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UBC Theses and Dissertations

Study of the field induced spectrum of hydrogen at high resolution Buijs, Hendricus Leonardus 1969

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A  STUDY ' OF  OF  THE  FIELD  HYDROGEN  AT  INDUCED  HIGH  SPECTRUM  RESOLUTION  by HEMDRICUS  A  LEONARDOS  BUIJS  B.A.Sco,  University  of Toronto,  1963  H.Sc,  University  of Toronto,  1966  THESIS  SUBMITTED  IN PARTIAL  •THE R E Q U I R E M E N T S DOCTOR in  FOR  OF  THE  F U L F I L M E N T OF DEGREE  OF  PHILOSOPHY  t h e Department of . ' PHYSICS  We  accept  required  THE  this  thesis  as c o n f o r m i n g  to the  standard.  UNIVERSITY  OF  BRITISH  December,  1969  COLUMBIA  In  presenting  this  an a d v a n c e d d e g r e e the I  Library  further  for  agree  in  at  University  the  make  tha  it  partial  freely  permission  this  written  representatives. thesis  for  It  financial  for  gain  of  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, C a n a d a  of  of  Columbia,  British for  extensive by  the  Columbia  shall  not  the  requirements  reference copying of  Head o f  is understood that  permission.  Department  fulfilment  available  s c h o l a r l y p u r p o s e s may be g r a n t e d  by h i s of  shall  thesis  I  agree  and this  be a l l o w e d  that  study. thesis  my D e p a r t m e n t  copying or  for  or  publication  w i t h o u t my  . • . ABSTRACT . The  static  hydrogen  has  reliable  frequency  1.5 to  amagat zero  the  The  to  amagat!.  f i t the  a  data  the  the  minimum  width  line  "collision the  of  width  at  The the  we  ) _Q 1  =  1.21  the over  2.5  classical  .  the  the  density  have  been  molecular have  simple the  amagat  range  from  constants  i s  doppler the  infrared.  for  compared profile  range  studied.  density until i t below  width  isotropic  with  extrapolated  been  density  of  and  dispersion  with  with  spectrum  resolution  the  profiles  i s consistent  obtain cm  obtain  minimum  in  high  over  decreases  about  3  ( <X  best  narrowing"  lines  to Line  however,  at  absorption  Frequencies  f u n c t i o n s and  increase again.  than  of  calibration  molecule.  linewidth,  reaches  of  28  induced  investigated  density i n order  various  seems  to  to  isolated  with  been  field  which  about line.  4  i t times  This  phenomena From  the  starts less  behaviour of  *  intensities  polarizability  ii  TABLE Abstract  '  Table  of  Contents  Table  of  Figures  List  of  CF  CONTENTS  .  x i i i i i  Tables  v  Acknowledgement  .  vi  Introduction Chapter  1  1  Experimental 1„1  The  absorption  1 2  The  interferometer  1.3  Detectors  1.4  Source  1„5  Data  collection  1.6  Data  analysis  1.7  Reliability  0  Chapter  2  Chapter  Chapter  Bibliography Appendix.  and  and  2.1  General  2.2  Frequencies  2.3  Line  3  cell  5 9  signal  frequency  conditioners  13  synthetizer  18 22  .  of  Experimental  3  4  procedure  .  2  frequencies  37  Results  remarks of  on the  45  the  quality  of  spectra  transitions  profiles  Discussion  of  Results  3.2  Zero density frequencies molecular constants  3.3  Absorption coefficients matrix elements  3.5  Line  69  shifts  profiles  Conclusions  50  69  Remarks  Frequency  45  57  3.1  3.4  6  v.s.  and  and  the  69  polarizability  density  75 81 8 3 94 96  iii  LIST  OF  FIGURES  FIGURE  1  Block diagram  of e x p e r i m e n t a l arrangement,  4  - 2a,b,c A b s o r p t i o n c e l l s ' .  6&7  3  Schematic diagram ferometer.  of o p t i c a l path through  4  S c a l e drawing ferometer.  5  Schematic  6  Infrared polarizer.  7  Schematic  8  Spectrum s e l e c t e d with frequency  9  Block diagram  of mechanical  arrangement of  interinter-  of d e t e c t o r e l e c t r o n i c s .  of f r e q u e n c y  10 11 15 20  synthetizer.  21  synthetizer.  23  of d a t a a n a l y s i s p r o c e d u r e .  28  10  Spectral d i s t r i b u t i o n s a r i s i n g during various s t e p s o f the a n a l y s i s .  30  11  Spectral d i s t r i b u t i o n before f o u r i e r ation.  34  12  Typical absorption features.  48  Log r a t i o p l o t s of a b s o r p t i o n f e a t u r e s shown i n F i g . 12.  49  14  Seguence of p r o f i l e s f o r Q^Cl) t r a n s i t i o n at different densities.  51  15  -Sequence of 4 p r o f i l e s f o r Q-^(l) t r a n s i t i o n at same d e n s i t y and d i f f e r e n t f i e l d s t r e n g t h .  56  16  Graph showing f r e q u e n c y d e n s i t y f o r 0-^(0) l i n e .  shift  and  l i n e width  v.s.  58  17  Graph showing f r e q u e n c y s h i f t density f o r 0^(1).  and  l i n e width  v.s.  18  Graph showing f r e q u e n c y d e n s i t y f d r Q-^2 ) .  shift  and  l i n e width  v.s.  19  Graph showing f r e q u e n c y d e n s i t y f o r Q-,(3)  shift  and  l i n e width' v . s .  • 13  transform-  59 60 61  iv  FIGURE 20  Graph showing f r e q u e n c y s h i f t v . s . d e n s i t y f o r the 5-^(0) and 3-^(1) l i n e s .  g2  21  Comparison o f observed p r o f i l e w i t h broadened L o r e n t z p r o f i l e and Gaussian p r o f i l e .  65  22  Graph showing l i n e a r frequency s h i f t c o e f f i c i e n t v . s . r e l a t i v e p o p u l a t i o n o f i n i t i a l states'. 84  .V  LIST  OF  TABLES  TABLE  I  List  TABLE  II  L i s t of frequencies of the at the various d e n s i t i e s .  TABLE I I I  TABLE  TABLE  TABLE  TABLE  IV  V  VI  VII  of values  f o r sample  interval lines  h  studied 55  L i s t of observed l i n e w i d t h and c a l c u l a t e d w i d t h and h e i g h t o f L o r e n t z p r o f i l e s that f i t the observed data. Also a l i s t of normalized integrated absorption coe f f i c i e n t s ; a l lrelated to density. Frequencies of the transitions polated to zero density.  Y  parameters  Comparison of pressure of line frequencies.  66  extra71  Comparison of zero density frequencies c a l c u l a t e d with newly e v a l u a t e d molecular constants a n d some p u b l i s h e d observations. L i s t of computed molecule.  53  73  f o r hydrogen 75  shifting  coefficients 83  vi  ACKNOWLEDGEMENT It i s a pleasure supervisor,  t o express my g r a t i t u d e t o my  Dr. H.P. Gush, f o r always g i v i n g t h e a d v i c e  needed i n p a r t i c u l a r d u r i n g  difficult  moments.  I a l s o l i k e t o extend my g r a t i t u d e t o t h e s t a f f of t h e computation c e n t e r standing during  f o r t h e i r patience  and under-  d e s p i t e the heavy demands p u t on t h e i r  data a n a l y s i s . •  duties  INTRODUCTION  The  spectrum  o f the hydrogen  extensively  investigated  red  as w e l l  regions  it  was  deemed  of  hydrogen  measure  Indeed  higher  this  obtaining the  highly  studied  symmetry  hydrogen  zero.  The molecule  infrared  spectrum.  absorption  frequency  tion  band  induced  spectrum  features  therefore  path.  however, An  arises  i n colliding  and i s n o t s u i t a b l e frequencies,  the  of intermolecular  study  pairs  i s characterized  molecular  and h a s been  because  "normal" quadrupole  dipole  of molecules; broad  i t i s o f much  forces.  using  i n the fundamental  this  absorp-  spectral  f o r the determination  although  electric  equal  observed  of electric  by v e r y  of  states  due t o  molecule,  time.  of the  a  to  l i n e s has  a centre  not display  absorption  with  i n addition  elements  spectrum  to  possible.  of spectral  possesses  does  lines  f o r the f i r s t  the matrix  An i n f r a r e d  also  before  different vibrational  i s allowed,  absorption  region  spectrum  i tpossible  f o r the hydrogen  narrowing  molecule  made  fruit:  frequencies  and consequently between  was  has borne  of collision  moment  moments  of spectral  precise  dipole  long  and shapes than  of this  the infrared  have  precision  infra-  In spite  techniques  i n the infrared  The  a  new  has been  and t h e  effect.  to reinvestigate  investigation  phenomenon  been  a s b y t h e Raman  the frequencies  considerably  i n the ultraviolet  worthwhile  because  molecule  of  importance i n  ~  The infrared field  dipole  which  predicted by  by  Condon and  MacDonald  Foltz  et  stronger the  Dagg  in at  this  can  less  in  an  tion  to  zero  quencies  gas  cell  be  carried  measurements  at  this  existence  collision  of The  ence. of  been  with  narrowing  was  permitted  of  one  approximately  determined  to  within  an  been  much than  atmosphere  and  an  /extrapola-  absorption It  or  fre-  was  because  that  the  revealed. were  to  0,006 better  carried  maximum be  cm  made ^',  than  and  is  absorption  possible,  meter  measurements  has  is  confidence. were  and  strengths  one  size,  Crawford  which  that  observed  density  interferometer  This  the  s p e c t r a l measurements  r e s o l u t i o n of  have  out  modest  first  (1959)  field  of  electric  was  by  absorption  means  an  experimentally  Church  pressures  of  low  the  static  recently  electric  of  a  exhibit  effect  phenomenon  This  at  to  in  This  (1959),  because  density  placed  more  this  absorption.  made  demonstrated  and  realizable  absorption  a. t w o - b e a m  is  be,measured  may  and  Terhune It  be  molecule.  (1953)  work  easily  quadrupole  spectrum  the  (1958),  can  i f i t i s  (1932)  a l _ (19.66) o  exploited,  molecule  spectrum  polarizes  Crawford  and  hydrogen  2  out  path with line  0,0,02  using differ-  a  limit centres  cra"\  3  1.  A mental  schematic  procedure  incandescent optical  passes  of  the  on  ferometer. the as  exit the  changed  and  ferogram.  the  path  gives The  incident  the  the  Fourier  difference by  light  and  this  the  ratio  of  switched  *  to  of  a  Fourier  off,  is  He-Ne The is  of with  laser  then  and  enters  a  two  one  one with  is  the  this  the  by  field  call to  of  inter-  is  recorded  i t switched  is interauto-  radiation  proportional optical  fringes  passes  with  the  through on  on,  yields  the  magnetic  360/67  static  path  produced  computer  numerically. the  on  varies  the  the  The  I.B.M.  is  intensity  also  evaluated  obtained  beam  i t i s hence  an  field  interferometer we  special  the  intensity  spectrum.*  which  a  radiation  static  interference  read  This  a  and  an  r a d i a t i o n In  proportional  interferogram  transform  spectra,  the  from  where  electric  experi-  p o l a r i z e r and  s i g n a l which  the  Transform  record  two  a  Light  measures  difference in  interferometer,  interferometer. tape;  detector  overall  lines.  interferometer;  i s monitored  from  a of  cell  i t then  the  1.  through  interferogram  function  to  Figure  absorption  and  rise  correlation on  showing  absorption  infrared  optical  Procedure  s e l e c t s bands  gas>  of  in  passed  hydrogen  the  side  is  the  An  drawing  shown  which  through  impressed  is  lamp  filter  vicinity  Experimental  The field  the  absorp-  A c o n s i d e r a b l e l i t e r a t u r e e x i s t s on t h e s u b j e c t . See for e x a m p l e a l e n g t h y r e v i e w p a p e r by V a n a s s e and S a k a i (1967).  FIGURE Block  diagram  of  i  experimental  arrangement.  A  _  J~  a 6.  UJ  a;  JJ.  Q-  UJ  r  I-  o CJjtfJi  1  a.'  ul m w.  <  Z o  Ul CO  a3  vj _} Iti X  DO  wo <C 3 Q  21  li)  UJ  ft. r 1j-  _1 r> o  >< al A-  it  A  _1 <: ) -  w 0-  j-  o  z  P-  I-  o o  vxr  O 1-  V? u) JUJ  -J _i  X ^:  U-l  O 00  <:  A o2 0  r-  <* O  o vD  N r  t-t  v. hi N < . —J  £  X  -  tion is  coefficient  a detailed  apparatus,  1.1  The  was  parallel  long  cells  range from  plate  from 30  where  were  generated  which  two  of the investigation  by  applying  electrodes  cell  4.5  to  kv./crn.  separated was  30  of by  found  a high the  a t an  cell  3 mm  that  guide  the use  without  sparking  the be  contaminated gas  amount the  i s reduced,  applied of  square  i n the event  the electrode  without  absorption  fixed-length The  decreases second  that  sparking  field  rapidly  cell  was  a As  allowable  strength  guide"  are formed  type  by  the  electrodes  electric spark  voltage  towards of  lower the  previousof  that  can  Because  to the density  the usefulness  also  had  fields  the pressure  i s reduced.  i s proportional  of the applied  high  surface.  t h e maximum causing  cm  pressure  field  of copper  the application of relatively  ly  the  100  (see F i g .2a).  allowed  even  was  i s of the " l i g h t  the l i g h t  two  path.  path  applied  electric  across  light  over  different  the  voltage  absorption  atm.  The  of the walls  It  of the  three  case  the absorption  adequate  atm.  In each  bordering  provided  electrodes,  parts  follows  analysis.  employed.  the f i r s t  t o 80  the various  I n what  cell  the course  In  are interested.  the numerical  absorption  absorption  we  description of  and  In  field  i n which  5  and  of a c e l l  the to of  pressure.  light  guide  type,  FIGURE  2a,b,c  Absorption  cells.  - 6 -  .CELL  E>  "<£>" '» PYREX TUBE 3  3  I  2  i f  •  j  4 4  C.»3,  END VIEW SHOWIMq LOCATIOM O F IMAGES OF SOURCE OKI M I 5  CELL  C  -  but  the electrodes  tube  so that  higher (see  field  Fig.  In  order  was  increased  to  10 mm  cone the  not take  strength  could  be m a i n t a i n e d  times  walls  3 x 3  absorption  1.7  t o 4.5  third  cell  either  end o f an a b s o r p t i o n  mirrors gence high  many  supplies, fixed (see  curvature light the  times  angle  of light.  This  cell.  section cell,  of the  light  maintaining cell  the pressure  using  o f 50 c m .  interferometer,  cell  provided  range  "multipass" mirrors,  as shown  from  In order  With  such  o f the. c e l l  t h e images  at  2c, the between t h e  due t o t h e d i v e r -  to retain  high  voltage  2.5 cm  i n size  small  arranged  i n Fig.  of the mirrors. 5.0 cm  o r "-White"  the space  of light  existing  2.5 cm x  ability  a  were, p l a c e d  height  2c) were  was  loss  beam.  the electrodes  gathering  the cross  i n the f i r s t  to traverse  without  strength  t h e maximum Fig.  thus  reflections o f f  while  spherical  c a n b e made  of the incident field  pressures  of the f i r s t  be reduced  used  By means o f t h r e e  light  long  a  atm.  c e l l .  incident  path  the solid  over  glass  a t lower  4 0 0 cm  vessel,  of a  and hence  d u e t o many  way  flux  spectra  place  a s i t was  could  incident  adequate atm.  mm,  In this  the c e l l  same t o t a l  losses  of the pressure  diameter.  entering  were  the absorption  light  from  The  P  The e l e c t r o d e s  t o reduce  glass  on t h e o u t s i d e  could  four  the  mounted  -  sparking  2b).  providing  were  8  a  power  apart  Mirrors with  mirrors, compatible  reasonably  and 2  this  and 3  a radius  of  t o make t h e with  of the source•formed  that at  of  mirror  1  should In  Roman of  of  and  3  and  forth  mirror  transfer  transfers,  mirror Fig.  of  44  The  of  of  and  gold  and  1. a l w a y s  coated  of  1  until  shown with  2 back  finally,  after  by  the  off  section  the  the  (source)  spills  in  curvature  Mirrors  i s determined image  with  images  versa.  aperture  mirror  as  labelled  centers  vice  attained  optical  A-A  multipass  of cell  mirrors.  in  arrangement  the  literature  of  the  optical  path  and  arrangement  have  been  parallel  the  I I I , the  aperture path  of  which  the  separated  severe  exit  using  respectively.  makes  II  markings  entrance  surface number  3  for  mechanical  prisms  the  diameter.  Mirror  but  "'diagram  being  mirror of  maximum  described  1967),  in  position  -  Interferometer The  been  the  mm  locations  on  the  the  meters,  The  2  5  9  mirrors.  centres  1 into  2c.  1.2  the  images  across  positions  was  are  least the  corresponding  surface  many  at  F i g . 2c  numerals  the  be  _  The  beams to  four have  sake  optical  i s changed  the  light  times  the  no  possible  of  requirements  path by  a  scale  increase in  3  two path  displacements  of  the of  the  slide  two  difference  interference,  precision  4  prisms  rotations  prisms  and  the  of  the  Gush,  the  between  the  Small  of  in Figs.  difference  has  schematic  drawing  repeated  and  state  on  the  the  displacing  the  interferometer  previously (Buijs  displacement. on  this  completeness  path,  effect large  of  of  the  which  without ways.  FIGURE Schematic  diagram  of  optical  3  path  through  Interferometer  FIGURE Scale  drawing  of  mechanical  4  arrangement  of  Interferometer  -  The  instrument  optical beams are  path  was  are aveiilable  50  cm  focal  at  their  these  the  focal  focal  fringe  with  length  used  interferometer  fringes mode  produced  He-Ne  pulses  which  infrared  gram. study  t h e A-D  path  difference  i s small, from  illuminate  the zero  white  placed  o f f axis.  The  carriage around  of the  difference,i n  mono-chromatic single  to a train t o measure  of the  location of the infrared  interfero-  o f t h e bands  path  difference  signal  i s driven  pulleys  by  of this path  a spring  at either  an  fringes  difference i s varied  of radiation  necessary  auxilliary v/ith  detector  continuously. wire  During  which  end o f t h e d i s p l a c e m e n t  light  detector  defines  The  to  white  a third  difference.  steel  under  location i s not  I t i s thus  with  light  the l o c a t i o n o f zero  path  used  i n  accurately  the interferometer  and d e t e c t  the  are placed  t o know  the interferogram.  source  imately  formed  stabilized  i s essential i n the analysis  I f the s p e c t r a l width  obvious  be  portion  are converted  converter  of  interferogram. It  zero  of a highly  The f r i n g e s  command  of  input  mirror  The path  b y means  output  channels  and  diaphragms that  of  Two  f r i n g e s may  to isolate  the light  era.  paraboloid  Appropriate  i s monitored  a range  a n d tv/o i n p u t  f o r observation.  by  laser.  t o +103  localized  i n order  over  of the output  an o f f a x i s  planes.  pattern  cm  Each  so t h a t  planes  -4  f o r detection,  available f o r sources. i s provided  -  to operate  d i f f e r e n c e from  beams  the  designed  12  approxa  scan  prism i s  guided  path.  One  -  of a  the  pulleys  i s  driven  by  set  of  reduction  gears.  found  to  fluctuate  by  various  °3  links  from  Detectors The  tion meter zero  are  background  the  for  detector, tried  the  and  a  as  former  performs  detector current  gave  of  1.5  but  1.5  swings  weak  radiation  for  analysis  cell.  Two  linear  by  mm  2  source,  circuits  in  Industries  the  B3  for  detector  dry  ice  top  at  and  only The Inc. was  of  z.p.d.  the  near a It  i s  information  linearly  Figs.  performed  detectors,  on  electrical in  radia-  intensity  into  an  form.  non-linearity  voltage  Infrared  , and  the  interfero-  numerical  v/hereas  performance.  type  of  the  the  from  converted  of  is  and in  away  source  constant  cooled  was  in  from  fringes  expressed  detector  Both  operation x  very  likely  at  backlash  cell  operated  adequately  ature  large  finally  voltage  through  carriage  obtained  the a  motor  carriage.  shown  as  the  to  pre-amplifiers,  source.  manufactured  the  fringes  by  of  of  due  absorption  sulphide  operates  detectors,  to  i n t e n s i t y be  most  lead  15%  successful  signal, The  In  the  speed  d.c.  conditioners  and  flux  radiation  electrical  were  the  difference,  imperative that  through  characterized  path  large  signal  interference  passing  -  motor  -  regulated  The  about  the  and  a  13  was  the  circuits  5(a)  and  constant  (b).  current  in  the  i s  essentially a  well  latter  for  circuit detectors For  room  chosen  operation  the  uncooled 5  (b) were temper-  with  an  area  the' t y p e  TI  was  -  used,  of area In  0„5  x  0„5  mm' .  the c i r c u i t  shown  i n Fig,  tional  amplifier  i s a high  a  low i n p u t  current  noise,  sources  of noise  very  noise  e  signal  Input  .  These  for circuit  voltage  sufficiently trolled  detector beyond  by  b y means  current  supply  i  , and  contribute  , out  ( i ) = i n n  R , . det.  c a n be  c o n t r o l l e d by  but input  current  In order  high  the bias  noise,  of the amplifier.  i n Fig,  of  the operational, a m p l i f i e r ,  to  (e  voltage  of the detector  For this side  R , , /AR.  reason  of the  In. c i r c u i t  i t was  output  found  through  This  the  was  diode  noise  -the o u t p u t  50000),  virtue  Any  at  side  by  5,  and  signal  and o n l y  appear  (A i s t h e o p e n  the s i g n a l i s taken  at the  loop from  to  accom-  of the feedback,,  ) will  con-  the noise  of a zener  diode  volta.ge  output  of the detector  the zener  equal  to the  cannot.be  current  by  portion  will,  noise  voltage  of the insertion shown  voltage  choosing  to limit  generated  a. r e l a t i v e l y  as  having  follows:  e  swing  opera-  type  low i n p u t  R, , /R. det, i n  extending  plished  q u a l i t y F. L'.T.-input  (e ) = e n n  to detector  the output  the input  , out  manner.  to pass  5,  e  large,  predominantly necessary  (a) as  noise  i n this  -  14  gain the  created appear a high = high  detector.  (b) t h e s o u r c e s  of noise  contribute  to  • Schematic  FIGURE of  5  detector  electronics  4- : 1  rA.D. CONVERTER, :4. DIGITS k SIGM W\TH SA.MPLE./HOLP  T R I A G E R.  AMPLI F l £ R  PULSE SHAVER, $ SELECTOR,  -AW-  X  I  ."OUT  - ' 16  the  output  Again of  signal  the ratio  voltage  across at  noise  For is  well  lead  known  sulphide  reason  three  and were X =  f  . out  (e ) = e n n  R^/R, . f det.  e  , out  ( i ) = i n n  R,_ f  i s made  R d  e  t  without  greater  effect  r e q u i r i n g an e x c e s s i v e  voltage  flux  of incident radiation i t  the area  i s obtained  germanium  imaged  condenser  factor coated  radiation  was  also  fringe  a speed  served  this  of the  elements  transmission  at  automatically  of wavelengths  less  by  of f / l . o  The condenser  f o r optimum  For  a  on t h e d e t e c t o r  having  o f 6.  from  i s a minimum.  defining the central  The condenser  to reject  allow  the  voltage  interference pattern  2.4 p.m„  time  detectivity  when  aperture  anti-reflection  to reduce  a high  total  detector  element  (a)  amplifier.  t h e same that  of circuit  .  small  a n d a t t h e same  a demagnification  f i l t e r 2  /  R  to that  e  of the  the exit  infrared a  i n a manner s i m i l a r  the detector  the output  -  than  as a about  p.. It  chopper  i s customary  to interrupt  when  the light  signal  alternating  signal  demodulated  to yield  a voltage  Intensity.  This  not necessary  because  from  using  was  the c e l l  the interference fringe  a PbS c e l l  t o employ  periodically;  i s then  synchronously  proportional i n these  frequency  the  to the  light  experiments  during  scanning  a  -  was  typically  where  about  35 s e c  PbS d e t e c t o r s  perform  thus  used  which  was  frequency  c u t o f f i n the range  frequency  half  shifts  were  shifts  i n the interferogram  the  kept  after  point  scanning  factor  the detector  full  signal  the  two l i g h t  the  room  than  to" n o i s e  a  z.p.d. time  high 5).  Phase  phase  by f l u c t u a t i o n s i n  path  increment  guide noise  of the cooled  of the spectrum.  used  cells, was  cells  determining  1/5000  about  and hence  was u s e d  detector  of the  i n conjunction noise  times  t h e amount  was  The  i n 20000  t h e r.m.s.  about  cell  t h e A-D  digital  the  i s one p a r t  d i f f e r e n c e so that  accurate  o f t h e A-D  ratio  the amplifier gain  not saturate  by t h e d e t e c t o r  longer  of the considerable  to increase  a more  (seeF i g .  generated  However,  t h e White  a smaller  ratio  will  and a  a low  i s no  When  detector  a t z.p.d.  Because  selected  noise  converter  the light  with  noise  absorption  through  through  tageous  guide  excursion  spectrum.  band  simple  undesirable  introduced  excursion.  temperature  detector  A  c.p.s.  t o avoid  to noise  o f o u r A-D  transmitted  o f ^.2  to the smallest  resolution  signal  well.  a t 70 c . p . s .  the electrical  i n the signal  scale  i n a frequency  the preamplifier with  t o a minimum  comparable  converter,  falls  speed.  When becomes  -  reasonably  amplifier  power  17  of  with of  the light  t e n times a  less  cooled  t o improve t h e improvement i t was  found  by a f a c t o r  the large  converter  representation  i n signal advanof 5 at  fringes at  while  a t t h e same  o f t h e low  level  signals  i s provided«  The g a i n  restored,  but the accuracy  precision  with  1,4  Source  studies  source few  by  absorption  narrow  spectral  only  some  This  i s troublesome  the  very  detector  radiation which  i s "loaded"  the spectrum  spectral  regions  profiles,  o f I t as p o s s i b l e .  been  achieved  a  increase  the fraction  employed  to pick  sorbed these  precautions,  parts  of the incident  when  the e l e c t r i c  interest.  must  be  of light  flux  field  from  was  less  absorbed  applied.  by  study,  to only  to  those  are being . studied. to obtain  one r e j e c t s  To  than  has  further was  i s maximally even  as  this  a polarizer  ' However, case  from  necessary  experiment  which  i s  because  under  naturally,  absorbed  cell.  was  coming  source  that  a  intensity.  synthetizer".  component  i n a typical  absorbed  the lines  lines  left,  "frequency  are only  spectroscopy  signal  In the present  field  there  I t i s then  absorption  out that  i n the static  between  but apart  much  with  large  implies,  continuum',  intensity  of the continuous  of the continuum line  In case  transform a  regions  i n which  some  of the incident  with  o f no  a s t h e name  from  the total  i n Fourier  restrict  precise  study.  fraction  i s essentially  Enough  absorbed  lines,  i n spectral  on t h e  i s known.  spectroscopy,  under  small  change  depends  synthetizer  the radiation  t h e sample  i s computationally  o f the spectrum  the gain  and. F r e q u e n c y  In one  which  change  ab-  with a l l about  1.6  the hydrogen  x gas  10  -  The lamp  operated  regulated 50  radiation  source  a t i t s maximum  d.c, supply  19  was  -  a small  allowable  tungsten  filament  temperature  from  ("Hanimex" p r o j e c t i o n lamp,  8  a  volts,  watts). The  was  polarizer,  constructed  reflecting angle.  as shown  to the high  h a s an  immediately  i n Fig.  the radiation  Due  polarizer  which  from index  efficiency  6,  followed  and o p e r a t e s  a silicon  slab  of refraction  o f about  the  source,  b y means  at the  Brewster  of silicon,  80% over  of  a wide  the  spectral  range. The at  radiation  the various  frequency  i s restricted  absorption  frequencies  s y n t h e t i z e r which  i s shown  The  instrument  consists of a grating  the  diffracted  rays  reflected a  back  s e t of small  rays  may  beam  splitter,  angular parts With and  *  be  i n the "exit  to the entrance spherical  separated  but here  separation  o f t h e two  of the grating a  6 0 0 &/mm  an e n t r a n c e  Mirrors each on  aperture  are spherical itself.  are  centered optical  i n Fig. i n which  o f a mask and  slit  more  t o make  convenient  grating, 3 mm,  i n order  using  high  with  a  an  different  and o u t g o i n g 10 cm  and  outgoing  of the entrance  beams,  x  rays. 13 cm  wide,  the s y n t h e t i z e r has  t o image  7.  selectively  The incoming  light  of 3 x  o f an  spectrometer  f o r the incoming  diffraction  bands  schematically  b y means  mirrors.*  i t was  by means  plane"  slit  i n front  to narrow  the collimator  a  - 20 -  -  light The  gathering  actual  shown  1.5  spectral  in Fig,  Data  we  be  out.  The on  carried  order  with  pulses  magnetic  an  having  instrument  (aperture  an  unit time  purpose  and  hold  the  which  of  unit,  to  the  instrument  are  or  can  be  a  digital  at  an  an  equals  has  is  required to  i s , the  can  be  taken,  Is  about  A-D  converter  to  follow  The  waiting  place, 10 a  full of  period,  before  yusec.  accuracy  settling  an  These scale 1  at  time  of  accurate  to  usee signal the a  sample  large  measurement  p r o p e r t i e s allov;  in  The  sample  look  sinusoidal  part  up  1  after  type  sign.  of  than  stored  speed  "Eeco"  built-in  less  are  system.  and  rate  the  time  of  an  digits  a  triggered  high  acquisition  converter  and  is  i s  interferogram.  large  time  taken  an  data  may  detector  "words",  aperture  has  with  by  decimal  second,  the  which  asynchronous  measurement). that  read  path  transform  reference  converter,  operate  with  from  converter  inter-  optical  Fourier  signal  this  infrared  of  A-D  four  per  the  points  laser  of  change  V  the  output  signal  frequency  with  numerical  electrical  analog  can  for  a  from  of  measurements  hold  discrete  describe here  The  30000  the interferometer.  mentioned  analog-digital  tape, We  at  The  measurements  760-A  obtained  already  that  generated  computer.  and  have  i s measured in  by  bands  with  8.  difference  measured  compatible  Collection As  ferogram  power  22  voltage  20000 f o r "P  the of less  ro  ' 4000  41oo  4 2 0 0  4-3.00  Z S P E C T R M ' COMTEMT  4-50O  44oo  OF 'SOURCE . . . 1  4 boo  c m  -1  41  OO  . 4-80O  -  than  about  derived the  150  from  fast  s e c ".  selected  sample  crossovers  and h o l d  unit,  a t p r e c i s e l y known  scanning  speed f l u c t u a t i o n s .  tape  digital  i n a form  digital  which  memory  and c o n t r o l  i s coupled  4  one, coded 20  As  wide  decimal long  converter for  into"  memory,  i n a  large  model  v i a a logic  to generate  despite  magnetic  i s a n Ampex  The c o n t r o l  of integrated  sign  i s taken,  register  I s moved  i t s register.  up When  by  circuit  which  buffer unit  I.B.M.  the r e g i s t e r s i s quickly  the four  binary by  o f t h e A-D wires;  16  digits  wires  a r e "pushed  a l l  existing  and t h e s i g n  i s pushed  registers are f u l l ,  the tape-transport  of operation  80  and t h e 1 7 t h f o r t h e s i g n .  the s h i f t  of  registers":  1 b i t wide  17 o u t p u t  positions,  measurements)  "shift  The output  on  author,  can store  sequentially while 4  the  and t h e o t h e r  bits.  b i tdigits,  measurement  tv/o m o d e s  long  simultaneously  four  the shift  20  20  are  on  processing  constructed  (B.C.D.) d i g i t s ,  appears  information into  i s recorded  required  b y 80 b i t s  to hold  the four, each  buffer  of 2 chains  bits  bits  unit.  c a n be  difference  converter  pulses  f r i n g e s , and  measurements  o f path  t o t h e A-D  logic  the trigger  tape. The  consists  values  information  a l l the functions  compatible  digital  The t a p e - t r a n s p o r t  TM7211  contains  with  of the laser  suitable f o r further  computer.  -  In conjunction  obtained  The  24  "pushed providing  i s started out" onto two  speed  and t h e tape.  (after content  There  ranges f o r  -  the  rate  of taking  /  into  measurement  has been  the  until  entered  start  a new  time  measurement  0 -  must  i s turned  on  after  i t i s not possible  c o n v e r t e r can keep  measurements from  case  the register  a n d 10 ms,  A-D  transport  i n which  measurement  tape,  -  measurements:  1) t h e t a p e  measurement,  25  f o r 15 ms, (5 ms,  of transport).  7,5  ms,  new  the 20th  transfer  to that  at i t s output  the time  be g r e a t e r than  a  Considering  one measurement  i s taken,  to enter  after  f o r data  t h e 20th  between giving  two  a range  of  130 m e a s u r e m e n t s / s e c . 2)  t h e tape  measurement:  In this  within  10 ms.  o f t h e 1 9 t h , and t h e time  cannot  be  less  than  transport case  5 ms.  i s turned  t h e 20th  thus  on  after  measurement  giving  between  a range  the 19th  must  occur  measurements  o f from  100  -  200 m e a s u r e m e n t s / s e c . By  virtue  "physical  tape  occupying  about  between of  20  about -10^  records  words  sing,  only  replaced  by  of the buffer  r e c o r d s ' * a r e 20 m e a s u r e m e n t s 0.1" o f t a p e . requires  requires  678000  words.  of the size  0.75" o f t a p e .  0.85" s o t h a t  measurements. I f a record  20 w o r d s zeros  tion);  this  tape.  The d i g i t a l  The stopping  A  3600'  reel  i s -"unreadable"  the phases  c o m p e n s a t e s somewhat recording  and  holds during  long  starting  every  o f 2400'  of information are lost  to retain  (words)  Thus  a reel  memory,  record holds  a maximum later  (and are  o f subsequent  f o r the i n e f f i c i e n t  system  was  of  proceslater informa use of  planned t coperate  at  a. r e l i a b i l i t y  level  interferograms bility  of  visible  of  due  1.6  Data  error.  to  one  is  assumed  the  ing  a  to  point  of  an  error,  an  interferogram to  our can  the  the  the  be  and  obtained  i n t e g r a t i o n at  be  path  located  by  to  within  spectral  lines  not  minimum studied. than  is  has  a  record  small  never  proba-  been  a  the  loss  of  informa-  has  been  recorded  in  digital  will  be  below.  A  second  procedure  the  number  of  In  samples  consistent our  the  a  cosine path  a  with  to  small  necessary  be  on  to  difference  zero  and  proceed  difference  of  the  otherwise  procedure  out  is  the  interferogram of  only,  path  fraction  The  (this  measurement)  spectrum,  width  inter-  transform  carried  the  the  by  the  difference, The  the  If  path  confirmed  in  procedure.more  absolutely  of  symmetric.  outlined  value  Analysis.  difference.  contained  of  only  to  even  zero  wavelength  tion  able  not  function  shortest  i s  there  Fourier  analysis,  maximum  must  z.p.d.  with  be  records.*  symmetric  in  spectrum  starting  retrospect,  to  Analysis  proceeds  ferogram is  In  high  measurements  unreadable  Once form  10^  indication  tion  sufficiently  the  to  to  the find  reducthe  spectrum  points  are  a c t u a l l y measured  define  the  spectrum.  e x c e p t f o r one o c c a s i o n d u r i n g which, f o r good parity generator of the d i g i t a l tape t r a n s p o r t an e x p e r i m e n t h a d t o be r e r u n .  The  reason, failed,  the and  riumber  of  :  points  procedure hydrogen  which  is  reduced  has  been  spectrum.  indicating  the The  spectrum  is  In  numerical  shown the  between  =  filtering  e s p e c i a l l y to  is in  Fourier  ( C )  B  9  steps  connection a  a  designed  Fig„  various  through  by  a  block  data  the  f i t  the  diagram  analysis.  interferogram  and  the  Integral:  I(S)COS(2.TT<0-£)CU -L  where ence  I( %  ) is  ,  and  0* i s  interferogram at  discrete  replaced  the  is  the not  points,  by  a  is and  hence the  domain  periodic  sufficiently one  finite  The  total  spectrum B((T). of  J  the  = £  i s  of  function  in  waves  of  per  continuously,  separated,  path cm.  but  the  differWhen  is  the  sampled  integral  above  ^ is  small,  period  then  Because  of  B ( O*) ;  in  by  1  N  The  w.i 11  only  is  spectrum  B(C  in  a  interval  h  only  number  of  finite  to  on  represent  the  l i e in  the  spectrum  i t has  been  points  required  on  interferogram  the  and  zero  required  lines  series,  non  dependent  hydrogen  true  coincide  i f the  a. f i n i t e  points  a. F o u r i e r  1/h.  i f B(CT)  markedly the  CT =  axis  and or  cos(£-n<Trih)  represented  frequency  number  h I(nh)  spectrum  domain,  is  measured  ( a*)'  periodic  of  frequency  equally  B(0 )'  spectrum  a  sum:  B The  i n t e n s i t y as  possible  to  actual distinct  reduce  below  that  the  )  certain is  in  either  domains. the form  of  regions number  usually  of  stated  FIGURE Block  diagram  of  data  9 analysis  procedure  -  2.8  -  Digital recording o f " 8 0 0 . 0 0 0 meas. o n mag. tape  Experiment Approx, z.p.d, info. Calculation of phase p l o t using 4096 p o i n t s near z.p.d.  Laboratory Program Tape reading numerical filtering and r e d u c t i o n o f d a t a t o 200,000 p o i n t s on mag. tape  I  #  1  Data  Manual v e r i f i cation of location of true  Precise z.p.d. info .  1. 2. 3.  z.p.d. 4.  5.  Program  #  Numerical filtering Interpolation Reduction of data P o i n t s bv factor 17/6, Fourier transforma t i o n o f 14Q000 points (70,000 f o r p o s . a x i s and neg. a x i s ) at f r e g . of interest Spectral data on cards or disc f i l e  Program  Program  4  Generation of synthetic spectrum including instrum. l i n e shape e t c . Iterative procedure to match width and h e i g h t o f exp. line  1. 2. 3.  Visual  Spectral interpolation to improve display Plotting Freg. determination  inspection  FIGURE 9  #  2  -  in  t h e sampling  frequency  in  Fig,  is  shown  the on  spectral  10a, where along  detector a wave  by  virtue  about  aliases.  laser  cm  fringes, added  4900  1  to the region  to digital  o f 2% i s o b t a i n e d  required. represent  At this  sample  an i n t e r f e r o g r a m  electrical  i s assumed  i s symmetric  i s assumed  f o r a sampled  inter-  of the spectra  10a, a sample  frequency  overlapping of  frequency  3000  of  p e r two  complete  t o 3950.72  of interest. to noise  information  of  drawn  cm"^  3 9 5 0 . 72 cm""'' t o a b o u t  of signal  o f two e q u a l  by  on the v e l o c i t y  t o one sample  the region  addition  the  spectrum  avoid  from  source  been  spectrum  a sample  from  (incoherent a factor  to Fig.  i n a band  a deterioration  analog  noise  The spectrum  corresponds  covers  depending  source  by s e l e c t i n g  the noise  cm"" ", w h i c h  allowing  by m u l t i p l y i n g  completely  -  *, w h i c h  has also  the interferogram  According  i s shown  generated  10b; t h e r e p e t i t i o n s  cm ''" w o u l d  However,  becomes  from  i n Fig.  aliases.  20000  that  i t s origin.  i s shown  about  7901.54  and t h e i n f r a r e d  of the fact  signal  below.  of the infrared  (thelatter  obtained  the highest  i s outlined  noise, spectrum  The r.m.s.  be p o s i t i v e  of  spectrum  mirror).  to  called  procedure  coefficient  t h e moving  .. b e i n g  of the analog  the r,m„s.  scale,  .. , CT  a suitable  of  are  content  and e l e c t r o n i c s  by  symmetric  This  the actual  with  number  frequency  ferogram  h <L 1/2 C*  theorem:  i n the spectrum. The  29  ratio  by a f a c t o r noise  o f 1 0 0 cm  800,000 path  by  i n going \[2  of  components)  i n t h e number  frequency  Thus  a saving;-  o f measurementsdata  points  difference.  FIGURE  10  Spectral d i s t r i b u t i o n s a r i s i n g during s t e p s of t h e  analysis  various  I  AMFLITUDE5  'lMFgAP,ED SIGNAL  P.C. D E C O U P L I N G  PETECTOft  1 !>  1  200O  6000  NOT TO SCALE  R.C. C U T O F F  hlOISB  8OOO  !ftif  10000  S A M P L E  cm  Fg.eaUE.NCY  2> II.  -JiLiL-Ll  ,  f t / •  \ \  /  1  1  » \  -r-  zr \:ALiAs  V*3 O  DITTO  i! l97S.38cv*'  £ L  L_  637.2 cm  1  J  tL.  l  i  - ' 31  In prior of  to  the  of  by  must  that  the  be  data  input  ferogram  has  can  now  be  the  previous in  a  sampled  the  a  200,000  points  the  one  form.  interferogram  as  frequency  numerical  shown  of  1975  in  this  the  number  two  additions  (one  and  quarter  the  points  200,000  800,000  in Fig.  on  magnetic i s kept tape  measurements  for is  are  occurs.  tape  to  10(d). in  a  future  of  aliases. number  These  highly reference,  reused. made  Using  along some  a of  of  inter-  operation  stored  z.p.d.  point  resulting  ^  pass  the  filtering  shown  before  band  i n F i g . 10(c) cm  so  very  overlapping  as  4000  of  without  from  tape  The  filter  possible  Interpolate  and  is  the  Gaussian  reduce  a  quantity  consist  a  of  data  as  difference  content  This  to  point.  content  laboratory generated About  path  input  i s reduced  are  using  the  means  the  points  multiplication  frequency)  i n i t i a l  By  by  large  will  p o s s i b l e to  per  a  data  points  deterioration  f u n c t i o n of  operation  zero  the  data  outside  while  of  attempting  i t was  at  sample  spectral  compressed  not  four  few  point.  frequency  measurements  having  by  (essentially to  as  filtering  i n c l u d e the  operation)  while  response"  per  to  performed  the  by  band  i s removed  Because  of  further  noise  10b)  "pulse  number  without  computer.  operation,  operations  Fig.  above  the  operation  f u n c t i o n and  points  Thus  (see  numerical  filtering  per  the  ratio,  represented  operations  f i l t e r  of  the  involved,  band  few  reduce  noise  filtering  read  data  to  interest  numerical  of  to  Fourier transformation  signal  region  being  order  typical these •  -  measurements a  along  with  about  low r e s o l u t i o n spectrum  and  sine  transformations  out  by t h e w h i t e  interferogram.  i|  /p  t  s  tudes  interferogram possible  an e q u a l  j  to locate  z.p.d.  spectral  i ti s possible  to within  ampli-  to find the  center  ( A = ~2~^ '•  center  ofthe  angle*  with  d i f f e r e n c e o f t h e assumed  cosine  singled  center  t h e phase  associated  z.p.d,,  Fourier  as t h e assumed  frequencies  t o the true  after  t h e measurement  by c a l c u l a t i n g CC  number  i s calculated using  fringes  S,  i n path  -  and u s i n g  ^ "/A »S1  at different  distance  is  Then  3 n~ [ 1  light  32  I  ofthe this  n  - 0.3% o f a  way i t  sample  interval. In  a second  is  c a l c u l a t e d from  by  200000  data  ing  operation.  the  filter  first at  z.p.d.  spectrum  sample  *  points)  b y means  In this  case,  o f another  this  filter  interferogram  phases  interferogram  operation  allowing  a further reduction  s t i l l  (represented  numerical  the pulse  i s c a l c u l a t e d a t such  a r e s e t t o zero  points.  a new  interferogram  however,  i n t h e new f i l t e r e d During  consequently  program,  the intermediate  function  point  computer  more  response o f so t h a t t h e  occurs regions  closer  i n t h e number  f i l t e r -  exactly i nt h e  aliasing  and  of required  •<  4> i s d e t e r m i n e d t o w i t h i n a m u l t i p l e o f 2TT , b u t b y d r a w ing a s t r a i g h t l i n e through a plot o f v . s . frequency t h e a b s o l u t e v a l u e o f <p i s o b t a i n e d f r o m t h e f a c t that = 0 at zero frequency. D i s p e r s i o n would cause a nonl i n e a r r e l a t i o n s h i p b e t w e e n <£> a n d f r e q . m a k i n g t h e above p r o c e d u r e difficult.  33  It a  multiband  are  Is possible narrow  chosen  band  amongst  lOd.  Then  gram  after  calculating  indicated such  different origin The  that  of frequency  spectral information  a r e no  obtained consist  longer s t i l l  tion apply  •arrays  Fourier  of data  the author  technique ing  o u t on  spectral  part  fast  that  b y means (buijs,  be  i n a  alias"  of the  the pulse with  different  of interest  need  blocks  to trans-  This  extended  i s calculated i n blocks. that  transforma-  Fourier  of this  must  transform  i t i s possible  ay means  thus  phases.  Fourier  has been  exact  response  and Tukey .(1965).  has the advantage  an  factor  cosine  o f complex  11.  i n this  different  o f a complex  (near  as i n F i g .  reduction  i n  completely  o f . a f a c t o r i n g technique  1969).  as  compromised  the Fourier  method  filter  interferogram  to lock  each  transformation  information  this  the "principal  function,  by C o o l e y  the spectrum  procedure  that  a real  developed  complex  means  as t h e r e a l  would  occur  The data  of  interfero-  related; nevertheless  o f numbers  the extremely  formation  sample  i s made  exists.  considering  carried  samples  bands  of the  o f t h e new  has n o t been  simply  of s i x sets  t h e same  now  response  as i n d i c a t e d i n  but the frequencies  i s 17/6 w h i c h  By  t h e bands  aliases  Then  scale)  parts  by  We  set of aliases.  relationship  where  many  the different  interferogram,  of  very  lOe.  final  is  filter  the spectral content  i n Fig.  a way  to calculate the pulse  the various  Fig.  -  to  method large  developed  factoring This  containing  blockno  n o t be c a l c u l a t e d , .  FIGURE Spectral  distribution  before  11 Fourier  transformation  - 34 -  -  which  are  i s not  the  case  In  the  Fourier  c a l c u l a t e d at  where  L  i s  cms.  This  the  the  spectrum  spectral data the is  length  and  the  only  single  a  slightly  point.  representation with  for an  In  analytically  c a l c u l a t e d at  four  times  as  background  intensity  "Calcomp"  plotter  frequency  scale  (for  0.0055  being  cm  narrow,  absorption  of  Because may  be  the  a  to  of  line  in  sharp  improve the  the spectral  calculated replica  and  the  final  frequencies  as  the  intensity  i s  p l o t t e d on  In  frequency  corresponds the  work  of  a  to  here,  wave  1  ratio  scale. cm  the  number  of  spectrum  spectrum  calibrated  in  limit  the  fraction  I n t e r e s t i n g to  very  the  of  graph  the  interferogram than  T.  cm  logarithm  hydrogen of  and  the  a  res.).  only  line  to  above  on ^  point  many  C.  amplitudes  to  d i s p l a y purposes,  function  this  a  order  shape  At  equal  of  of  spectral  less  line  one.  program  ended  instrumental  original  i t  intervals  representation  just  i s convolved  original  transformation,  of  i s  the  is  the  frequency  spacing  resolution,  with  35  ^  =  of a The  18"  spectral near  lines  each  i s plotted.  complexity compare  of  the  the  above  numbers  of  analysis, computations  •i  involved  in 1)  double points:  ended  the  above  analysis  S t r a i g h t complex interferogram  with  a. f e w  Fourier  simpler  alternatives:  transformation  c o n s i s t i n g of  1.6  x  10^  of  data  a  98  x  8192  x  6  x  2000  x  14 x 196  2  x  =  22.6  x  10  (blocks  2 =  4.7  x  10^  (spectral  =  2 7.3  x  10  total (this  a l t e r n a t i v e would  6  require  o f T.&  C„  transforms)  assembly)  calculations  double  the quantity  of  input  data). 2) polation  Numerical  to obtain  a  f i l t e r i n g reduction  symmetric  of data  interferogram  with  and  inter-  known  center: 70000 18 6  x  x  116  8192  x  14  X 2000  x  36  x  2  total  =  8.1  x. 10  =  4.1  x  10  .4  x  10^  12.6  x  10^  =  3) A n a l y s i s  (numerical (blocks  6  filtering)'  o f T.&  (spectral  calculations  as d e s c r i b e d  above:  x  20  =  4.0  x  10  6  (1st filtering)  70000  x  29  =  2.0  x  10  6  (2nd  =  4.1  x  10  (blocks  .4  x  10  (spectral  10.5  x  10^  calculations.  x  8192  x  14  5  x  2000  x  36  x  total  One of  =  "calculation" one  The  often  been  time  B.C.  I.3.M.  and  consuming  of cosine completely Most  new  i n t h e above  multiplication  evaluation have  2  360/67  computation  center.  consists  and  data  have  this  transforms)  (such  transfer  been  roughly  and i n d e x  calculations  installation Since  C.  assembly)  i n t h e above  spectra  computer  o f T.&  additions  auxiliary  functions)  recently,  filtering)  comparison  several  ignored  transforms)  assembly)  200000  18  C.  changes. as  operations  comparison. obtained  using  the  i n the' U n i v e r s i t y o f  i s a time  sharing  -  installation, dollars"  computation on  an  hourly  different  aspects  of  the  (see  9)  0,9 of  Fig, (the  the  tape at  c  costs  cost  reading same  about  reduced  reduced)  priority used.  Reliability  Provided  transformation  calibrated  when  (frequency)  in  produced  a  becomes the  the  established  the  air,  on  highly  the of  at  a  a  fast  Program  #  2  are  the  the  the #  1  level  of  priority  required  machine, language about  levels  costs,  of  Program  costs  Priority  each  priority  as  very  for  used.  factor  the  per  i n t e r f erogram  spectrum of  this  frequency  the  on  of  C$  54.00  0.4  or  0.6  spectrum.  the  light  refractive  The  the  in  from  on  which the  through  the  complete-  can the  latter which be  central  knowledge  was  rate  fringes  the  with  the  interferometer  is  the  frequency  with  frequency  sample  and  precision  i s known, passing  The  a.t  digital a  spectrum  laser,  sample  index.,of  Irregularities  He-Me  a  l i e on  i s known.  accuracy  line  since  the  sampled  from  i s derived  mean  the  will  Hence  standard.  of  i s  resulting data  stabilized  laser  finally,  the  a  experiment  depends  of  and  one  this  value  direction  meter,  by  linear.  frequency  absolute  frequency  the  i s highly  by  30,00  using  that  Fourier  ly  schedule  "computer  in  frequencies  intervals,  that  evaluated  C$  These  regular  scale  are  rate  level.  of  -  installation  subroutine.  commonly  ^  is  task, i s  the  are  i  based  tasks  37  of  interferooperated  air.  sample  interval  arise  from  in  -  noise  in  the  phase  shifts  tuations  reference due  are  dependent  measurements  For  path  will  each  to  is  M  the  the  sample  e  ing  of  x  is  10^  the  strong  *  This best  Then  after  which  the  measurement  fluci n -  taking  N  magnitude of  path  measurements  the  r.m.s.  deviation  same  a  h  (say £ ) then  the  r.m.s.  is  deviation  in  _  = vie"- -VsT € • • r.m.s.  so  due  deviation  that  to  about  would  spectrum  the  random  6  x  be  in  variations in for An  at  an  the  the  1st  mean  individual  interferogram  additional effect  reduce  particularly  be  uncertainty  10'  to  will  s i g n a l to  overtone  consist-  of  noise  sample ratio  frequencies  of  features. The  laser  accumulated  measurements.  irregularities of  another..  interval.  .1  frequency  5  statistically  sample  ,  /h  measurements  and  These  the  fractional  Typically  electrical  is  •  |  V / S e and  the  from  be  the be  and  fluctuations.  random  to  where  of  signal  speed  be  -  difference during  nh  assumed  L  of  to  sample  linearly,  difference  L =. £j  one  fringe  mirror  believed  from  increases  to  38  having  laser a  is  highly  a  "Spectra  stabilized  Physics" tunable  type  119  c a v i t y , but  He-Ne  G'.W.  without  i s a n a l o g o u s t o f i n d i n g t h e e r r o r i n t h e s l o p e o f -the s t r a i g h t l i n e w h i c h g o e s t h r o u g h a number, o f p o i n t s .  -  X  the  servo  option.  Using  checking  out  the  maintain  the  frequency  (particularly  X. s e r v o  in  the  a  39  -  monitoring  operation,  of  the  later  laser  work,  system  suggested  i t was  found  output  to  after  easy  to  within  gaining  for  -  15  Mc  experience)  20 of  the  transition  infrequent radiation  manual was  vacuum,  (see  Mielenz  et  mator, focal fringe  point  must  be  in  precisely  in  When  i s the  experienced  et  =  al  Ne  The  line,  (1965),  image  -  of  to  the  case,  the  of  limiting the  the  laser  specify wave  the  n X represents  number  radius  of  of  laser  the  collimator. above  and  may  as  shift  the  length  rays  laser in  - 1  (1966)  and  (1  Due  to can  the be  times  sample  and- f  m - ~ r  carried  f u n c t i o n of  of  out  center  path  the the  and  the c o l l i -  same  with  the  interval reference  path  laser.  difference  2  )  c difference  wavelength,  the  smallness  f r e q u e n t l y the a  path  i s  the  of  be  1 ^  the  of  other  optical  -  extent  light.in  of  will  observed  fringes  aperture  alignment  precision  only  the  cm  plane  each the  average  infrared  the  focal  •  a  of  ,0005  Engelhard  concentric with  order  terms  by  through  S = n X where  with  frequency  15798,0012  aperture  passing  pattern  this  CT  circular  the  plane  the  (1968)),  light  and  as  Mielenz  al  of  adjustments.  taken  The infrared  frequency  focal the  with of  length  i n terms i s of  dimensions, only  the  difference.  the the the  limited  fringe  pattern  of  _•  Looking one  observes  through  two  t h e two  superimpose  the fringe  of  mirror two  ence"  will  center of  motion.  would  images  fringes  mirrors  never  when  occur  0^  aperture  " a " c a n be  (i.e.  A  aperture then:  and f r i n g e  and  laser  adjusted"  path  differ-  side  with  the  fringe  from  the  approach  direction  (a) o f the  of the collimator.  In this  b y means  of adjustment  difficulty.  X  cos  0  between center center.  image  direction  adjacent  cos  i s the angular  center  The path  aperture  i n case  inter-  of the differof  mis-  and a p e r t u r e i s n  and t h e f r i n g e  then, t h e  of  of the infrared  i s the angle  image  9 0 ° away  of closest  without  image  images  and  the separation  reduced  30 }i  of laser  laser  of observation,  plane  I f these  but "zero by  side  seen  i s "poorly  are side  i n a. d i r e c t i o n  6 = where  superimpose,  from  as  s t a t i o n a r y and i n t h e  The d i s t a n c e  at the center  alignment  difference,  t h e images  i s obtained  t o about  path be  the exit  of the source  I f the interferometer  i n the focal  ferometer  ence  will  to the direction  observation.  two  at zero  will  occur  images  from  of the interferometer.  pattern  images  respect  arms  -  the interferometer  coherent  exactly  of  the  into  40  8. i  T  the center 9 ^  and Now  infrared  i s the angle  l e t A=  d i f f e r e n c e between measured  of the  towards  between  ( @ -j- - © L A T I T U D E the  infrared  the fringe  center)  cos 6 j  -  o  =  =  and It  ^ = can  be  change  X  n  fringe  seen  ties  in  maximum  of  sign.  -  sin  -  2  -\ A ) aperture  movement  ^  of A  value  of  the  be  aperture  variation  in  ^) b u t  8  =  L  causes  this a  be  the  center  a/nX  center  may  considered  and  during  the  a  in  path  as  the  the  an differ-  uncertainThe  relative  laser  scan  value.  cause  interval.  from  fractional  towards  function of  sample  a.  shift  direction  estimated  A  tan  5  the  as  average  can  0  "constant"  In  must  A  '  Q  a  terms  of  A  sin  misalignment  and  in  0  a A  -  2  i s measured  the  -  A tan  both  of  severe  A  variation  value  positions most  A  hence the  |  difference  since  unpredictable and  -  that  center,  ence  (1  X ( 1  n  A  41  cos  n A  in' p a t h  However,  cos  -  image  would  be  and  the  reversal  Thus,  + °  .  a A ,  x.  5  «§ »y\asc. By  displaying  image, cases  to  align  improved  %  =  hence  projection  magnified  also max  a  70  about  their with  b=  cm  ^  =  of  the  twenty  centers  times, to  -  n X ( l -  4  x  ~ — c  For 10~  -  and  i t was  within  experience).  n X ( l  aperture  A  0.2  8  ~  5.7  4  x  10~ )  4  (this x  x  8  laser  possible in mm  =  m  the  10~^  most  alignment and  10~ ) 8  -  5.7  n X  x  10~  8  -  All ferometer  experiments  surrounded  temperature  pressure  during  the  vacuum  wavenumbers,  known  at  two  laser  value  times  the  prevailing  of  .d  the  For  index  i n  of  the  a i r of  frequency  x' v a c . LT. A CT  then  I R  v  a  C  =X v a c , LT. = —  o  IR  working  in  IR  In S  IR  terms  vac,  evaluating S  O  t  h  a  t  of  will  this  ^ I R  =  rX'  up  to  third  a i r must  to be  The  i s equal  measured  m2 _  _  4 x  line,  a  relative  to  in  the  .„-8, 10 )  distance  n  • -  4  x  10~ ) 8  IR  S - n  -  1;  IR  very d  U  +  S  T  order  known  calibration  r  r 2 7^f p  - 47"  V3.G  approximation  not  X'vac.L.  2  product,  vac.  exact  corrections;  L  T  the  infrared.  light  refractivity  vac.L.  was  inter-  be;  h  1  the  of  i n cms,  laser  Yjr*" " v a c . L ,  the  2X  i n the  1 ( i _ _  (  / v  refraction  infrared  axis  which  frequency  aperture  an  with  atmosphere,  interval  IR  where  of and  sample  plus  out  of  precise  2 Xvac.L, -  =  carried  laboratory  frequency the  -  composition  the  atmosphere  frequency  along  and  wavelength  , h  The  the  experiment.  the  absolute  by  were  42  o  i-j  o  in  L  IR  nearly cancels "  S  IR  }  i  s  a  9 ° •  S.  o  d  with  •  -  According and  pressure  wavelength directly  on  the  to  the of  be  for  computed S-^  index  a i r are  -  -*-  S^ ^ i  s  r  that  p  (S  S  is  in  torr.  =  364.5  -  (S  -  T  variations R  ) .  highly  may  be  applied  Variations in dependent  S  p r o p o r t i o n a l to  given  by  )  (S  T C 1  =  IR  For  S j  temperature  a i r are  wavelength  c t l y  e  L where  these  of  of  the and  must  separately,  R  constant  Hence  effects  refraction  somewhat  and S-TR  a i r .  of  so  -  3  (1966),  difference (S^  proportionality  standard  Edlen  independent  composition  the  to  .  4  p  the  p  conditions  -  T  S  L  =' 760  -  40  pressure  T D  )  x  IR torr  with  in  0 001388  p  o  s  ^  and  —8 -  T  T D  )  J-K  Li  IR  vac.  S  will  x  10  , the  = (cr;  The  t  found  to  with  i s  by  temperature  The about  extreme of  18  air. air  18.6  A and  -  I  R  )  S  t  =  (S  L  -  Then  a  s  of  temperature  pressure  J R  in the  -  the  19  in  io~ ) s  x  refractivity  ) ^  x  (1  +  the  laboratory  variation  ( C r  iRvac»s  water  x  vapour  (Clark's, tables  in. r e l a t i v e partial the  a i r i s given  ( 1  of  _„ IR  vac.  Edlen  1 0  pressure  "  in  a i r at  21°C  8 >  Therefore  could  a  of  difference in by  *  2  cause  water  1  was  (1957)).'  humidity  pressure  1  of  .00367t)~  be  saturated  the  vac.  variation  1.5°C.  will  torr  in  ^  The  formula.for dry  IR  O'lRvac "  changes  torr  -  L  21.5°C  •  is  (S  i n °C.  be  vac.  temperature  i s given  )  n  IR  where  with  be  <r__  air  variation  variation  vapour  in  the  refractivity  of  moist  (1966)  as:  -  Cn-, where  L  S  ~  S  where 18  Applying  IR f )  =  (  S  L  "  S  i n ja m" ,  the correction  )  +  f  term  i s  (CTt )„ •= ( ( £ „ ) IRvac H 0 IRvac D  ft  2  According in  ( C  partial  i n moisture  2  - CT  0<rkS<1.9  refractivity  (1966)  normally  o f a i r which  vapour  changes  and h e n c e  In  summary  provided  accurately  located  the absolute  on  x  I R  2 ) x  10  content;  10"~  for  8  8  0 < f <  IRmeas  of this  the effect  of  i s much  than  less  c a n be that  10  ±  6 x  10~ 8 10 8  changes a change i n  that  due t o  ignored.  a spectral axis,  frequency  3 x  x  8  cause  -  -22  10" ).  encountered,  the frequency  value  1 IRvac  ( 1 + 1.9 x - 0 0  to Edlen  concentration  water  in  10  torr.  Hence  the  variation  °-0457  x  ) x  and f t h e  1  t h e above  IR  -  - 0 . 0 4 5 7 O*  = - f ( 5 . 722  CT i s t h e f r e q u e n c y  pressure.  (  - n)  44  line  c a n be  the uncertainty  will  be  due  to laser  due  to aperture  due t o i n d e x vari ations.  >  adjustment alignment  ofa i r  -  -• 4.5  2. 2.1  General  Experimental  remarks  The  on  results one  of  about  1969.  By  a n a l y z i n g the  upon  the  next  ful  feedback  and  data to  and  make  the  correct the  was  the  study  obtained because  for of  the In  the  and  two  (1), Q  Of  these  x  a  few  (2), Q  appear  lines to  were  arise  the  long  field.  In  order  to  lines  this  where  more  re-  gradually  too  approach,  generally  ''Also,  simpler,  expected.Only became  use-  collecting  arose.  density  lines  set-up  1,  A. J =  (4), Q S-^  there  (0)  too  from  the  1  +2)  weak the  to  spectra  reliable,  ±  to  was  be  quadrupole  any  of  (& v =  (0)  and  detected and  seen.  these  the  spectral  1,  Q-^  The  i.J=  S  1  (1).  in  only  (4) S  0)  a.nd  lines  rather  lines  were  externally details  for "  (0),  the  transitions  because  presence  provision  namely;  (5), S  line  weak  eliminate  was  transitions  induced-dipole transitions r e g a r d l e s s of  embark-  provide of  they  absorption path,  always  present  as  spectral  of  are  ( A V= ]  mainly  technique  were  the  to  a  September  before  possible  higher  the  ( 3 ) , Q_  with  run  to  over  experience.  s i x of  1  at  obtained 1968  each  quickly  result  densities  transitions,  spectra  (5)  than  1  until a  transitions  spectra  were  the  lines  experimental  observation of  Q  broad  improved  the  S^  started  As  lower  of  i t was  improve  reduced  effectively.  here  observation of  were and  density  results  hence  of  from . September  spectrum,  i n i t i a l  strong  year  f o r problems  measurements  latively  quality  presented  period  ing  the  Results  applied  that  are  not  related  molecules a  the  spectrum  of  the  S  with  lines  fact  to  fringes" but at  the  13  the  of  local high  of  the  spectra; axis  the  to  a  that  intensity  should  beam  the  fringes  the  sinusoidal  i t  was  the  Fourier  near  felt  any  without of  the  i n the  case  plot.  spectra  complicated  in by  the  of  features of  the  interferogram  factor  of  These  the  of  their  location  of  in  the  along to  turn  the  applied lines  of  ratio the  of  path  causes  shift  the  to a l l to and  I t was  resulting  and  background  two differ-  expansion  phase  contains  interest,  the  sinusoidal  spectrum.  field)  on  sinusoid  thermal  transformation the  from  surface  effect  no  This  due  back  proportional  intensity  taking  centered  arise  component  amplitude  zero  and  fringes  sinusoidal  an  60  from  analysis a  about  "secondary  f r i n g e s are t e m p o r a r i l y set  appropriate to  to  set  varies  component  two  off  a  which  secondary  (spectrum  features  somewhat  when  exact  in  during  of  amplitude).  disappear  these  these  add  large  separating plate,  zero  the  reflected  having  the  when  log-ratio  in  hydrogen  field  seen  a  An  the  the  except  difference.  of  ground  by  of  i s studied,  was  ( i . e . at  a  however,  that  with  log-ratio  main  they  spectrum  of  spectrum  spectrum  not  lines  path  intensity  component  a on  separating plate.  parts  ence  the  due  shows  at  of  induced  interferogram contained  cm  spectrum  the  are  i n magnitude  interference of  which  resembling  about  of  field  taking  each  reduced  field  the  isolate  that  the  log-ratio  The order  to  no  shifts found to backsharp  consequently with  respect  -  to  the  spectrum  sinusoidal  figure  =  of  plotted  that  spaced  tained gram  during  would  data  function.  the  the of  spectrum. each  from  of  the  should  coefficient can  be  the  limit  profile  of  due  by  obvious  that  The  wavelength  on  actual  data  points  i n Fig.  noise  the 12  the  features  than  the  i s  "analyzed" 13  be  by  i s  directly  the  gas. some  width  poor  shown  sections the  at  the of  in  the  of  same  a .plot  shown  of  line  p r o p o r t i o n a l to  resolution  the 12.  Apart  profile, the  absorption  detail  while  i t i s  other  transitions.  i s high,  signal  to  small  noise  do  not  line  possible  distortions  ratio  these  the.Q^(l) only  as  log-ratio  be  the  that  Fourier  I t can  for  seen  spectrum  resolution  in Fig.  instrumental  the  suitable  limit  the  ob-  interfero-  but  a  a  points  display  with  this  from  data  of  above  this  from  improve  wider  typical  derived  The  to  a  in  obtained  interpolation  or  resolution to  not long  intervals  spectral  line  the  background.  s p e c t r a were  used  Fig.  studied with  estimate the  of  bring  structure i s established before  broadening  features  0.2"  Note  and In  the  are  relatively  apart.  width  noise  transformation,  to  sections of  corresponding  (Calcomp)  points  scanning  because  order  small  components  obtained  same  shown  These  at  are  the  in  Fourier transformation  spectrum  of  the  0.05"  occur  additional  are  are  graph  the  -  phase.  their  1.5").  computer are  12  with  because  amount  in  sinusoidal  ( X  scale  Fig.  along  mentioned  small  component In  spectrum  a  47  Since of  the  preclude  to  FIGURE 12 Typical absorption  features  FIGURE Log  ratio  plots  of absorption  13 features  shown  i n F i g .  T  .8219  4125.8573  QlC3)-  .8927  .92.81  -  the  accurate  weak  lines.  than  the  determination Hence  Q^d)  Fig.  14  transition  demonstrate as  list  determination In  the  the  the  different this  reason  they  2.2  Frequencies  ferogram  The  field  have  the  by  the  index  amplitude.  The  the  taking zero  occurs,  the  frequency to  used  principal  alias  and  frequency. principal question becomes  If  the  alias, is  an  additive  was  the  frequency  correspond  to  densities,  and  for  areas.  computer  number at  of  which  on  starting  term.  original  not  very  the  this  occur of  for  the  from  of  profile  the the  by in  the  sample  the  alias  point the  data  points  ratio  frequency  recipes  identifying  computer  describing  not  simply  here.  center  frequency  zero The  did  inter-  corresponding  spectral  points  line  the  an  program  from  the  multiplying  the  were  i s described  number.of  to  for  to  central  performed  determined  original  assigned  and  calculated  the  then  the  profiles  the  in  are  point,  total  and  frequencies  of  the  densities  result,  relation  ratio  complete  profiles  filtering  Frequencies by  of  numerically  amplitudes  the  width  different  analysis  to  to  i s more  the  transitions  As  related  a  sequence  strengths  quite  of  parameters.  different  at  frequency  frequencies  taken  density.  obtained  central  a  line  of  -  i s shown  Fourier  spectral  of  other  interferogram. the  the  in  electric  The  of  change  a .function of  of  50  and  in thus  evaluation  of  FIGURE  14  Sequence of p r o f i l e f o r Q-. ( 1 ) t r a n s i t i o n  at d i f f e r e n t  density  the  frequencies  of  39,0 1 7 , Oh 38.0 17,Oh  and  CT  where  2.0 h  = h  is  very  the  laser  of  the  profile  corrections  a  way  vacuum value  of  h  for of  =  8  for  of  vacL  is  used  the  (1  for  a l l  to  eight  number  the  an  of  incorporated  line  is  h  are  used  at  the  different  - .4 x  when  value  is  8  -  is  above  of  are  and  the on  (S  S__))  -  h  in  in the also,  resolution.  based  T  the  aperture  of in  the  of  corrections,  used  center  Aperture  the  limits  and  N  effect  different  h  the  and  different  for  10  to  the  evaluated these  wavelength  alias.  in  of  values  the  points  and  line  Q.lines  integer)'  interval  frequencies,  -  times  principal  Because  of  line  6^0 1 7 . Oh  observed  list  (0)  t h e S-^Cl)  frequencies  of  for  for  the  in  are:  x  equal  sample  each  a  6_^0 17,Oh  x  x  lines  necessarily  numbers.  gives  X  1)  n  the  are  h  N  a i r are  diameters  evaluation  1)  the  values  I  N  points  different  Table  (n  (not  that  wave  1)  nearly  of  refractivity such  -  light,  number  various  (n  (n  +  of  total  +  the  actual  the  relation  (see  text)  -  53  TABLE r  G"'  cm  -1  h  4125 414 3 4155 4161 449S 4712  (S  i n ja  S _.)  o f H^O  Av a c L  6 3 2 9 9 1 4 ja  -the t e x t  may  x  10  spectral ratio  762  axis  t  3  cm  lines  -  1  1  -  a t 4 1 5 0 cm c a n be  by  5.06391180 1182 1183 1183 1216 1221  -  -O  21.5 C  L  -S  8  IR  364.9 364. 7 364.5 364.5 359.9 356.9  partial  scanning  set of data  The  bisector  of this  its  predominant  was  precisely  position  b y means  with  which  profile  i s then  The f r e q u e n c i e s thus  taken  obtained  of the  was  of interpolation  i s drawn  the  of the  the spectrum  t h e "Calcomp  to  to noise  width  the log-ratio  by  of  corresponds  the center  describing  plotted  plotted  10^ w h i c h  extent' on.the  and then  earlier  i n the calibration  depends on t h e s i g n a l  of four  function  as mentioned  The a c c u r a c y  a n d t o some  determine  a factor  „  located  the"number o f p o i n t s  increased  To  of h  i n 3 x  profile,  profile.  }  an u n c e r t a i n t y  line.  enlarged  torr  of 1 part  i n the spectrum  known  S  h  10~  torr  observed  a  mm x  = 0. 5 0  m,  cause  1.4  at p =  10  r  5.06391023 1024 1025 1025 1048 1064  i n t h e above v a l u e s  frequency  + -  =  mm  mm  Uncertainties  the  = „ 75  m  h  5.06390888 889 890 890 912 928  pressure  in  r  mm  h  i s taken  T  500  = .91  m  m  5.06390169 5.06390170 5.06390171 5.06390171 5.06390193 5.06390209  -  T  r  = 1,5 ram  m  I  of  v/ith  this  plotter".  i n by hand  and  as t h e c e n t e r o f t h e were  graded  with  -  small the  letters  bisector  0.004 l i s t  cm  - 1  of  ,  to is  c  at a  to  5.90  =  within  some  check  for  spectra  the  so  that  same.  found  to  for  plot  a  indicate field  be  of  that  same  of  correlated  with  these  tion.  no  i s  a  shown  In  i f there  period  a  of  be  cm  shift from  - 1  each  exists  about  20  nearly are Fig.  This  test  as  function  a  strength,  to  but  establish  15  seems  regular  appear  a  data  See  a  at  The  very  .  in  particular  Q^(l)- lines  lines.  to  repeated  recorded  would  frequencies  insufficient  is  strength.  0.0005  field  been  were  -  deviations  applied  II  results.  four  frequency  observed  the  the  field  Q-^ ( 1 )  ='within  1  to  of  density  be  slightly  the  accuracy  this  correla-  The  pressure  is  of  have  the  within  However,  the  results  to  -  densities.  conditions of  band  cm " ', b  Table  determine of  frequency  0.001  spectra  to  a  In  c o l l e c t e d over  group  there  of  function  was  this  dependence  of  a  ).  - 1  spectra  four  frequencies  strength.  cm  wide  various  strength  as  the  =  reliability  atmospheric  The  within  densities  field  shift  hours  (a  the  density,  frequency these  how  0.008  at  the  amagats  different  over  located.*  frequencies . At  order  indicate  54  of  values  the  of  hydrogen  the gas  density in  the  pressure-temperature-density  tables  *  S  t h i s was results.  not  done  for  the  lines  were  obtained.from  absorption of  the  and  cell  National  some  of  the  the  using Bureau  last,  the of  TABLE List  of  frequencies  densities.  of  the  II lines  studied  at  various  TATJLE  •'AG A T  2 6.1 2 5 .4 2 2.4 17.8 1J! 3 10.2 3.22 7.73 13 90 90 90 90 5.90 5.26 5.26 4.62 4.62 4.62 4 .00 A  .CO  3.40 2 .90 2.4 5 ,08 , 70 .53 .53 1.94 1.50 1.50 1.10  .7S  APP.r-'I'iLD KV/cn  A5S.PATH  75.3 71.3 . 57.5 71.8 64.6 68.9 50.6 57.5 50.3 4 6.7 9.33 16.8 22.4 . 27.1 18.7 24.6 35.8 21.0 25.6 2 7.6 2 5.2 2 5.2 25*.2 2 5.1 25.6 2 5.6 16.8  0 ITI 0 0 0 0 0 1.0 1.0 1.0 1.0 4.0 4.0 4.0 4.0 4.0 4.0 1.0 4.0 4.0  C O 16.4 16.4 15.4 16.4 16.4  c (i)  C, ( 0 )  cm" 4161.1056° .113S .1179? .12 54° .1363 . 1420° .14 70° . 1 4 4 7° .14 73° .1500 a  C  a  L  cm-1  1  cm"  n-1  4155.1639° . 1774 . 1332 - 1 9 4 9,° :109^  d a  .22 72° .2250° -> p q t ) . <_ c. J L.  3  414 3 . 4 1 2 9 5 .4199 .42 7 2 .4 309^ .4 335= .4403° .4465." .44 52° .4494° ,4511 C  a  .2 3 1 4 .2345  d  1  412 5 . 8 0 8 7 .8304.' .823 .84 0 .848 .3557 .8565 .852 .853 .862  a  I  a  !a " b • b .1541° .1531° .1568 .1560° .1563 .1578° .1601° .1601 . -1 .-5 -9 3 ? . 1 6 1 0^b ° .159 1  5  4  3  1  5  3  9  i  _  a  ,a  i3  a  .2381  ci  a  >  a  a  5.  a  ,1592 ,1600 , 1 6 30  a )  .246 .24 7 .246 .247 .247  !246  !4554° '.4557^ .4547° .4547°  a  _  .861 _  36 6 53 .. 8  I  ^4600° .4 6 1 4 * . 4 62 5 ° .461  !8654^ .3690° .8697° .864  .364  .463  .459 ^455  —  .  0.028  .8835  0.014  .3917 .8898 .8922 .897 .892 7 .394  0.007  .8987 .8988 . .8985 .8951 .8962 .8967 .8962 . .899 7 .8995 .897 .  .398 4497.835 .84 0  .038 .854 .840  \  RESOLUTION -1  4712.8504 .8604  -.  5;  .4537° .45 70* .4600°  ! 4 61 _  ^  ".361 .364 ° .8658° .8643  (1)  (0)  0 (3) 1  1  .Tl  4.0 4.0 4.0 44.0 44.0 44.0 44.0 44.0 44.0  II  If It  " If  0.014  0.007 0.007 0.014 0.007 II II tt II II  0.0055 tl  .895  .899 .897 .897 .892  LIMIT  It  11 It tt  VJ1  F^GURE_15  Sequence o f 4 p r o f i l e s f o r 0 ^ ( 1 )  transition  same d e n s i t y and  strength  different  field  •Standards.  The  were  measured  -  accuracy.  5%  measured o f -  1%  below with  with  with of  a  a  0  a. M e r c u r y  16,  density  figures  other  investigations  Line  are  were  •In shape  geometrical  ness  of  length  to  measured -  300  about  -  1%  18,  19  for  the  different  of  the  and  some  of  hydrogen  at  psi  20  an  were accuracy  densities  Bourdon  the  are  gauge  measured  shown  lines  the  about  simultaneously  of  17,  shown  with  spectra-  giving  pressures  gauge  0  was  not  made  profile  to  beam  the  density  gauge  experiments  were  recorded  been  the  later  and  highest  density,  Bourdon  limit  has  related  Bourdon  the  functional  line  psi  general,  the  line  also  five  value.  plots  of  studied.  results  In  obtained  by  spectrum,  profiles In  spectra  In  accurate  these  2,3  psi  pressures  Figs,  the  amagats  Manometer  ' vs.  for 1000  11  scale.  pressures  frequency  -  -• 300  amagats,  In  0  Below  full  2.4  giving  pressures  form to  on  of  the  correct the  Fourier  enough  form  effect of  the  quality  of of  "fringe  achieved.  the the  the  the  Instead  alignment  It  and. of  the  the  attempt  instrumental of  as,the  the  an  feature.  the  (i.e. i t  depends on  the  instrumental  absorption  such  which  reveal accurately  independent  optics  with  However,  of  instrument  visibility",  The  to  spectroscopy  function i s essentially arrangement  resolution  profiles.  the  transform  splitter,.etc.). the  low  line  for  actual  of  on  is-not  flatness the  maximum  of  steadipath  interferometer  during  FIGURE Graph  showing  density  frequency  f o r Q^(0)  line  16  shift  and. l i n e  w i d t h vs.-.  FIGURE Graph  showing  density  frequency  f o r Q,(1)  line  17  shift  and  line  width  vs.  'A 155-2.5  ^FREQUENCY ^.S. DENSITY Q / i ) "^.FROM DISrogTEP SPEC TEA, .. FINK £.TM- (\<j(=5)  •lAr-  41 5 5. 2 5 4 3 * . o o o 5  cm'  .22.  .2!  I T - .  PoPPLEE. WIDTH  04.  ©  S3  -.o3  ~.02.  o  DMEWlDThl  t .  A  J  i  QiCl)  CORRECTED  OTUH  \  V.S, D E N S I T Y  CORRECTED  O-BTMK<Eb-FR0M-BI8rogTg.P  \ I  v  v  1.  20  AMAGAT  FIGURE Graph  showing  density  frequency  f o r Q (2) 1  line  18  shifts  and  line  width  vs.  FIGURE  Graph showing f r e q u e n c y d e n s i t y f o r Q-, (3) l i n e  19  s h i f t and l i n e w i d t h .vs.  FIGURE 2 0  Graph showing f r e q u e n c y s h i f t S (0) 1  and S ^ l ) l i n e s  .vs. d e n s i t y f o r t h e  -  each•experiment amplitude  of  i s  the  steady.  Since  passing  through  a  reduction  difference ference the  reference  the  where  the  aperture.  Then  v i s i b i l i t y  representable  (interferogram)„  most  probable  width  and  or.  The  procedure  a  line  and  height  /  "i  to  r  i  mCJ/lCaOL A  in  ri (CF)/£tCT)|_  like  0  The an  e B S  A ,  equal  A^ls  oBS  exponential  absorption  of  by  the  This  accomplished  by  simply  Fourier to  transform that  which  of  the  feature  broadened  similar  be  inter-  surface  of  upon by  this  to  an profile  as  the  to  the  trans-  determine  was  for  ... ' •  i s  the  form  the  i t s Fourier  used  -tfV|^ln2)  e  ground, i s  of  profile  possible  In  2) looks  broaden  truncation  Q  the  instrument  and  the  assume  to  over  path  the  follows:  profile,  the  and  observed  height.  • i  (i.e.  of  i s  long  that  i s  form  i t s width  small  the  attenuation  specify  towards  of  interferogram  remained  Interferometer  effect  because  We  the  the  which  the  intensity  uniform  long  1)  of  so  of  amplitude total  occurs  become  means  longer  infinitely  form  the  by  no  spectral profile,  of  this  aperture  fringes  i s  monitored  records  entrance  fringe  -  fringes;  detector  condition  actual  continuously  the  in  63  Gaussian  for  Lorentzian  above a  function,  unity  instrumental  this  takes  in  for  line  attenuating absorption  place  in  the  height  and  shape  estimate  estimate,  which backfunction.  truncating  feature  in  a  manner  interferometer..  3)  The  log ratio  of t h i s  compared w i t h the observed  profile.  c o m p a r i s o n o f peak h e i g h t the parameters of the  and  analytic  of  the broadened  coincide. 21  Fig. and  success  where the  Lorentz p r o f i l e the d e n s i t i e s  of t h i s  solid  curves  profiles  seems t o be  procedure indicate  i s indicated the  The  quite reliable reliable  width  at h a l f  f o r the  the d i f f e r e n t  transitions  profile.  and  width  and  A l s o shown i n T a b l e  the  then  line,  be  seen,  thus  the width  of  the  f i t for  underlying  can  of  para-  be  obtained  are not  because of poorer  densities  in  observed  a list  but  I I I i s shown a l i s t  the s y n t h e t i c p r o f i l e path,  can  height v a l u e s  s t r o n g 0-^(1)  In Table  tion  i n form,  f o r t h e weaker l i n e s  uncorrected  of the  t h a t f i t the data best  noise ratio.  observed  As  should  synthetic profiles  t h e most s a t i s f a c t o r y  are Lorentz p r o f i l e s  compiled.  width  observed  spectrum  I f i t i s assumed t h a t t h e  meters f o r the p r o f i l e s  of  observed  s y n t h e t i c spectrum.  shown.  until  function i s correct,  t h e d a s h e d s e c t i o n s show t h e d e p a r t u r e  spectrum from the  adjust  and  f u n c t i o n matches the  s y n t h e t i c s p e c t r u m and  The  simple  t h e peak h e i g h t  the c h o i c e of i n i t i a l  graphs of the  a  1%.  t o w i t h i n about If  first  f u n c t i o n of the p r o f i l e  means o f s u c c e s s i v e i t e r a t i o n s analytical  At  h a l f w i d t h i s used to  by  values  broadened f e a t u r e i s-  signal  are  too to  linewidths for  including  the  of the best s y n t h e t i c  I I I i s the i n t e g r a t e d i n t e n s i t y  d i v i d e d by  square of the f i e l d  the  l e n g t h of the  s t r e n g t h and  absorp-  the d e n s i t y .  FIGURE Comparison profile  and  of  2!  observed p r o f i l e  broadened  Gaussian  with  broadened  profile  Lorentz  ~ 65 -  0.007 C W  QiCl) ©  i.50 IWAkGkT  V_ ^ ——  FIT."OFL"OR.EMTZ PROFILE _  FIX  7PA5H&D  LIME  CORRESPONDS  o,oo7c  m"  ."QiCl, cp I.IP AMA^M"  OF  TO  qAUS.SlAN  PROFILE  TABLE List  of  observed  height  of  Also  list  a  Lorentz of  coefficients;  linewidth profiles  normalized a l l related  III and  c a l c u l a t e d width  that  f i t the  integrated to  density.  observed  absorption  and data.  TABLE I I I  c (o) 1  D E N S I T Y A.'VvGAT  O S S . W I D T H -1  cm  C A L C U L A T E D W I D T H  cn  O B S .  H E I G H T  -1  I N T . A 5 S .  log(I / I ) o m J  m  B / J 1 S  WIDTH -1  2  cn  (1)  l  0 ^ ( 2 )  C A L C U L A T E D WIDTH  H E I G H T  „ -1 cm  l o q t l /I) ^ o m  O R S . I N T . A B S . B / f  IE.  W I D T H  2  Q  C A L C U L A T E D W I D T H  -1  -1  cm  H E I G H T  log(I 3  cm  /I)  INT.ABS. B/j>lE  W I D T H  2  WIDTH  -1  cm ^ -  cm  o  1  ( 3 )  C A L C U L A T E D  OBS.  H E I G H T  log(I /I) 0  IHT.ABS. B/j>lE 2  n  2 8 . 4  . 0 8 5  . 0 7 7 4  . 1 2 4  2 . 1 4  . 0 6 3 8  . 0 5 4 8  . 8 2 3  1 0 . 1  . 0 8 7  . 0 7 9  . 0 9 7  1 . 7 1  . 1 4 1  . 1 3 5  . 0 5 2  2 5 . 4  . 0 8 5  . 0 7 6 8  .  2 . 1 6  . 0 6 7 3  . 0 5 5 5  . 7 2 0  1 1 . 0  . 0 9 2  . 0 0 5  . 0 9 1  2 . 1 4  . 1 2 0  . 1 2 1  . 0 4 7  . 1 3 5  . 1 3 5  . 0 3 6  2 . 4 1  . 0 8 9  . 0 0 1  . 0 5 4  1 . 7 1  . 0 7 0  . 0 4 3  1 . 9 5  . 0 4 8  . 0 4 5  1 . 5 9  102  1 . 5 •  6  1 . 5 7  2 2 . 4  . 0 8 4  . 0 7 7 7  . 0 7 0  2 . 6 5  . 0 6 2 3  . 0 5 2 1  . 4 7 1  1 2 . 0  . 0 8 5  . 0 7 9  . 0 6 4  2 . 5 0  1 7 . 3  . 0 6 9  . 0 5 9 2  . 1 0 2  2 . 3 7  . 0 5 5 3  . 0 4 2 8  . 6 4 3  1 0 . 8  . 0 8 2  . 0 7 4  . 0 8 4  2 . 4  1 3 . 3  . 0 5 2  . 0 3 8 0  . 0 7 5  1 . 8 5  . 0 4 5 4  . 0 2 9 1  . 4 9 7  9 . 4  . 0 5 2  . 0 2 8  . 0 5 7  1 . 3 9  . 0 7 0  1 0 . 2  . 0 3 3  . 0 3 0 2  . 0 9 0  2 . 0 2  . 0 2 7 7  . 0 2  . 7 0 4  1 2 . 6  . 0 3 6  . 0 3 4  . 0 8 5  2 . 1 2  . 0 4 9  . 0 4 1  . 0 3 9 8  . 0 4 6  3 . 1 5  . 0 2 6 2  . 0 2 0 3  .  342  1 1 . 9  . 0 3 1  . 0 2  7  . 0 4 4  2 . 0 5  . 0 4 9  . 0 4 9  . 0 2 6  2 . 1 7  . 0 2  300  . 0 2 6  8 . 2 2 -  58  39  •  7 . 7 3  . 0  . 0 4 2  1 . 5 2  . 0 2 6 6  . 0 2 1 6  .  1 1 . 8  . 0 3 0  . 0 2 3  . 0 2 3 4  . 0 4  2 . 2 9  . 0 2 4 8  . 0 1 8 7  . 3 0 1  1 1 . 3  . 0  5 . 9  . 0 2 8  . 0 2 3 4  . 0 4 1  2 . 7 1  . 0 2 4 8  . 0 1 8 5  . 2 2 8  1 1 . 8  4  . 0 2 7  . 0 2 1 7  . 0 2 7  3 . 5 3  . 0 2 3 0  . 0 1 4 0  . 1 5 2  . 0 2 3  . 0 2 2 5  . 0 4 8  3 . 2 4  . 02  . 0 1 6 0  . 2 8 5  4 . 0 0  . 0 2 0  . 0 1 8 2  . 0 5 8  3 . 7 3  . 0 1 4 8  . 0 1 1 8  . 3 7 3  1 5 . 6  . 0 1 8  3 . 4 0  . 0 1 8  . 0 1 5 6  . 0 5 4  3 . 5 2  . 0 1 5 2  . 0 1 1 7  . 3 4 4  1 6 . 8  . 0 2 1  . 6 2  30  •  7 . 1 3  4 . 0 0  . 0 1 9  . 0 1 6 8  . 0 1 6  . 0 1 3 4  2 . 0 8  . 0 1 5 8  1 . 7 0  . 0 1 2  2 . 9 0 '  Q  2 . 4 5  9  . 0 4 1  3 . 3 8  . 0 4 1  3 . 2 4  . 0 1 3 2  . 0 4 1  3 . 5 9  . 0 0 7 1  . 0 2 0  1 . 1 6  '  .  •  34  *  . 0 5 0  1 . 8 5  . 0 3 5  . 0 3 3  . 0 3 3  1 . 5 0  . 0 2 5  . 0 3 6  1 . 8 2  . 0 4 3  . 0 4 1  . 0 2 4  1 . 9 8  . 0 2 9  . 0 2 4  . 0 3 7  2 . 5 5  . 0 3 7  . 0 3 4  . 0 1 7  1 . 6 3  1 3 . 7  . 0 3 5  . 0 3 1  . 0 2 2  4 . 5 0  . 0 3 5  . 0 3 4  . 0 1 6  3 . 2 6  1 3 . 6  . 0 2 9  . 0 2 4  . 0 4 0  2 . 8 7  . 0 2 9  . 0 2 4  . 0 2 9  2 . 1 0  . 0 1 6  . 0 4 1  2 . 3 4  . 0 1 9  . 0 1 7  . 0 3 0  1 . 9 9  . 0 2 0  . 0 3 7  3 . 2 0  . 0 2 4  . 0 2 4  . 0 2 7  2 . 6 2  . 0 1 4 2  . 0 1 0 9  . 3 0 1  1 6 . 1  . 0 1 3 1  . 0 0 9 2  . 2 6 0  1 4 . 0  . 0 1 4 2  . 0 1 0 9  . 2 0 7  1 4 . 9  . 0 1 4 2  . 0 1 0 8  . 1 4 7  1 2 . 8  30  . 0 1 4 •  . 0 1 4 . 0 1 8  .  3  -  -  . 0 1 0 2  . 0 3 4  2 . 0 3  _ -  - . 0 0 9 8  . 0 3 6  2 . 3 1  . 0 1 8  . 0 1 6 3  . 0 1 8  2 . 3 8  -  _ . 0 1 6  -  _ . 0 2 2  -  2 . 3 1  ' -  -  The  length  of  accuracy  of  accuracy  with  earlier.  The  intensity  of  the  absorption  about  .5%  for  which  the  density  greatest the  voltage J.  was  read  supply.  Fluke the  linearity  work  and  an  i t  a  H.P.  the  be  supply  discharge  electrodes  of  the  very  uniform.  4. m  cell  was  but  because  potting  of  may  cross  section  believed  have  that  the  1  long  The  gap  of the  M  to  The  cell  was  between .5  mm  presence  of  a  glass  electrodes distorted of  high against  of  the -  the  scale. net-  applied  3%.  However,  used  between  3.12 the  the  in  series  large currents  gap  -  somewhat  was  of  divider  Thus  to  12  the  end  within  due  to  calibrated  resistor  damage  knowledge  voltage  be  between  been  a  discussed  regulated  lower  The  absolute  applied  our  the  the  an  used.  been  our  voltmeter.  c e l l .  m  to  at  with  100  the  in  to  ~  .09  the  mm  and  e l e c t r o d e s of and  was  cylinder the  these  was the  fairly and  field  (see  when  rubber  in  F i g . 2b  cell).  Because  factors  field  strength  quoted  is  accuracy  of  line  width  of  plot  uniform,  the  gas  for  i t i s  accurate  to  about  only. A  by  in  the  compound  a  in  were  accurate  prevent  measured  space  10%  tube  occurs  not  -  vacuum  to  of  cell  has  voltage  dial  checked  that  error  The  supply  measured  i s known  readings  be  be  absorption  of  was  noted  can  however,  the  dial  i s believed to  should  with  from  voltage  Then  voltage  lies,  field.  The  high  each  source  .lines  -  path  -  applied electric  electrodes  a  the  67  above  test  of  the  analysis  i s  the  the  continuity  a  obtained of  line  -  wjidth jvs.... d e n s i t y .  65  The u n c o r r e c t e d l i n e v,d.dths f a l l on a  h i g h l y d i s c o n t i n u o u s c u r v e because o f t h e a b r u p t changes i n t h e l i m i t o f r e s o l u t i o n a t w h i c h s p e c t r a were r e c o r d e d . Fig.  In  17 b o t h t h e u n c o r r e c t e d and c o r r e c t e d l i n e width, as a  f u n c t i o n o f d e n s i t y a r e shown f o r . c o m p a r i s o n .  I n F i g s . 16,  18 and 19 a r e shown, graphs o f l i n e w i d t h v s . , d e n s i t y f o r the other  transitions.  >  69  Discussion  of  Results  Remarks  3.1  From possible  In  what  the  results  compiled  to  deduce  various  quantities.  1)  f r e q u e n c i e s as a f u n c t i o n o f gas d e n s i t y and i n p a r t i c u l a r extrapolated values f o r zero density,  2)  t h e w i d t h and a f u n c t i o n of  3)  the  possible  about  actions  with  will  compared,  other  3„2  be  free  These  to  i t s neighbours,  of  extract  molecule  wherever  line  intensities  attempt  the  Chapter  shape of the density,  integrated  f o l l o w s 'we  in  in  of  are:  the  information and  Our  p o s s i b l e , with  as  lines.  as- m u c h  gas..  i t is  profiles  hydrogen  the  2  i t s  inter-  conclusions  those  reached  density The  frequencies  energy  level  and  terms  state  the for  molecular the  constants  hydrogen  (ground, s t a t e )  are  molecule  given  by  equation  (Herzberg, w  T  (v,J)  -  w  =  G  (v)  +  Fv(J)  (v  +  3 2 ^) 2  +  w  1950) (v  e  J  B  +  (J +  .1 2  TT)  1)  x e e D  J  2  (J +  I )  2  +  y e e H  (v  J  3  (J  and B  V  by  writers.  Zero  G(v)  as  B  e  ot  e  (V  +  7  )  +  E  ( V  +  w )  o  o  o  1 %•) 2  + +  l )  3  +  the  in  70  D  = D  v  e  +6  = H  (v +  e  i  and  H  The  transitions  v  *  e  -i-e tS (v2 +. i ')  2  observed  i n these  J * * = J'' f o r J ' = 0 ,  J'  =0,  The  v  ,  1  = 1 with  where  2  H , .  v"  lo  -  &. J  J takes  values  AJ  = 2 transitions  1,2,  = 0 transitions  i s t h e quantum  and  experiments  number  occurring  are v' = 0 to  3 a n d J'» = J  vibrational  i n the initial.state,  are indicated  +2 f o r  by Q ( J )  are denoted  of the final  1  by S (J)„  and then  I t may  v  state  be  shown  that: • ^Q., ( 0 ) "= <3. . = w -2w x 1 1-0 e e e  +  J  Q"Q (1)  = CT _  Q (2)  = O-3 _  1  Q J  1  ^"c^O)  1  0  0  1  1  ,  1  +  (B -B )6  1  + 63  0  = Q^ _o  +  1  2  1  equations  B  +  0  1  1 4 4 D  x  1  Q  + 1728H  make u s e o f t h e r e l a t i o n s  = 0 6B  ^ ( 1 )  -°V3)  ^ ( 2 )  - ^ ( 4 )= % ( 2 )  =  %  U  )  =  1 0 B  3 6 D  0-  = " B  0  (3)  +  (4)  - 2B  1  we  0  (1-^-1-^)216  (^-1-^)1728  (5)  f o rthe various  -°S (0)  (2)  Q  1  solving  - ^ ( 2 )  1  (D -D )144  In  ^ ( O )  (H -H )8  +  Q  - 360^^ + 2 1 6 H  l  (1)  (D -D )36  0  1  w y e e  1  0  ]  /4  <- ( D - D ) 4  Q  1  0  5  ' S (1)  (B -B )2  = CT _ + ( B - B ) 1 2 +  .^S-^CO) = ( T _  Q  +  1 3  + 4D  constants  0  1 4 0 D  Q  +  2 1 6 H  0^  - u 364D  0 +  -  8H (6) Q  i n t h e above  0  1 7 2 0 H  Q  ( 7 )  0  ( 8 )  7784H . 0  (9)  71  From  these  constants  three  equations  B^, D Q a n d  we c a n o b t a i n v a l u e s  which  can then  (2), (3), (4) a n d (6) t o s o l v e f o r given a cy  a list  least  of frequencies  squares  fitting  D  ]L  be used  and H „  f o r the i n equations  I n Table  1  extrapolated t o zero  IVi s  d e n s i t y by  o f a quadratic expansion  f o r frequen-  v.s o d e n s i t y : TABLE I V Frequency  Line Q (0)  4161 .1653  +  .0006 c m "  Q (l)  415 5 .2543  +  .0005  0,(2)  414 3 .4664  +  .0009  4125 .8696  +  .002  s (o)  4497 .8405  +  .002  a)  4712 .9008  +  1  1  Q l  (3). 1  S ]  Note:  ,001'4  t h e t o l e r a n c e i s t h e computed r.m.s. d e v i a t i o n f o r t h e data used i n t h e l e a s t squares program. From  there  t h e above  a r e no d a t a  cannot ences cies  1  available  be o b t a i n e d computed  rotation  a small  results  i n agreement  apparent  frequency  values  f o requation  f o rB Q , D Q and HQ„  we f i n d  obtain  of frequencies i t i s clear ( 9 ) , and a  However,  i n ( 7 ) a n d ( 8 ) may b e c o m p a r e d  o f t h e pure  corrected  list  lines  obtained  systematic  with Fink  N  and H . n  solution  the differ-  with  frequen-  by S t o i c h e f f  (1957).  i n Stoicheff s  e t a_l ( 1 9 6 5 ) .  of Stoicheff  f o rB „ , D  shift  f o r Cfg ^ ) They a r e :  w  Using the e  c  that -  a  n  t  n  e  n  -  72  B  =  Q  Present  results  59.3344  -  DQ  = +0.04560  HQ  = 4.1  x  10~  - 8 x  x  should  equations  cm"  4  10~  10""i4.8  It in  6 x  Stoicheff  noted,  has been  reflected  i n the accuracy  Introducing (2),  measured  •  H Q .  (3) and  ±  and  H  X  quoted and  w y from e e  0% n 3- 0 We  =  case  poorly.  of B  -w  e  x  e  whose  This i s  = +0.04416  -  1 x  10~  4  era"  1  3.95 1  6  »  1  x 1  6  10" 5  -  3  4 x  -  5  6  x  10~  10~  6  cm"  4  cm  for B Q ,  D Q  equations  may  obtain  new  2w  x e e  values  e  -  6w  -  12w  .+ 1 3 / 4 w y ee  x e e  J  +  31/2  w  x e e  +  171/4  = 4401.1177  i  .03  =  -  .02  e  e  y  e  w y . e e  121.284  cm  1  cm"  1  - 1  1  f o r t h e o v e r t o n e s , Q^-O*  -  3w  e  line  and D Q i n t o  ,  Q  find: w  frequencies  obtained  equations:  =  a  1  = 2w  H 7 8 2 . 351  cm  the difference  cm"  e  n  10"~  4  =  1- 0 - - 8087.006 2- 0  that  x  10~  = 4 1 6 1 . 165 3 = w  n  =.5.2  - 1  -  e t a _ l , we  the  Q  2 x  frequencies  by F o l t z  H  1  cm  -  4  using  = +0.04599  =-56.37600  ^ l - O "  Now  rr,  1  Q  cm"  obtain:  B D  D  5 9 . 3392  relatively  values  ( 4 ) we  Q  of the values  •  t h e new  B  (8) i n v o l v e i n each  frequency  and  - 1  1 0 " cm"  be  (7) and  cm  5  1  ^3-0' for w  a  s  ,  w  x G  e  -  w w  e e  i  .03  cm  121.284  -  .02  era"  -  .003  x ' = e  constants previously  Table  V  a r e shown  .8048  frequencies  with  1  from  the above  the present  and  V  Frequencies calculated  cm" ,  results. -  TABLE Line  1  calculated  and compared  published  -  4401.1177  w y = e e In  73  present  Fink  cm  et a l  1  Church  3  Stoicheffk  0,(0)  4161.1653  .1653  ••181  .170  .138  0,(1)  4155.2541  .2543  t .2586  .246  .208  Q,(2>  4143.4665  .4664  T.4664  .468  . 392  0,(3)  4125.8693  .8696  T.8710  .871  .835  S,(0)  4497.8389  .8405  .8385  .835  S,(l)  4712.8989  .9008  t.9066  .846  S , (2 > 4 9 1 6 . 9 6 3 5  17.0118  .873  S,(3)  5108.2505  .4066  .286  Q (0)  8087.006  2  *  t h i s value i s taken Foltz et a l .  86.94  from  the f i e l d  induced  spectrum  of  -»  t  t h e s e v a l u e s a r e b a s e d on t h e r e s u l t s o f F i n k e t a l , b u t c o n s t i t u t e a s l i g h t l y improved e x t r a p o l a t i o n to zero d e n s i t y c a r r i e d o u t by F o l t z e t a l .  a)  these f r e q u e n c i e s have been e x t r a p o l a t e d t o zero d e n s i t y u s i n g known f r e q u e n c y s h i f t c o e f f i c i e n t s and a s s u m i n g m e a s u r e m e n t s w e r e made a t 19 a m a g a t d e n s i t y .  b)  these f r e q u e n c i e s have been f r o m 2 amagat d e n s i t y .  extrapolated  to zero  density  The  results  from  measurements  near  1  set  amagat.  of  of  obtained  from  the  reported  data  somewhat  an  at  zero  improved by  Q^(0)  line  and  seems  in  that  Church  very  well  i s  poor  Brannon,  l i t t l e  to  the  quoted  i s  about  atically  in by  present Church  same.  Raman  0.045  cm  - 1  approximately  hydrogen  we  of  -  and  0.02  cm  More  .  connection  In that  only  spectrum  present in  1  list  Table  -  to  cm" , a  his  be  of VI  seems  to  Foltz  shifted  are  add  by system-  this  0.0015  agree  accuracy  measured  with  comparison  believed  cm ,  to  although  - 1  i s better,  i s clear Dunham's (see  of  of  data  the  spectrum  as  of  results  seem  frequencies  within  0.0008  molecule  our  density  recent  frequencies  were  Considering  because  to  another  frequency  1  (1968)  Church  The  the  results.  Peters  of  zero  measurements  appear  from -  our  quote  improvement  effect  remembered  reproducibility  the  densities  frequencies  that  results.  results  c o r r e c t absolutely to  the  This  with  accuracy  be  for  a l .  to  the  Finally  et  obtained  at  a_l ( 1 9 6 5 ) these  due  should  being  density,  entirely  i t  the  be  -  et  e x t r a p o l a t i o n to  Fink  an  were  spectrum  notes  older  the  (1966)  one  the  by  Stoicheff  fc'oltz  agreement  quoted  al  when  quotes  with  et  quadrupole  though  questionable  the  Fink  the  Even  frequencies  of  from Y  Dunham,  Table  IV.  parameters 1932):  -  75  TABLE w  Y  e w x e e  10  ~Y  20  Y  w Y  e B  Y  e *e  -  tfe  Most by  4401.118  =  121.284  30  01  Y  l l  Y  21  Y  he  =  values H  Q  Pe  .8048"  He  =  3.02 58  "  .0345  "  .0048  - .002  Y Y  H  1  e  =  31  -  parameters  e t a l (1966)  parameters  obtained  "  cm"  Y  e  60.8380  exceptions.-aretwo  D  - 1  =  o f these  Foltz  cm  VI  agree  "  0.144 0.0  22 ~"  Y  0 3  Y  13  7I 5  ;  -  =  e  with  (1959).  x 10~  2  cm  2  .2  x 10~  with  those The T  n  5  5  obtained notable latter  e  the values  of H  The complete  list  of  f o rH i s : v  = 4.1 x  10  5  - 4 x  10~  5  cm  3.9  10  5  - 4 x  10"  6  cm"  ^  1  present H.  10~  - .0001  and  H  x  4.2 5 x 1 0 "  =  well  e  consistent  a n d Howe  12  4 4 . 6 32  e t a l (1965).  .the p a r a m e t e r s  by H e r z b e r g  ~  very  and F i n k  a x e more  02  x  1  results  J  H,  H  4  3.72 x  10  =  3.48 x  10  3.4  x  10  3.3  x 10*  H, H  6  3„3  -5  =  =  passing  -1 ^  -5 Herzberg  -5  Absorption The  cm  coefficients  amount  through  and p o l a r i z a b i l i t y m a t r i x  of absorption  a sample  a n d Howe  experienced  o f hydrogen  by  elements  light  gas c a n be expressed  by  -  a  simple  loss  i n .  i s the absorption coefficient  tion  path.  with  a particular  T h e amount  i s obtained  j  =  8 K  <TN  where j j i s t h e d i p o l e state,  frequency, in  and N  the state  the  dipole  vibrational  band  .  E 2  0  0  1  1  E  2  2 -<S— 2  E  2  3 -+~  3  E  2  •3—  0  E  2  1  E  2  3 (See  rule"  CT  6  i sthe  i s the transition per unit  of the matrix  volume  elements  of  rotational-  following:  Matrix  Element  J  r  2  golden  jn'  i n the fundamental  are the  Squared  state,  «r)) d<r  n>\  o f molecules  The squares  arising  t r  o f t h e system,  i s t h e number  moment  (cr)/i,  "Fermi's  JT \  |  i s the final  | n'^> „  Transition  J  moment  \n>  n (i.  by u s i n g  |.<n  he  length associated  p ' r o f i l e "m  £  absorp-  equals:  1  B ( <T ) d 0 profile  and £ i s t h e  per unit  transition  theoretically  B'  i n i t i a l  of absorption  molecular  = i  B'  It  (<r). e  (cr) = i .  tr. B(tf)  -  equation:  i,  where  76  Appendix  A  CcO  2 0 1  [ ( CX )  2 Q  [ ( cX )  2 Q  [ ( cX )  1  Q  i  )  (tf  + 8/22.5  (  *  + 8/315  (  tf  +  2  4/45 ( 4/75  1  ) 2  )  2  oi.l oJ  16/675  2 0  )  1  2 Q  1  f o r the derivation  of these  matrix  elements)  77  The  number  states  of  particles  i s given  by  per  the  unit  volume  Boltzmann  in  each  of  the  initial  distribution:  -YWkT N  p  =  "  .where  is  the  Loschmitt's which  i s  3  ( 2 J  "° . Z vJ  density  of  at  a  temperature  in  the  We  find  J  (para =  J=0 1  J=2  N  have  in  J  (ortho  and  3  independent pointed  observe  of  y  E  in  our.observations  decreases saturation  smaller  This  trend  including  N  0  x  O  ^  :  NQ  is  nuclear  statistic  and  for N terms  o  1  1  were up  to  for computed 2000  cm"  5  x  0.6617  =  £ N  Q  x  0.1155  J N  x  Q  0.0866.  frequency and  Cr" , t h e  E.  the  i n the  values  B'/y  top  less.in  at E  2  than  at 2  bottom.  our  results  ,2  $  e t a_l  exhibit  large values  I I I where  to  B'/  Foltz  lines  of-B'/^E  i n Table  from  value  However,  hydrogen  of  i s much  1  Q  that  shown  3  f N  values  monotonically effect  r  hydrogen)  =  J  of  out  $  =  - =  particular  they  ,  7  the  Values  c o n s i d e r a b l e ."saturation",.and hence  2  V  amagats,  represents  of  ~  €  values:  N  (1966)  gas  ( J )  function.  J  be  g  hydrogen).  N _  should  1)  the  295°K  N  a  e  +  g(J)  following  At  ( J )  (2J  values  T  partition the  q  of  and  f o r odd  values  1 }  r  ^  number  even  +  of  lower can  the  be  ^  E  2  values noted  product  j> E  Even, t h o u g h  the  (because  most  2  1  -  measurements reported a  were  by F o l t z  function of  obtained The  values  ° E  2  linear  values  of  j E  than  E  line  by  linear  dependence  f o r the stronger  Q, ( 1 )  w  s  extrapolation.  i s significantly  line.  a  as  The  non-  extrapolated  are: .  B'  !$  .6  X  10  1.5  X  . .6  X  10"  1 5  X  10"  1 5  Line 0,(0)  3.0  0,(1)  13.8  Q,(2)  2.5  V  1.9  From  lower  2 B'/^E v/as p l o t t e d 2 2 for B'/^E a t 5* = °  and a v a l u e spectral  of this  only  a t much  et al) nevertheless  f o r each  slope  zero  taken  78  3  )  these  + + +  .5  values  - 1  ^  cm  - 1  /(volt  cm" ) 1  cm  2  , -15 0  i t follows  by  straightforward  calculation  that '  ( oL )'  ( CX ) ^ ,  + 8/225  (# ) '  (o( )  + 8/315  (  0  ( OL  If  we  then  ! 0  )  ,  01  +  i t c a n be  )'  #  seen  2 Q  =  1, 16  ' =  1.18  Q  1  ~2—  16/675(  assume, t h a t  )  + - .12  1.23  01 1  x  10  ,08 x -  10'  .12  x  10  .12  x  10  1  01  1.21  78,  01 that  as q u o t e d  i t contributes  -25  by  •25 2  5  -25  cm  3  cm cm cm  Church  only  (1959),  about  2 to  3%  2 to  (OC)  take  i n each  the average  estimate  o f oc ^  of the above  value .  oc  01  on  expressions.  the right  V7e o b t a i n : + 1.20 - .1 x  10  hand  -25  side  3 cm ,  Hence as  a  we good  can  79  A  comparison  both  of  this  theoretically  value  and  f o r OC  with  values  experimentally/follows:  Investigator  0  et  (1966)  al  '  and  Ishiguro  e_t a l  was  not  (1952  elements  vibrational  states  because  obscured  by  the  spectrum  and  the  spectra,  have about can  30  relate  data  which  that  which  that  between  an  the  field  v  (calculated).  estimate 0  =  Induced  and S  appearing  the  the  product  to  observed  v  for  lines  the  1  =  were  i n both  the  value  line  width .06  is f £E  cm  to  2  of  resolution  i t i s evaluated,  density  the  of 1  .  peak  x  1 0 ~  isotropic  with  which  recorded.  Lorentz  Using  the  limit  are  the  the  this  We  profile width,  absorption  at we  from  our  yields : In  where  j> i s  E  applied  the  ,1  background.  from  the  obtain  S. l i n e s  i s related  amagat  1. 39  the  quadrupole  appears  observed  --t-  3  .97  )  p o s s i b l e to  matrix  polarizability  ~  C M  1,10  (1958)  MacUonald  anisotropic  the  25  ^  X  .97  Crawford  It  01  (1959)  Church  It  6  1,20  present Poltz  obtained  the  (I /I) 0 max  density field  that  f o r example  near  this  density  =  n  for  in  amagats,  in volts the  there  L54  cm  lowest is  a  1  „  0  peak  the  From  value  1  ? £ E -> 0  2  absorption this  of  absorption  i t can E  used of  path be by  about  and  seen Foltz 8 3%.  -  Because  of the non-linear  feature  and  ing on  by  In  saturation  between  has been  =  0  and v  of the quadrupole  Q-^(l)  and Q^(2) l i n e s obtained  and  Coolidge  the  matrix  element  path,  =  we  profile. when  S-j(l)  line  appear  White  weakly  '1  lines  taken  a t 2,56  rough  from  According  moment  5  measure-  "background" t o James  i s related  ~R  to  by:  i ^iV]  5  5hc  amagat  moment  i n some  4TX CT M.  J  (1) $  ~  • -  ) 4 1 2  x  10  ,0036  x  10  <  'Q (2) ! /  T<\  a n d f o r 50 m  n>)  2  absorption  -1 cm  /amagat  cm  /amagat  cm  -1 cm  -3 '  values  those  the  This  the quadrupole  absorption  of the quadrupole  =  states  and from  cell.  the integrated  B(cr)dc-  I  a  i  The  influence  find:  'Q  B'  the broaden-  strong  to obtain  1 vibrational  -3 B  absorption  of the quadrupole  -3 B  a  disappear  possible  which  1  spectrum  =  with.the  (1938)  B.  a  have  of the l o g r a t i o  element  ments  From  the  absorption,  will  therefore  found  o f the matrix the v  spectra  between  resolved. It  estimate  should  -  strong  profile  of the integral  effect  fully  relation  a t such  the instrumental  the value  are  (I^/I)  80  (l)^S  =  o(  - S31  x  )  f o r t h e 0.^(1)  obtained  line  i s about  will  be  by F i n k  from  -1 cm  and S ^ ( l )  "/amagat lines  e t a l (1965),  6 0 % a s much  ignored  10  here  cm.  agree  The v a l u e  as t h e value, o b t a i n e d on.  (very poor signal to n o i s e ratio)  By  very  well  with  f o r t h e Q^(2) by F i n k  straightforward  and  arithmetic  -81  we  obtain  f o r G-^^Q/e  This  compares  Fink  and -59.3 x  James a  Frequency The  line 17,  v/ith  these the  shifts gas  over  effect.  amagat  with  up  foreign  For postulated isotropic the  were  Raman  vibrational  pretation  in  amagats.  to  favour  1965).  shown  range  shifts  covered amagat  of  have  range  over  small  a n d May  been  each  i n Figs.  of  at different  hence  frequency i n the  studied  e t a l '(1964) range  16,  which  and  encountered  the density  hydrogen  a t 300°K  the frequency scattering motion  o f degree  [<rQ(j)] v/here. Q ( J )  seem  frequency  of the behaviour  density  from  more i n the  less  temperatures  than  and  =  expresses  (  J  )  +  f  i s the zero  by  density  9  v/ith  perturbations of  For a quantitative  i n the  Q  May h a s  associated  are caused  he  two  and 85°K  shifts  only.  of the shifts  polynomial  by  mixtures.  pure  that  A" .  t h e v/ork o f  et a l ,  i s relatively  e t a l (1961)  t o 800 gas  (Fink  10  obtained  2  calculations  the density  taken  frequency  They  X  3  from  i s clearly  However,  b y May  10~  of the central  the complete These  o f -90.8 x  v.s. density  are not indicative  extensively  100  2  i n density  and 20.  phase.  Raman  recent  10  variation  measurements  data  o f -100 x  More  shift  value  as c a l c u l a t e d  -120 x  changes  1 8 , 19  %  10"  o f about  average  n  a value  and C o o l i d g e .  value  3•4  with  a  -  inter-  the frequency  as a  density:  J ?  +  b  j ?  frequency  2  a n d J> i s t h e d e n s i t y  -  He suggests term  that  that  i n i t i a l  first  i s  aj  points  can  be  rotational  as  contribution a  "coupling  to  state,  of  =  O  T  that  expanded  proportional  a  The  out  82  a  -  the  into  the  J  dependence  a. c o n s t a n t  number  of  to  a.  effect".  the  intermolecular  the  internuclear  In  this  +  X  a  the The  linear  term  Quadratic  in  shift  could  constants  potential  term, '  then  a.,  a  and  a  separations.  By  form  potential  the  expressed  a,  as  contribution, giving ence  a  small  a^.  With  coefficient  tions are  to  was a  listed  for  the  each  sum  the  that  a,  making  is  cross  use  of  in  a the  an  model  he  are  T  u  expressing expansion  in  molecules.  related  to  the  bj  to  term  In  the the  inter-  Lennard-Jones  potential,  relatively  temperature  then  b  of  " a t t r a c t i v e " and a  interpreted  pair  the  intermolecular  of  by  series  separation,  first  considerably  this  power  be and  c  interacting  consisting.of  but  and  May  "repulsive" large  value  dependent  attempts.to  has  predict  differthe  bj.  The density  an  out  to  c  quantities a  internuclear  nuclear of  as  of  i t turns  the  r  ( n . /n) „ u  c  meaningful  distances  expansion  a-  i.e.:  to  physically  term  molecules  1  related  of  frequency  found  by  quadratic ble  a  of  each  least  squares  function. VII,  line  along  The with  as  a  function  f i t of  of  the  a l l the  observa-  c o e f f i c i e n t s so  obtained  the  r.m.s.  deviation.  - 8 3  TABLE  -  VII  present results J  Q  (J)  l  a., x  10  May  3 J  b  x  10  6 e  J x 10  Foltz et a l  et a l  3  b  x  10  ajX  0  4161 . 1653  -2.44^.14.  14  i  5  -2 .35  5. 6  -2.34  1  4155 o2543  -3.58i.ll  18  i  4  -3 . 14  4. 86  -3.25  2  4143 .4664  —2„62i„22  30  i.  8  -2 .07  5. 77  -2.02  3  412 5 .8696  -l.42i.45  15  i  15  -2 .25  6. 79  -  From  a plot  of  r  obtained.  On  considerably  a  T  of  ag,  we  as  t h e components  i t appears from  by well  that  a.  and  1  a^ f o r J  the predicted value  May as  (see F i g . 22).  and  using  =  were  c  3 i s  f o r a^  the present  a l lthe values  Then  a  quoted  based,  values by  May  d i s r e g a r d i n g our value  o f a-^,  obtain:  and  a  These fact he  given  a.^,  and  Foltz  plot  different  the r e l a t i o n  and  v . s . n^./n J  this  on  a,  J  .185  c  values  obtained higher  -  0.15  x  10~  cm  -  /amagat,  =  -  0.25  x  10~  cm  -  /amagat.  -2.35  agree  the value  predicts  =.-2.15  closely  for a  using  The  reason  3.5  Line  those  i s here  those  somewhat  the Lennard-Jones  f o r the b  than  c  with  coefficient  by  closer  discrepancy  over  i s not  May to  potential.  are generally  o b t a i n e d .by May  for this  given  the The  3 to 4  a wider  and i n value values times  density  range.  clear.  profiles The  full  width  at half  t h e peak  intensity  (HIV/) o f  FIGURE Graph  showing  relative  linear  population  22  frequency of  initial  shift states  coefficient  vs,  - 84 -  lERESE-UT .-RESULTS. F.OLTZ ET AL MAY  E.T AL  . .  -  the  profiles  have  been  range  18  and  graph in  lines  each  the  Due  case  the  width  of  to  a  linearly part  measurements lines  (1966) The  The  line by  narrowing  suggested  case  by  noise  f o r these in  f o r the than  equals  cm  lines,  which  to  zero  Cooper  Raman  et  effect  to  less  a  width  Wiggins  (1953).  (1968)  than  by  the  consistent on  lines-due He  the to  pointed  that observed  "doppler"  these  which  i s  i t Is  about  possible  constant  3  and  4  qualitatively  and  towards  width  some m o n o t o n i c a l l y  emission  (1963)  spectral  Dicke  a l  a  between  o b s e r v a t i o n s agree by  into  plus  However,  width  at  - 1  other  width  the  classical  the  increasing  i n  17,  the  noteworthy  i n t e n s e than  dependence  of  uncorrected  0.041  are  16,  lines.  line,  goes  results  ratio  line  the  density  in Figs.  Q^(l)  density  the  These  I t i s also  less  Raman  of  to  reduction  stimulated  and  over  plotted  signal  (even  i s , furthermore,  Rank  been  lines  considerable scatter  a  which  spectra  amagat.  density  of  0^(3)  the  i n the  the  28  and  of  made  narrowing  Q^(l) made  on  a  width  the  the  These  ' S Q ( I )  poorer  vv.s.  lines  more  decreasing  to  have  occurs  trend  In  decompose  plus  and  the  line  these  times  observed  i s considerably  frequencies. five  the  ~  ( 1 ) , 0.^(2)  i s unmistakable.  of  width)  ITI  to  Q  amagat  width  density  minimum  line  1.5  there  line  0^(0),  from  i n Table  of  lower  about  19.  weaker  the  deduced  from  recorded  of  85  on  the  with S^(0)  Lallemand of  amagat.  and  e t a_l  the  (1)  doppler  width  with  observation  an  quadrupole  of  Q^(l)  pressure  was  out  when  that  line. the  line.  first many  86  elastic over  collisions  a distance  spectral  and n o t by  rate  i s much doppler  results.  that  the  the thermal than  t h e mean  shift  will  be  the coherence  auto  This  consequently  thermal  function  or emitted  results  ( i . e .Galatry,  1961, G e r s t e n  Rautian  and Sobel'man,  1966) have  both In  doppler  each  of these  perturbation time  broadening  caused  (assumption  reduces, finding  a s was  of c l a s s i c a l  shown by A n d e r s o n  the autocorrelation  radiation  field  emitted  by  to  t h e F.T. o f t h e a u t o c o r r e l a t i o n  of  account.the  the internal  broadening state  was  Several  i n  made  that  function  the  the radiating i s then  function.  due t o c o l l i s i o n a l  place. the of  problem  t o the problem  The spectrum  of the molecule,  which  take  of the amplitude  i t undergoes  into  which  the case  so t h a t  while be  of the  broadening  (1954),  o r absorbed  of  1968 a n d  i s a definite  function  collisions.  field  so  each  the length  and F o l e y ,  treated  path)  at  o f the spectrum.  the assumption  by c o l l i s i o n s  line  amplitude,  molecules,-  and " c o l l i s i o n "  treatments  result-  are usually  of the e l e c t r i c  authors  diffusion  the  Is reduced  by t h e s e  the  a narrower  of reducing  i n a broadening  the  velocity,  i n the o s c i l l a t o r  of the oscillations  molecule  diffusion  Since  collisions  has the e f f e c t  absorbed  by t h e s e l f  and hence  elastic  shifts  correlation  radiation  less  of a  of the radiation,  velocities.  less  by phase  collision.  the'displacement  i s determined  In practice,  accompanied  during  , the wavelength  distribution  rate  ing  X  occur  In  of  of the system taken  taking  perturbations  t h e model  of  impact  -.87  broadening the It  i s used.  molecule c a n be  This  that  both  the  case  o f a hydrogen  The  mean  free  packet  path  thermal  the  uncertainty  The  effective  hydrogen and  molecule  much  less  therefore tained  ing  most  cases  pressure, time  t o compare  v/ith  some  t h e "time between  i n some  of Rautian  appropriate i n that  motion  spectrum  transformation  collisions.  detail  they  Followinq  the treatment  Kui)  = ~  where  _(()  =  • j and  E(t )  (D  wave  made  treat  radiated  of Rautian  h  R e f 4>(r)  <F. (iff.  .e  and l u j r  ( t +V))  w,\ > i W t + i k r.(t) = A(<J)Q) e 0. n  f o rthe pressure,  It  appears ob-  by t h e above (1966)  a number o f  limit-  here.  of a  function by  when  value.  the results  and Sobel'man  of the autocorrelation  of the light  units  of collision" i s  i s o b t a i n e d b y means  amplitude  at the  potential  c a n be r e c o g n i z e d as a p p l i c a b l e  The  a n d a wave  at atmospheric  of the predictions  The treatment  that  pressure  300°K.  1 0 % o f i t s mean  hence  which  i s small.  at  a few Angstrom  i s about  6  molecule  equilibrium  of the intermolecular  t h e mean  valid  here  authors. seems  than  over  during  are reasonable In  trans 1ational  extends  i s about  somewhat h i g h e r  assumptions  1000 AVatm.  i n momentum  range  the time  another  gas i n thermal  the free  speed  that  with  these  i s about  representing  average  implies  Is i n "collision"  seen  -  Fourier  of the  a moving  oscillator.  Sobel'man:  dz? , (< > = t i w i e ave.)  -  r(t)  i s the location  follows  0  '  simplify  and  studied.  Sobel'man  VQ),  which  distance the  •  we  have  To f i n d  W  0  < e  r  was  of the line  identified  M  t.  I t  t acquires  function  which  that  set A  f  a molecule  = 1  Rautian  ( r ,v, t ; moving  v when  2  line i s  above,  function  and i t s  V  we  spectral  values  a velocity  satisfies  + v  >  n  profile,  a distribution  at the origin  distribution  k  '  the probability  r i n a time  i  the expectation  introduce  gives  particle  This  i e  the discussion  0JQ = 0 after  being  at a time  that 2  and  -  of the o s c i l l a t o r  $ 0 0 = A (oo ) To  88  a  initially  was V Q .  velocity  the kinetic  equation:  f = S,  at where  S i s the c o l l i s i o n integral.  solve  f o r f , then  (pit)  = <e"  i  k  r  (  Z  it'follows  r  )  >  The  autocorrelation  the  phase  This  a manner  effect  similar  i s also  l  i s taken  after  a time  equation.  t .  k  f  r  (r,v,r;v ) 0  affected  into  dr  by changes i n as a r e s u l t  account  b y R.  of  a n d S.  t o t h e above ,  )  f  i  of the o s c i l l a t o r  ( 4 ,"C ) i s t h e d i s t r i b u t i o n  where  e  0  function  to  that  Jdv J dv J  o f the amplitude  collisions. in  =  I f i ti s possible  f i s again  The' c o m b i n e d  function  obtained  effect  from  of motion  f o r t h e phase  the kinetic and c o l l i s i o n s c a n  then  be  CD (£0  treated  = \e  in  a  unified  •  -  89  way  so  / =  e  -  that:  - i k r - i iy  f ( r , v ,  V,t-)dvdrd'4y  t  or  4>(f)  e  =  l  k  ( r , v , "C  f  r  ) dv  dr  where . We  can  f  now  choose  model  of  here  which  to  the  of  of  treatment  i k  atom. is Its  ),  this  + v  •at  can  leads  to  V  f  be  of  complex  we  of  after  so  by  that  collisions of  limits  of  shift  will  velocities The  i s of  order  Also  independence"  1/S)  we  in  which  at  a collision,  velocity  of  the  V  as  defined  that  remains noting  assymmetric  a  broadening.  distribution.  phase  provided  of  collision i s  distribution  the  case  "strong-collision"  "statistical  verified  the  the  doppler  redistribution  correlation  to'an  within  case,  before  for  c o l l i s i o n frequency.  i s applicable  validity  observed  the  the  ( i . e . phase  dependence  In  that  the  velocity  i s independent  This  large  to  and  velocity  for this  choose  (P+  equation  equilibrium  initial  time  of  the  velocity  related  i s assumed  kinetic  that  w h e r e "\5 I s the  ) d^V  (r,v,iy  the  an  the  characteristic  ^f  treatment  the  establish  regardless  i t  1  c o l l i s i o n broadening  assumes  independent tend  -  formulate  combination We  = j e  after  that  line  emitting  many  above  collisions)  statistical  profile  which  our  experimental  f  w (v)  i s  not  error.  have:  = -( P +  i M  f  -  \>  -  m  \ f  (r,v',t)  dv'  -  where The  w  (v)  m  i s the  equation  i s  ecmilibrium  solved  by  R.  90  -  distribution  and  S.  by  Fourier  transform  method  which  Fourier  transform  of  distribution  to  the  the  following expression  making  yields  for  the  of  velocities, use  directly  of  the  space-time  f u n c t i o n and  line  the  which  leads  profile:  W(v) c i v (w)  I  -  r-i(co-L-kv)  Re 1  .  o Y  Since we  in  may  this  for  A =  0  the  case  (see  section  that  damping decay  i s  discuss  3.4  of  the  are  the  or  the  account  doppler the  Since  oscillator  about of  a the  the  the  line of  product  to  profile  the  the  a  or  collision by  processes,  convolution and  the  in  the  i t can  and  exponential  When  broadening  In  radiation  simply  spectrum.  collision  with  autocorrela-  simple  be  are  of  the  taken the separated  expression,  W ( v ) dv  l(<o)  which  r7rc dio' \ r .+ (co-cu )  =  2  is  1  the  2  1.  Re  convolution  K  of  a  V - i(uj'-kv)  t -  V  doppler  J V - l ( U J - kv) 1  profile  A  auto-  broadening  "guenching"  corresponds  frequency  shift).  v,  of  doppler  the  autocorrelation function, independently  broadening above  shape  independent  function i s simply  the  symmetric  f o r d i s c u s s i o n of  and  broadening.  of  motion  in  P  line  f u n c t i o n associated with  collision  into  the  simplicity  correlation tion  case  WWccvv) d vf J V + r - L(uj-A-k.v)  and  /  another  ,  -  profile.  Thus  consists  simply  of  quenching  broadening  the of  to  broadening  a  profile  the  Lorentz width  consists  of  a  We  of  f u n c t i o n and  then  upon  .velocities (i.e. to  the  the  Y"  V  to  the  rate  changes  be  at  to  0. AuJ  A  to  =  assume  the  gas  so  that  the  doppler  When  of V  taking  I(u) ) s i m p l y with  V  2  1^2«  The  depends  parameter take  be  on  the  y  increases  should  V>>Au> (Acj  become =  form  of  magnitude  in  the  to  gas.  of  the the  velocity number  collisions  i s defined,  i t i s  the  the  different  of  there  changes  with  The  the  velocity  densities  the  i s proportional  equal  linearly  case  for  the  nature  i n weak  the  detailed on  0  Lorentz  also  d u r i n g which  before^the manner  "Y*  place  taken  However,  different  The  =  reduces  the  intensity  at  cases  collision  half  collisions  profile  limiting  The  strong  at  the  i s  depends  y  case  profile  width  doppler  distribution  first  constant  that  of  effect  the  This  collisions  whatever  and  the  broadening.  several collisions In  effect  contribution  second.  add  various  Maxwell  doppler  ^j-,'  which  For  per  stantially. able  the  the  the  the  may  function.' i n  persist),  c o n s i d e r a b l y , i t may  collisions may  £  i s  proportionality collisions.  of  broadening  relative  in  (we  complex  the  contribution  profile),  treat,  velocities  V  for  this  find  Using  collision  profile  doppler  of  to  can  ( v ) , and  i n i t i a l  due  P »  doppler the  for w  convolution  profile when  i t .  of more  expression..  broadening  -  collision  general this  91  subreason-  density  of  forms  of  apparent.  0.025  cm  - 1  f o r hydrogen),.the  .  92  2  p central the  part  simple  of the doppler  dispersion  From the is  Qd this  = we  (CO) ,  than  Lorentz  the  observed  that  V  which  may  of 1/V J C  be  v  by n o t i n g  of the line  a l l components  1  being  the case  t h e sum  I t i s found  width  when i n Fig„  17  of the p r o f i l e the t o t a l  width  o f the widths  from  2 t o 3 amagat,  that  of the  the observed  2 ^  ,006  cm  of  data 1  amagat.  2 - 1 .025 cm 7006"  -  ,-1  amagat  o  n  =  time  .  of velocity  change)  finds:  e  3.3  x  with  10  ^  s e c amagat  t h e mean  time  betv/een  collisions  i s , =  the correlation  collisions. i t  for V  i s simply  from  compared  £*  Thus  - ^ „ .  T  (the characteristic  Z^  This  on  that,  Expressing terms  cm This  spectrum  •V o  in  -  a value  0,025  profiles.  i n the range  ) takes  •*  components.  follows  i  d e c r e a s i n g component  much.less  individual  V  can deduce  monotone  are  It  2  ( f o r t o ~ <.< ^  form,  x  where  profile  c a n be  With  seen  .6  lO " "^ -  1  s e c amagat.  of velocity  this  that  x  value  extends  f o r9  the assumption  over  about s i x  as a f u n c t i o n V »AU)  ; 1 )  of  j_ valid s  density over  the  -  entire  range  Sobel'man  of  densities  further  93  studied  observe  that  in  when  this  work.  ~Y >-^-&.LO„  Rautian  the  and  profile  i s  2 expected for  the  occurs  to  of  to  the  noise  should the  ratio  density  be  dispersion  lines  such  obtained.  predictions treatment  made  of  coefficients function  of  n  at  at  the  the  the  1  to  covered  profile.  shown  These by  This in  and  (1961)  following i s obtained  from  i s a  away  1  be  and  i s too  the  i s  here,  line  i s confirmed F i g . 21  value  far  removed  Foley less  slope  (1968)  to  that should  detailed a l l spectre  whereas  the  Q,(0)  .003  cm  /amagat  0,(1)  .0021  cm"" /amagat  0,(2)  .0036 - 3 x 1 0 ~  0,(3)  .0055 - 5 x 1 0 ~ .  1  4  4  with  the  here.  collision of  a  signal  qualitatively  density: - 1  then  from  applicable  of  the  profile  applied  agree  the  this  expected  the  1/LO  OJ  from  studied, because It  to  o J d e p e n d e n c e  spectra  This  list  the  this  crn  observations  Gersten  opposed  density  density.  range  i s  0.1  amagat  line  as  observed  about  adequate.  as  wings,  However,  not  Galatry  The  l  with  of i s  the  comparison  »  start  linearly center  in  profile.  profile  over a  1/^4  f o r U) > V  only  increases from  as  dispersion  dependence center  vary  line  broadening width  as' a  -  4.  The in  a  static  resolution  infrared  electric using  an  frequencies  have  literature,  which  molecular  was  was  was  our  been  of  noise  deduce of  values  hydrogen.  in  of  inevitably there  has  the  The  values,  being been  of  the  It  not  been order  determinations  in  made.  reason  under in  time to  the  for  the  future  in  value  with  and  this  the  line the  improved line It  theoretical  lines  element i s  i t  of  the  higher  a t t r i b u t e d , to  interferometer resolution  been  poorer  this  has  the  than  not  been  illumination  this  using  point of this  the  which  signal might  unambiguouscharacter-  of  background  have  at  one  dynamical  precision  experiments  the  profiles.  high  continuous  in  recent  Nevertheless,  strong  high  precise  induced  is  gas  detail.  obtained  has todowith  the  some  matrix  ,to i n v e s t i g a t e  improve  More  reported  the  g i v e n "the  probably  flux  of  using  s p e c t r a has  detector  large  In  the  and  established.  istics  for  measurement  have  studied  intensities  at  collisional  measurements  quality,  expected,  of  the  the  hydrogen  e v a l u a t i o n of  phenomenon  spectra obtained  ratio  the  compare  measurements  have ly  good  those  was  accurate The  to'  The  method,,  than  permitted  previously reported more  the  obtained  of  investigated  and  p o s s i b l e to  than  has  From  polarizability  been  observed  p o s s i b l e to  predictions.  has  spectrum  interferometric  been  -  Conelusions  absorption  field  constants.  broadening  94  the spectrum;  thoroughly. frequency  apparatus,  several  modifications  obvious  one  in  i s the  a vacuum  control clear,  on  The  laser  against  precise  a  as the  from  s c a n n i n g mechanism to  a  the  reduce  out.  i s the  optical  actually  used  there  laser.  should  be  constructed  speed  It i s  small  Lastly,  fluctuations  servo  should  are  to  path  a  reference.  laser  the  most  adoption of  frequency  laser  The  entire  standard, because  frequency  interferometer  of  second  used  furthermore, that  i n the  carried  installation  chamber. the  calibrated ences  s h o u l d be  for of  be differ-  a  more  the  the  moving  mirrors. This  work  can  obviously  nuclear  diatomic molecules  also  of  be  vibration remains at  interest spectrum  t o be  densities  measure expect less  the that  of  done below  1  In  of  as  pure  extended  D ,  the  to  and  0  weak  .  some  i t would  parahydrogen, broadening  It  further  be  would  work  measurements of  interest  because  would  homo-  rotation-  particularly  Also  other  allowed  addition,  itself,  collisional  be  one  to  might  slightly  pronounced.  s h o u l d be form  our  expectations.  described  electrodes was  investigations  done  the.  i t  HD.  amagat.  spectrum the  measure  w i t h H2  If-these work  to  such  be  i s too  difficult  on  the  i n the In  to  multiple thesis  particular  large  f o r the  attain  are  carried  pass  out,  White  cell,  d i d not  really  the  between  power  adequately  gap  supplies large  some  live  further  which up  to  the  available,  field  in  and  strengths.  -  BIBLIOGRAPHY  :  Anderson, Brannon,  Buijs,  P.W.,'  1954.  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Nauk.  6,  APPENDIX  Determination the  induced  dipole  We respect  a  moment  define  dipole  diagonal  axis.  moments  elements  between  and w i t h  In the (x'y'z') are related  components  frame  ( x y z ) may  be.obtained  R(ot,^ y  ),  carries  (xyz)into (x'y'z').  a  ^  being  (x'y'z')  system  fixed  of stateE  with  p a r a l l e l to the  t h e components  of  components v i a  consisting  o f the hydrogen  of the dipole  rotational  to the field  of the principal  molecule,  \0 The  different  t h e z' a x i s  p o l a r i z a b i l i t y matrix  polarizabilitxes  o f the components  a c o o r d i n a t e -system  to the molecule  internuclear the  of the matrix  <*„/ moment using  i n a  the rotation  the Euler We  laboratory  angles  fixed  matrix  of a rotation  which  find,  R  R • *  \ 0  0  6  E  Y  11  where R  ( c * ^  I ) =[ coscx. \  sine*-  0\  s I n oL  c o s oc  0  0  0  • 1  / cosf 0 -sin|b  0  s i n p\ 1  /  0  0 c o s |>y  1  t  sm^  0\  -sing  cos^  0  0  1  c o s  0  we r e q u i r e  Since moment  between  harmonics, of  the matrix  wave  functions  moment  t h e components  l  \  i s also  i l i t y  R  U •'•R  the  customary  matrix  t o express  i n two p a r t s ;  anisotropic  i  - i  0  o)  0  1  U  the diagonalized  polarizab-  polarizability  and  polarizability:  (1 2  C  <  J.  f-1  0\ i i  + <*«  V0  -ex a.  J 0(  i s the isotropic  anisotropy (0<  0  WJ  the isotropic  0 \  where  vectors  that,  J It  ba.sig  \  = —  \ }- J  i t follows  =  U  dipole  spherical  to express  where  v  \ Pi J  U -1'  of  i n the set of spherical  u  this  of the induced  consisting  i t . i s more c o n v e n i e n t  the dipole  From  elements  >r\c<  )  a  polarizability  of the polarizability. n  d  U  R  U  =  D  - ( ^ i f o f t  >  and where  We n o t e hence,  that  U  ^  i sthe U  =  D . 1  f-  \  1  DVCX^V-  =  \P  X  1  j (.  ) u  -1  1  E  W  \ B  1  where  o  y  -1  •u  / -1 u =  -l  2  /  V  V  Then e v a l u a t i n g D  ^  j  -1  -1  )  _1  <*,M ) ^ T f  d 1  I  orn an  1  e x p r e s s i o n f o r D"" g i v e n by Tinkham i t i s seen t h a t y" appears 1  = 1, and t h e r e s u l t i n g  only i n expressions l i k e e ^ x e ^ x  1  f u n c t i o n s o f O N and j?> c a n be w r i t t e n as s p h e r i c a l Harmonics of order 2 „  Hence,  f  (~) E l  =  V^l  E  o  V  3  5  j  w  Y  2,0  Y  2  - f  3  ^2 , - 1  2 Y„  ,1  Y 2,2  ~f  3  X  Y  ~ {?,  N  2,l  ~  Y Y  2,-1  E,  2,0  I t i s a l w a y s p o s s i b l e t o choose t h e x y z c o o r d i n a t e system such t h a t E = E Q „  Then t h e components o f t h e d i p o l e moments  are: Y,  p  ^  Q  +1  E  "  Q  3  +  *  V5  V~5~  Y  E,  _1  2,0  2,1  2  v  E  0 J  J  0  We must now e v a l u a t e t h e m a t r i x e l e m e n t s f o r t h e s e components o f t h e i n d u c e d d i o d e  moment i n , t h e d i r e c t i o n o f  the  electric  work  field  presented  parallel  to  of  here,  the  the the  static  incident incident  field.  radiation. light  Thus  we  was  In  plane  a l l the polarized  require,  <*r. i " o i ™ > . . - « * < > «-\ €> *U* <F£  <€> i A  y  0  The  first  The  second  Eckart  term term  as  and  be  which  and  m'„  a  We  the  reduced  a  dependent  J  right  evaluated  of  find  us  the  "reduced  matrix  hand  allows  a product  coefficient m  the  can  theorem  elements  of  on  the  side by  to  making  express  in  terms  this  m'  m,  =  |J-2|^J'  J  f o r the  J+2  for  C(J»2J;000) i s  zero  and  J'  ^  =  = .0 t o  the  ^mm'"  I  Wigner-  matrix  which  is  independent  expression  of  coefficient  a  C-G  for and  factor,  i t i s apparent  J'  of  T  explicit  x  From  use  6 J  Clebsch-Gordan  element"  following  oCEQ  these  appropriate  matrix  element  equals  J  =  0  that  we  isotropic  the when  have  i s not  =  the  selection  contribution  anisotropic J»  C ( J ' 2 J ; m'Om).  J±l  allowed  and  contribution.  so  that  for  the  J'  rules  = J  Also or  J-2  anisotropic  part.  i  


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