7.  F. X. P o w e l l and D a v i d R. L l d e ,  8.  R. T. M e y e r and R. J . M y r e s ,  9.  Or. E h r e n s t e i n , P h y s . R e v . 13_0,  4201  C. H. Townes, and M. J . S t e v e n s o n , P h y s . R e v .  (1959)  (1965).  J r . , J . Chem. P h y s .  J . Chem. P h y s .  42,  J4, 1074 (1961).  669 (1963).  10.  P r i v a t e communication: P a u l E . Cade and W i n i f r e d Huo, L a b o r a t o r y o f M o l e c u l a r S t r u c t u r e and. S p e c t r a , P h y s i c s D e p a r t ment, U n i v e r s i t y o f C h i c a g o , C h i c a g o , I l l i n o i s .  11.  N. F. Ramsey, M o l e c u l a r Beams ( C l a r e n d o n P r e s s , O x f o r d ,  1956), p . 231.  91 CHAPTER V  CONCLUSION AND SUGGESTIONS FOR FURTHER STUDY T h i s work h a s r e p o r t e d linear  Stark  diatomic and  splittings  molecule.  field  theoretical  served  resulting  i n the Z  2  electric  transitions  77  The e l e c t r i c  electronic  electronic  a means o f d e t e r m i n i n g  the e l e c t r i c  the e l e c t r i c  electronic  s t a t e s h a v e been  Suggestions  there.  ing  used here  d i p o l e moment  d i p o l e moment  provide  f o r short  Furthermore, w i t h o f a molecule  i n excited  f o r f u r t h e r work  most i n t e r e s t i n g  topic  f o r f u r t h e r study would be the  components o f s e v e r a l l o w J l i n e s  i n t h e CH, 2^L~-~* 7 T , Ji3900^.band f o r an e l e c t r i c 2  120  these  determined.  o f the f o r b i d d e n Stark  exceeding  o f t h e OH  s t a t e a n d o f t h e CH m o l e c u l e i n  states are given  techniques  observed  \  one d e g e n e r a t e  d i p o l e moment  and c h e m i c a l l y r e a c t i v e s p e c i e s .  fading  the  a r e summarized a t t h e e n d o f  T h i s w o r k h a s shown t h a t t h e t e c h n i q u e s  The  from  d i p o l e moment, when t h e ob-  involve at least  Derived values  chapter.  7 T and A  lived  broadenings  f e a t u r e s a r e In agreement w i t h t h e  a permanent  state.  the p r e v i o u s  2  spectra of a  p r e d i c t i o n s f o r the Stark s p e c t r a of a diatomic  having  electronic  the  i n the e l e c t r o n i c  The o b s e r v a t i o n s have a l s o shot^m  A l l these  electronic  molecule  produced  successful observation of  induced-parity forbidden lines  Stark e f f e c t .  molecule  the f i r s t  kV/cm.  the s t a b i l i t y  Such a s t u d y would p r o b a b l y  o f the cathode  i n the discharge  field  i n v o l v e improvtube.  Per-  92. haps a n a l t e r n a t i v e could  technique  be d e v e l o p e d .  f o r producing  However, a d a p t i n g  large e l e c t r i c  the present  spectrograph  f o r p h o t o e l e c t r i c d e t e c t i o n may overcome  the present  sities  fields.  encountered  a t very high  allow  studies at high  tube.  Further study  electric  t r b n i c ' • and v i b r a t i o n a l and P-LU) l i n e s  2  and  R (D  lines.  2  f i e l d s with  o f the s l i g h t  moments d e d u c e d f r o m d i f f e r e n t  R (l)  electric  state i s advised  and f o r t h e CH,  In doing  this  2  I  This  would  the present  going  discharge the dipole  t o t h e same  elec-  f o r t h e OH, 2  TT,  TT,  P (D, 2  i t w o u l d be i m p o r t a n t  p a r t i c u l a r a t t e n t i o n to e l i m i n a t i n g sources  e  low Inten-  d i f f e r e n c e between  transitions  fields  t o give  o f Impurity  lines.  

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