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Nonlinear resonant photoionization in molecular iodine Sil, Georgena Sarah Petty 1976

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NONLINEAR  RESONANT PHOTOIONIZATION IN MOLECULAR  IODINE by  GEORGENA SARAH PETTY SIL B.Sc,  U n i v e r s i t y o f Saskatchewan,  A THESIS SUBMITTED  1973  IN PARTIAL FULFILLMENT OF  THE REQUIREMENTS  FOR THE DEGREE OF  MASTER OF SCIENCE  in THE FACULTY OF GRADUATE STUDIES Department o f  Physics  We accept t h i s t h e s i s as conforming to the r e q u i r e d standard  THE UNIVERSITY OF BRITISH COLUMBIA September,  ©  1976  Georgena Sarah P e t t y S i l ,  1976  In  presenting  requirements British freely that  this  in p a r t i a l  f o r an a d v a n c e d  Columbia,  I agree  degree  that  scholarly  for extensive  purposes  ment o r by h i s  copying  may be g r a n t e d  representatives.  p u b l i c a t i o n of  this  Department  of  thesis  Physics  The U n i v e r s i t y o f B r i t i s h 2075 Wesbrook P l a c e V a n c o u v e r , Canada V6T 1W5  of  shall I  this  Columbia  is  further thesis  for  understood  it agree for  Depart-  that  f i n a n c i a l gain  permission.  of  make  by t h e Head o f my It  the  at the U n i v e r s i t y  the L i b r a r y  n o t be a l l o w e d w i t h o u t my w r i t t e n  Date  f u l f i l l m e n t of  a v a i l a b l e f o r r e f e r e n c e and s t u d y .  permission  i n g or  thesis  copy-  shall  -  i  -  ABSTRACT Strong molecular  photoionization  Iodine  ultraviolet. ture of  following  of  g  of to  Vibrational  x e  of  0.58  Franck-Condon intensities that  analysis  the  cm"*.  are  compared  internuclear  the  near  power,  and  the  indicates  an e l e c t r o n i c  analysis  separation  r  g  in  two energy  constant  vibrational  theoretical  struc-  ioniza-  co  e  constant  done  by  the r e l a t i v e e x p e r i m e n t a l  with  in  e x c i t e d by  vibrational  Rotational  method, whereby  in  state  c m " * , and an a n h a r m o n i c  ± 0.06  been o b s e r v e d  with three-photon  a harmonic  -  ± 0.4  upon l a s e r  intermediate  53 , 5 6 2 . 7 5 ± 1 c m * ,  241.4 e  i n an  have  excitation  are c o n s i s t e n t  t i o n w i t h resonance  T  laser  The d e p e n d e n c e  the s p e c t r a  photons.  spectra  values,  the band  indicates  the resonant  electronic  0  state stant has,  i s 2.567 ± 0 . 0 0 2 A , c o r r e s p o n d i n g to a r o t a t i o n a l c o n B of 0.04029 ± 0.00007 c m . The new e l e c t r o n i c s t a t e e - 1  with high p r o b a b i l i t y ,  the d e s i g n a t i o n  1 .  Several  im-  y  purity cm"  1  lines  (half  were o b s e r v e d  w i d t h 8.09  2 7 , 3 4 3 . 9 6 ± 1 cm The f e a t u r e s formed been  -1 1  .  likely  in reactions  identified.  nonlinear vicinity  at e x c i t i n g  cm" ), 1  The  signal  from complex  of 80,000 c m "  1  varies molecular  high temperature  exhibits  with  of  l^,  as  I  2  total  at 02  .  species and  have  e f f i c i e n c y of  an a p p a r e n t  i n terms  and  1  The p h o t o i o n i z a t i o n  absorption  26,297.14 ± 1  26,915.22 ± 1 c m " ,  impurity  arise at  at  energies  not  in  resonance  in  the  molecular  energy.  TABLE  ii _  OF  CONTENTS  Chapter  p  1.  INTRODUCTION  2.  THEORY AND ANALYTIC TECHNIQUES  !  2.1  Theory  of N o n l i n e a r  2.2  Coarse  Structure:  2.3  Fine S t r u c t u r e :  2.4  S e l e c t i o n Rules  2.5  The  Molecule  25  2.6  V i b r a t i o n a l A n a l y t i c Techniques  30  2.7  Franck-Condon  Iodine  Optics  7  Vibrational Analysis  .  12  . .  17  Radiative Absorption.  21  Rotational for  Rotational  Analysis  Analytic  Techniques 2.8  30  Electronic Configurations  and  Band  Contour 3.  34  INSTRUMENTATION AND EXPERIMENTAL  DESIGN 3 9  3.1  Introduction  3.2  C a l i b r a t i o n and O p e r a t i n g  Character-  istics 3.3 4.  a g e  Signal  42 Processing  57  DATA ANALYSIS 4.1  Introduction  4.2  Power-Dependence Signal  65 of the  Photoionization 69  - i i i TABLE  OF  -  CONTENTS  (cont.)  Chapter  5.  Page 4.3  Vibrational Analysis  72  4.4  Rotational Analysis  85  4.5  Band C o n t o u r A n a l y s i s  93  4.6  Impurity  99  Lines  DISCUSSION 5.1  Results  and C o n c l u s i o n s  5.2  Future Research  101 106  Appendix A  CALIBRATION OF PHOTOMULTIPLIER FILTERS  . . .  108  Appendix B  DETAILS OF BRANCH CONTOUR  . . .  Ill  REFERENCES  CALCULATIONS  ,,,  LIST  iv -  OF  TABLES  Table I  Page V i b r a t i o n a l Energy  Levels  o f t h e Ground  Electron ic State of II  27  Power-Dependence o f t h e P h o t o i o n i z a t i o n S i g n a l  i  n  III  . .  F r i n g e S e p a r a t i o n o f t h e ( 0 - v ) and (v - 0 ) Bands o f I  77  0  IV  C a l i b r a t i o n of the Fabry-Perot Interferometer  i  n  V VI  E x p e r i m e n t a l E v a l u a t i o n o f co  i  (v-0)  Progression  i  e  F r i n g e S e p a r a t i o n o f t h e ( 1 - v ) and (v - 1 ) Bands o f ^  VIII  E n e r g y S e p a r a t i o n o f t h e ( 1 - v ) and (v - 1 ) Bands o f ^  (v X XI XII  80  81  i  II  i  79  i  VII  E x p e r i m e n t a l E v a l u a t i o n o f co i e  82  Using the  -1) Progression  Energies  83  o f the Observed  Resonances  in  . . . .  84  R e l a t i v e E q u i l i b r i u m Population of V i b r a t i o n a l S t a t e s i n t h e Ground E l e c t r o n i c S t a t e o f . . . Relative I n t e n s i t i e s of the Photoi©nization Bands o f I  87  2  XIII  78  Using the  II  IX  . .  E n e r g y S e p a r a t i o n o f t h e ( 0 - v ) and (v - 0 ) Bands o f I 2  71  T h e o r e t i c a l Franck-Condon Vibrational Resonant  Transitions  Factors  90  f o r Selected  Between t h e Ground and  E l e c t r o n i c States  of I„  91  LIST  OF  v -  TABLES  (cont.)  Table XIV  Page Comparison Ratios  of the I  With the R a t i o s  Franck-Condon XV  Experimental  2  Density  Factors  o f ND F i l t e r  Intensity  of the T h e o r e t i c a l 0  From 3 = 0 . 0 9 6 t o 0.104A #3.0  as a F u n c t i o n  . .  of  Wavelength XVI  Total  109  Density,  Materials  92  as  a F u n c t i o n of Wavelength,  Shielding  P h o t o m u l t i p i i e r EMI  of  6256S  . .  110  LIST  OF  FIGURES  vi  -  AND  ILLUSTRATIONS  Figure  Page  1.  The A p p a r a t u s  2.  Circuit  40  Diagram  o f SLO-SYN T r a n s l a t o r  DC Power  Supply  46  3.  SLO-SYN S y n c h r o n o u s  4.  EMI  5.  L i n e a r i t y of  6.  L i n e a r i t y of Chart  7.  Photoelectron Signal  Diagram  Voltage  P u l s e Shape a t T e r m i n a t i n g 58  of the Iodine  for a Typical  Band  Contour  Band a t 100°C  Dependence  10.  Typical  P h o t o e l e c t r o n Spectrum of  o f t h e Peak S i g n a l  20°C A c c o m p a n i e d by L a s e r  100°C A c c o m p a n i e d by L a s e r  Intensity.  Iodine  Iodine  14.  f o r the  (1-0)  Electronic  Transition  at  Higher  Fringes  . .  68  Power  Band  Factors Against  N o r m a l i z e d Band C o n t o u r  Vapor  67  on L a s e r  70  R a t i o of Normalized I n t e n s i t i e s Franck-Condon  15.  Intensity  64  at  Output  R e s o l u t i o n A c c o m p a n i e d by F a b r y - P e r o t  Illustrated  Vapor  .  66  the P h o t o e l e c t r o n Spectrum at  of S i g n a l  63  Output  T y p i c a l P h o t o e l e c t r o n Spectrum of  Dependence  53 56  Voltage  13.  . . .  Ktt  Dependence  P o r t i o n of  6256S  Recorder  9.  12.  52  P h o t o m u l t i p i i e r Tube EMI  100  Illustrated  11.  47  6256S P h o t o m u l t i p i i e r Tube C i r c u i t  Impedance 8.  Motor W i r i n g  to T h e o r e t i c a l  Final  Energy  o f t h e 0 * ->- 0 9 g  . . . .  94  +  96  FIGURES  AND  vi i  -  ILLUSTRATIONS  (cont.)  Figure 16.  17.  18.  Page Normalized  Band  Electronic  Transition  Normalized  Band  Electronic  Transition  Electronic  Potential  Approximate  Contour  Contour  Potential  of the 0  of the 0  Diagram  +  9 +  g  -> 1 9 + 2  g  Including  States  on I  98 the  o f t h e New S t a t e  on t h e Known V a l e n c e - S h e l l  97  Superimposed 0  104  -  vi i i  -  ACKNOWLEDGEMENT  With p l e a s u r e stimulating research was  thank  Professor  advice, assistance  project.  Professor  discussions. Herman B l e s s  Also  M.H.L.  contributions.  Dr.  F.W.  Dalby  and e n c o u r a g e m e n t  for  is  his  during  this  c l o s e l y a s s o c i a t e d w i t h the p r o j e c t  P r y c e , who made i n v a l u a b l e t h e o r e t i c a l C. T a i  is  t h a n k e d f o r many h e l p f u l  The t e c h n i c a l e x p e r t i s e o f John Lees  and  also appreciated.  The N a t i o n a l financial  I  support  Research  Council  o f Canada  provided  i n the form of r e s e a r c h g r a n t s  and  scholarships. I most  also  t h a n k my husband  Ashok f o r what may be t h e  important c o n t r i b u t i o n of a l l :  unfailing  good humor d u r i n g  his  moral  support  the c o m p l e t i o n of t h i s  and  thesis.  -ix-  To  my  Father  1.  INTRODUCTION  A number o f n o n l i n e a r since All  phenomena  the i n t r o d u c t i o n of the l a s e r  o f t h e e a r l i e s t work was  generation  of s e c o n d - o r d e r  conversion  was  ated n o n l i n e a r  that  component  dispersion  t h e o n l y means  practical stals  magnitudes  i n w h i c h , upon  indices  of  (Baldwin,  (1962). is  Young ilar  was  1969  1973).  techniques  becoming  1970.  not o n l y  generation  of  is  to  Most o f  of the n o n l i n e a r  and  interest 1973  were p u r s u e d  in which phase-matching  of gases.  cry-  possible  and H a r r i s ,  was  the work,  response  and sim-  achieved however,  through  at  w i t h an a t o m i c o r m o l e c u l a r s t a t e , made  w i t h the development of t u n a b l e ,  circa  to  discovered  output  became m a t e r i a l s o f  enhancement  one r e s o n a n c e  soon  The i n e r t g a s e s  e t a l . , 1973)  precise mixing  gener-  of the r e f r a c t i v e  (Miles  practical  was  the n o n l i n e a r  a few c a s e s  i n v o l v e d enhancement  lasers  It  In  through  et a l .  by i n t e r f e r e n c e due  r o t a t i o n , matching  in s o l i d s ,  the  parametric  i n t e n s i t y of the  limited  tool.  t o employ s t r o n g l y b i r e f r i n g e n t  and Z e r n i k e ,  later.  and  by F r a n k e n  t h e i n c i d e n t and g e n e r a t e d waves  to those  least  others,  of enhancing  i n which  harmonics  The  investigated  a spectroscopic  of the m a t e r i a l .  a t o m i c and m o l e c u l a r v a p o r s somewhat  as  been  in s o l i d s  optical  a c h i e v e d , among  ( 1 9 6 1 ) and G i o r d m a i n e  t h e normal  done  have  This a means  coherent  narrow-bandwidth  resonant-enhancement of  technique  parametric conversion  f a r - u l t r a v i o l e t r a d i a t i o n in  is  and gases  and v a p o r s , tion  about  little  but a l s o atoms  work  has  2 -  a means o f g a i n i n g  and m o l e c u l e s  heretofore  been c a r r i e d o u t  other experiments,  DC-induced  to date  the  low-lying  and Wi11iams The subject  were g e n e r a t e d  vapors, only  the l a s t  Cs2»  and K e l l y  et a l .  as  excita-  Rousseau  wherein  nonlinear  phenomena  or so.  et a l . (1972),  in  The m u l t i p h o t o n  field  et a l . LuVan  of o p t i c a l  the energy  of  (1974)  work  has  (1973),  is  He,  K,  ionized  frequency,  several  quanta  laser and  interest investiand been Collins  and M a i n f r a y Na,  i o n i z a t i o n process  When a m o l e c u l e  and  gases  Theoretical  the elements  the  tunable  r e c e i v e d renewed  (1972), C o l l i n s  upon  is  absorption  the i n f l u e n c e of  four years  (1972)  follows.  electromagnetic arise  multiphoton  ( 1 9 7 5 ) , and e x p e r i m e n t a l  Delone  N^ and W^.  described  by  i n t e r a c t i o n which  been c a r r i e d o u t by L a m b r o p o u l o s  (1974),  and LuVan  vapors  Resonance  two-photon  been s t u d i e d  i o n i z a t i o n has  done by Bakos e t a l . et a l .  and  in atomic  (1974).  following  has  is  under  As w i t h most  have  Pindzola  work  of molecules  during  et a l .  in  (1974).  multiphoton  gations  Iodine  E state  of the present  radiation.  Among  (1971),  particular nonlinear  ionization  field.  and Ward  by Hodgson e t a l . ( 1 9 7 4 ) and Leung  of  this  by F i n n  components  tion  in  Very  generation  third-order  in molecular  inaccessible.  harmonic  observed  fluorescence  informa-  second  t h e i n e r t g a s e s was optical  spectroscopic  Cs, is  in a  a situation turns  out  (1972),  strong may  t o be  - 3 equal In  to the energy  this  case  multiphoton  o f t h e bound  the i o n i z a t i o n w i l l resonant  state  tion  of  have  the c h a r a c t e r of a m u l t i p h o t o n  1972).  new and s i g n i f i c a n t  obtained  regarding  parameters a variety scopy.  if  reasons,  Transitions  processes the  states  using  excited state  energy.  advantage  of a l l o w i n g  population  of both p a r i t y - f o r b i d d e n  be a c c o m p l i s h e d  example, states was  electrical  only  spectroone-step  spectroscopy  number  above  the  of quanta  has  the  of  sources.  high-energy In  the  other  The s u b s e q u e n t  past,  states  excitation  i n w h i c h many  of  additional  and h i g h - e n e r g y  excited.  for  (for electronic re-emission  e x t r e m e l y c o m p l i c a t e d and t h e a s s i g n m e n t s  ambiguous.  In  contrast,  can s e l e c t i v e l y p o p u l a t e ference  spectroscopic  in  a t an e n e r g y  light  et a l . ,  resonant  absorption  by h i g h - e n e r g y  discharges)  were s i m u l t a n e o u s l y  generally  at best  visible  also  and  detailed investigation  using  can  inaccessible,  spectroscopy  states  ioniza-  i n f o r m a t i o n may be  in multiphoton  t o an even  Multiphoton  and  (Delone  parity-forbidden  lies  stages,  an i n t e r m e d i a t e  which are  electronic  could  transition  conventional  which are  ground s t a t e c o r r e s p o n d i n g incident  stage  spectroscopic  may be i n v e s t i g a t e d  resonant  the m o l e c u l e  the e l e c t r o n i c s t r u c t u r e  of m o l e c u l a r of  via  electrons.  i n two  The s e c o n d  When i o n i z a t i o n o c c u r s  state,  the  proceed  e x c i t a t i o n of  the e x c i t e d m o l e c u l e .  of  from o t h e r  multiphoton  such f o r b i d d e n  electronic states.  states  were  experiments without  Multiphoton  inter-  spectroscopy  - 4 also  has  Doppler  the advantage broadening  experiments  also  the advantage  i n a p p l i c a t i o n s such  (Bloembergen,  Molecular  has  Iodine  1965  is  as  and Cagnac  of  reducing  double-beam et a l . ,  1973).  the s u b j e c t of the p r e s e n t  photon  investigations.  higher  valence-shell states  multi-  The n a t u r e and i d e n t i f i c a t i o n o f and t h e R y d b e r g  states  the  of  r e m a i n c o n f u s e d and c o n t r o v e r s i a l , -and even some a s p e c t s the  lower v a l e n c e - s h e l l s t a t e s  Iodine  has  are in c o n t r o v e r s y .  Molecular  been e x t e n s i v e l y s t u d i e d b o t h i n a b s o r p t i o n  in emission,  and a g r e a t many p a p e r s  of  and  have been d e v o t e d  to  the c o r r e l a t i o n of e x p e r i m e n t a l e v i d e n c e w i t h p r e d i c t i o n s the p o t e n t i a l c u r v e s electronic  states.  statements  regarding  recent LeRoy  literature.  and o t h e r f e a t u r e s Nevertheless, this  (1971), conflict  (a)  on t h e  a number o f c o n t r a d i c t o r y  o f H a r a n a t h and Rao  Mathieson  Nobs and W i e l a n d  (1966),  and Rees  Mulliken (1970)  in c e r t a i n regions o f bands  of  into  systems,  the f i n a l  states  fluorescence (c)  (1958),  points:  t h e s p e c t r u m , and t h e a r r a n g e m e n t  (b)  (1956),  and V e n k a t e s w a r l u  t h e number o f band s y s t e m s  these  numerous  m o l e c u l e e x i s t even i n t h e more  The a n a l y s e s  (1970a and 1 9 7 0 b ) ,  of the  on  the b a s i c rotational  i n the u l t r a v i o l e t resonance  systems,  spectroscopic constants  (vibrational  and  frequencies, electronic potential-wel1  -  5 -  m i n i m a , and d i s s o c i a t i o n and l o w - e n e r g y (d)  and d i s s o c i a t i o n  products  states.  amply d e m o n s t r a t e s  trum i s  o f b o t h h i g h-  states,  electronic configurations of the upper  This  energies)  that  a good c a n d i d a t e  for  with i t s  very  investigation  by  complex  spec-  multiphoton  techniques. In  the present work,  the near  u l t r a v i o l e t with a pulsed,  narrow-bandwidth Iodine  changes  laser.  pure  cell.  It  is  Iodine  excited  t h a t the spectrum  t h e e x p e r i m e n t a l work was  v a p o r w h i c h was  distilled  i o n i z a t i o n of the  are  Iodine  i n t o an  such  in  tunable,  of f o r e i g n gases such  The e x p e r i m e n t a l c o n d i t i o n s  tripie-photon  molecule i s  continuously  known  i n the presence  and n i t r o g e n , and t h u s in  the Iodine  of  as  argon  performed evacuated  t h a t we e x p e c t  molecule via  the  reaction: I  2  + 3v •* I  accompanied  by a v e r y  sociation.  As  occursin  will  discussed  by two p h o t o n s . 27,397 c m  - 1  .  small  + 2  + e"  ,  percentage  of t r i p l e - p h o t o n  i n C h a p t e r 2 , any  correspond The r a n g e  resonances  t o an i n t e r m e d i a t e s t a t e of e x c i t i n g energy  Thus t h e a c c e s s i b l e  resonant  is  state  and whose  energy  lies  which excited  26,316  transitions  those which are p a r i t y - f o r b i d d e n from the ground  dis-  are  electronic  between 52,632 and 5 4 , 7 9 4 cm~^.  In what f o l l o w s , v i b r a t i o n a l and r o t a t i o n a l a n a l y s i s  is  - 6 carried out, tion I2  is  via  resonant This  information research  is  the e l e c t r o n i c  a t t e m p t e d , upon a new e l e c t r o n i c s t a t e  signal.  scopic  and t h e a s s i g n m e n t o f  of  enhancement  research the  expected  which, to have  the  nonlinear  contributes  to the  Iodine molecule,  contributes  tool  of  in  view of  its  significant  observed  in  photoelectron  spectroscopic  b u t more  to the development  configura-  important,  o f a new  sensitivity applications.  and  this  spectrosimplicity,  - 7 -  2. 2.1  Theory  THEORY AND ANALYTIC TECHNIQUES  of N o n l i n e a r  The d i e l e c t r i c r e l a t i o n TJ = e t |E|.  is  constant  in general  The n o n l i n e a r  quencies,  Optics  however,  terms  e in Maxwell's  a f u n c t i o n of the f i e l d  are very  and t h u s  constitutive  small  at o p t i c a l  t h e i r experimental  a f t e r the development of p o w e r f u l  pure e l e c t r i c  dipole  zation as  transitions  lasers.  i n t e r a c t i o n s , which form the i n m o l e c u l e s , we may expand  P i n a power s e r i e s  fre-  discovery  occurred only  optical  strength  For  strongest  the p o l a r i -  i n the a p p l i e d e l e c t r i c  field  E  follows: ?  F o r any  VoX  E(I  +  X  (X)* (X)  +  ... ).  3  +  t  atom o r m o l e c u l e , t h e p a r a m e t e r s  on t h e o r d e r o f t h e m a g n i t u d e  a-j , a , 2  of the e l e c t r i c  (2  a ,  etc.  3  field  .V)  E  m  are  inside  Q  the atom o r m o l e c u l e , t y p i c a l l y a b o u t (Bloembergen,  P -  0  1965).  x l  ( ,  the r a t i o  powerful  lasers  response  is  very  +  X  +  l^l/E  ( X ) v  available  t  m'  < 3 x 10"  ( X )  2  x  3  m  3 +  i n the focus  (Bloembergen,  . . . ) .  /  1965),  o f t h e most the  nonlinear  small.  Each o r d e r o f n o n l i n e a r i t y r e q u i r e s for  volts/cm  Thus we may w r i t e  m Since  3 x 10  t h e s u s c e p t i b i l i t y x>  its  own  expression  and t h u s x must t a k e t h e f o r m  of  - 8 a t e n s o r when d e s c r i b i n g expression the  n o t a t i o n of the  where t h e f r e q u e n c i e s  one  t o .= 0  light  phenomena.  The  general  f o r a s u s c e p t i b i l i t y c o e f f i c i e n t of N  standard  satisfy  nonlinear  to i  + <JJ  *'"+  +  is  used,  Thus, the e x p r e s s i o n s polarizations  all  for  Since  u>^.  U> I ,<D  in t h i s  w.. a r e e q u a l  >  2  in • • • > <J  fields  research  only  and hence t o = N w . 0  the s u s c e p t i b i l i t y c o e f f i c i e n t s  l i n e a r , second  applied electric  X ( - D ° ;  u . of the a p p l i e d e l e c t r i c  2  source  l i t e r a t u r e is  order  order,  f i e l d £(to)  and t h i r d o r d e r  in  for  the  may be w r i t t e n ( G u c c i o n e - G u s h  e t a l . , 1967 , L a m b r o p o u l o s ,  1974 , Leung  et a l . ,  1974):  LINEAR  .  , -<^[«K>  X(-w; wj <* TT) ng SECOND ORDER  77Y  C Q  -"  ,  -  x( 2 ;  w j  ,  <ji«i*x;i»iO  -I  < » t g - -) o>ng - 2 . r  THIRD ORDER  x(-3-i «. is  the e l e c t r i c  The s t a t e l * £ ^ '  .)  (=  - .)«!.„  £ g  dipo1e-moment  operator  |ij; ^>is the ground s t a t e  '^m^"'  0  '^n^  a  r  e  e  i  9  e  n  s  t  a  t  e  s  - 2«)(a  n 9  of s e c t i o n  of the s y s t e m , o  f  being  the f i n a l  state  When a b s o r p t i o n  leads  to i o n i z a t i o n , t h e m a t r i c  3.)  2.4  and  succeedingly  energies,  -  in absorption  higher precesses  element  <i|j 1 ft 1IT ip° 0  n  g  included  > between t h e f i n a l  -  and i n i t i a l  i n the s u s c e p t i b i l i t i e s .  example defined  9  has  energy  An u p p e r  and  hcco^  states  lifetime  need n o t  state, r £  ~^»  be  for  and ft  by:  The f o r m o f t h e s u s c e p t i b i l i t y c o e f f i c i e n t s i n d i c a t e s  that  the n o n l i n e a r  a  resonance  p o l a r i z a b i l i t y may be e n h a n c e d  i n one o f t h e f a c t o r s  susceptibility  occurs.  the a p p l i e d f i e l d of a resonance third-order ject at  of t h i s  least  These  i n the denominator  Such a r e s o n a n c e  f r e q u e n c y co i s  f a c t o r in  the  relationships  f o r example, which for  resonance  R  e  (  %  "  w )  °»  R  e  (  %  "  2 w )  =  R  e  (  %  "  3 w )  =  =  °  °'  o  °'  are e q u i v a l e n t  to:  co0 Jo  -  co  g  =  co  ,  or  co  -  co  g  =  2co,  or  -  co  =  3co  co  n  g  .  r  r  the  whenever  vanishes.  following:  m  of  such t h a t t h e r e a l  r e s e a r c h , we r e q u i r e  one o f  occurs  the denominator  nonlinearities,  whenever  is  part For  the  sub-  enhancement  -  10  n m I ground  EIGENSTATES OF THE As w e l l ,  t h e a p p r o p r i a t e m a t r i x e l e m e n t s must  section  order  t h a t the i n c i d e n t  scattering  from resonance the s t a t e  l ^  0  On t h e o t h e r  or  with regards ^ is  both of  may be r e s o n a n t ,  final  state  tion  process,  be g a i n e d  is  1^°^  if  to the f i r s t  a virtual  hand,  or  s t a t e and  real  we must  second  necessary  the energy  the energy the  resonant  state,  of  states  d i f f e r e n c e between  i n the  the  photoioniza-  state.  photon  since  information  |ii)°>  would  T h u s , we as  the  m  enhancement  |^^>  and  However,  excited state  the fundamental  away  0.  resonant  resonant  tune  lost  |(co„ - co ) - co I >>  spectroscopic  were t h e o n l y  on t h e d i s c r e t e  state  n o t be  Thus  states.  a continuum  energy  1 r  twice  (see  excited state.  the uppermost  no s i g n i f i c a n t this  light  linear absorption,  |ijj°>  focus  not vanish  2.4). In  through  SYSTEM  occurring  becomes  when  equal  to  and t h e g r o u n d s t a t e  of  molecule: 0J  Two-photon  resonance  investigation  m  has  - co  g  = 2co  .  the advantage  of e l e c t r o n i c s t a t e s  of a l l o w i n g  which are  detailed  symmetry-  forbidden section photon  in l i n e a r  2.4.  (one-photon)  The o r d e r  resonant,  11  of  -  spectroscopy,  the s t a t e s  tripie-photon  is  as  then,  ionization  of  shown  for  in  two-  the  Iodine  ± 10  cm )  molecule:  The  use  n  continuum  m  resonant  £  virtual  g  XOg  of a tunable  dye  electric  field  function  of wavelength  dye,  provides  and hence  as  photoionization the  intensity  equation  Thus  - 1  ground  laser  as  the source  an a b s o r p t i o n over  of  the  of  spectrum  the u s e f u l  a function  When N p h o t o n s a r e  order  75,814  the as  range of  a  the  i d e n t i t y of the  applied continuous laser resonant  \ty^> •  states  of  (>  2.1  depends if  C is  signal I  of  i n which  involved  intensity the  in  S depends  incident  light.  the n o n l i n e a r  upon t h e N  t h  power  a proportionality S = C  I  o  N  the  transition, upon t h e This  the e l e c t r i c  constant  we may  power  t h  follows  pol a r i z a b i 1 i ty  of  N  the  in  field  from  N^*  1  vector.  write:  .  3 The  signal  of our in  is  expected  photoionization  the f o l l o w i n g  to vary signal  manner.  as  I  q  .  The  may be measured  When a number  power-dependence experimentally  n of c a l i b r a t e d  neutral  - 12 density  filters,  attenuate  each o f t h e same d e n s i t y  the l a s e r  beam b e f o r e i t e n t e r s  then the p h o t o i o n i z a t i o n s i g n a l S = C i or,  i n a more c o n v e n i e n t  N o  S is i  0  "  K  (  A  )  n  Coarse  K(X) i s  I )  -  N  Q  -  known.  K(\)nN  first-order perfectly  Vibrational  The an h a r m o n i c  approximation  o s c i l l a t o r model  t o any p h y s i c a l  increasing  actual  binding  to z e r o , r a t h e r than distance  provides  oscillator,  if  only a since  linearly proportional in nature.  t h e a t t r a c t i v e f o r c e between any  tends  versus  Analysis  t h e a m p l i t u d e o f v i b r a t i o n , do n o t e x i s t  molecule  intensity  oscillator  e l a s t i c f o r c e s , which are  particular,  of a  We h a v e :  The s i m p l e h a r m o n i c  with  K(A)nN  i n t h e p a t h o f t h e i n c i d e n t beam,  Structure:  2.2.1  follows:  ,  N  of the l o g of the p h o t o i o n i z a t i o n s i g n a l  the d e n s i t y  chamber,  N may be d e t e r m i n e d f r o m t h e s l o p e  t h e number o f f i l t e r s  2.2  Iodine  a t t e n u a t e d as  = constants The power dependence  the  are used to  form:  log S = log(C  plot  K(>),  In  two atoms  increasing  to  of a  indefinitely,  from the e q u i l i b r i u m p o s i t i o n .  f o r c e must be r e p r e s e n t e d by power s e r i e s  The in  powers  of the d i s p l a c e m e n t  requires force  13  -  f r o m e q u i l i b r i u m , and  b o t h even and odd t e r m s .  The o n e - d i m e n s i o n a l  of a d i a t o m i c m o l e c u l e , i n the absence  applied f i e l d s , is  where r i s  Term + A n h a r m o n i c  - r )  + k (r  e  and k^,  2  - r )  2  g  k ,  - k (r  p o t e n t i a l energy  nature,  i n w h i c h t h e n u c l e i i move  1  - r )  2  e  For small  anharmonicity  the e i g e n  energies  r  f u n c t i o n , which  v  - k /3(r 2  - r )  3  g  where h i s  + H)  e  Planck's  is  is  - hca) x (v e  constant,  e  c is  •••  the e q u i l i b r i u m The  corres-  electronic  + k /4(r  + k)  - r )  3  o f t h e o s c i l l a t o r (Ik^l  of the Schroedinger  = hcw (v  g  +  3  g  in  is: +  4  g  <<  |k |  •••  <<  2  | k-| | )  e q u a t i o n may be d e t e r -  mined w i t h a ' p e r t u r b a t i o n c a l c u l a t i o n t o E  - r )  3  k^ a r e f o r c e c o n s t a n t s .  2  ponding  U = k /2(r  externally  Terms  the i n t e r n u c l e a r s e p a r a t i o n ,  separation,  of  binding  thus:  F = Harmonic = -k^r  asymmetry  2  be: + hcw y (v e  e  the v e l o c i t y of  + k)  3  +  •••  light, v  is  t h e v i b r a t i o n a l quantum number , and co , co x , co y , . . . ^ e e e e e are c o n s t a n t s c h a r a c t e r i z i n g the m o l e c u l e , p r o p o r t i o n a l to force  constants.  measure  of the anharmoni c i t y of  the harmonic (co  g  The q u a n t i t i e s co x , co y , . . . e e e e  approximation  = / k ^ / u , where y  is  are a  t h e m o l e c u l e , w h i l e co  to the o s c i l l a t o r  the reduced mass).  g  is  frequency A more  useful  the  expression  in spectroscopy  i n wavenumber G(v)  units  = u (v  given + H)  e  is  14  the  "vibrational  term"  G(v)  by  - ^ x (v e  + %)  e  2  + ^ y (v e  e  + %)  3  +  ••• (2.3)  for  the anharmonic  motion  is  frequency with  still is  amplitude-dependent, amplitude.  potential  curve,  the o s c i l l a t o r i s for  almost  FIRST  the  vibrational  the time average  a l l molecules, of  i n wavenumber  or  the f r e q u e n c y  Furthermore,  no l o n g e r  The s e p a r a t i o n described  Although  s t r i c t l y p e r i o d i c , the n a t u r a l  increasing  of the  oscillator.  resonant  decreasing  due t o t h e of  asymmetry  the p o s i t i o n  the e q u i l i b r i u m p o s i t i o n ,  is  greater  successive units  (<r>  > r  but,  ).  vibrational  by t h e  of  levels  is  following  DIFFERENCE AG  = G(v+1)  V j V + 1  = a)  -  G(v)  - u x ( 2 v + 2) e  + w y ( 3 v + 6v+13/4) +  •••  2  e  e  e  (2.4) SECOND DIFFERENCE A 2 G  v,  V +  2  E  A G  V,V 1  = 2 oj x e  where  v is  vibrational  "  +  e  A G  v l,v 2 +  +  - w y ( 6 v + 9). + • . . e  by d e f i n i t i o n t h e quantum state  may be p o s i t i v e  involved  (2.5)  e  number  of the  i n the comparison.  or n e g a t i v e ,  co x e  e  is  positive  lowest  While  " y e  for nearly  e  all  diatomic molecules levels  draw t o g e t h e r  number,  this  work,  a d o p t e d whereby involved  transitions  v  1  section  into  2.4  Thus t h e  represents  involves  vibrational  spectroscopic  the upper,  vice  upper  versa)  for a discussion  quantum  notation  and v"  transition.  a single  (or  vibrational  a continuum.  the standard  adjacent lower states See  1950).  in a v i b r a t i o n a l  which  -  with increasing  and e v e n t u a l l y merge In  state  (Herzberg,  15  is  the  lower  A series  state  and  termed a  of v i b r a t i o n a l  is  of several  progression.  selection  rules. 2.2.2  Thermal  According applied  d i s t r i b u t i o n of the v i b r a t i o n a l  to the Maxwel1-Boltzmann  t o quantum m e c h a n i c s  equilibrium,  under  distribution  conditions  t h e number o f m o l e c u l e s  N  y  states  of  law  thermal  i n each o f  the  vibra- E/ kT  tional where ture  states k is  is  the Boltzmann  in degrees  (Herzberg, measured  proportional  constant,  K e l v i n , and E i s  1950).  If  E is  from the f i r s t  referred  in  t o t h e number  the a b s o l u t e  the energy  of  ,  tempera-  vibration  the v i b r a t i o n a l  energy  -  G(0)  G (v) 0  factor  numbers o f m o l e c u l e s  factor e  state,  the Boltzmann  T is  d e f i n e d as  E = G(v)  then  to the Boltzmann  ~Go ( ) A T v  e  gives  the  relative  the d i f f e r e n t v i b r a t i o n a l of molecules  in the lowest  levels vibrational  level.  When G ( v )  substitution N  If  we w i s h  v  all  is  expressed  of the c o n s t a n t  _  v  in  t h e gas  required  1  /  0  the  units,  then  result  ^  r e l a t i v e to the t o t a l  sample,  i n which  i n wavenumber  c m *  Q  y  -  k gives  -G (v)/(0.6952  to determine N  molecules Q  is  Q  16  the s o - c a l l e d  the Boltzmann  number  partition  factors  are  N of  function  summed  over  states: Q  v  = 2 e v  -G ( v ) / ( 0 . 6 9 5 2  cm /°K)T _ 1  0  Then t h e f r a c t i o n a l number  of molecules  in v i b r a t i o n a l  state  vis N  N  v _ e  -G  Q ^v  In most system  diatomic gases, only  normally  the v i b r a t i o n a l tively  heavy,  cm'VlOT  (v)/(0.6952  appears, quanta  leading  vibrational  states  temperature  (see  of  Table  a d d i t i o n to the v"  one p r o g r e s s i o n  t h a t with v"  are  small  because  t o an a p p r e c i a b l e  XI).  = 0 to v  Thus, 1  it  = 0,  1, = 1,  the p r o g r e s s i o n s  v"  higher)  = 0,  appear  1  For  Iodine,  the m o l e c u l e population  the ground e l e c t r o n i c s t a t e  progression, to v  = 0.  n will  is  of at  n  however, rela-  the  upper  room in  absorption  3, 4 (and  i n our  band  is  predicted that  2 2,  of a  data.  possibly  2.3  Fine  Structure:  The  simple  approximation cule.  In  17  -  Rotational  rigid  Analysis  r o t a t o r model  to the  rotational  motion  model  we c o n s i d e r  the  this  a t t h e ends o f a w e i g h t l e s s ,  and y i e l d s  Schroedinger  rigid  the e i g e n e n e r g i e s  of  first-order  of a diatomic of  is  The  r  apart  solution  comparatively  rotation,  mole-  reduced  at a d i s t a n c e  rod.  equation  a  two atoms  mass y t o be p o i n t - l i k e and f a s t e n e d  appropriate  provides  in  of  the  simple  wavenumber  units: F( J )  = BJ ( J +•  1)  ,  .  —^—j  B E  4iTCyr  J is  the  rotational  separation. reciprocal accurate that  The  rotational  moment o f  a vibration t h e moment  i n e r t i a of  and v i b r a t i o n  period, of  the  tional  take  2  period.  B  y  essentially  the n u c l e i i . into  internuclear  consideration  place  i n e r t i a and r o t a t i o n a l  constant  B are  very  the  simultaneously. and  is  the  F o r a more  distance  small  During  consequently changing.  compared  a mean B v a l u e  fact  to  i n the  the  vibra-  considered: B  O/r  B is  the  internuclear  r o t a t i o n , we must use  state  and r i s  constant  the p e r i o d of v i b r a t i o n  p e r i o d of  where  number,  t r e a t m e n t , we must t a k e  rotation  Since  quantum  ^ is is  v  =  - i -  4ircy  the time average somewhat  smaller  V  2  of than  1/r  2  during  the  the c o n s t a n t  B  vibration g  evaluated  a t the e q u i l i b r i u m s e p a r a t i o n tion,  because  tion will tory)  given  B  e  = B  v  brings  e  - a (v  r .  t h e mean n u c l e a r  To a f i r s t  e  (usually B  ,  a  <<  e  o f t h e d a t o m i c m o l e c u l e as  satisfac-  B  Therefore  a nonrigid  rotator  c o r r e c t i o n term f o r c e n t r i f u g a l  solution  with increasing  the r o t a t i o n a l c o n s t a n t  number J , d e c r e a s i n g  J.  r o t a t o r model  is  The r o t a t i o n a l  moment  of r o t a t i o n .  Although requires  quantum  an  exact  t h a t the  i n powers  obtained using only  force,  the  a f u n c t i o n of  i n an i n f i n i t e power s e r i e s  good a c c u r a c y terms.  energy  B is  with increasing  of the n o n r i g i d  be e x p r e s s e d  vibra-  .  g  t h e i n t e r n u c l e a r d i s t a n c e , and c o n s e q u e n t l y increases  separa-  i n the  y  vibra-  by:  + %)  in a small  inertia,  ratic  than  state v is  whereby  very  , since with increasing  of the a n h a r m o n i c i t y ,  be g r e a t e r  Consideration  of  r  -  a p p r o x i m a t i o n , the r o t a t i o n a l c o n s t a n t  tional  also  18  energy  of J ( J +  t h e l i n e a r and  term f o r the n o n r i g i d  1),  quad-  rotator  becomes: F (J) y  = B J(J v  4B D  where oo i s In t r e a t e d as  v  the v i b r a t i o n a l the models  revolving  - D J (J + l ) , 2  2  V  3  2  (2.6)  frequency.  of the s i m p l e  p o i n t masses.  the e l e c t r o n s  u  + 1)  Typically D  rotators,  y  <  t h e atoms  1 0 ~ were  A c t u a l l y , t h e mass d i s t r i b u t i o n about  t h e two n u c l e i i must be  y  of  taken  .  into  account.  The moment o f  19  -  i n e r t i a of these e l e c t r o n s  much s m a l l e r t h a n t h e moment o f t h e two n u c l e i i a b o u t c e n t e r of mass, owing In  s p i t e of t h i s ,  t o t h e much s m a l l e r mass o f  the c o r r e s p o n d i n g  t h e same o r d e r o f m a g n i t u d e more r a p i d l y .  The model  since  angular  of a symmetric  (two o f t h e t h r e e p r i n c i p a l moments  equal).  For a g i v e n  external  torques,  magnitude ft a b o u t  electronic state,  the t o t a l  axis  is  constant  In  angle  J" w i t h t h e f r e q u e n c y o f  about  f a c t , the f i g u r e  The e n e r g y  levels  F (J)  = B J(J  y  v  + 1)  rotates  is  t h e moment o f  constant  Thus t h e r o t a t i o n a l as  those  nitude  (Herzberg,  2  y  1950)  the  are:  + (A - B ) f t  2  of  y  2  ,  ft A = . 4  T ire  i n e r t i a of  and has  axis. only  (2.7)  I„  the e l e c t r o n s  For a g i v e n a small  about  an  electronic  (integral)  value.  l e v e l s o f t h e s y m m e t r i c t o p a r e t h e same  of the s i m p l e  (A - B ) f t  in  nonrigid  V  p a r a l l e l to the f i g u r e  s t a t e , ft i s  but not  from s o l u t i o n  in  momentum  the v i b r a t i n g  - D J (J + l )  with  axis  constant  constant  J *  n  of  at a  that result  wave e q u a t i o n o f t h e s y m m e t r i c t o p  I  diatomic  i n the absence  i n magnitude  axis  of  i n e r t i a are  momentum 3 i s  angular  direction.  where  of  the  and d i r e c t i o n , w h i l e t h e e l e c t r o n i c a n g u l a r  the f i g u r e  rotator.  the e l e c t r o n .  r o t a t e much  top f i t s  molecule  the  momenta a r e  the e l e c t r o n s  is  r o t a t o r except for a s h i f t  in  mag-  c h a r a c t e r i s t i c of the e l e c t r o n i c s t a t e ,  and  except that l e v e l s Since tional rise  r  is  less  broad wavelength  f o r the t o t a l Q  variable.  = v  is  y  for  a b s o r p t i o n , where v  ing  the s m a l l  for  the ground  = v In  lines ing  the ground  constant  f o r a given  Q  + F ,(J') v  Q  is  -  In  the + v  band  v  •>  while  F „(J") V  c a l l e d t h e band o r i g i n .  - B ')fi' v  2  and n o t i n g  v  \ ^ we t h e n  + B 'J'(J +l) ,  v  + B 'J'(J'+1)  processes, 2.4)  Neglect-  t h a t ti" = 0 have:  - B " J " ( . J " + 1)  - B "J"(J"+1)  V  (section  formulae  1  + f(n')  two-photon  head).  which  Q  e l e c t r o n i c s t a t e of + (A  0  (band  (bands)  of a t r a n s i t i o n , v = v  c o r r e c t i o n term i n D  Q  regions  gives  We may w r i t e v = v  v = v  edge  energy  + v  g  vibra-  r o t a t i o n - v i b r a t i o n spectrum  have a t one end a s h a r p  the q u a n t i t y v v  absent.  r o t a t i o n a l q u a n t a a r e much s m a l l e r t h a n  t o more o r  expression  -  w i t h J < Q, a r e  q u a n t a , a combined  usually  20  .  V  we may e x p e c t up t o f i v e b r a n c h e s  whose  (J represents  wavenumbers  are given  of  by t h e f o l l o w -  t h e r o t a t i o n a l quantum number  of  state) :  AJ = + 2 S(.J)  = v  + f(fi') + 6B '  + (5B '-B ")J  + (B '-B ")J  2  (2.  + f(fi') + 2B '  + (3B '-B ")J  + (B '-B ")J  2  (2.  y  Q  v  v  v  v  AJ = + 1 R(J)  = V  q  V  V  V  v  v  -  21  -  AJ = 0 Q(J)  = v  AJ = P(J)  f(fi') + (B ' - B ")J + (B '  +  Q  v  v  y  - B ")J  2  (2.10)  - B ")J  2  (2.11)  y  -1  = V  q  + f(ft')  -  (B « + B ")J  + f(n')  + 2B '  y  v  + (B/  v  AJ = -2 0(J)  = v  Q  A band head i s quadratic Case  I.  terms If  equations  B ' v  2.8  .  forms  In  signs.  < B "  y  Case  (but 3 B '  v  t o 2.12  v  II.  to l o w e r - e n e r g y , When B  branches,  1  > B ",  t h e heads  v  .  i.e. heads  All  if  it exists,  branches  2  v  and  seen  of  from  the side  sometimes t h e band a r e  to the r e d . a r e f o r m e d i n t h e P and 0  f o r m a h e a d , as  i n case  o f t h e band a r e d e g r a d e d now t o w a r d h i g h e r  2.4  B ")J (2.12)  f o r m e d i n each o f  now l y i n g t o t h e l o w - e n e r g y  The Q b r a n c h may a l s o  the  easily  l y i n g to the high-energy  a d d i t i o n , the Q b r a n c h , to v  -  y  the l i n e a r  > B ") i t is  t h a t a head i s  b o t h heads  + (B '  v  V  formed i n a branch i f  a head v e r y c l o s e  degraded  (3B ' + B " ) J  i n J have o p p o s i t e  R and S b r a n c h e s , of v  -  v  s i d e of  I.  energy,  All  v . Q  branches  i.e.  to  violet. S e l e c t i o n Rules If  for Radiative  a system e x i s t s  Absorption  i n an u n p e r t u r b e d s t a t e  s e n t e d by one member o f a c o m p l e t e o r t h o n o r m a l  set  repreii> °(r,t)} n  - 22 of  stationary-state  wavefunctions,  then i n t e r a c t i o n of  s y s t e m w i t h an e l e c t r o m a g n e t i c wave 1 c r e a t e s and c o n s e q u e n t l y may a l w a y s  a change-of-state  be e x p r e s s e d Y(r,t)  as  = Z C (t)  any  new e i g e n s t a t e ,  external tion  of  matrix and  radiation field  is  given  the c o e f f i c i e n t s C „ ( t ) elements  initial  associated first  under  m  O  states  ° I E '^n°^ of  w  the system,  w i t h the p e r t u r b a t i o n  approximation,  eigenstates:  make a t r a n s i t i o n  the i n f l u e n c e of by C  m  involves  H  m  the  n  system w i l l  say ^ ° ,  of  n  e  r  (t)C (t).  a c a l c u l a t i o n of » is  E (Penner,  the m a t r i x elements  Determina-  m  e  and  i n t e r a c t i o n o f t h e wave w i t h t h e  to  the  of  a  the  r  e  t  '  the  ^ " ''  i e  1  n a  Hamiltonian  1959). the  In  a  interaction  o f an e l e c t r o m a g n e t i c wave w i t h a d i a t o m i c m o l e c u l e to the  which  ^ °(r,t)  n  The p r o b a b i l i t y t h a t t h e  a perturbation,  to the s t a t e ¥ ( r , t )  a "mixture"  this  (variable)  reduce electric  d i p o l e moment M o f t h e m o l e c u l e whose components a r e N E u b (M » M s i m i l a r ) where t h e e. a r e t h e c h a r g e s |< = 1 K K y z K on t h e N p a r t i c l e s o f c o o r d i n a t e s x ^ , y ^, z ^. Then f o r  M  =  e  x  x  small  perturbations,  time,  P  n+m  , is  the t r a n s i t i o n  constant  and i s  t The  radiation density  3fi  is  p v  mn  given  3  p r o b a b i l i t y per  unit  by: J  2 V"m " l^n '  %  n  s t r i c t l y a property  of  the  applied  field,  characterizes  while the  the  is  no s p a t i a l  region  tion  of  is  valid  the dipole-moment  results  rest  variation  charge  is  in  element  the e l e c t r i c in which  appreciable  wavefunction  i n any  matrix  upon t h e a s s u m p t i o n  the d i a t o m i c m o l e c u l e  of e l e c t r i c  electronic  -  molecule.  The p r e v i o u s there  23  is  large).  but e x c e p t i o n a l  spectroscopy  we a r e c o n c e r n e d  and  radiation  (that  cases  with  field  t  over  the  distribu-  is,  where  This since  that  the  approximation in  molecular  ultraviolet,  visible  o  infrared  (A > 1000A)  so t h e w a v e l e n g t h s  are  o  large  compared w i t h m o l e c u l a r  variation molecule for  of the e l e c t r i c is  not  dipole,  However,  the m a t r i x  of  moment,  able only  electric  hence  when  in  the  of  by e q u a t i o n  2.13  leads  to c e r t a i n s e l e c t i o n  transitions  between  for  of  the  of  the  moments. a r e many  the are  dipole observ-  forbidden.  transition  rules  this  is  the  expression  moments  transitions  transition the  If  higher  the h i g h e r  be n o n z e r o  element  and  the m a t r i x element of  that  given  vanishes  appear  the c o r r e s p o n d i n g  The r e q u i r e m e n t  many w o u l d - b e  2A).  the dimensions  quadrupole,  than  the d i p o l e  the d i p o l e m a t r i x  there  elements  ten s m a l l e r  and  over  (-  p r o b a b i l i t y , m a t r i x elements  magnetic  powers  field  neglected,  the t r a n s i t i o n  dimensions  probability  the combining  P  states  based on t h e e v a l u a t i o n the given  dipole matrix  i d e n t i c a l l y , and t h e t r a n s i t i o n  is  m  states.  of  For  element termed  forbidden.  For example, a homonuclear no p e r m a n e n t e l e c t r i c tions  nor  does n o t tional  rotations  d i a t o m i c m o l e c u l e such as  d i p o l e moment and n e i t h e r  induce a d i p o l e  r o t a t i o n a l spectrum.  (M 5 0 ) .  However,  its  has vibra-  Therefore a pure  it  vibra-  such m o l e c u l e s  do  e l e c t r o n i c s p e c t r a w i t h v i b r a t i o n a l and r o t a t i o n a l  structure  (bands),  changes d u r i n g accompanies conforms of  -  i n t e r a c t w i t h r a d i a t i o n to produce  or  exhibit  24  the  to Hund's  The component axis,  cule  ^5  ized  under  the i n s t a n t a n e o u s  coupling  atoms  of t o t a l ft,-is  dipole  r e d i s t r i b u t i o n of e l e c t r i c  the e l e c t r o n i c t r a n s i t i o n  the s e p a r a t e  nuclear  because  case  persists angular  charge  i n w h i c h t h e L-S  momentum a l o n g  which  1964).  when t h e m o l e c u l e i s  well-defined.  the t r a n s i t i o n s  c,  (King,  moment  the  coupling formed.  inter-  For the d i a t o m i c mole-  w h i c h a r e a l l o w e d may be  the f o l l o w i n g s e l e c t i o n r u l e s  f o r the  categorquantum  numbers: 1.  VIBRATIONAL-ELECTRONIC TRANSITION Av = 0 , ± 1 , ± 2 ,  ...  f o r the anharmonic  oscil-  lator. 2.  ROTATIONAL-ELECTRONIC TRANSITION In  t h e s y m m e t r i c - t o p m o d e l , AJ = ±1 i f ft = 0  i n both  u p p e r and l o w e r s t a t e s ,  (excluding  J = 0  t h e two s t a t e s 3.  J = 0)  has ft f  ELECTRONIC TRANSITION Aft = 0, ±1 .  0.  and AJ = 0 ,  i f a t l e a s t one  ±1 of  - 25 The  parity  must The  change: parity  reflection 0  +\*  +  may  state  (non-resonant)  I  2  ground  in  The  has  state must  must be  state.  upon change:  selection from  rules  the  ±1, ±2.  have  and  branches.  from  go  previous r e s u l t s . ground  0*,  the  "g" and  1^,  ±1, ±2, g i v i n g  first  "u" w h i l e the  absorption  or 2g. rise  second  therefore  the c o n f i g u r a t i o n  to 0*,  in  f o r two-photon  S i n c e the  symmetry  o f symmetry  therefore  investiga-  are symmetry-forbidden  the c o n f i g u r a t i o n  Starting  f o r J a r e A J = 0,  The  which  i s 0,  rules  2.5  parity).  wavefunctions  v i a c o n v e n t i o n a l one-photon  m o l e c u l e may  0  u (odd  p r o c e s s e s a l l o w the  be deduced  of  (resonant) state inaccessible  inversion  i n a p l a n e o f symmetry must not  states  easily  a l l o w e d change  electronic  the  of non-degenerate  spectroscopy.  resonance The  g (even p a r i t y )  resonance  of e l e c t r o n i c  one-photon  under  0".  Two-photon tion  o f the w a v e f u n c t i o n  from 0* , the  The  to S,  is  selection  R,  Q,  P  Iodine Molecule 127  Diatomic has  Iodine, I  the e l e c t r o n i c  vibrational 1950):  and  2  with  reduced  mass 63.466  ground-state configuration  rotational  c o n s t a n t s as  Og  follows  amu,  with (Herzberg,  =  "  CO  e  26  214.57  cm  0.6127  "eX "  cm  e  ».V  =  -0.000895  cm  Ve"  =  -0.0000187  cm  B  e"  "." D  0.03735  cm  0.000117  cm  4.5  e"  10"  cm  9  o  2.666 Note  that  D " e  is  According quantized  units  c a l c u l a t e d using to  the  vibrational  electronic  state  A  of  energy  diatomic  = 214.57(v"  -0.000895 later  second the  use,  the  (equation  2.3)  Iodine  given  six  are  + \) 2' (v"  energy  differences,  first  effects  o s c i l l a t o r model,  is  of  the  in  the  ground  wavenumber  by:  G(v")  For  anharmonic  expected  in  0.6127(v' " v  + J-)  levels  AG(v")  vibrational  -  and  the  \ )  G(v")  plus  G(v"), of  I^  spectrum  of  (v"  the  are  in  2  2  + 0.0000187  3  A  levels  +  +  \)  first  tabulated  Table  Iodine,  I.  No  since  and for isotope the  127 isotope  I  1974).  The  2  has  abundance  quantized  better  rotational  than  energy  99.9%  (Robinson,  (equation  2.7)  of  V  e  (cm 0  a) x (v+h) e e  w (v+k) - 1  )  e  e  (cm )  (cm )  -0.1532  -0.0001  - 1  107.29  w y ( v+J§)  3  ow (v+3s) e  (cm )  - 1  - 1  -  4  AG(v)  6(»)  (cm  - 1  )  (cm ) - 1  107.14 213.34  1  321.86  -1.379  -0.0030  0.0001  320.48 212.11  2  536.43  -3.829  -0.0140  0.0007  532.59 210.87  3  751.00  -7.506  -0.0384  0.0028  743.46 209.63  4  965.57  -12.41  -0.0816  0.0077  953.09 208.39  5  1180.14  -18.53  -0.1489  0.0171  1161.48 207.13  6  T394.71  -25.89  -0.2458  0.0334  1368.61 A =1.24  cm"  2  Table  I .  Vibrational  Energy L e v e l s  of the  Ground E l e c t r o n i c  S t a t e of  I. 2  1  the ground e l e c t r o n i c s t a t e F (.J") V  =  x lo"  1  (Myer  photon  i o n i z a t i o n of the I  2  2  t h e number  research I  the  is  + Nv -> I  of photons  Iodine  the  reaction:  , simultaneously  The f u n d a m e n t a l  provided  laser  requirement  to date.  13,514 c m "  The < v.<  1  27,  x  w i t h Nv > 7 5 , 8 1 4 ± 10 is  satisfied  lowest-order choose  N = 3.  for  the v a l u e s  nonlinearity  where  N = 3,  will  2  + 3v -*- I  the e x c i t i n g energy  + 2  4,  cm"  required  is  cm"  frequency range  commercial  1  Since  intense, is  the  we  then  , v > 25,271 ± 3 c m " o  which corresponds  to photons  by  1  5 and 6.  reaction  + e"  by  778  be t h e most  The p h o t o i o n i z a t i o n I  is  l i e w i t h i n the s p e c t r a l 1  1)  Venkateswarlu,  3600-7400 A (27,778 - 13,514 c m " ) dyes a v a i l a b l e  +  (2.13)  and  absorbed  process.  i n c i d e n t l i g h t must  J"(J"  by:  to o b t a i n m u l t i p l e -  + e"  + 2  units  .  2  molecule via  2  i n the p h o t o i o n i z a t i o n  v of  + 1)  2  and Samson, 1 9 7 0 ,  The aim o f t h i s  I  i n wavenumber (v"+ i)  J" (J"  9  1970).  N is  given  i o n i z a t i o n p o t e n t i a l of molecular  7 5 , 8 1 4 ± 10 c m "  where  is  -  0.03735 - 0.000117 - 4.5  The  28  o f w a v e l e n g t h ^ 3957 ± 1 A.  1  In  principle, non-linear  to  the n o n - l i n e a r  and d i s s o c i a t i o n tion  occurring  1970),  I will the  thresholds  are  The  will  occur  the in  •* I  +  +  the s p e c t r a l  small  Mathieson  Iodine  b e l o w 10%, (Myer  Samson, non-  however,  1956,  since  compared t o a  and Samson,  1970),  investigated.  2.1). Iodine  According (Haranath  M u l l i k e n , 1934  1 966 , and V e n k a t e s w a r l u ,  n o t be  1 970),  to  lost  of  from the ground  l^.  and Rao,  and 1 9 7 1 ,  state  appear,  between t h e  state  1958,  Nobs  t h e r e appear  No bands  of  previous  i n t h e v i s i b l e and n e a r - u l t r a v i o l e t  (sing1e-photon)  absorption  dissocia-  and  not c o i n c i d e w i t h a resonant  (section  and R e e s ,  spectra  of  and s c a t t e r i n g , t h e w a v e l e n g t h  of d i a t o m i c  band s y s t e m s  tion  range  linear absorption  investigations  in  percentage,  o r d e r t h a t the i n c i d e n t l i g h t energy  diatomic  ous  (Myer  - 1  ionization  I"  a very  i n c i d e n t l i g h t must  Wieland,  the  i n t h e same o r d e r o f  p h o t o i o n i z a t i o n y i e l d of 80-100%  through  contributes  s i m i l a r , the onset  photodissociation yield f a l l s  In  I^  reaction  c o n t r i b u t e only  throughout  of  Since  at a p p r o x i m a t e l y 71,300 c m  + 3v -> I*  2  photodissociation  photoelectron signal.  both processes  linearity.  29 -  and  numerabsorphowever,  wavelengths  o  3957 A, t h e  longest  wavelength  possible  for  triple-photon  o  ionization laser.  of  Thus,  I^,  and 3600 A, t h e l o w e r l i m i t  i f a laser  dye i s  chosen  of the  which l a s e s  dye  below  o  3957 A, we e x p e c t t o a c h i e v e  triple-photon ionization with  30  -  -  no c o m p l i c a t i o n s f r o m s i n g l e - p h o t o n r e s o n a n c e s . ant  enhancement o f t h e p h o t o i o n i z a t i o n s i g n a l  expect  two-photon resonance  symmetry 2.6  "g"  When r e s o n -  o c c u r s , we  t o an i n t e r m e d i a t e s t a t e  of  f o l l o w e d by p h o t o i o n i z a t i o n .  V i b r a t i o n a l A n a l y t i c Techniques In  ecular  t h e v i s i b l e and n e a r - u l t r a v i o l e t s p e c t r u m o f  Iodine,  t h e band heads a r e c l e a r l y  (Venkateswarlu,  1970,  will  Since  (section  2.8),  e n e r g i e s may be i g n o r e d i n t h e v i b r a t i o n a l  T h u s , once t h e v i b r a t i o n a l t r a n s i t i o n s have been a s i m p l e measurement o f a chosen  a maxi-  o c c u r i n each v i b r a t i o n a l  band a t a b o u t t h e same e n e r g y o r J v a l u e rotational  developed  and P e t t y e t a l . , 1 9 7 5 ) .  mum o f i n t e n s i t y (band head)  progression  mol-  analysis.  assigned,  t h e s e p a r a t i o n o f t h e band heads  will  yield  values  in  f o r the v i b r a t i o n a l  c o n s t a n t s to , co x , e t c . f o r t h e c h o s e n e l e c t r o n i c s t a t e , e e e according  to equations  2.4  and 2 . 5 .  Furthermore, i t w i l l  d e m o n s t r a t e d t h a t t h e head o f any band l i e s v e r y c l o s e  to  the  band o r i g i n  of  the  potential  (section 4.5),  well  and t h u s  t h e minimum T  g  be  o f t h e u p p e r e l e c t r o n i c s t a t e may be f o u n d  w i t h i n a few wavenumbers. 2.7  Franck-Condon  R o t a t i o n a l A n a l y t i c Techniques  D e t e r m i n a t i o n of the r o t a t i o n a l c o n s t a n t s through  analysis  of r o t a t i o n a l e n e r g i e s  is  B '  and  complex.  The  v  r ' g  o  laser's  b a n d w i d t h (-  0.2  A)  is  broader than the l i n e w i d t h o  of  a single  resonance  line  in I  ?  (-  0.03  A, e s s e n t i a l l y t h e  Doppler  width)  out  rotational  the  found  than  so  that  The transitions population and  (b)  analysis,  approach  of  the  intensity  the o v e r l a p  of  of the  two v i b r a t i o n a l  factor  is  2.2.2. is  relative  relative  vibrational  states.  of  ficult  determine state.  under  of  i ndependent  probability of  the of  relative molecule,  distribution  functions  a $  d i  these  state  s  c  u  s  The  e  (  i  n  the s t a t e s , r  and  1 g  molecular  $  e  c  first  the  obtained  and  in  the  and  the  elec-  e  were  n  the  are of  constant  I o d i n e was  is  o  depends  constants  upper  approach  i  r "  rotational in  t  integral,  f r o m a measurement  Since  the m o l e c u l e  J  the o v e r l a p  Franck-Condon f a c t o r s  from the  s  co ' and co " o f e e  The one a s s u m p t i o n o f t h i s  ionization  is  the  positions  may be c a l c u l a t e d  size  rotational  consideration.  c m " /°K)T  band i n t e n s i t i e s .  the  the  1  frequencies ^  the  (a)  states  probability  equilibrium  to measure,  must be  vibrationa1-electronic  second f a c t o r ,  the e x c i t e d e l e c t r o n i c  of  carry  results.  g o v e r n e d by  When t h r e e o f  fourth  the r e l a t i v e  precise  of  states  the  To  Franck-Condon f a c t o r s  Franck-Condon f a c t o r of  upon t h e  known t h e  the  G  The s q u a r e o f  of  vibrational  -G (v")/(0.6952  e  termed the  tronic  is  initial  resolved.  the s e p a r a t i o n  with very  in absorption  not  a d i f f e r e n t approach  The measurement  relative  -  t h e band i s  of measuring  energy l e v e l s . an a l t e r n a t i v e  that  31  used  difto  electronic that  the  resonant excited state  is  v'.  We may a p p r o x i m a t e w i t h the e i g e n f u n c t i o n s  of  the l o w e s t - l y i n g the  harmonic  vibrational  oscillator  states  model.  These a r e  -  the Hermite orthogonal  The n o r m a l i z e d tronic  32  state  vibrational  is  functions  wavefunction  (Herzberg,  1950).  i n the ground  elec-  then: •aX /2 2  * .i v  (x)  where x. i s  [*  J  2  the d i s t a n c e  v"/2  H „(/crx) v  AT  from the e q u i l i b r i u m s e p a r a t i o n , of  II  t h e n u c l e i i , a = y u ) /fi , and H ( / c T x ) i s vll  g  nomial  of v - t h degree.  normalized  vibrational  In  a Hermite  poly-  the e x c i t e d e l e c t r o n i c s t a t e  wavefunction  the  is: •3y /2 2  *. .ty) where y i s  the d i s t a n c e  The H e r m i t e function factor  H (u) n  between  (-1) n  =  states  ,v")  3 represents  positions  e  v  /v  from e q u i l i b r i u m  polynomials  F(v'  where  /2 29 v ' -  ( * )  v  1  a r e o b t a i n e d from t h e g e n e r a t i n g 2 2 u ( d / d u ) e -u The F r a n c k - C o n d o n n  Pryce  n  and v  is  * I I ( X ) •i|; , (x-3) V  the d i s t a n c e  v  between t h e  dx  equilibrium  i n t h e g r o u n d and e x c i t e d e l e c t r o n i c  The method o f e v a l u a t i n g of  and  (1976),  the o v e r l a p  in which a g e n e r a t i n g  whose c o e f f i c i e n t s a r e  proportional  between t h e d i f f e r e n t v i b r a t i o n a l  states.  integrals  f u n c t i o n was  to the o v e r l a p  states.  The  is  that  derived integrals  Franck-Condon  - 33 -  factors  take the form: PD /2 P e" " " 2  Ftv'.v")  < ^ 1 ^  -  !  2  >  v where 6 ( v ' , v " ) of  is  the c o e f f i c i e n t of  t  function H(s,t): -Q'Ds Q"Dt 2Pst H ( s , t ) = e e e  \  »  /  2  v"  1  s  /  (G(V.V)  r  in the  expansion  the g e n e r a t i n g  The q u a n t i t i e s P, electronic  Q'  positions  2  and Q" a r e c o n s t a n t s  s t a t e s , whi1e  equilibrium states.  R,  e  Rs  e  -Rt  2  f o r any two  D v a r i e s w i t h the s e p a r a t i o n of  given the  i n t h e u p p e r and l o w e r e l e c t r o n i c  The d e f i n i t i o n s a r e : n  =  h  InU'/oo")  P = sech n R = tanh n -n/2  Q'=  e  s e c h ri n/2  Q"=e  sech n  D = 9 / m/h The f i r s t  (OJ'CO'T  4  few c o e f f i c i e n t s G ( v ' , v " ) G(0,0)  =  G(1,0)  =  -Q'D  G(2 ,0)  =  %Q D  G(l,l)  =  2P -  G(2,l)  = - 2 P Q ' D + JgQ ' Q " D  G(2,2)  =  are:  1  1 2  + R  2  Q Q"D 1  2  2  2P  2  - R  2  +  3  + JsRQ" D 2  2  RQ"D - J^RQ' D 2  +  -  2  %Q Q" D , 2  2  2PQ'Q"D 4  2  2.8  Electronic In  resonant  34  Configuration  the t h r e e - s t e p two-step  -  and Band  ionization  transition  Contour  of  from the  arising  l^, X 0  state  +  from a  t o some  9  intermediate ionization,  even-parity i t would  be u s e f u l  prediction concerning rotational  state,  the  structure.  f o l l o w e d by t o have  intensities  The  non-resonant  firm theoretical associated  intensities  of the  with  the  individual  r o t a t i o n a l members w i t h i n a g i v e n v i b r a t i o n a l band a r e p r o p o r t i o n a l to t h r e e f a c t o r s : (a) a B o l t z m a n n f a c t o r -F (J")hc/kT v  e  , (b)  (c)  the  the t r a n s i t i o n  states.  probability  The d e p e n d e n c e  used i n t h i s  research  is  The  only  ^ g  4%.  ' I ^m]>  by a n a l o g u e s  ional of  and  frequency  on J  is  weighting ition The fore  f a c t o r of  probability  intensity resembles  is  the  the  range  since  the  variation  is  that  part  is  of  represented  a heavy  molecule,  high  even  within  in  the  onerotat-  vicinity  to the Honl-London for  large  (2J+1),  essentially  closely  over  in  rotational  distribution  rotational  appearing  the analogues  of  and  factors  encountered,  multiples  two  and J " , and  1  may be used i n t h e i r a p p r o x i m a t i o n are a s y m p t o t i c a l l y  the  probability  Since  numbers a r e  peak,  the t r a n s i t i o n ,  between  to t h e H o n l - L o n d o n  quantum  v of  may be n e g l e c t e d ,  depends  absorption.  t h e band  on t h e  transition  which  M  photon  frequency  the  states.  constant  J.  These  factors  statistical Thus t h e  i n each  a rotational  the p o p u l a t i o n  factors  branch.  branch  distribution  trans-  of  therethe  initial  rotational  -  states: i(J)  The r o t a t i o n a l  35  -F  = C(2J+1) e  term F ( J " )  (J")hc/kT v  of equation  2.7  simplifies  since  2  the s y m m e t r i c - t o p electronic D " v  is  state  term (A" of  negligible  transitions  I,  single i(J)  Since  t h e bands o f  distribution f u n c t i o n of  spectrum,  laser  small  ground  correction  term  The r e l a t i v e i n t e n s i t y  branch  of  by  the  (J=J"):  v  are  unresolved,  may be t r e a t e d as  the  an e s s e n t i a l l y  intensity continuous  J. of a s i n g l e  the i n t e n s i t y  approximated  The c o n t o u r  the  in the  i s then d e s c r i b e d -B "J(J+l)hc/kT = C(2J+1) e  Iodine  The c o n t o u r convoluting  B ")•  7  vanishes  B^")Q"  and s i n c e  2  (=10~  o f any  -  I(v^)  frequency  as  b r a n c h may be d e t e r m i n e d  distribution  i(J)  a square-topped  of a branch  expressed  w i t h the  wave  as  1.5  is: J2  I(v ) 4  =  J  i(0)  dJ  Jl  k T  hcB/  a(e where  -Jjd^ a =  e  -B "J(J+l)hc/kT v  + D/a  - e  kT/hcB " v  -J (0 2  + 2  D/a  )  laser  cm *  a function  by  -  of  wide.  The  limits  width.  of i n t e g r a t i o n  36 -  a r e d e t e r m i n e d by t h e l a s e r  band-  Thus: J and  J  2  1  =  J(v  =  J(^  The l i m i t s o f i n t e g r a t i o n equations  2.14 t o 2 . 1 7 .  the r e s u l t s  + 0.75 c m " ) , 1  £  - 0.75 c m " ) . 1  £  f o r each Placing  a r e as f o l l o w s  b r a n c h may be deduced  the zero  f o r the case  of  from  at v / 2 ,  |AB|<<B : 1  v  0-BRANCH J  2B ' - J L . AB  =  Q  / /2B ' \ j (—v-) V \ AB /  ±  2v„ - 2B _ * AB  2  +  1  (2.14)  P-BRANCH J p  .  V  /  t  ^  V  AB  \AB /  (  ,  1 5 )  AB  R-BRANCH B ' J  R  = -  AB  ±  / /  /B ' \ (—1 \AB /  V  2  +  2v„ - 2B — * AB  1  (2-16)  S-BRANCH 2  Oc = -  Q  4  The r e q u i r e m e n t upon t h e  intensity.  / /—v'\ H 2B  /  V  V  o f t h e Q-BRANCH i s  jI (/v )\ ions  ,  ±  AB  5  The c o n t o u r  V  . . /1.5\ ^ -  = 9 2a s i n h  t h a t J be r e a l f o r which  +  2v  * "  AB /  v'  (2.17)  places  restrict-  6B  AB  simply: j  e  " V 2  a A B  and p o s i t i v e  there are contributions  to the  Prediction electronic requires  over  all  a knowledge  possible  possible  calculations  f o r the  various  i n the r e s o n a n t  of the r e l a t i v e branch  electronic configuration  a t the two-photon  lowing  -  o f t h e band c o n t o u r s  configurations  For a g i v e n  37  it  is  intensities. necessary  intermediate electronic states analogues.to  the Honl-London  were c a r r i e d o u t by P r y c e  state  to  to  sum  arrive  factors.  (1976) w i t h t h e  The fol-  res u l t s :  ^Transition 0  Branch""  +  g  -  0 g +  g J(J-2). (2J-1)  P Q  0 (2J+1)  (a+23)  2  2  3(2J+l) 2(2J-1)(2J+3)  In  3(J-1)(J+2)(2J+1) 2 ( 2 J - 1 ) ( 2 J + 3)  1  R S  (J-2)(J-3) 4 ( 2 J -1)  %(J+1)  2J(J+1) ( a - g ) 3(2J-1)(2J+3)  + f  9  %(J+3) (J+l)(J+2) (2J+3)  the 0  -> 0  (a-g)  (J+l)(J+3) (2J+3)  ( J + 3) ( J + 4) 4(2J+3)  t r a n s i t i o n , a and g a r e c o n t r i b u t i o n s  from  intermediate  0* and l  2  3a  may,  for large  (1)  + 4ag + 8g  o f J as For  The r e l a t i v e b r a n c h  rotational energies,  value  depends  be e x p r e s s e d  a positive  are  3:2:3  is  and  q u a n t i t y whose  The e x t r e m e band c o n t o u r s  equally  y  are t o t a l l y absent,  intermediate  F o r 0* -> 2  and a  e n t i r e l y Q-1 i k e .  strong.  the r a t i o s  is  absent  and t h e o t h e r  0:P:Q:R:S = are  branches  1:1:0:1:1.  0:P:Q:R:S =  1:4:6:4:1.  y  Once t h e r o t a t i o n a l a n a l y s i s band c o n t o u r  independ-  the  Og ->• l g t h e Q b r a n c h  are a l l  strengths  on d e t a i l s o f  contour which  has  been c a r r i e d o u t ,  the  f o r each e l e c t r o n i c c o n f i g u r a t i o n may be  p r e d i c t e d by summing All  so  follows:  states.  (3)  =1.  = 3:2+x:3 where x i s  actual  For  r e s p e c t i v e l y , normalized  Og -> 0^ t h e R and P b r a n c h e s  0:Q:S  (2)  states  u  -  2  that  ently  38  the c o n t r i b u t i o n s  bands o f a v i b r a t i o n a l  progression  of a l l  branches.  w o u l d be s i m i l a r  in  contour. It  is  noteworthy  configurations  that for  become Q - l i k e  (pure -2v  I(v ) £  In  a p l o t o f 1n ( I )  slope  at high  but w i l l analysis.  serve  <*  against  energy. to check  very  large  J, all  band  exponential):  /aAB  e v  £  we may d e t e r m i n e AB f r o m t h e  The method  in  inherently  the Franck-Condon  approximate,  rotational  3. 3.1  39  -  INSTRUMENTATION AND EXPERIMENTAL DESIGN  Introduction The  light  a Molectron nitrogen  source  used t o p h o t o i o n i z e  DL-300 t u n a b l e  dye l a s e r  l a s e r , which provided  the Iodine  was  pumped by a UV-1000  5-nsec p u l s e s  of  bandwidth  0  0.2A.  A digital  grating  drive mechanically  Triple-photon  i o n i z a t i o n of  citing  _> 25 ,271  energy  +.3  the  Ig  molecule  cm ''' ( s e c t i o n -  tuned the requires  2.5),  laser. an  which  ex-  corres-  o  ponds chosen  to photons was  Butyl  of wavelength PBD  in  <_ 3957 ± 1A.  the s o l v e n t  The l a s e r  p-dioxane  which  dye  lases  over  0  3650-3800A; t h i s able at present The  dye p r o v i d e s in  laser  this  beam was  between t h e e l e c t r o d e s vapor  at  its  sensitivity  was  built  over  quired  the  pressure  Iodine  possible cell  for  power  avail-  spectrum.  cell  by f o c u s i n g  the l o n g e s t  output  w i t h a 9 3/4  electrode in order  cm q u a r t z  containing (Figure  the  laser  Iodine  1).  Great  very  close  to a c c e l e r a t e the distance.  product  An oven  the p r o d u c t i o n  lens  of  was  high-  spectra.  The s i m u l t a n e o u s laser  focused  vapor  achieved  to house t h e  temperature  of  of a g l a s s  saturated  to the n e g a t i v e electrons  region  the h i g h e s t  output  along  both f o r  heads and f o r  monitoring  of a small  w i t h the p h o t o i o n i z a t i o n  c a l c u l a t i o n of  portion  signal  t h e wavenumbers  of  d e t e r m i n a t i o n o f t h e r e l a t i v e band  Thus a beam s p l i t t e r  of  low r e f l e c t i v i t y  was  was the  of  the  reband  intensities.  required  immed-  \  - 40 o o  r-VvVHl"  cc  o  t— o << C vO CC o  x O  cr: — CJJ LU CC  m  h < CL.  Z  <  CC  LU CQ  Q  n: < cr: u 1 o 1 c_> o O "5  < < _ > rsl  LU CC  3  fD CL CL <  o  —  <  3  Q: 1<  <2>  I  E  0 0 : 0 X C3 O L U CC CQ ( < Z CL.  O  o 1 cn  o  Z1  z  c;  LU CO CO . <  E  O 1  ANODE j  CATHODE  -  LU CC \LU < H- I f— CL. — _l Q_ LU  CO I— —  2:  O ZD  < LU CQ  _1  CC C O LU  CC UJ  1— O X  a_  —  LU  —  CC LU rLU  Lu  z:  O  —  —  1< ZD  LU  LU  <  z  C zO LU  < _1  z  ATT A 1 1  to a. v D — u-\ r— rsi _ i vO ZD  2: O  1 — _l  CO co  a:  < C3  CC LU O CC LU LU :C Q_ O I CC >- LU CC U_ CO cr: LU U.  1—  <  \-  1z  lately 4.3  in f r o n t of  the l a s e r .  mm s e r v e d w e l l .  ative  band  41  A lucite  To f a c i l i t a t e  p l a t e of  thickness  d e t e r m i n a t i o n of  i n t e n s i t i e s , the d i r e c t r e f l e c t e d l a s e r  m e a s u r e d w i t h p h o t o m u l t i p i i e r t u b e EMI  6256S.  the  rel-  light  was  Attenuating  materials  were used t o s h i e l d  eliminate  o p t i c a l s a t u r a t i o n of the p h o t o m u l t i p i i e r .  materials,  namely a h i g h - n e u t r a l - d e n s i t y  i n some c a s e s  two, sheets  of d i f f u s i n g  a t t e n u a t i o n on t h e o r d e r o f i n t e r f e r o m e t e r was beam ( F i g u r e number plate  the photocathode  1)  as a v e r y  separation  filter  glass,  10^ ( A p p e n d i x  introduced  in order  and o n e ,  A  tuned,  was  i n t o the path of the r e f l e c t e d  of the p h o t o i o n i z a t i o n - b a n d  pressure.  the i n t e r f e r o m e t e r p r o v i d e d  whose s e p a r a t i o n  an  a c c u r a t e means o f m e a s u r i n g  at atmospheric  and  Fabry-Perot  the  heads.  s e p a r a t i o n was a d j u s t e d t o 0 . 0 5 0 2 0 cm; t h e gap  the p l a t e s  These  provided  A).  to  The between  As t h e l a s e r  closely-spaced  c o u l d be a c c u r a t e l y c a l i b r a t e d .  wave-  was  fringes A 4 cm 2  glass  lens  of the lens  was  used to expand  interferometer plate.  c o l l e c t e d the l i g h t  the c e n t e r of the f r i n g e s ceeding  A second,  from the  cell  signals  focused  i n aluminum f o i l  f r o m t h e p h o t o m u l t i p i i e r and  integrators  glass  pre-  of the p h o t o m u l t i p i i e r .  were f e d t o two s e p a r a t e  The b o x c a r  7 cm  large-diameter  boxcar  the  integrators,  e a c h t r i g g e r e d by t h e s y n c h r o n o u s o u t p u t o f t h e laser.  roughly  i n t e r f e r o m e t e r and  on a p i n h o l e  the a t t e n u a t i n g f i l t e r s The p u l s e d  Iodine  t h e beam t o f i l l  nitrogen  c o n v e r t e d the r e p e t i t i v e  - 42 waveforms  t o dc s i g n a l s  number o f p u l s e to-noise played  in analogue  example lens  peaks,  improvement  Fused  consisting  of the t i m e - a v e r a g e  t h e number d e t e r m i n e d by t h e  desired.  The b o x c a r  f o r m on a t w o - c h a n n e l  q u a r t z was  employed  i n t h e window o f  beam i n t o t h e  t h e window o f  the oven,  since  The o p e r a t i n g major 3.2  pieces  Iodine  far  into  dis-  recorder. for  cell,  the  and  is  in  excellent  the u l t r a v i o l e t .  c h a r a c t e r i s t i c s and c a l i b r a t i o n of is  described  C a l i b r a t i o n and O p e r a t i n g  the  in the f o l l o w i n g  section.  Characteristics  Laser  The l i g h t DL-300 p u l s e d design  were  places,  the t r a n s m i s s i o n  1965)]  of apparatus  3.2.1  signal-  the p h o t o m u l t i p i i e r t u b e , in  the l a s e r  1 cm ( K o l l e r ,  chart  in c r i t i c a l  focusing  [98.9% a t  outputs  of a  s o u r c e was  a state-of-the-art  tunable organic  follows  Hansch  (1972)  dye l a s e r , whose  Molectron engineering  pumped by a UV-1000  nitrogen  0  laser  a t 3371  repetition  peak  anywhere  design  provides  occurring  of  1 MW per p u l s e  t o a l l o w dye  5-nsecpulses  between 5 and 50 p p s ,  power o u t p u t  channel  power o f  designed  The l a s e r  rates  time-averaged discharge  A.  laser  a t 10 p p s .  interchange,  the  at the r a t e  the n i t r o g e n  thus  at highest  10 p p s .  The  delivers a  The dye l a s e r achieving  is  the wide  0  tuning  range  of  3 6 0 0 - 7 4 0 0 A , f o r w h i c h t h e o u t p u t power  pends upon t h e p a r t i c u l a r dye and s o l v e n t  chosen.  de-  A high  dis-  persion  echelle grating  43  -  i n L i t t r o w mount f u n c t i o n s  length-selective  end r e f l e c t o r i n t h e dye l a s e r  of  is  t h e dye l a s e r  grating.  In  accomplished  the absence  by a s i m p l e  of a F a b r y - P e r o t  as  a wave-  cavity.  Tuning  r o t a t i o n of  the  intercavity etalon, o  the bandwidth of the d y e - l a s e r -1  or  1.5  a t 3750A. narrower  photoelectron tercavity quality  is  approximately  0.2A,  0  cm  slightly  output  This  b a n d w i d t h may i n p r a c t i c e be  due t o t h e t h i r d - p o w e r dependence  signal.  The beam d i v e r g e n c e  beam e x p a n d i n g  is  of  2 mrad.  t e l e s c o p e t o g e t h e r w i t h the  d i f f r a c t i o n grating  provides  the An  in-  high  e x c e l l e n t wavelength  rep-  0  roducibility is  also  ensured  magnetically in order rival  (0.01A)  from shot  from shot  to s h o t .  to shot  t o r e t u r n t h e dye t o o p t i c a l  term, however,  as  ities  i n the form of d i s s o c i a t i o n Molectron  mole/liter ies  or  as  required  i n 2 cm  lifetime  o f a sample  six  insensitive  t o dye d e c o m p o s i t i o n . 3.54 3  not s t a b l e  mg o f  over  w i t h i n t h e dye  sol-  impur-  products.  in solvent  to small  of B u t y l use a t  of  At t h i s PBD  of  impurit-  weight  dye B u t y l  PBD  are  c o n c e n t r a t i o n , the  in p-dioxane  10 p p s .  5 x 10  amounts  With a m o l e c u l a r  the o r g a n i c  of s o l v e n t .  hours o f c o n t i n u o u s  ar-  a f t e r Hansen ( 1 9 7 2 ) , t h e r e l -  c o n c e n t r a t i o n o f dye  3 5 4 . 4 5 gm/mole,  cell,  before the  t h e dye c o n c e n t r a t i o n and i n t r o d u c e s  recommends,  being  stirrer,  i n a 2 cm  homogeneity  photodissociation  both decreases  high  an a u t o m a t i c  The a m p l i t u d e i s  ution  atively  by u s i n g  d r i v e n , t o c i r c u l a t e t h e l i q u i d dye  o f t h e n e x t pump p u l s e .  the long  Amplitude s t a b i l i t y  is  The peak  approximately power  obtained  from a f r e s h  sample  o f dye  44  is  -  20 x 10  joules  per  pulse,  0  o r 40 KW p e r p u l s e ,  a t 3760A.  The e m i s s i o n  curve over  the  0  useful that  range  3650-3800A i s  the emission It  is  beam changes was  varies  wavelength stepping  of the  as  grating  c o n c e r n , however,  as  rotations  Scanning  scanning  assembled,  as  in a continuous  of the I o d i n e  system  applications. at rates pulse  of v o l t a g e ,  a means o f c h a n g i n g and smooth manner.  is  requirement is  ripple was  of  built  5%. is  volts  in  requires  printed  diagram  Figure  assembly.  circuit  a SLO-SYN motor  The e x t e r n a l  10 v o l t n e g a t i v e 30  in  the motor  change  ysec.  a power s u p p l y  dc and + 12 v o l t s  The c i r c u i t given  width of  module  this  per second.  an 8 t o  the  Synchronous  B i d i r e c t i o n a l o p e r a t i o n of  and a minimum p u l s e  -25  is  laser's  translator  a plug-in  up t o 2000 s t e p s  of  the  by SLO-SYN) were used f o r  The t r a n s l a t o r module can p r o v i d e  This  chamber.  f o r the g r a t i n g  board w i t h l o g i c c a p a b i l i t i e s f o r d r i v i n g  triggering  rotated.  i t was e x p e r i m e n t a l l y  motor HS50 and t h e a c c o m p a n y i n g  possible  laser  System  The t r a n s l a t o r module  is  is  of the  i n t e n s i t y of the p h o t o e l e c t r o n s i g n a l  STM1800C ( m a n u f a c t u r e d  stepping  Note  dye.  the l a s e r  to s m a l l  was  w i t h t h e age  10 and 1 1 .  s1ightly  A mechanical dye l a s e r  Figures  t h a t the output angle  determined t h a t the  3.2.2  in  conceivable  o f no p r a c t i c a l  insensitive  given  which  dc w i t h a maximum  o f t h e power  supply  2 (Mi 11 man and H a l k i a s ,  which  1972).  -  45  The w i r i n g c o n n e c t i n g lator  module  is  shown i n  current-limiting required tors  t h e SLO-SYN m o t o r t o t h e  Figure  resistors  3.  Two h e a v y - d u t y  (shown as  5.5ft w i t h i n a b o u t The w a v e l e n g t h  trans-  5.5ft  R in the F i g u r e )  t o i n t e r f a c e t h e m o t o r and t r a n s l a t o r .  used a r e t e n - o h m v a r i a b l e  quired  -  resistors  The  are resis-  reduced to the  ± 5 % , and a r e r a t e d a t 225  increment produced  re-  watts.  by t h e d i g i t a l  scan-  0  ning  system  step over  in t h i s  t h e range  p a r t i c u l a r a p p l i c a t i o n was o  3650-3800A. Since  0.00383A  the l a s e r ' s  per  bandwidth  0  was  roughly  achieved.  0.2A,  The w a v e l e n g t h  The s t e p a n g l e shaft  an e s s e n t i a l l y  makes  continuous  output  was  increment  is  c a l c u l a t e d as  o f t h e SLO-SYN m o t o r  is  1.8°  200 s t e p s  per r e v o l u t i o n .  so  follows.  t h e motor  One r e v o l u t i o n o f  the  o  grating first  crank  advances  order.  Since  dye used i n t h i s crank  is  equal  the  laser's  wavelength  the d i f f r a c t i o n o r d e r  research o  to 14.3A.  is  seven,  by 100A  in  appropriate  to  the  one r e v o l u t i o n o f  the  T h u s , when t h e m o t o r d r i v e s  the  grato  ing  directly,  each s t e p  advances  n o t v e r y much s m a l l e r t h a n system of  four  gears,  the  however,  the wavelength  laser  bandwidth.  the step  s i z e was  by  0.0715A,  By u s i n g  a  reduced  by  0  a factor step  (64/32) x (112/12)  (3740 s t e p s  per r e v o l u t i o n ) .  the s m a l l e s t  step  laser  losing  before  a stepping  = 18.7  possible  Molectron  f o r the g r a t i n g  a c c u r a c y due  speed o f 400  to the v a l u e  steps  specifies  crank  to s l i p p a g e  per r e v o l u t i o n  0.00383A  of the  corresponds (Reynolds,  per  that dye to 1974).  gu re  2.  Circuit  Diagram  of  SLO-SYN  Translator  DC  Power  Supply  Figure  3-  SLO-SYN  Synchronous  Motor W i r i n g  Diagram  -  -  After  careful  limit  was e x c e e d e d by a f a c t o r o f t e n .  scanning fringes  adjustments,  48  system of  is  Figure  however,  this  quoted  The q u a l i t y o f  i n d i c a t e d i n the F a b r y - P e r o t 1 2 , where o n l y  performance  occasional  the  interference  slippage  is  apparent. 3.2.3  Iodine  The g l a s s photoionization  Chamber  cell  containing  occurred is  Iodine  shown i n  p y r e x window t h r o u g h  which the l a s e r  a v i r t u a l l y constant  transmission  vapor  Figure  in which  1.  the  The 2 mm  beam e n t e r e d t h e c e l l  o f 92% ± 1% o v e r  has  3650-  0  3800A, t h e s p e c t r a l laser  beam was  a r a t e d by 1.1 to  focused cm.  of  interest  ( K o l l e r , 1965).  could  A F l u k e 415B  to the s e n s i t i v i t y  H.V.  dc power s u p p l y  Lower v o l t a g e s  higher  voltages  o b t a i n adequate  after  Brackmann  caused  an a r c  was  project  voltage  an a d e q u a t e  signal,  In o r d e r  temperatures, this  to  range  V.  ( 1 9 5 8 ) , who o b s e r v e d  that his  Iodine  which employed t h i s metal  the g l a s s  used  t o -400 V  constructed with s t a i n l e s s - s t e e l  had t h e l o n g e s t  through  -200  instability.  s e n s i t i v i t y at high  violet-photon-counters electrodes  the range  d i d not p r o v i d e  had t o be e x c e e d e d up t o -430 The c e l l  in  was  sep-  potential difference.  d e s i r e d , the e l e c t r o d e  be a d j u s t e d t o any p o i n t  (20°C).  The  between p a r a l 1 e l - p l a t e e l e c t r o d e s  m a i n t a i n the e l e c t r o d e s at a c o n s t a n t  According  and  range  lifetimes. of our c e l l  for  The t u n g s t e n through  a  electrodes ultratheir leads  standard  - 49 Stupakoff the  seal.  Iodine  a long that  distilled  stem c o n t a i n i n g  the v a p o r  pressure  of  the s o l i d the c e l l ination high  was  The c e l l  Iodine  it.  a reserve inside  when p l a c e d  inside  used t o h e a t  (maximum  supply  thick  to the h e a t i n g  DCR150-15A w h i c h  supplies  the temperature  was  important  on t h e c e l l  than  to ensure  isolate  that  of  contam-  d i d not o c c u r  Iodine  cell  asbestos  when  120°C).  current  constructed  sheeting,  cemented  The d i r e c t  e l e m e n t was  high  was  current  a S o r e n s o n NOBATRON at  low v o l t a g e .  s t a b i l i t y was w i t h i n 0 . 2 ° C  to prevent  solid  window and e l e c t r o d e s .  Iodine  In  over  from  one  in order  to  of s o l i d  Iodine  the c e l l  at a lower  i n t h e stem o f  the remainder dimensions  tered through  of  the c e l l .  5 3/4"  a 1.5  x 5 3/4"  The  upper  x 6".  deposi-  Thus t h e oven  w i t h two c o m p a r t m e n t s  quartz  to  vapor  the remainder  designed  inner  so  operation. It  than  with  Iodine  o f t h e stem s e r v e d  the  temperature  ting  fitted  taken.  w i t h epoxy  hour's  before  the s a t u r a t e d  window and e l e c t r o d e s  inch  oven  was  of s o l i d  always  the oven,  o f one and o n e - h a l f  this  torr  6  Oven  The oven  power  supply  temperature  t e m p e r a t u r e s p e c t r a were 3.2.4  to 10~  The c e l l  was  The l e n g t h  at a lower  of the c e l l  evacuated  into  pressure  Iodine.  was  -  isolate  the  supply  temperature  compartment  The l a s e r  was  has  beam e n -  inch diameter aperture covered with a  p l a t e to m i n i m i z e  heat  loss.  The l o w e r  compartment  -  50  -  w h i c h h o u s e s t h e stem o f t h e c e l l IV  x 4"  wire  x 4".  a t seven  terior.  270"  is  partments  and i n t h e l o w e r , 2 6 " ,  about  1.3  is  Nichrome  i n the upper for a total volume  the  in-  compart-  of  173ft.  i n the upper  com-  i n t h e l o w e r , t h e two com-  m a i n t a i n a s u f f i c i e n t t e m p e r a t u r e d i f f e r e n c e even  t h e u p p e r one must  loss.  From t e s t s  upper  over  per u n i t  times t h a t  though  the  dimensions  ohms p e r f o o t wound many t i m e s a r o u n d  t h e power d i s s i p a t e d  partment  inner  e l e m e n t f o r t h e oven  The l e n g t h o f N i c h r o m e w i r e  ment i s Since  The h e a t i n g  has  3.2.5 EMI  22° -  is  about  1.13  times  a greater  heat  the t e m p e r a t u r e that  i n the  in  lower  100°c.  Photomultiplier  t u b e 6256S used t o m o n i t o r  a 1 cm c a t h o d e ,  13-stage  the l a s e r  photomultiplier with  window.  With a r i s e  currents  up t o 300 mamp, t h i s  operation.  sustain  done on t h e empty o v e n ,  compartment  the range  necessarily  t i m e o f 7 nsec  The e n d - w i n d o w ,  adequate  semi-transparent  is  fused-quartz  and a c a p a c i t y f o r  tube i s  t h e v e n e t i a n - b l i n d t y p e dynodes  intensity  for  peak  pulsed  photocathode  a r e c o a t e d w i t h CsSb  and  which o  has  a flat  of l a s e r 0.13 is  response  dye PBD.  ± 3%.  designed  t o have  over the  spectral  range  The quantum e f f i c i e n c y i n t h i s  The n o i s e  0.5 myamp a t -1000 tect  curve  c h a r a c t e r i s t i c s are good.  very volts.  low anode  dark  A mu-metal  the d e t e c t o r from s t r a y  magnetic  current,  s h i e l d was fields.  3650-3800A range  is  Tube  6256S  less  than  used to  The dc  pro-  voltage  applied was  51  to the p h o t o c a t h o d e ,  supplied  by R e g u l a t e d  -  t y p i c a l l y on t h e o r d e r  H.V.  Supply  RE-1602  of  -600  (Northeast  V,  Sc.  C o r p . ). F o r good l i n e a r i t y and g a i n drawn  from t h e power s u p p l y  materially  change  by t h e dynodes  the v o l t a g e  r e q u i r e m e n t means t h a t  s t a b i l i t y , the  this  must  current  not  between t h e d y n o d e s .  anode  current  I,  This  must  be  a  considerably  smaller  the p o t e n t i a l I  <_ 1^/10.  providing  that  divider. Pulses  that  few s t a g e s ,  than  A good r u l e o f  of  large  by-pass  where  the b l e e d e r c u r r e n t  capacitors  current  are  that accommodated  used between t h e  are g r e a t e s t ,  <I  through  is  a m p l i t u d e may be  the c u r r e n t s  t h e mean anode  thumb  I^  > satisfies  and  last  providing  t h e above  re-  a  quirement. pulses this  Measurement  of l a r g e  end c h a i n  and b y - p a s s stages  of  amplitude resistors  capacitors  the l a s e r ' s and v e r y  short  were c h o s e n  were c o n n e c t e d  o f t h e p h o t o m u l t i p l i e r was  involved  duration,  such t h a t  of the p h o t o m u l t i p ! i e r c i r c u i t  linearity  intensity  <  I  >  tested  to 1^/50,  =  a  m  between t h e (Figure  and a  x  last  4).  The  using  four  four  0  identical  neutral  very  the l a s e r ' s  near  linear,  as  saturation distance density  of  density  shown i n  peak  Figure  filters  at wavelength  intensity. 5.  In  order  The r e s p o n s e to a v o i d  of the p h o t o m u l t i p l i e r , d i f f u s i n g 2 cm f r o m t h e c a t h o d e ,  filter,  were used t o s h i e l d  3760A,  optical  glass  f o l l o w e d by a the c a t h o d e .  is  at a  high-neutralThe  total  52  1 OOK  f  —  -  A  A  A  r  Photocathode  MEG  Dynode 1  560K  D  2  D  9  D  10  560K  0.01  yF 560K  D 11 0.01  yF 560K  D 12 0.01  yF 560K  D 13  0.08 yF 560K  Load  F i g u r e k.  EMI  Anode  6256S P h o t o m u l t i p l i e r Tube C i r c u i t  optical  54  -  a t t e n u a t i o n o f t h e s e m a t e r i a l s as  wavelength  is  3.2.6  presented Boxcar  Two b o x c a r A p p l i e d Research  in Appendix  a function  of  A.  Integrator  integrators Model  160,  were e m p l o y e d :  with input  (a)  impedance  Princeton lOOKft  "normal  r e s o l u t i o n " mode, and w i t h maximum a c c e p t a b l e  voltage  o f 200V p e a k , was  used t o p r o c e s s  signal,  and  CW-1, w i t h i n p u t  (b)  maximum v o l t a g e  PAR Model 200V p e a k ,  f r o m p h o t o m u l t i p l i e r EMI The p u r p o s e  of a boxcar  waveform from n o i s e . consisted signal  was  integrator  is  impedance the  lOKft and  signal  d e t e c t o r was  needed.  to e x t r a c t a r e p e t i t i v e  t h e two s i g n a l s  of r e p e t i t i v e pulses  input  photoionization  used to p r o c e s s  6256S when t h i s  Since  the  in  mentioned  above  f o r which the r a t i o of  t i m e t o dead t i m e was on t h e o r d e r o f  10  useful  t o 1 and  -4 10  to 1 r e s p e c t i v e l y , the boxcar  useful  i n our In  signal can  essence,  the boxcar  synchronously  samples  an  using a v a r i a b l e - w i d t h , v a r i a b l e - d e l a y gate,  signal.  integrator proaches ture  research.  be f i x e d a t any  input  i n t e g r a t o r was p a r t i c u l a r l y  p o i n t on, or  The b o x c a r  circuit  the e x t e r n a l to c o n t r o l  event  uses n e g a t i v e  scanned feedback  which  across in  v a l u e of the i n p u t s i g n a l -over A trigger  under  the t i m i n g of  study  pulse which  is  If  apthe  aper-  synchronized  can be a p p l i e d t o t h e  the gate.  the  an  so t h a t t h e o u t p u t a s y m p t o t i c a l l y  the average  time i n t e r v a l .  slowly  input  the gate  is  boxcar  f i x e d on  with  a single rise  point  of the input  asymptotically  toward  signal  a t t h e sampled  across  the input  reproduced  If  value  the gate  output  will  of the input  i s being  scanned  is  linear  ±0.5%.  settings.  i s the real  to reach  to w i t h i n ±0.25% o f f u l l - s c a l e ,  a r e two i m p o r t a n t  control  improvement  time r e q u i r e d  ratio T  relationships  The o b s e r v e d  63% o f i t s f i n a l  0  time c o n s t a n t  f o r the processed  value,  and t h e  (SNIR) a r e e x p r e s s e d C  between t h e  as  The c o n t r o l  settings  follows: {  a r e d e f i n e d as  TC = s e t t i n g f = pulse  All 3.2.7  Chart  The model a wide v a r i e t y inches  -  1  )  follows:  repetition  dial.  frequency.  t i m e , or gate  parameters  3  (3.2)  of the time constant  AT = a p e r t u r e  sig-  signal-to-noise  ( f ) ("AT)  =  (OTC),  output  SNIR = / 2 x OTC x f  ten  be  at the output.  There  nal  the boxcar  the average  point.  and has g a i n s t a b i l i t y  which  signal,  s i g n a l , , t h e s y n c h r o n o u s waveform w i l l  The b o x c a r  boxcar's  55 -  are valued  width.  i n sec or sec  Recorder  used  (Kent)  of s e n s i t i v i t y  allowed reasonable  was a t w o - c h a n n e l settings. accuracy  A l i n e a r i t y c h e c k was p e r f o r m e d  recorder  The c h a r t in the  with  span o f  measurements.  on two o f t h e s e n s i t i v i t y  10  10  INPUT F igure  6.  SIGNAL  (ARBITRARY UNITS) Test  INPUT SIGNAL  L i n e a r i t y o f C h a r t R e c o r d e r a t Two S e n s i t i v i t y (a) 10 V o l t s Maximum, and (b) 5 V o l t s Maximum  (ARBITRARY Scales:  UNITS)  scales  (5 and 10 v o l t s  57  -  maximum)  used most o f t e n .  p u l s e s were f e d t h r o u g h  boxcar  o u t p u t was  a p p l i e d to the c h a r t r e c o r d e r ;  pulse  subsequently  a m p l i t u d e was a l s o  oscilloscope. voltage  is  possibly 3.3  i n d i c a t e d in  required  in the boxcar  The main s o u r c e p i c k u p w h i c h was  was  r e s p o n s e to  and  linear.  from the  PAR 160.  in the instruments  signal  improvement  r a t i o was  only  impedance  was  recorder.  was  electrical  signal Since  careful  a  resolution large  of the  lOOKfi on t h e c e l l , The p u l s e  i n the scanning  shape,  the boxcar  integrator  Figure  The a p e r t u r e w i d t h o f t h e b o x c a r  and t h e TC p a r a m e t e r was  set  mode,  a t 0.1  is  could  photo-  by t h e b a n d w i d t h o f t h e of  of  not r e q u i r e d , t h i s  to o b t a i n a r e s o l u t i o n  bands l i m i t e d  off-  the o p e r a t i o n  against  desired.  Iodine  The  extent through  averager,  improvement  had h a l f - w i d t h 70 p s e c .  10 y s e c  is  so t h a t no dc o f f s e t  i n t e g r a t o r must b a l a n c e  With a t e r m i n a t i n g  signal  integrator  r e d u c e d by a l a r g e  be s a c r i f i c e d i n o r d e r  7.  applied  Except f o r the f i r s t ,  i n t e g r a t o r or t h e c h a r t  As w i t h any  signal-to-noise  pulse  6.  negligible  of noise  the s i g n a l - t o - n o i s e  ionization  i n d e p e n d e n t l y on an  of the e l e c t r i c  done w i t h b o x c a r  signal  the boxcar  the  Processing  resonant  shielding.  Figure  CW-1 and t h e dc  i n c h of c h a r t , the response  The p r o c e s s i n g chamber was  measured  The c h a r t r e c o r d e r ' s  the l a s t ,  Signal  integrator  Voltage  the  laser. signal  reproduced  by  i l l u s t r a t e d in  integrator msec.  At  was the  \  - 5-8 -'  (MILLISECONDS) Figure  7 •  Photoelectron  Signal P u l s e Shape I m p e d a n c e 100 KQ  at  Terminating  repetition  frequency  to e q u a t i o n s o f 4.5 ively  3.1  10 pps  and 3 . 2 ,  processed  over  signal  of the  pulses.  analysis  perimental  measurement  ionization  bands.  the l a s e r  of  energy  12.  The  A sample  instruments  of  Perot signal  value,  pulse  recorded  on a t w o - c h a n n e l  presented  in  Figure  fringes  integrator  - 8 0 0 V , was  CW-1.  integrator  CW-1.  weak,  r e q u i r e d on  of the  Fabry-  improvement  lowest The  f r o m t h e p h o t o m u l t i p i i e r was  the  resolution  signal-to-noise its  photo-  inter-  i n t e r f e r o m e t e r was  set at  ex-  fringes  i n t e g r a t o r was good  than a l a r g e  msec, on b o x c a r  of the s i g n a l  optical  The aim i n t h e p r o c e s s i n g  rather  pulse  a portion  a Fabry-Perot  the data i s  Thus t h e TC p a r a m e t e r was 0.1  of the  s e p a r a t i o n w h i c h were  voltage,  w i t h the boxcar  of the f r i n g e s  the  of  the i n p u t  measurement,  scanned,  the o u t p u t of the F a b r y - P e r o t  photomultipiier.  ratio.  this  6256S and b o x c a r  a r e l a t i v e l y high cathode  of  a delay  used t o r e c o r d t h e F a b r y - P e r o t  were p h o t o m u l t i p i i e r EMI Since  of  w i t h the p h o t o e l e c t r o n s i g n a l  recorder.  effect-  The m a g n i t u d e  separation  passed through  f e r o m e t e r , y i e l d i n g , as  chart  of 1 second,  ratio  of the spectrum r e q u i r e d the  To f a c i l i t a t e  constant  according  aperture.  of the energy  l i g h t was  gave,  improvement  between t h e b e g i n n i n g  of the boxcar  Vibrational  simultaneously  this  was m a x i m i z e d by i n t r o d u c i n g  and t h e o p e n i n g  essentially  laser  time constant  ten l a s e r  a p p r o x i m a t e l y 3 ysec  of the l a s e r  -  a signal-to-noise  and an e x p e r i m e n t a l averaging  59  possible  half-width 6.8  ysec  at  a terminating  impedance  the boxcar  integrator  the output  signal  of  was  set at  was m a x i m i z e d 0.8  pulse.  settings  The q u o t e d  d u c e d an e x p e r i m e n t a l  of the l a s e r about  each  was  the p o t e n t i a l  at  was  set  20°C.  ation,  as  litude,  sensitivity was  very  high  these  The  (-400  of  conditions  the weaker  during  necessary  In  this  were  10%  and  of the  Iodine  threshold  the v i s i b i l i t y  saturation  of  unimportant  on w h i c h  fringes,  application,  below t h e a r c  the  in this  applic-  5 volts  FSD,  PAR  160 was  varied  amp-  recorder  the p h o t o i o n i z a t i o n  at  w h i l e the between  in order  to  signal sensit-  1 volt magnify  bands. f o r a d e t e r m i n a t i o n of  of  strongest  than t h e i r  The c h a r t  a complete scan  photoionization  The d a t a  was  was  sensitivity  increase  be m e a s u r e d .  integrator  FSD  just  rate  Fabry-Perot  the bands, r a t h e r  on t h e c h a n n e l  and 100 m v o l t  V),  pro-  the f r i n g e s  the  12).  input  The s c a n n i n g  the e l e c t r o d e s  inevitable  the item of  boxcar  and a  a m p l i t u d e between  taken to  of  of  (Figure  d i f f e r e n c e across  r e c o r d e d was m a i n t a i n e d  ivity  1 second  of  aper-  the CW-1  recorder  a fringe  scale  the p o s i t i o n s  was  of  of  integrator  r a t i o of 4.5.  and c h a r t  giving  chart  bands.  under  boxcar  the r e c o r d i n g  T h i s a c t i o n was  t h e weaker bands  In  the boxcar  from the b e g i n n i n g of  of  The m a g n i t u d e  by d e l a y i n g  such t h a t t h e p e r i o d o f  FSD,  20% o f t h e f u l l  10 y s e c .  time c o n s t a n t  sensitivity  5 volts  cell  ysec  improvement  24 s e c o n d s .  the boxcar  -  10 Kft , and t h e a p e r t u r e w i d t h  ture approximately  signal-to-noise  60  the  band  intensities  r e q u i r e d , along  the s i m u l t a n e o u s Fabry-Perot reflected  laser  this  light  -600  of the  The  characteristics.  Since  the l a s e r  The b o x c a r  10 u s e e so t h a t  of  the s i g n a l - t o - n o i s e  the e x p e r i m e n t a l and 3 . 2 ) ,  effectively  processed  signal  sensitivity recorder,  photoionization between -200 ing  and -400  instruments  (boxcar)  and  signal,  FSD  vapor.  laser  0.5  d a t a were a l s o  The l a s e r  i n t e n s i t y was  frequency 14  and  On a l l  volt  FSD  and  of  the  was  of the  in t h i s  recorded  gate scans of  varied  a t 100 mV  produced  3.1 The  the sampling  the r e c o r d i n g  recorder),  and  pulses.  input pulse.  throughout  (chart  resolution  (equations  V, and t h e s e n s i t i v i t i e s  Photoionization Iodine  100  of  slowly  r a t i o was  the e l e c t r o d e v o l t a g e  were c o n s t a n t  5 volts  In  a  repetition  by d e l a y i n g  FSD.  In  were TC = 1 msec  o f t h e b o x c a r was  1 volt  is  10 s e c o n d s  over  of the  PAR CW-1.  signa1-to-noise  improvement  was m a x i m i z e d  recording  10 and 1 1 ) ,  at the pulse  was  direct  6256S a t a c a t h o d e  e x c e l 1ent  averaging  0.8 usee f r o m t h e b e g i n n i n g  the c h a r t  The  intensity  (Figures  time constant  the  c h a r a c t e r i s t i c s were  settings  gate width  the  so t h a t  integrator  signal-to-noise  c o u l d be s a c r i f i c e d t o a c h i e v e  taken  intensity.  be r e c o r d e d .  f u n c t i o n of wavelength  10 p p s ,  laser  removed  V f o l l o w e d by b o x c a r  importance.  varying  signal,  used were p h o t o m u l t i p l i e r EMI  a p p l i c a t i o n the  prime  could  -  w i t h the p h o t o i o n i z a t i o n  i n t e r f e r o m e t e r was  instruments voltage  monitoring  61  for  record-  FSD application. heated  simultaneously  as  described  erature  is  above.  desirable  in order  in d e n s i t y ,  practical. the  intensity,  vibrational  of the m o l e c u l e .  however,  states As  so t h a t v e r y  compartment.  volts  d c ; t h e oven drew 0.69  within  the l o w e s t  was  sensitivity  t h e oven w h i c h  raised  (Gerry  signal of  was  up t o - 4 3 0  three voltages  in Figure  integrator FSD  not  of  was  performed at 20°C.  as  the  signal 9.  intensity  V. is  mm a t photo-  The o v e r a l l increased  over  Electrode  volt-  (2-0)  saturation. change band  at  de-  exponential  as  throughout  PAR 160 and c h a r t r e c o r d e r were 100 (all  by  The v o l t a g e  The s e n s i t i v i t i e s  respectively  heat-  pressure  d i d not  i n d i c a t e d f o r the and -430  120  27 mm Hg, g o v e r n e d  instruments  of  the  and G i l l e s p i e , 1 9 3 2 ) , and t h e  between -150  o f t h e peak  and 1 v o l t  in  V were p o s s i b l e - w i t h o u t , e l e c t r i c a l  electrode voltage,  boxcar  to a l m o s t  8 i l l u s t r a t e s t h a t t h e band c o n t o u r  illustrated  are  housed  amp o f c u r r e n t t h r o u g h The s a t u r a t e d v a p o r  the r e c o r d i n g  ages  pendence  100°C  c o n s i d e r a b l y weakened.  used i n e x p e r i m e n t s  with  in-  decrease  r e q u i r e d an a p p l i e d v o l t a g e  173ft.  that  Figure  the vapor  t e m p e r a t u r e i n t h e o v e n , compared w i t h 0.2  room t e m p e r a t u r e ionization  This  impedance  the c e l l  the  h e l d at a temperature i n the v i c i n i t y  upper  u n i t of  of  high temperatures  90°C, which produced a temperature of about  ing  temp-  change  recombination processes  The l o w e r c o m p a r t m e n t o f  I-£ chamber was  high vapor  to c r e a t e s i g n i f i c a n t  the upper  ground e l e c t r o n i c s t a t e  the s i g n a l  -  T h e o r e t i c a l l y , a very  in the p o p u l a t i o n of  creases  62  of  the  mvolt  bands on s c a l e a t -340  V).  - 63 -  ~v  Figure 8 .  *-  Voltage Dependence of the Iodine Band Contour I l l u s t r a t e d f o r a T y p i c a l Band at 100°C  -  Gk  -  1000  (A  o >  <  too 9  cn CL O  10  9 9  9  100 APPLIED  Figure 9 •  200  300  VOLTAGE  V o l t a g e-Dependence of the Peak Intensity  Signal  4. 4.1  65  DATA  -  ANALYSIS  I n t r o d u c t i on Strong  resonant  f r e q u e n c y was  scanned.  The s p e c t r u m c o n s i s t s spaced  signals  The o f f - r e s o n a n t of a s e r i e s  violet-degraded  presented Figure  in Figure  were f o u n d as  bands.  laser  v o l t a g e was  of a p p r o x i m a t e l y  A typical  10, and a t y p i c a l  11, accompanied  the  by t h e l a s e r  negligible.  equally  s p e c t r u m a t 20°C  hot  scan  output.  {-  100°C)  is in  No bands were  o  f o u n d t o t h e r e d o f 3800A i n  s p i t e of the c o n s i d e r a b l y  greater  laser  A p a r t of the spectrum  shown  at  power i n t h i s  higher  region.  resolution  in  Figure  12.  duced a t t h e peak o f t h e s t r o n g e r 10  per pulse  1 2  a t -350  photons plus  4.2)  bands  is  pro-  on t h e o r d e r  laser  power-signal  t o g e t h e r w i t h the f a c t t h a t s i n g l e  were e n e r g e t i c a l l y u n a b l e  the assurance  ions  of  V.  The a p p r o x i m a t e l y c u b i c (section  The number o f  is  from the ground s t a t e  reasonable  to a s s i g n  the observed  and  to i o n i z e t h e  t h a t no r e s o n a n c e s  absorption  relation  can o c c u r  (section  2.5),  resonance  double  molecules, for  one-photon  make  signal  as  it two  "  photon  resonance  ground s t a t e  to a v i b r a t i o n a l  s t a t e o f symmetry an i o n i z e d s t a t e . peaks, as  from the v i b r a t i o n a l  v  v  A f t e r some t r i a l  in Figures  10,  and e r r o r  at the assignment 1 1 , and 12.  +  o f t h e X 0^  o f an i n t e r m e d i a t e  g f o l l o w e d by a n o n r e s o n a n t  one q u i c k l y a r r i v e s  presented  level  i  level  transition  to  to a s c r i b e  the  of the  transitions  Detailed vibrational  Figure  10.  T y p i c a l Photoe1ectron Spectrum of Iodine V a p o r a t 20°C A c c o m p a n i e d by Laser Output  Fi gure  11.  T y p i c a l P h o t o e l e c t r o n Spectrum o f Vapor at 100°C Accompanied byLaser Output  Iodine  Figure  12.  Portion  of  the P h o t o e l e c t r o n Spectrum at Higher Accompanied  by  Fabry-Perot  Fringes  Resolution  and r o t a t i o n a l a n a l y s i s and t h e p o s s i b l e are e x p l o r e d . cussed 4.2  -  t h e band s y s t e m  is  carried  electronic configurations  of  t h e new s t a t e  The e f f e c t  of  impurities  Power-Dependence single-  unable  observed  i n the sample  to  of  the P h o t o i o n i z a t i o n  and d o u b l e - p h o t o n  is  dis-  i o n i z e the  resonance  signal  I  molecules  2  must  (section  ionization  the i n t e n s i t y  was measured  to  allowed  (4-0)  were t h o s e  of  the  (v  i n c l us i ve, p 1 us  the  (1-1)  investigation  (unattenuated) signal  was  signal  strengths.  d e t e r m i n e d as  w h i c h were i d e n t i c a l ,  slope  of a p l o t of the log of  beam ( s e c t i o n  A sample  2.1).  plot is  - 0)  This  choice  over a range of  filters. K(x)  from  the  varied The  as  of  output with  filters,  noted  the p h o t o i o n i z a t i o n s i g n a l  of f i l t e r s  (Figure  bands.  progressions  band.  light,  in  N may be d e t e r m i n e d f r o m t h e  The r e l a t i o n s h i p  given  photo-  incident  i n t e n s i t y was  density  The power d e p e n d e n c e  t h e number  any  the  of s e v e r a l  each have a d e n s i t y  II.  versus  of the  The m a g n i t u d e  the l a s e r  Table  2.6),  I ^ of  o f t h e power dependence  up t o f o u r c a l i b r a t e d n e u t r a l  tensity  I  e x p e r i m e n t a l l y a t t h e peaks  The bands c h o s e n  energetic-  be t h e ' r e s u l t o f e x c i t a t i o n by  The p o w e r - d e p e n d e n c e  s i g n a l , upon  Signal  e x c i t a t i o n are  t h r e e o r more p h o t o n s .  (0-0)  out,  briefly.  As ally  of  69  13)  a t t e n u a t i n g the is  (equation  f o r the  (1-0)  in-  laser  2.2):  band.  - 70 10  i  —  0  1 Number  Figure  13.  Dependence o f  2 of  F i 1 ters  3 -»-  S i g n a l I n t e n s i t y on L a s e r f o r t h e (1-0) Band.  Power  Illustrated  -  Band  A  LASER o  (A)  Table  71  -  Fi1ter Dens i t y  Power Dependence N= - s l o p e / K ( X )  K(A)  (0-0)  3733.10  0.164  2. 34  (1-1)  3731.18  0.164  2. 50  (1-0)  3716.44  0.166  2.23  (2-0)  3699.98  0. 167  2. 31  (3-0)  3683.76  0.168  2.69  (4-0)  3667.78  0. 169  2. 75  II.  Power-Dependence of the P h o t o i o n i z a t i o n  Signal  - 72 The p o w e r - d e p e n d e n c e 2 23 I  '  -  of the chosen  I  *  (Table  band, the l e s s e r electric  signal  tripling  process  breakdown,  is  II).  In  g e n e r a l , the s t r o n g e r  the power-dependence  because  the r e s u l t s  of  possible  minimum e n e r g y determined  Analysis  T  bands,  oo e  (resonant)  described  o f t h e heads o f  in section  2.6.  passed through  Fabry-Perot  were  the is  n  ( 1 - v ) and resolved  (v  bands,  i  of  taken laser  interferometer, simultanmeasurements f o r the  and a r e t a b u l a t e d i n T a b l e VII  -1) bands o f  l^-  from the accompanying  the  corres-  recorded the  2  i  of  photoioniza-  in units  fringes,  each o f w h i c h  a Fabry-Perot  the  e o u s l y w i t h the I photoionization signal. The from the t h r e e c h a r t s are t a b u l a t e d i n Table III (v - 0 )  may be  Measurements  t o t h e number  from t h r e e d i f f e r e n t c h a r t s  I  the  electronic state  ponding  of  avalanche 3  and w x„ , p l u s e e ^  o f t h e p h o t o i o n i z a t i o n band h e a d s ,  ) and  and  the  i  spacing  II  the  w i t h the expected  i  the s e p a r a t i o n as  the  As  of the e l e c t r o n i c p o t e n t i a l w e l l  g  f o r the upper  by m e a s u r i n g  measured.  saturation  are c o n s i s t e n t  The v i b r a t i o n a l c o n s t a n t s  (0-v  from  may n o t be p e r f e c t l y l i n e a r l y r e l a t e d t o  relat ion. 4.3 Vibrational  light,  varies  2 75 to  tion  bands  Each o f t h e  i  (v - 0 )  i  (v  for  -1) bands  band, w h i l e  the  II  bands o f  the  Hence T a b l e wavelength  (1-v ) progression VII  contains  tuning  only  are only  occasionally  selected entries.  s y s t e m o f t h e dye l a s e r  distinct.  Since  was pushed  the  beyond  - 73 -  its  quoted  this was  performance  system  was  t h e main  separation  at  1% o f  of  The  in Tables  between  Fabry-Perot  in  the o p e r a t i o n  erratic.  This  III  two a d j a c e n t  of  the  of  effect  t h e measurement  The m a g n i t u d e  presented  the d i s t a n c e  3.2),  slightly  uncertainty  the bands.  t h e measurements  (section  some p o i n t s  source  of  limit  of  the  uncertainty  and V I I  is  in  better  than  bands.  i n t e r f e r o m e t e r may be c a l i b r a t e d by II  comparing  the spacing  vibrational  levels  are d e s c r i b e d calibration  of  i  (v  -0)  and  and  the  tronic using  in  i  (v  of  four  the  2.6  the f r i n g e s -1)  The c a l c u l a t i o n s  ) bands w i t h t h e electronic state  and l i s t e d i n  is  constants  bands,  are  of  \^  I.  from  presented  (0-0)  to  in Table  (0-4) IV  the  of  the  units,  the upper  i n t e r f e r o m e t e r was  which  Once  t o wavenumber  calculated for  Fabry-Perot  of  Table  well-known  c o m p l e t e , the s e p a r a t i o n  bands may be c o n v e r t e d  The  pairs  (0-v  the ground  section  vibrational state.  of  elec-  calibrated  inclusive.  and y i e l d an  aver-  age c a l i b r a t i o n o f 9.961 ± 0 . 0 3 4 c m * p e r f r i n g e . Applying t h i s c a l i b r a t i o n f a c t o r , t h e s e p a r a t i o n i n wavenumber u n i t s -  II  of  the  over  (0-v  ) and  three charts,  (v  i  -0)  is  photoionization  given  in Table  V.  bands o f  Similarily,  n VIII  contains  i n wavenumber  the s e p a r a t i o n  of  the  (1-v  averaged  l^,  Table  i ) and  (v  -1)  bands  units.  i  i  was  C a l c u l a t i o n of the v i b r a t i o n a l c o n s t a n t s u and w x c a r r i e d o u t s e p a r a t e l y w i t h t h e (v - 0 ) p r o g r e s s i o n and  the  (v  &  i  -1)  progression  of  I. ?  Consider  first  the  g  (v  i  -0)  e  bands.  - 74 Table  V contains  energy  -  the s e c o n d - d i f f e r e n c e s  which, according  to e q u a t i o n  in the v i b r a t i o n a l  2.5,  are  in a f i r s t  i approximation second  to 2 u x e  differences is  determined is  equal  0.06  value of  1.195  The a v e r a g e  -  constant  was  of  c m ' ' ' , and t h u s  vibrational  electronic state  then  these  used  measured  the e x p e r i m e n t a l l y  -  the anharmonic  cm "*" f o r t h e u p p e r  vibrational  .  e  constant  of  I2  " x e  e  This  i n the c a l c u l a t i o n of  the  i harmonic the  vibrational  first  two t e r m s  constant  u  as  e  of equation  follows.  2.4,  Keeping  only  the f i r s t - d i f f e r e n c e s  e x p e r i m e n t a l v i b r a t i o n a l e n e r g y may be e x p r e s s e d : A G = o> ' - w „ x (2v +2) E e e e ' where v i s t h e quantum number o f t h e l o w e r v i b r a t i o n a l i n v o l v e d i n the c o m p a r i s o n . Thus,  in  the  u>  e  v  Q  C  ' = AG  E  C  +  co  x (2v' e e  + 2) . _ i  1  Using  the e x p e r i m e n t a l  v a l u e <±> x e  state  = 0 . 0 6 0 cm  e  , several  •  calculations the  (v  for  a>  -0)  of oo  progression  The a v e r a g e  analysis  Calculation  of  p r o c e e d e d as of  of  and  its  position  the anharmonic  follows. the  a double-quantum  (1-1)  transition.  f o r bands  the v a l u e s  is  of  determined  2 4 1 . 4 5 cm  the  (2-1)  cannot  vibrational  From d a t a and  VI  c a r r i e d o u t on bands o f t h e  was more c o m p l e x , s i n c e  from (1-0)  separation  in Table  upper e l e c t r o n i c s t a t e  Vibrational  resolved  are presented  progression.  of the  e  g  (3-1)  be  is  Thus, using  is  -1)  not  measured.  constant  in Table VII, bands  band  (v  the  "J x g  e  fringe  47.894 f r i n g e s the n o t a t i o n  of  for  - 75 -  Table V I I I ,  we ha ve : 2x:•+ 2y = 4 7 . 8 9 4  We a l s o  know t h e f o l l o w i n g  .  second  (4.1) differences  9 . 9 6 1 ( 2 x - 2y) = 2u> x ' e  9.961 where UJ X e e equations solved  value  Table  VIII,  The o n l y  ,  e  units.  (4.3)  The s e t o f t h r e e  unknown  i s 0.897 c m  using  i s 2.13 c m * . -  - 1  .  of value  One o t h e r  is 2w x e  ( 4 - 1 ) and ( 5 - 1 )  Thus t h e a v e r a g e  the c a l c u l a t i o n s  leading  constant  o f t h e (v - 0 ) b a n d s .  value  w  bands.  of  w x e  e  i s 0.76 cm  to a determination  , s i m i l a r to the an-  Two e v a l u a t i o n s  of u  e  are a v a i l -  d i r e c t l y f r o m t h e t a b l e , w h i l e a t h i r d may be o b t a i n e d  follows.  The  expressions:  9 . 9 6 1 ( 2 x ) + 3.04 = w ' 9.961(2y) from Table  VIII  plus  ,  (4.4)  + 4 . 5 6 = o> '  (4.5)  equation 4.1:  2x + 2y = 4 7 . 8 9 4 give  three equations  substitution average  f o r oo  in three  ,  i s a v a i l a b l e d i r e c t l y from the  the ( 3 - 1 ) ,  vibrational  e  evaluation  f r o m t h e bands o f t h e (v - 1 ) p r o g r e s s i o n  IX c o n t a i n s  alysis  as  be i n wavenumber  d i f f e r e n c e 2w x e e  of the harmonic  able  e  the s o l u t i o n  data of Table  obtained  (4.2)  (2y) - 237.19 = 2 u , x '  by s u b s t i t u t i o n .  the second  This  ,  e  VIII:  i n t h r e e unknowns, 4 . 1 , 4 . 2 and 4 . 3 , may e a s i l y be  f o r which of  must  from T a b l e  unknowns w h i c h , when s o l v e d by  , y i e l d the value  2 4 2 . 3 3 cm  of the e x p e r i m e n t a l l y determined values  . The of u  e  is  - 76 then 242.76  the  (v  i  cm" . 1  The v i b r a t i o n a l -0)  i  and  (v  iu ' = 2 4 1 . 4 5 c m " e oj x e e  1  = 0.60  evaluations relied  given  cm of  1  -1  -1)  least-squares  progressions  versus  cm  0.76  f i t of = T  given  observed  in  I>  l a s e r must  be e s t a b l i s h e d .  2  equal  Ebert  spectrum. position  in the  I  The l e a s t - s q u a r e s E(v')  2  laser  1  analysis  2  output  of Pryce  (0.58  the  of the  dye  transition (1976)  r e l a t i v e to  the  results:  (241.4 ± 0 . 4 ) ( v "  ± 0.06)(v'  relative errors.  the  not w e l l - d e f i n e d .  (1976) g i v e s +  using  reference  from the f a c t t h a t  s p e c t r u m was  (Pryce, of  (0-0)  and T a i  a n i c k e l arc  function:  h)  positions  of the  by D a l b y  = 5 3 , 5 6 2 . 7 5 ± 0.35  quoted are  +  e  c a l i b r a t i o n was done  resonance  The e r r o r s  - « x '(v' e  is  by a p p l y i n g a  to a q u a d r a t i c  The e n e r g y  error arises  at which the  comparison  s t a t i s t i c a l weight  spectrometer plus  The l a r g e  the peaks  however,  the wavelength  placed at 53,576.00 ± 1 c m "  and oo x„ e e, The  to determine the a b s o l u t e  resonances  a 3-meter  w e  These  with c a l c u l a t e d energies  + h)  e  ± 1% and  1  procedure.  consistency,  + w '(v'  e  with  well:  respectively.  the o b s e r v a t i o n s  w i t h each o b s e r v a t i o n  was  -1  very  constants  averaging  internal  order  agrees  242.76 c m "  the v i b r a t i o n a l  E(v')  In  c a r r i e d out s e p a r a t e l y  t r a n s i t i o n energies  greater  1976).  analysis  ± 1% v e r s u s  upon a s i m p l e  o f measured  -  + h)  Since  2  the  +  cm" . 1  absolute  h)  -  Band  77 -  S e p a r a t i o n o f S u c c e s s i v e Band Heads Chart A  Reverse Chart B Chart C Scan on A (Number o f F a b r y - P e r o t F r i n g e s )  Average  (0-4) 10.553  *  10 .553  10.577  *  10 .577  (0-3) (0-2) 10.705  10.614  10 . 660  10.600  10.743  10 .672  (0-1) (0-0) 12.212  11.931  11.986  12 . 043  11.847  12.175  12.071  12 .031  12.047  11.841  11.914  11 . 934  11.915  11 .885  (1-0) (2-0) (3-0) 11.824  11 .918  11.883  11.759  11 . 588  12.063  (4-0) 11 .803  (5-0)  * Bands n o t  distinct.  Bands n o t marked were n o t i n c l u d e d  n  Table  III.  i n the scan.  i  F r i n g e S e p a r a t i o n o f t h e ( 0 - v ) and (v - 0 ) Bands o f I  Band  Separation in Number (n) of Fabry-Perot Fringes (Table III)  True Fringe Spacing (2n) of Vibrational Levels  Calibration of Fringes = AG/2n  AG 1  (cm  )  (Table I)  (cm  _i  per f r i n g e )  (0-0) 10.672  2 1 . 344  213.34  9.995  10.660  21.320  212.11  9.949  10.577  21.154  210.87  9.968  10.553  21.106  209.63  9.932  (0-1) (0-2) (0-3) (0-4)  Mean = 9.961 cm  Table  IV.  C a l i b r a t i o n of the F a b r y - P e r o t  _l  Interferometer.  per  ± 0.034 fringe  Band  Separation in Number (n) of Fabry-Perot Fringes (Table IV)  Fringe Separation of Bands f o r Double-Quantum Transition (2n)  Experimental Energy Separation l AG (cm )  Second Difference A  2  G ^ E c  2CJ  _i (cm )  £  x ' e e  (0-4) (0-3) (0-2) (0-1) (0-0) (1-0) (2-0) (3-0) (4-0) (5-0)  10.553  21.106  210.24  10.577  21.154  210.71  10.660  21.320  212.37  10.672  21.344  212.61  12.043  24.086  239.92  12.031  24.062  239.68  11.934  23.868  237.74  11.885  23.770  2 3 6 . 78  11.803  23.606  235.14  T a b l e V.  Energy S e p a r a t i o n of the (0-v  II  0. 24 1. 94 0.96 1.64  I  ) and (v - 0 ) Bands o f  I  - 80 -  AG Band  E  ( T a b l e V)  E x p e r i menta 1  X= 0.60(2v'+2)  E v a l u a t i o n o f co e (AG +,X) E  (cm" )  (cm )  239.92  1 .20  241.12  239.68  2.40  242.08  237.74  3.60  241.34  236.78  4.80  241.58  235.14  6.00  241 . 14  Experimental  E v a l u a t i o n o f co  1  (cm )  - 1  - 1  (0-0)  (1-0)  (2-0)  (3-0)  (4-0)  (5-0)  Table  VI.  (v'-0)  Progression  1 g  U s i ng t h e  1  -  Band  8 1  -  S e p a r a t i o n o f Band Heads from (0-0) Chart A  Reverse Chart B Chart C S c a n on A (Number o f F a b r y - P e r o t F r i n g e s )  (1-5)  *  (1-4)  -30.435  (1-3)  *  (1-2)  *  (1-D  1.412  (2-1)  **  Average  -30.435  1 .436  1 . 300  1 . 383  *  *  *  25. 271  25.330  (3-1)  25.389  (4-1)  37.224  37.365  37 .213  37. 143  37.236  (5-1)  49.024  49.118  49 .042  48. 957  49.035  *  Band n o t d i s t i n c t . Bands n o t marked were n o t i n c l u d e d i n t h e s c a n . Fabry-Perot fringes  Table VII.  erratic.  F r i n g e S e p a r a t i o n o f the (1-v") and ( v ' - l ) Bands o f I„.  Band  Separation in Number (n) of Fabry-Perot Fringes (Table VII)  Fringe Separation of Bands f o r Double-Quantum Transition (2n)  Experimental Energy Separation AG  E  (cm  Second Difference 2  E  1  l  (cm  )  e e )  (1-4) 31.818  63.636  638.88  2x  9.961(2x)  (1-D (2-1)  2^ e xe Q  2y  9.961(2y)  (3-1)  2w e xe Q  11.906  23.812  237.19  (4-1)  2 .13 11.799  235.06  23.598  (5-1)  II  Table VIII.  Energy S e p a r a t i o n of the (1-v  I  ) and (v - 1 )  Bands o f  I  -  83 -  Experi mental  X= Band  (Table  VIII)  E v a l u a t i o n o f co (AG + )  e  0.76(2v'+2)  E  (cm" )  X  (cm" )  1  1  (cm" ) 1  (1-D 9.961(2x)  3.04  9.961(2x)+3.04  9.961(2y)  4.56  9.961(2y)+4.56  237.19  6.08  243.28  235.06  7.60  242.66  (2-1)  (3-1)  (4-1)  (5-1)  Table  IX.  Experimental Using  Evaluation  the ( v ' - l )  o f co  1 g  Progression.  1  - 84 -  Transition Band  Energy  1/A i n vacuum  (cm ) - 1  Observed  Calculated  A  (0-4)  52 , 7 3 0 . 0 8  52 , 7 3 0 . 22  -0.14  (1-5)  -  52,762.07  -  (0-3)  52,940.32  52,939.85  0.47  (1-4)  52,969.68  52,970.46  - 0 . 78  (0-2)  53,151.04  53,150.72  0. 32  (1-3)  -  53,179.09  (0-1)  53,363.40  53,362.83  (1-2)  -  53,390.96  -  (0-0)  53,576.00  53,576.17  -0.1 7  (1-1)  53,603.56  53,603.07  0.49  (i-o)  53,815.92  53,816.41  -0.49  (2-1)  -  53,842.15  -  (2-0)  54,055.60  54,055.49  0.11  (3-1)  54,080.62  54,080.07  0.55  (3-0)  54,293.34  54,293.41  - 0 . 07  (4-1)  54,317.82  54,316.83  0.99  (4-0)  54,530.12  54,530.17  -0.05  (5-1)  54,552.88  54,552.43  0.45  (5-0)  54,765.26  54 , 7 6 5 . 7 7  - 0 . 51  (6-1)  -  54,786.87  -  T a b l e X.  0. 57  E n e r g i e s of the Observed Resonances i n  I  - 85  -  p o s i t i o n was e s t a b l i s h e d much l e s s separations,  the a b s o l u t e  Table X l i s t s in which  error  the p o s i t i o n s  The a g r e e m e n t  4.4  (Table  Rotational  vapor  levels it  is  regarding  that B'  confirms  closely  expected that B '  The s e p a r a t i o n  of the  The d e g r a d i n g > B "  1  the r o t a t i o n a l  that B  as  appearance the  bands  2.5).  The  the t e m p e r a t u r e of  > B ".  1  of  (section  v  o f t h e bands  o f t h e bands  are very  energies  Analysis  in the s l o p e  narrowness  have  X).  indicates  increases  in  transition.  o f t h e m o l e c u l e may be drawn f r o m t h e  the v i o l e t  decrease  (0-0)  .  absolute  and c a l c u l a t e d t r a n s i t i o n  of the p h o t o i o n i z a t i o n bands. to  - 1  resonances  a p p l i c a b l e , t o t h e one  Some q u a l i t a t i v e c o n c l u s i o n s constants  band  1 cm  o f T a b l e V and V I I I  a v a i l a b l e , t h a t of the  of observed  least  f e  t h e band s e p a r a t i o n s  energy  i s e x c e l 1ent  in t .-is at  of the observed  been added or s u b t r a c t e d , as reference  a c c u r a t e l y than the  Furthermore,  v  the  i n d i c a t e s t h a t the r o t a t i o n a l spaced is  (equations  only  Iodine  slightly  nucleii  2.8  energy  t o 2.12)  larger  and  than  i n the upper  the  B ". v  (resonant) 0  electronic  states  separation  i n the ground  tional  analysis The  is  is  thus  slightly  smaller  electronic state.  done by t h e F r a n k - C o n d o n  intensity S , v  v  „  of a v i b r a t i o n a l  the t r i p l e - p h o t o n i o n i z a t i o n spectrum of p o p u l a t i o n of  than  the i n i t i a l  level,  ^  2.666A,  Detailed  the  rota-  method. transition depends  the Frank-Condon  upon  factor  in the  - 86  between t h e v i b r a t i o n a l  -  states,  the l a s e r  power N, and t h e p h o t o i o n i z a t i o n an unknown number  f u n c t i o n of  and o f  intensity  efficiency P(v',v)  the u p p e r - v i b r a t i o n a l - s t a t e  the m o l e c u l e ' s  total  energy  prior  to a which  is  quantum  to  ionization.  We may w r i t e : 2  V,v" Since  K  =  <VlV>  the l a s e r  wavelength  power-dependence adopted ing  is  N is  saturation  conversion  of S , y  the c o n s t a n t parameters voltage  v  „  there  includes  influence  and t h e c u r r e n t  at  Iodine  the p o p u l a t i o n electronic this  state  temperature  were o b t a i n e d -430  vapor of  at  2  range. 100°C,  erature,  function of  the bands,  intensity  the e f f e c t of  Two s e t s  represent-  is  the  of  experimental  i n d i v i d u a l l y since  a t low e l e c t r o d e v o l t a g e s .  cell.  experimentNote  in the  (Table  at e l e c t r o d e voltages  t h e bands d i f f e r e d much more  Iodine  100°C.  intensity  in  electrode  levels  measurably  The  contained  were measured  20°C and  or  process.  such as  vibrational  increases  the  a minimum o f o p t i c a l  intensities  of  power-dependence  a m p l i f i c a t i o n w i t h i n the  V; t h e s e were a n a l y z e d  bands were v i s i b l e  is  temperatures  I  The  for a l l  intensity,  the higher of  varying  the assignment  to a b s o l u t e  The r e l a t i v e band ally  2.7  E  in the p h o t o i o n i z a t i o n  K which  which  11),  value  i n which  electrical  a slowly  not c r i t i c a l .  an a v e r a g e  conditions  P(V.V)  is  10 and  -G(v")hc/kT  7  V  intensity  (Figures  2  XI)  that ground over  measurements -300 most  V and of  At room  in magnitude  than  the tempat  v"  Vibrational Energy G(v")-G(0)  e  87 -  Relative Population -[G(v")-G(0)]/kT  Fraction of Total Sample  (cm" )  (%)  1  I. 0 1 2 3 4 5 6  0 213.34 425.45 636.32 845.95 1054.34 1261.47  VAPOR TEMPERATURE 20°C 1 0.351 0.124 0.0441 0.0158 0.00567 0.00205  64.9 22.8 8.05 2.86 1.03 0.37 0.13  Partition Function = 1.54  II. 0 1 2 3 4 5 6  0 213.34 425.45 636.32 845.95 1054.34 1261.47  VAPOR TEMPERATURE 100°C 1 0.439 0.194 0.0860 0.0384 0.0172 0.00773  56.2 24.7 10.9 4.83 2.16 0.97 0.43  Partition Function = 1.78  Table XI.  Relative Equilibrium Population of V i b r a t i o n a l States i n the Ground E l e c t r o n i c State of I . 0  higher  temperatures,  and  i n t e n s i t y measurements ferent  88  i t was  necessary  from s e v e r a l  electrode voltages.  strongest  -  photoionization  voltage  -200  V.  In  mediate e l e c t r o d e voltage -400  V,  putting  provided  the  data f o r  the remaining  bands were d e t e r m i n e d  is  band.  In  sufficed  accompanying  the s t r e n g t h  voltage  i n both  transition  cases,  is  of  had a s i m i l a r  upon  of  shape  saturation.  the l a s e r  vibrational  level  power and was  under  however,  t h e band vapor  removed  the  it  heads,  as  the  temperature  The dependence upon  When  vibrational  spectrum,  at a given  divided  transitions.  of the  the a m p l i t u d e of  "  values  inter-  the r e l a t i v e i n t e n s i t i e s  rotational  photoionization  i n the absence  initial  elec-  taken at the  bands o f f - s c a l e  the  data  a t t h e low  V and t h e maximum  of a v i b r a t i o n a l  t o measure  amplitudes  difof  from  t h e r e f o r e d e t e r m i n e d from the area  the  bands a l l and  is  at  bands.  unresolved,  transition  -240  c a l c u l a t i o n of  the v a r i o u s  a band  saturation  a d d i t i o n , scans  strong  The s t r e n g t h among  scans o b t a i n e d  the  The r e l a t i v e i n t e n s i t i e s  o b t a i n e d w i t h minimum e l e c t r i c a l trode  to combine  of the  the p o p u l a t i o n  to a r r i v e  at  band of  experimental  2  S , v  v  efficiency However,  c c  <l  i J  P(v',v)  'l'J j^ J  v  >  v  is  the e f f e c t s  t o be l a r g e initially  „  P(v',v).  not w e l l of  this  The  established  p a r a m e t e r were n o t  f o r the m a j o r i t y of the bands,  assumed c o n s t a n t .  photoionization for  The a b s o l u t e  the  molecules. expected  and P ( v ' , ) v  was  intensities  were  not  required  was  carried out,  utions  in the r o t a t i o n a l for  each  from a s i n g l e  litudes  89  set  analysis.  o f d a t a , by summing  progression  i n the chosen  set  and d i v i d i n g  by t h i s j resulted  value,  and I  Si v  sities  which are d i r e c t l y comparable  y  ii  ,v  „ = 1.  This  Rather,  so  all  that z  in experimental  •  .  factors,  <s2  K$> i I nP"  2  v"  v  1.  =  v  Table calculated  XIII  f o r which I * < ^ V '  The r e s u l t s  contains  in the harmonic  the  contrib-  band  amp-  S , „ = , v ' , v" band i n t e n -  1  w i t h the t h e o r e t i c a l  . Franck-Condon  normalization  2  , 14> V  =1  are presented  theoretical  and  V  in Table  Franck-Condon  approximation  according  XII.  factors  to  the  method o f s e c t i o n 2 . 7 , f o r t r a n s i t i o n s between t h e g r o u n d " -1 -1 (o> = 2 1 4 . 5 7 cm ) and t w o - p h o t o n r e s o n a n t (to = 241.4 cm ) e l e c t r o n i c s t a t e s o f Ir,. I t i s c l e a r from d i r e c t comparison 1  e  of  the Franck-Condon  factors  w i t h the experimental  band  in-  0  tensities  that  ] A r[  (ors)  lies  however,  t h a t the t r a n s i t i o n  rational  transitions  respect Condon  vary  t o one a n o t h e r . factors  provide  the e x p e r i m e n t a l  between 0.075 and 0 . 1 2 5 A .  strengths  r a p i d l y , as  of c e r t a i n of a f u n c t i o n of  Thus, the r a t i o s  The f o u r most  3,  of c e r t a i n  a much more s e n s i t i v e  data.  the  vib-  with  Franck-  comparison  sensitive  Note,  ratios  with are 0  presented Comparison imental  in Table of  XIV  these  intensity  f o r a narrow  range  theoretical ratios  ratios  yields  four  of  3 (0.096 -  w i t h t h e mean  values  of  0.104A).  exper-  .3 w h i c h a r e  in  0  close  agreement.  Thus, the  We may c o n c l u d e  internuclear  separation  that  | A r | = 0.0988A ± 2%.  i n the resonant  electronic  Band  Relative  (0-0) (1-0) (2-0) (3-0) (4-0) (5-0) (0-1 (1-1 (2-1 (3-1 (4-1 (5-1 (6-1  90 -  ) ) ) ) ) ) )  Intensity  Bands a t 20°C  Bands a t 100°C (-300 V)  Bands a t 100°C (-430 V)  Mean  0.17 0. 39 0.31 0.11 0.022 0.004  0.1 1 0.20 0.27 0. 23 0.15 0.048  0.13 0.25 0.28 0.21 0.10 0.027  0.14 0. 28 0.28 0.18 0.090 0.026  0.32 (0.22)  0.19 (0.12)  0. 24 (0.13)  0.25 (0.16)  (0.071) (0.024) (0.006)  (0.11)  (0.12) (0.080) (0.051 )  (0.093) (0.070) (0.029)  (0-2) (2-2) (3-2)  0.36  (0-3) (2-3)  0.42  1.23 (0.15)  (0-4) (1-4)  0. 26 (0.22)  1 .36  (1-5)  (0.27)  0.40 0.15  0. 30 (0.17)  0. 35 0.15 (0.17)  0.42 (0.24)  0.69 (0.19)  0.40 (0.098)  0.68 (0.16) (0.27)  B r a c k e t e d v a l u e s have u n c e r t a i n t y up t o a f a c t o r A l l o t h e r s a r e a s s i g n e d an u n c e r t a i n t y o f 30%.  Table XII.  Relative Bands o f  Intensities I„.  of the  o f 2.  Photoionization  -  Band  91  -  '  Franck-Condon Factors  6 = 0.075 I  6 =0.100 A  6 = 0.125 K  (0-0) (1-0) (2-0) (3-0) (4-0) (5-0)  0.299 0.338 0.213 0.097 0.036 0.012  0.117 0.236 0. 252 0.189 0.112 0.056  0.035 0.111 0. 180 0. 204 0. 178 0. 129  (0-1) (2-1) (3-1) (4-1) (5-1)  0. 383 0.012 0.090 0.197 0.166 0.092  0. 267 0.152 0.005 0.045 0.1 32 0.153  0.125 0.193 0. 109 0.01 3 0.011 0.070  (0-2) (2-2) (3-2)  0.222 0.138 0.000  0.287 0.114 0.110  0. 214 0.000 0.073  (0-3) (2-3)  0.076 0.006  0.194 0.103  0.236 0.087  (0-4) (1-4)  0.017 0. 170  0.092 0.201  0. 188 0.041  (1-5)  0.057  0.177  0.135  (1-D  Table XIII.  T h e o r e t i c a l Franck-Condon Factors f o r S e l e c t e d V i b r a t i o n a l T r a n s i t i o n s Between the Ground and Resonant E l e c t r o n i c States of L .  Theoretical  F ( 0 - 0) F ( 3 - 0) F ( 0 - 0) F ( l - 1) F ( l - 0) F ( l - 1) F ( 0 - 1)  Ratios  0  0  0  0  3=0.096 A  3=0.098 A  3=0.100 A  3=0.102 A  3=0.104 A  0.943  1.111  1.296  1.500  1. 724  1.154  1.279  1.437  1.611  1.803  2.013  1 .353  0.509  0.576  0.645  0.718  0.793  0. 561  0.450  0.509  0.571  0.635  0.702  0.636  O  F(l-l)  Franck-Condon-Factor  Mean Experimental Intensity Ratios  T a b l e XIV.  Comparison of the I Experimental I n t e n s i t y Ratios w i t h the Ratios of the T h e o r e t i c a l Franck-Condon F a c t o r s from 3 = 0.096 t o 0.104 A . 2  -  93  "  o  I  state  is  r  stant  is  B ' = 0.04029 ± 0 . 0 0 0 0 7 c m " , and A B / B "  A plot, of  = 2.567 ± 0 . 0 0 2 A .  g  The  upper-state  rotational = 0.079 ±  1  g  as  a function  of  t h e mean e x p e r i m e n t a l  total  molecular  energy,  band  intensities  con-  of  to the  the  3%.  ratios  corresponding  0  theoretical indicates constant  Franck-Condon  that  the  between  independently (3-0), for  (1-0)  1  Each o f these  and  and t h u s  (section which  tional  contours  energy,  have  observed  energy  in  the  plateau  I  is  2  Figure.  roughly  The  i n the  vicinity  downward  trend  by Myer  progressions  ratios  and  exhibit (0-0),  were t h e  between 8 0 , 3 6 0 region  not  uncertainties  The t r a n s i t i o n s  where  (1-1),  basis and  the  constant.  analysis  to the branch  of the f i v e  the  a slight  total  the  B contains  intensity  distribution  upper  formulae  of  electronic section  o f each  one may c a l c u l a t e  rotational  these  the  distribution  spectrum,  separate  of  contour  intensity  w i t h the l a s e r  Knowing  as  the  is  Analysis  4.4)  Appendix  is  absorption  the r o t a t i o n a l  and S.  Typical in  14),  of  resonance  whose i n t e n s i t y  lie  convolutes  branch  there  (Figure  P(v',v)  indicated  an a p p a r e n t  six  y i e l d of  Applying  2.8,  (0-1),  Band C o n t o u r  state  are  two f e a t u r e s .  |Ar|,  photoionization 4.5  has  molecular  determining  81,550 c m "  values  Thereafter,  1  Samson ( 1 9 7 0 ) .  yield 1  yield  increasing  3 = 0.099A  8 0 , 0 5 0 and 8 2 , 2 5 0 c m " .  of 80,000 c m " . with  at  photoionization  i n the e x p e r i m e n t a l photoionization  factors  branches  intermediate between  the  0,  P,  rotathe Q, R  calculations. branches,  \  - 3k- -  RATIO OF NORMALIZED INTENSITIES TO THEORETICAL FRANCK CONDON FACTORS AGAINST FINAL ENERGY  8  v •  ©  © y  =o  x  v'  = I  •  v  = 2  A  V  = 3  o  V  = 4  v  v  = 5  x •  cm-I  80 000  81000 3T/  82000  LASER  +  F i g u r e ]k.  G  83000  discussed  in d e t a i l  tributions plicable  -> 2  bands o f  one may t h e n sum t h e  to a resonant  +  are p o s s i b l e :  2.4).  The 0  +  -> 0  g contributions  The c o n t o u r s  contour  +  varies  o f t h e 0* and  l  band c o n t o u r s  occurring t h e Og  of  1.5  the r e s o n a n t are found  observed  in general  cm  - 1  ,  are  depicted  lies  of  very  t h e t h e o r e t i c a l band  a smooth  t h e peak  s t a t e of  rise  the e l e c t r o n i c certain  improbable.  The  numerous e x p e r i m e n t a l t o t h e peak  side.  It  is  2g t r a n s i t i o n may be r u l e d o u t s i n c e  band c o n t o u r  shows f e a t u r e s  of the peak,  contrary  of equal  to o b s e r v a t i o n .  is  side,  hesitation  probable  that  the t h e o r e t i c a l  prominence It  spectra  on t h e s t e e p  drop-off with a s l i g h t on t h i s  con-  However,  l^.  t o be h i g h l y  in our  by e x p o n e n t i a l near  states.  The peak  s i m i l a r to i n d i c a t e d e c i s i v e l y  of the t r a n s i t i o n s  to the r e l -  0  At a r e s o l u t i o n  of  15,  v .  3  followed  an i n t e r m e d i a t e c a s e  f o r each e l e c t r o n i c t r a n s i t i o n  t o t h e band o r i g i n  configuration  Figures  intermediate  u  electronic transition.  have  in  g  15 f o r t h i s  are too  +  according  in  t h e band c o n t o u r  three  possible  a t 20°C a r e p r e s e n t e d  plus  Figure  state,  +  The two e x t r e m e c a s e s  tours  ap-  -0„ -> 0 „ , 0„ -»- 1 , and g g g g of the p h o t o i o n i z a t i o n  K  transitions  16 and 17.  close  con-  t o . a r r i v e a t t h e band c o n t o u r  p r e d i c t e d f o r each of the t h r e e  electronic  ative  2.8,  absorption  transitions  (section  y  branches  two-photon  electronic y  in s e c t i o n  to a p a r t i c u l a r e l e c t r o n i c t r a n s i t i o n .  In  0  of a l l  95 -  on b o t h  also  sides  evident  - 96 -  - 98 -  that  contributions  equally  shared  to the 0  between 0  in a purely  Experimental  investigation  in  firmly  rules  -  -> 0  +  g  and l '  u  would r e s u l t  process  99  g  u  o u t t h e 0*  of the e f f e c t the l a s e r  observed  ability,  the d e s i g n a t i o n  1^.  measured  in the v i b r a t i o n a l  this  requires  exciting It  an e x a c t  on t h e  light  not  in  analysis  photoionization 1976)  Thus,  with high  prob-  t h e band p o s i t i o n s  f r o m t h e band peak  , no c o r r e c t i o n was a p p l i e d t o T knowledge  this  (Dal by e t a l . ,  Ir, h a s ,  Although  as  observed.  0* e l e c t r o n i c t r a n s i t i o n .  t h e new e l e c t r o n i c s t a t e  v  be  intermediate states,  Q-1 i k e b a n d , w h i c h i s  I ^ of p o l a r i z i n g  f r o m t h e band o r i g i n  t r a n s i t i o n may n o t  +  of the bandwidth of  were  rather g  as  the  energy. was  noted  in section  2.8  that at c o n s i d e r a b l e  dist-  ance f r o m t h e band o r i g i n , a l l band c o n f i g u r a t i o n s become - ( v / 1 0 2 ) ( B ,,/AB) Q - l i k e w i t h contour I(v^) ^ e a t 20 C, where is  expressed  estimated  i n wavenumbers.  f r o m t h e band s l o p e  Thus t h e r a t i o A B / B „  at large  ( 3 - 0 ) , ( 2 - 0 ) and ( 0 - 3 ) , l n [ I ( v )] was f r e q u e n c y v , each p l o t y i e l d i n g AB/B JO  method i s  well  w i t h t h e more p r e c i s e  4.6  gives  J.  For bands  (4-0),  plotted against laser „ = 0.07. Although V  this  which  may be  v  inherently approximate,  AB/B „  Impurity Several  v  the r e s u l t s  Franck-Condon  = 0.079 ± 3% ( s e c t i o n  rotational  compare analysis  4.4)  Lines peaks  occur  a p p a r e n t l y a r e n o t members  i n the p h o t o i o n i z a t i o n data of the resonance  spectrum of  which I  os  -  100  -  b e i n g n e i t h e r b a n d - l i k e i n shape to  nor of the c o r r e c t  f i t the v i b r a t i o n a l p r o g r e s s i o n s .  clearly  v i s i b l e , and p o s s i b l y  by t h e s t r o n g  Iodine  signal.  terms of e x c i t i n g energy  (in  Three  vacuum)  = 26,297.14 ± 1 c m  v  2  = 26,915.22 ± 1 c m "  1  v  3  = 27,343.96 ± 1 c m "  1  of the f e a t u r e s  exist  the  on t h e is  Iodine  v a p o r was c o o l e d .  (1-0)  band o f  l^* and i s  prominent  in very  high  has  - 1  ,  H a l f w i d t h 8.09  not been  Peak v  2  v e r y weak.  voltage scans,  low t o a l l o w a c c u r a t e measurement  :I  laser  v  of i t s  The s i g n a l a t v j 2 02 i n t e n s i t y t o t h e power l ' - 16:1  a t 20°C.  n  in  1  remained  is-superimposed Although  its  cm"  identified.  peak  intensity is  power  dependence.  The r e l a t i v e i n t e n s i t y o f t h e two p r o m i n e n t p e a k s I  masked  o f t h e peaks  The f e a t u r e s were d e v e l o p e d w i t h t e m p e r a t u r e , and after  are  are:  V!  The s o u r c e  s u c h peaks  a d d i t i o n a l peaks The p o s i t i o n s  energy  depends  is upon  the  v  3  too  5. 5.1  Results  and  Quantum possess states  1971).  electronic  state  the t e c h n i q u e s requirements  order  For has  yield  of  Iodine  at higher the f i r s t  energies,  by R y d b e r g  time, a single  spectroscopy.  conservation,  the n o n l i n e a r  high-energy in  Iodine  is  was  Since  insignificant  that of  triple-photon  is  vibrational state  reasonable bands o f  t o an  I  transitions  parity-forbidden, been o b s e r v e d  ?  2  both  dissociation comparison  the s p e c t r a l  range reaction  ionization: + 3v  •+  to a s s i g n  two-photon molecular  I  + 2  + e  transitions  s t a t e of  . resonances  from the  g symmetry.  Furthermore,  has the  not  to  ground  Since  t o such a s t a t e  intermediate state  in absorption.  -  the observed  from the ground s t a t e this  triple-  were  and Samson, 1970) , t h e p r e d o m i n a n t  I It  the in  the  third-  principle,  the p h o t o i o n i z a t i o n - y i e l d throughout (Myer  using  experimental  photoelectric signal In  states  From b o t h  and f r o m  intensity.  must  electronic  been s e l e c t i v e l y p o p u l a t e d  of m u l t i - p h o t o n  of m o l e c u l a r  photon  molecule  valence-shell  in the p h o t o e l e c t r i c s i g n a l .  investigated  X 0*  the  i o n i z a t i o n and t r i p l e - p h o t o n . d i s s o c i a t i o n  present  was  number  i n the a p p l i e d f i e l d  photon  with  large  of energy  confirmation,  DISCUSSION  shows t h a t  f o l l o w e d , mostly  (Mul.liken,  -  Conclusions  theory  a rather  101  singleare  previously  intermediate  state  has  no c o u n t e r p a r t  The v i b r a t i o n a l upper  analysis  102  -  in emission was  {T  + G(v  g  The r o t a t i o n a l a n a l y s i s Franck-Condon  was  (0.58  ± 0.06)(v'  complex,.as  the  the  I  molecule  2  separation  i n the resonant 0  g  B  = 0 . 0 4 0 2 9 ± 0.00007 c m " .  = 2.567 ± 0 . 0 0 2 A , whereupon  with  the observed  bands  at large  slope  J.  cm" . 1  2  were  of  The  unre-  results  the Q - l i k e  The s i z e  obsersize  internuclear established  the r o t a t i o n a l  These  1  e  + h)  bands  e l e c t r o n i c s t a t e was  at r  the  h)  +  to d e t e r m i n e the  i n the e x c i t e d s t a t e .  I  for  f a c t o r s were c a l c u l a t e d f r o m t h e  ved r e l a t i v e band i n t e n s i t i e s , and used of  literature.  )}:  = 53,562.75 ± 1 + (241.4 ± 0 . 4 ) ( v " -  solved.  i n the  s t r a i g h t - f o r w a r d and gave  v i b r a t i o n a l - s t a t e energies E(v')  spectra  are  contour of  constant  is  consistent the  Iodine  d i f f e r e n c e of the m o l e c u l e  in  the  0  upper  s t a t e compared t o i t s  indicates  t h a t the resonant  a Rydberg  state.  energy state  ground  electronic state  t o make t h e c a t e g o r y  e x t r e m e l y p r o b a b l e , as in  Ig,  (Venkateswarlu,  all  a large  at energies  and 0  +  g  absorption 2 . g  is has  0.1A  smaller)  most  probably  electronic  of a  Rydberg  number o f Rydberg above  51,500  cm"  states  1  1970).  Three e l e c t r o n i c t r a n s i t i o n s photon  (nearly  F u r t h e r m o r e , t h e new s t a t e  s u f f i c i e n t l y high  are observed  state  to a r e s o n a n t  Each t r a n s i t i o n  are p o s s i b l e  state:  has  0*  0*,  in  two-  0g -> l g ,  a c h a r a c t e r i s t i c band  contour.  The  103  -  t h e o r e t i c a l l y p r e d i c t e d band  resolution tronic  of  cm  configuration  comparison ition.  of  which  zero  of  state  rules  information  The e l e c t r o n i c  out only  was  with  gained  Thus i t  is  of  potential  Figure  18 as  a function  internuclear  to the  known v a l e n c e - s h e l l  Mulliken parity  potential  (1971)  are  states  energy  i n which  shown by f u l l  those  are  zeroth  order  experimental state  has  a minimum  which  and  The  approximations  data.  is  are  energy  of  in  curves those  accurately  l  g  .  in  relation The from  even  states  rather  of  new  state, shown  of  for  curve  cannot  Iodine.  except  The p o t e n t i a l  trans-  t h a t the  is  states  potential  The  l^.  state  reproduced  for  elec-  the d e s i g n a t i o n  of m o l e c u l a r  lines,  by d a s h e d l i n e s .  in  at a  polarization  separation  for  parity  X 0* and t h e B s t a t e s y  from  function,  diagram  the  t h e 0* -»- 2g  concluded  the curves  (u)  state  t h e new Rydberg  by a h a r m o n i c of  similar  decisively  high p r o b a b i l i t y ,  potential  very  electronic  approximated  valence-shell  are  resonant  the resonant  momentum. has,  indicate  the observed  show t h a t  angular  electronic  and do n o t  - 1  band c o n t o u r s  Additional  studies, have  1.5  contours  of  of of  (g) odd  Mulliken the  ground  known  t h e new  53 , 5 6 2 . 7 5 ± 1 cm "'' a t -  from  Rydberg inter-  0  nuclear  separation  2.567 ± 0 . 0 0 2 A .  The p h o t o i o n i z a t i o n has  a broad  (Figure  functional  14),  absorption  exhibited  efficiency  dependence  on t o t a l  independently  progressions.  P(v  ,v)  observed  molecular  be each  The p h o t o i o n i z a t i o n  of our  in  Iodine  energy six  efficiency  ex-  -  F i gure  18.  104  -  E l e c t r o n i c P o t e n t i a l Diagram I n c l u d i n g the A p p r o x i m a t e P o t e n t i a l o f t h e New S t a t e S u p e r i m p o s e d on t h e Known V a l e n c e - S h e l l S t a t e s o f I. 0  hibits  the s l i g h t  energy  observed  apparent  downward  by Myer and Samson ( 1 9 7 0 ) .  resonance,  resonant  which  is 1  Since  observed,  i n terms  of three photons,  only  these  The r e s o n a n c e unidentifiable molecular  in the c o n t e x t of Further  I  2  this  2  neither band-like  to f i t the v i b r a t i o n a l  purity  f e a t u r e was o b s e r v e d  t o o weak  field  with  h a l f - w i d t h 8.09  cm  sible  - 1  .  cm  is  required  t h a t a d d i t i o n a l peaks  of  to  in the  i n shape  w h i c h was  nor o f  photo-  temperspec-  the  correct  One p r o m i n e n t  second-order  in  The p o s i t i o n is  of  being  the  pro-  26,297.14 ± 1 c m  and 2 7 , 3 4 3 . 9 6 ± 1 e x i s t masked  im-  the  impurity features  The two w e a k e r f e a t u r e s - 1  quoted.  of the resonance  of e x c i t i n g energy  occur at 26.915.22 ± 1  , v)  was  absorption.  i n t e n s i t y , the remaining  i n terms  is  progressions.  f o r a c c u r a t e measurement.  m i n e n t peak  lower than  feature appearing  t o be members  energy  applied  respec-  - 1  f e a t u r e s were d e v e l o p e d w i t h  a t u r e w h i c h do n o t a p p e a r 1 , being  to e l e c t r o n i c  known e l e c t r o n i c s t a t e s  i n nonlinear  spectral  photon  of the resonance  investigation  in  energy.  o f one  or 80,000 c m  tail  occurs  molecular  i n t h e p h o t o i o n i z a t i o n y i e l d P(v  i o n i z a t i o n y i e l d of  trum of  - 1  may be c o n s i d e r a b l y  the nature of  Several  of t o t a l  corresponding  the h i g h - e n e r g y  values  Iodine.  understand  a d d i t i o n , an  heretofore unobserved,  i n the v i c i n i t y of 26,700 c m  tively.  In  molecular  s t a t e may o c c u r e i t h e r a t t h e l e v e l  or at the l e v e l energy  -  trend with increasing  the v i c i n i t y of 80,000 c m " This  105  cm" . 1  - 1  observed It  by t h e s t r o n g  is I  ?  possignal.  Identification ject  for  of  future  the source  research.  o c c u r at the l e v e l  of  may be i d e n t i f i e d v i a since  and s i n c e  (the  tables  Future  of the  If  the  Iodine arise is  the  probably tions  it  energy  is  is  unlikely  a subalso  that  or m o l e c u l a r wavelength  of e m i s s i o n  spectra  are  far  they,  tables,  in t r a d i t i o n a l  d i p o l e - d i p o l e • t r a n s i t i o n is  of s u b j e c t s  directly  for  i d e n t i f i c a t i o n of  arise  the  absorption  parity-forbidden), from c o m p l e t e .  with  functional  of the p h o t o i o n i z a t i o n which appears  among t h e e s t a b l i s h e d  research  species  dependence  work.  or  data  is  the  on t o t a l  has  most  formed i n  no  valence-shell  reac-  investig-  molecular  e f f i c i e n c y of m o l e c u l a r  i n our  Rydberg  molecular  l i n e s , which  Another  l^-  in  experimental  impurity  from complex m o l e c u l a r  the broad  the resonance  future  from the p r e s e n t  at high temperatures  a t i o n of  lines  i m p u r i t y resonances  two p h o t o n s , atomic  impurity  Research  A number  One  -  the t r a n s i t i o n would not e x i s t  apectroscopy  5.2  106  Iodine;  counterpart states  of  I2  o  The n o n l i n e a r offers  absorption  wide s c o p e In  techniques  spectroscopy information  will  of  to the  red of  view,  it  is  3800A  c l e a r t h a t the  laser-induced  nonlinear  y i e l d new and s i g n i f i c a n t  from a g r e a t  (Venkateswarlu,  Iodine  also  investigation.  a more g e n e r a l  resolution  forbidden  for  of  number  o f atoms  and  states.  absorption  spectroscopic molecules  1 9 7 6 ) , e s p e c i a l l y when a p p l i e d  and h i g h - e n e r g y  high-  The e f f e c t s  to  parity-  of  pertur-  -  bations,  Stark  vestigated accessible.  shifts,  107 -  level  crossings,  i n a t o m i c and m o l e c u l a r  e t c . may  states  be  heretofore  -  108 -  APPENDIX  A  CALIBRATION OF PHOTOMULTIPLIER In o r d e r multiplier,  to avoid  optical  one o r two s h e e t s  density  filter  portion  of the l a s e r  3500-4000A.  saturation  of d i f f u s i n g  of the photoglass  N.D.#3.0 were used t o a t t e n u a t e  with a densitometer 0  FILTERS  beam.  The m a t e r i a l s  s e t to give  The q u a n t i t y measured  neutral  the r e f l e c t e d  were  a continuous  plus  calibrated  scan  between  i s c a l l e d the d e n s i t y  K,  K whereby  the f i l t e r ' s  density  w h i c h may be m e a s u r e d  whi,ch has a d e n s i t y  attenuation  greater  c o u l d be c a l i b r a t e d o n l y reference  is  10 .  Since  t h e maximum  i s 2 . 0 , N.D. f i l t e r  than  four  by p l a c i n g  beam o f t h e d e n s i t o m e t e r .  i n the u l t r a v i o l e t ,  two e x t r a  filters  The two e x t r a  (N.D.#0.9 and N.D.#1.0)  had t o be c a l i b r a t e d a l s o  XV).  of the m a t e r i a l s  The t o t a l  density  one o r two p i e c e s 0  20A  intervals  of d i f f u s i n g  in Table XVI.  glass  #3.0,  i n the  filters (see Table  f o r the cases  were used i s g i v e n  i n which at  -  109 -  D e n s i t y o f ND # 3.0 With #0.9 and #1.0 i n Reference Beam of Densitometer (c)  D e n s i t y of Reference Filters  A 0  ND #0.9  (A)  ND  (a)  #1.0 (b)  1.566  (sum a , b , c )  4.543  3600  1.307  3620  1.287  1, 648  1.537  4.472  3640  1.270  1.625  1.512  4.407  3660  1.258  1.604  1.497  4. 359  3680  1.245  1. 589  1.480  4.314  3700  1. 232  1. 573  1.468  4.273  3720  1.223  1.560  1.459  4.242  3740  1.213  1.546  1.450  4.209  3760  1.204  1.532  1.446  4. 182  3780  1.194  1. 520  1.411  4. 155  3800  1.185  1.511  1.436  4.132  3820  1.174  1.499  1.429  4.102  +  1.670  Density of ND #3.0  +  f  t  Uncerta i nty in  each measurement  i s ± 0. 002  tt  Uncertai nty in  total  ± 0. 006.  Table  XV.  density  D e n s i t y o f ND F i l t e r Wavelength.  is  #3.0  •  as a F u n c t i o n  of  + +  -  A 0  (A)  Density of Diffusing Glass  110 -  D e n s i t y of ND Filter #3.0  Total Density Including One S h e e t Di f f u s e r  Two S h e e t s Di f f u s e r  6.017*  7.491  4.472  5.946  7 .420  1 .474  4.407  5.881  7.355  3660  1 .474  4. 359  5.833  7 .307  3680  1 .471  4.314  5.785  7.256  3700  1 .469  4.273  5.742  7.211  3720  1 .469  4.242  5.711  7.180  3740  1 .469  4.209  5.678  7.147  3760  1 .470  4. 182  5. 652  7 .122  3780  1 .471  4.155  5. 626  7.097  3800  1 .471  4. 132  5.603  7.074  3820  1 .471  4.102  5. 573  7.044  3600  1 .474  3620  1 .474  3640  f  +  4.543  + t  Uncertainty  i n each measurement i s  Uncertainty  is  **  ± 0.001.  ± 0.006.  * U n c e r t a i nty i s ± 0.007. *  Table  XVI.  Uncertainty  is  ± 0.008  T o t a l D e n s i t y , as a F u n c t i o n o f W a v e l e n g t h , o f M a t e r i a l s S h i e l d i n g P h o t o m u l t i p l i e r EMI 6256S.  - Ill APPENDIX  B  DETAILS OF BRANCH CONTOUR CALCULATIONS The r o t a t i o n a l calculation tional I(v  of the contours  branches  )of a single  intensity  analysis  expected branch  2.8.  i n two-photon  £  B ''= 0 . 0 3 7 3 5 e  cm"  1  B '=  cm"  1  where  0.04029  Bandwidth  = 1.5 c m "  1  c o m p l e t e l y by: e  (-0.75,0.75]  in  wavenumbers.  1  The c o n t o u r s  described  1  -(0.124)v = ( 5 4 6 2 ) ( 1 - 0.911 e ),  the l a s e r  as  = 204 c m " a t 20°C  o f t h e Q-BRANCH i s d e s c r i b e d  = (1018)  The c o n t o u r  involved are: 1  Laser The c o n t o u r  spectrum,  AB = 0 . 0 0 2 9 5 1 c m "  e  Q  absorption.  was d e t e r m i n e d by c o n v o l u t i n g t h e  The p a r a m e t e r s  kT/hc  4.4 a l l o w s  o f t h e 0 , P, Q, R and S r o t a -  d i s t r i b u t i o n with the l a s e r  in s e c t i o n  I (v )  of section  -(0.124)v. e '* , frequency  e  [0.75,-)  i s expressed  o f t h e 0 , P, R and S b r a n c h e s  were  determined  from: I ( v ) = 5462 (e £  with  the l i m i t s  ±0.75 intensity  - J ± ( J i + D/5462 • . " -• ' >•' J  of i n t e g r a t i o n ,  c m " from e q u a t i o n s 1  distribution  e  and J  2  - J ( J + 1 )/5462 ) 2  , c a l c u l a t e d at  2.14 to 2 . 1 7 .  i s an e s s e n t i a l l y  2  Since the  continuous  function  -  of r o t a t i o n a l integral  -  quantum number J i n t h e s p e c t r u m o f l^, n o n -  values  The r e s u l t s  112  o f J are c a r r i e d through  the c a l c u l a t i o n .  f o r each b r a n c h a r e :  0-BRANCH The O - B r a n c h  forms  a head a t v,  cm  1 . 0 6 0  The  two components o f t h e b r a n c h a r e d e s c r i b e d b y : (a) J  2 7 . 3 1  2  Ji  J  / 1 2 2 6 . 8  +  6 7 7 . 7  v  2 7 . 3 1  2 7 . 3 1  (b)  +  2  ( - 1 . 8 1 , - )  e  ( - 1 . 8 1 , - 0 . 3 1 ]  Z£ +  / 2 1 0 . 2  = 2 7 . 3 1 - /1226.8 =  0  e  +  6 7 7 . 7  v,  + 677.7  0 . 5 0  £  £  v„  £  ( - 1 . 8 1 , - 0 . 7 5 ]  v  £  [ - 0 . 7 5 , 0 . 7 5 )  E  ( - 1 . 8 1 , - 0 . 3 1 ]  E  [ - 0 . 3 1 , 0 . 7 5 )  V  £  Jx = 2 7 . 3 1 = 27.31 -  /210.2 + 6 7 7 . 7 v ,  ( - 0 . 3 1 , o o )  P-BRANCH The P - B r a n c h  also  forms  a head, a t v  • 0 . 2 7 5  cm  The two components o f t h e b r a n c h a r e d e s c r i b e d b y : (a) J  1 3 . 6 5  2  +  / 6 9 4 . 6  +  v  6 7 7 . 7  £  1 3 . 6 5  (b)  J  2  E  ( - 1 . 0 2 5 , ° ° )  £  ( - 1 . 0 2 5 , 0 . 4 7 5 ]  =  1 3 . 6 5  +  / - 3 2 2 . 0  +  6 7 7 . 7  v  £  E  [ 0 . 4 7 5 , - )  =  1 3 . 6 5  -  / 6 9 4 . 6  +  6 7 7 . 7  v  £  £  ( - 1 . 0 2 5 , 0 . 7 5 ]  e  [ - 0 . 7 5 , 0 . 7 5 )  0  v  1 3 . 6 5  =  1 3 . 6 5  -  / - 3 2 2 . 0  +  6 7 7 . 7  v.  £ (-1.025,0.475] e  [ 0 . 4 7 5 , 0 . 7 5 )  -  113  -  R-BRANCH No head G  2  Ji  = -13.65 =  is  formed.  +  Z667.3  + 677.7  v  £  0 13.65  + Z-349.3 + 677.7  v  £  ,  v  e  (-0.71,oo)  ,  v  e  (-0.71,0.79]  ,  v  £  e  [0.79,-)  ,  v.  e  (-0.63,-)  ,  v  £  e  (-0.63,0.87]  ,  v  £  e  [0.87,-)  £  z  S-BRANCH No head i s 0  2  Ji  = -27.31  formed.  + /1172.2  + 677.7  v  = .0 = -27.31  +  /155.6  + 677.7  v  £  -  114  -  REFERENCES Bakos,  J.  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