UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Investigation of the selfpressure broadening of the Ne [Lambda] 6074.3 A° line profile by Zeeman scanning Burnett, John Crawford Duncan 1969

You don't seem to have a PDF reader installed, try download the pdf

Item Metadata

Download

Media
[if-you-see-this-DO-NOT-CLICK]
UBC_1970_A6_7 B87.pdf [ 2.86MB ]
Metadata
JSON: 1.0084802.json
JSON-LD: 1.0084802+ld.json
RDF/XML (Pretty): 1.0084802.xml
RDF/JSON: 1.0084802+rdf.json
Turtle: 1.0084802+rdf-turtle.txt
N-Triples: 1.0084802+rdf-ntriples.txt
Original Record: 1.0084802 +original-record.json
Full Text
1.0084802.txt
Citation
1.0084802.ris

Full Text

AN  INVESTIGATION  OF THE  PRESSURE ' BROADENING Ne\6074.3 A  LINE  0  BY •- ZEEMAN  SELF-  OF  THE  PROFILE  SCANNING  by JOHN  C.  B.Sc, U n i v e r s i t y A  THESIS THE  BURNETT of B r i t i s h Columbia,  SUBMITTED  IN  REQUIREMENTS MASTER  PARTIAL  FOR OF  THE  FULFILMENT DEGREE  SCIENCE  i n t h e Department of PHYSICS We a c c e p t t h i s required  THE  thesis  as c o n f o r m i n g  tothe  standard:  UNIVERSITY  OF  November,  BRITISH 1969  1959  COLUMBIA  OF  In p r e s e n t i n g t h i s  thesis  an advanced degree at the I  f u l f i l m e n t of  the U n i v e r s i t y of B r i t i s h  L i b r a r y s h a l l make i t  freely available  f u r t h e r agree that p e r m i s s i o n  for  the requirements f o r  Columbia,  I agree  f o r r e f e r e n c e and  f o r e x t e n s i v e copying of  that  Study.  this  thesis  s c h o l a r l y purposes may be granted by the Head of my Department or  by h i s of  in p a r t i a l  this  written  representatives. thes,is  It  for f i n a n c i a l  is understood t h a t copying or p u b l i c a t i o n gain s h a l l  not be allowed without my  permission.  John C. Burnett)  Department of  Physics  The U n i v e r s i t y of B r i t i s h Vancouver 8, Canada  Date  10 NOV, 1969  Columbia  - i i -  Abstract  The- s h a p e o f t h e Ne.X6074.3 A° a b s o r p t i o n  line  has been i n v e s t i g a t e d u s i n g t h e Zeeman s c a n n i n g Neon g l o w d i s c h a r g e s  at three pressures,  50 T o r r ,  and 100 T o r r , w e r e u s e d a s a b s o r b e r s  Geissler  t u b e was u s e d as t h e s o u r c e .  broadening the  of t h e observed  r a t e of b r o a d e n i n g  profile  technique.  2 Torr, while  a 2 Torr  The s e l f - p r e s s u r e  l i n e was c l e a r l y  o b s e r v e d and  compares w e l l w i t h t h e o r e t i c a l  made f r o m t h e i m p a c t t h e o r y w i t h a v a n d e r W a a l s  estimates  interaction  assumed. No s h i f t was d e t e c t e d , This  l a c k of s h i f t ,  i n c o n t r a d i c t i o n to the theory.  and t h e r a t e o f p r e s s u r e  observed,  were i n agreement w i t h t h e r e s u l t s  regarding  the s h i f t  by n e o n .  and b r o a d e n i n g  broadening o f S m i t h (14)  o f t h e Ca. X 6 5 7 3 A°  line  - i i i TABLE  OF  CONTENTS  Chapter  Page Abstract T a b l e of C o n t e n t s L i s t of F i g u r e s L i s t of R e f e r e n c e d E q u a t i o n s Acknowledgements  I II  III  i i i i i iv v vi  Introduction  1  Theory . A. S p e c t r a l L i n e A b s o r p t i o n and T r a n s m i s s i o n Curves B. L i n e B r o a d e n i n g : P r e s s u r e Independent E f f e c t s C. L i n e B r o a d e n i n g : P r e s s u r e Dependent E f f e c t s D. S e l f A b s o r p t i o n B r o a d e n i n g E. V o i g t P r o f i l e s F. Zeeman S c a n n i n g and I n h o m o g e n e i t y Broadening  4 4 9 12 18 21 24  Apparatus A. S o u r c e B. S c a n n i n g E l e c t r o m a g n e t C. A b s o r p t i o n Tubes , D. O p t i c a l S y s t e m E. E l e c t r o n i c D e t e c t i o n  27 27 27 28 30 32  IV  Experimental Procedure.  33  V  Method of A n a l y s i s A. C h o i c e o f M o d e l B. S p e c i f i c P r o c e d u r e  34 34 35  Results A. D e t e c t i o n o f B r o a d e n i n g B. D e t e c t i o n o f S h i f t C. L i n e Shape D e t e r m i n a t i o n D-. R a t e o f P r e s s u r e B r o a d e n i n g Comparison w i t h Theory E. V a l i d i t y o f R e s u l t s  37 37 41 41  Concluding Discussion.  53  Bibliography Appendix I F l o w c h a r t : Computer C a l c u l a t i o n of T r a n s m i s s i o n C u r v e s  57  VI  VII  42 46  58  -ivLIST  OF  FIGURES  Figure  Page  1.  T r a n s m i s s i o n Curve Parameters.  7  2.  S p e c t r o s c o p i c D e s i g n a t i o n and Zeeman E f f e c t f o r NeX6074.3 A .  25  3.  A b s o r p t i o n Tube C o n s t r u c t i o n .  29  4.  Experimental Arrangement.  31  5.  Transmission Curves f o r D i f f e r e n t P r e s s u r e s ( t = 0.16).  38  Transmission Curves f o r D i f f e r e n t P r e s s u r e s ( t .= 0 . 3 3 ) .  39  Transmission Curves f o r D i f f e r e n t P r e s s u r e s ( t = 0.53).  40  T r a n s m i s s i o n C u r v e : T h e o r y and E x p e r i m e n t (P = 2 T o r r ) .  43  T r a n s m i s s i o n C u r v e : T h e o r y and E x p e r i m e n t (P = 100 T o r r ) .  44  0  Q  6.  Q  7.  0  8. 9. 10.  Transmission Half Width Transmission  (Theory  versus  and E x p e r i m e n t ) .  11.  Rate of P r e s s u r e  Broadening.  12.  E f f e c t of C u r r e n t R e g u l a t i o n F a i l u r e .  45 47 50  -vLIST Equations  OF  REFERENCED  EQUATIONS Page  I, I I  4  III  5  IV  6  lV(a)  8  V  9  VI  11  VII  14  VIII  15  IX  19  X  21  XI  23  XII  24  -vi-  Acknowledgements  I w i s h t o e x p r e s s my a p p r e c i a t i o n t o D r . R. N o d w e l l f o r his  e n c o u r a g e m e n t and s u p p o r t , b o t h o f my g r a d u a t e w o r k i n  g e n e r a l and t h i s  experiment.  for  and a d v i c e i n t h e p r e p a r a t i o n o f t h i s  h i s guidance  A d d i t i o n a l thanks  I a l s o w i s h t o t h a n k D r . J . Meyer thesis.  a r e due t o :  - Mr. B a r r y S t a n s f i e l d  for his initial  w o r k s e t t i n g up t h e  Zeeman s c a n n i n g s y s t e m and d e m o n s t r a t i n g i t s f e a s i b i l i t y . - Mr. Bar.ry S t a n s f i e l d  and D r . W.  S e k a f o r much  helpful  d i s c u s s i o n and a d v i c e . - Mr. J . L e e s f o r h i s e x p e r t c o n s t r u c t i o n and f i l l i n g t h e s o u r c e and a b s o r b e r Finally  of  tubes.  I w i s h t o e x p r e s s my g r a t i t u d e t o my w i f e , S y l v i a , f o r  h e r c o n t i n u i n g p a t i e n c e and s u p p o r t .  -1-  CHAPTER  I  INTRODUCTION  Spectral lines, characterized strength.  b o t h i n e m i s s i o n and a b s o r p t i o n , a r e  by t h e i r  shape,  f r e q u e n c y , and i n t e n s i t y  The s h a p e o f a s p e c t r a l l i n e  d e t e r m i n e d by t h e p h y s i c a l e n v i r o n m e n t particular  For  and e l e c t r i c  of i t s source, i n  or magnetic  most h i g h t e m p e r a t u r e p l a s m a s  electromagnetic f i e l d s by t h e t e m p e r a t u r e it  i s primarily  the temperature, n e u t r a l p a r t i c l e  electron density,  u s u a l l y most  density,  fields present.  i n t h e absence  t h e shape o f t h e l i n e  and e l e c t r o n d e n s i t y .  i s the temperature  or  of s t r o n g  i s determined  At lower  and n e u t r a l p a r t i c l e  temperatures  density which are  significant.  G e i s s l e r t u b e and g l o w d i s c h a r g e p l a s m a s , w h i c h b e l o n g t o the  latter  c l a s s of lower temperature plasmas,  are frequently  e m p l o y e d i n s p e c t r o s c o p i c work as s o u r c e s o r a b s o r b e r s o f spectral lines.  F o r e x a m p l e i n two r e c e n t e x p e r i m e n t s a t t h e  U n i v e r s i t y of B r i t i s h Columbia  t h e a b s o r p t i o n i n glow  d i s c h a r g e s of l i g h t  e m i t t e d by G e i s s l e r t u b e s has b e e n  used  to  transition  One  measure r e l a t i v e  experiment spectral  probabilities  i n neon.  compared t h e a b s o r p t i o n s t r e n g t h s o f v a r i o u s  l i n e s ( l ) w h i l e t h e second  i n a. g l o w d i s c h a r g e t u b e ( 2 ) .  u t i l i z e d Faraday  rotation  I n b o t h e x p e r i m e n t s i t was  assumed t h a t t h e a b s o r p t i o n and e m i s s i o n l i n e  shapes  were  G a u s s i a n , due t o t h e r m a l D o p p l e r b r o a d e n i n g a l o n e . A p p r e c i a b l e  - 2 -  departure validity  from  the  of t h e s e  Estimates impact  theory  interaction, t h e r e may the  indicate  assumption  discharge  line  and  not  had  the  transmission to  the  transmission  this  decrease  to  alter  theory i n the  examine a t l e a s t  shapes but  plasmas  of  also  one  are too  of  is isolated  such  examination. f o r a range  an  of  the  The  employed.  as  the  be  spectral of a  absorber  a  variable t o . scan  fractional  source  absorption l i n e .  generally reflect  narrow  The  techniques  I t should  employed  through  be  that with  cr-component  and  i n glow  ) is  (3)  et a l (4)  a single  the  lines  (—£10  neon  the  narrow to  by S t a n s f i e l d  shape o f  such  to t e s t  spectral  resolution  Bitter  exact  i s obtained  curves  Waals  broadening  In a d d i t i o n  to  high  under  the  glow d i s c h a r g e c o n d i t i o n s  pressure  I t i s passed  span t h e  der  conventional spectrographic  technique  absorption line  sufficient  tube  technique  source.  a van  dependent,  been d e m o n s t r a t e d  n o r m a l Zeeman t r i p l e t  of  However t h e  of v e r y  to d i s c e r n  frequency  the  made a c c o r d i n g t o  o n l y to check the v a l i d i t y  s t u d i e d by  With t h i s  could a f f e c t  line.  line  Geissler  Zeeman s c a n n i n g  lines.  pressure  desir^able  equipment  possible  sufficient  predictions.  conveniently  It  t h a t under  of G a u s s i a n  theoretical  assumption  spectral  thus  glow d i s c h a r g e  broadening,  significantly.  of the  I t was  unless  be  a slight,  frequency  assumed  results.  under the  shapes  predicts  shapes  of p r e s s u r e  indeed  line  Gaussian  frequencies  resultant  shapes  of b o t h  the  -3-  s o u r c e and t h e a b s o r b e r and a r e s e n s i t i v e t o v a r i a t i o n s i n either;,  By c o m p a r i n g t h e s e r e s u l t s t o t h e p r e d i c t i o n s o f a  s i m p l e model t h e l i n e be  s h a p e s o f s o u r c e and a b s o r b e r  may  extracted. As e m p l o y e d i n t h i s  experiment  t h e t e c h n i q u e seemed  c a p a b l e o f d e t e c t i n g c h a n g e s i n t h e w i d t h o f an a b s o r p t i o n line to  as s m a l l as 2 mA°  (which f o r the l i n e  10% o r l e s s o f t h e h a l f w i d t h ) .  corresponds  I t a l s o seemed c a p a b l e o f  q u i t e a c c u r a t e d e t e r m i n a t i o n of t h e l i n e Zeeman s c a n n i n g a p p a r a t u s  studied  i s composed  shape.  Because t h e  of equipment  usually  a v a i l a b l e i n a l a b o r a t o r y or e l s e o b t a i n a b l e at low c o s t , the t e c h n i q u e seemed a t t r a c t i v e  as a s i m p l e , e c o n o m i c means o f  s t u d y i n g t h e shape o f a n a r r o w l i n e  f r o m a neon g l o w d i s c h a r g e .  -4-  CHAPTER  II  THEORY  A.  S p e c t r a l L i n e A b s o r p t i o n and As  radiation  passes  medium t h e f r a c t i o n  Transmission  through  an  element of  of t h i s r a d i a t i o n  p r o p o r t i o n a l to the absorbing the l e n g t h of the a b s o r b e r  Curves absorbing  absorbed  is directly  ' s t r e n g t h ' o f t h e medium  and  traversed.  = - k(?> )dx  dlJjLl  I  )  l(y  ) i s the i n t e n s i t y frequency  k(^)  i s the the  dx  f o r a homogeneous a b s o r b e r intensity  by  l^(j?  absorber  will  itself  traversed.  of l e n g t h  ) and  J.  and  the t r a n s m i t t e d  i s i n t e n s i t y m o d u l a t e d and  d e t e c t i o n system.  .  j).  This  However  a lock-in amplifier  the t r a n s m i t t e d i n t e n s i t y .  e m i t t e d by t h e a b s o r b e r  phase s e n s i t i v e  at frequency  c o m p a r a b l e t o 1^ (1?)  the  determine  II  emit- l i g h t  have an i n t e n s i t y  ated l i g h t  7^ .  k{f)J]  light will  employed t o  of  Ij(7?):  by  source  ('strength'  l e n g t h of a b s o r b e r  = I.(>>)exp{ The  at  .  absorber): at frequency  the i n c i d e n t  intensity  radiation  absorption constant  i s the elemental  Integrating denoting  ~P  of the  The  unmodul-  i s r e j e c t e d as n o i s e by Since the l o c k - i n  is  the  amplifier  -  used  improved  emitted  consideration.  Hence E q u a t i o n  from  -  the s i g n a l - t o - n o i s e  more, t h e l i g h t  emergent  5  ratio  by a f a c t o r  by t h e a b s o r b e r  an a b s o r b e r  may be o m i t t e d  i  .  I n t h e r e g i o n o f an a b s o r p t i o n l i n e dependence p e a k i n g  indicated  below. k(  from  I I gives exactly the i n t e n s i t y  of l e n g t h  frequency  o f 100 o r  at the l i n e  k ( ^ ) will centre  have a  ^  as  )\  o.-  2  A u s e f u l measure o f t h e w i d t h is  the half  width  width  which i s here  a t t h e half-maximum o f If  o f an a b s o r p t i o n  d e f i n e d as t h e f u l l  ) - see a b o v e .  a band o f r a d i a t i o n w i t h f r e q u e n c y  by t h e shape I ^ ( ^ - ^ specified  by k ( ^ ) s  of t h e a b s o r b e r ,  then  line  ) i s passed  through  k ( y - % ) where the resultant  mean  characterized  a length 1  of absorber  i s the c e n t r a l  frequency  intensity  at frequency  is: I  f  (/)  =  I^Z-^s  )exp { - k ( / - ^  III  -6-  i \  \  \  1  i  ^- exp{-k(  l.o-  iJ-tiU}  V  • • '•  1  \ \ \  1  1  \ \\  \  •  1  1  ''•  1  •  1  \  i \ i i\  i ;  The i n c i d e n t or source  <>—~  —  i  flux i s :  s(^)  =  y I (> -^)dy ,  i  ?  ,  o oO  w h i l e the t o t a l  flux transmitted  is:  0 o  The f r a c t i o n a l t r a n s m i s s i o n i s the r a t i o  tit) =  ^M  1  IV  s(i )  C o n s i d e r i n g the absorber transmission w i l l vary with This  of these two f l u x e s :  frequency  j) as a constant 0  the  % , the mean frequency of the  source,  i s d e p i c t e d s c h e m a t i c a l l y i n F i g . 1. The width of t h i s t r a n s m i s s i o n curve w i l l  the f u l l width at  ' half-minimum'  Several salient  - At-  be d e f i n e d as  as i n d i c a t e d i n F i g . 1.  f e a t u r e s of such t r a n s m i s s i o n curves  are:  -7-  -*» : t :  Fig.  1  Q  At  = line  centre  At (minimum)  = transmission  Transmission  Curve  *•  half  transmission  width  Parameters  -8-  (a) F o r f i x e d  t ,  w i d t h and t h e a b s o r b e r (b) F o r f i x e d i n c r e a s e as (c)  by  will  i n c r e a s e as t h e  source  width increase, source  and a b s o r b e r  i s i n c r e a s e d ( i . e . as t F o r an i n f i n i t e l y  lA?'-%)  Q  widths,  At  will  decreases).  narrow source  =  represented  then:  0{? ,?.) t  Hence:  At  t ( ii)  = I exp{ o  =  exp{  Thus f o r a s u f f i c i e n t l y  -  k(/>,-  k ( ^ - ^ )£}  IVa  s  n a r r o w s o u r c e t ( ^ ) and  depend on t h e shape o f t h e a b s o r p t i o n l i n e  only.  At  -9-  B.  L i n e Broadening: P r e s s u r e Independent (1) No  an  Natural  its  own  Broadening:  spectral  isolated  l i n e can  be  perfectly  oscillator is still  radiation.  i n the  spectral  Effects  monochromatic.  p e r t u r b e d by  C l a s s i c a l l y t h i s can  distribution  of  be  the  shown (5)  of  to  result  •i  where T half  reaction  intensity:  i(y-&)  The  the  Even  i s the  w i d t h of  lifetime  of  the  oscillator.  this distribution,  natural l i n e width, i s :  referred  _  to  as  l  * ~ T The  normalized  intensity  is:  (1?-%)  27T  T h i s i n v e r s e s q u a r e f o r m of o r i g i n a l l y derived b e e n named t h e The the  A.  states.  for  sum  b e t w e e n s t a t e s m and  n:  V  and  has  was  since  profile.  of  the  a l l transitions  Thus f o r  2  L o r e n t z i n 1906  intensity distribution  L\tfv e q u a l s t h e  (ML)  f r e q u e n c y dependence  quantum m e c h a n i c a l t r e a t m e n t of  probabilities final  H.  'Lorentzian'  same f o r m of  that  by  +  2  t h i s problem and  furthermore  spontaneous  M = LA^ 1  initial  from a  and  transition  + z  A , nn  n'  +  shows,  transition  from both the  a line resulting  yields  1  T  n  -10-  where:  and A ,  are the appropriate E i n s t e i n  n n  A-coefficients. T ° m  T  and  a r e t h e ' l i f e t i m e s ' o f t h e two  n  In the o p t i c a l r e g i o n the n a t u r a l n e g l i g i b l e compared t o t h e e f f e c t s mechanisms.  X6074.3 A  For the  been m e a s u r e d t o be: natural  width, of  0  of other  braodening  sec ( 7 ) .  This yields a  ^ 6*10 ^ cm ^ = 0 . 0 6 mK.  By c o m p a r i s o n  the Doppler  (2) D o p p l e r Relative observer w i l l  width  motion  (see below) i s :  between a source o f r a d i a t i o n  cause a f r e q u e n c y  ~ 50 mK.  l i n e being  and an  s h i f t of the observed  The random t h e r m a l m o t i o n s  radiation particles w i l l  spectral  _  Broadening:  (Doppler e f f e c t ) . of  frequency  radiation#  o f an a s s e m b l a g e  r e s u l t i n a broadening  of the  observed.  F o r a v e l o c i t y component a l o n g t h e l i n e o f s i g h t Doppler  usually  l i n e o f N e l t h e l i f e t i m e has  5*10"  A^  l i n e width, i s  states.  v , the  shift i s :  w h e r e )l i s t h e u n s h i f t e d  frequency.  I n a n a s s e m b l a g e o f p a r t i c l e s o f mass M w i t h a M a x w e l l i a n velocity d i s t r i b u t i o n characterized  by a t e m p e r a t u r e  T, t h e  f r a c t i o n w i t h a l i n e o f s i g h t v e l o c i t y component b e t w e e n v  and s  v  + dv i s : s s  -11-  N i s t h e t o t a l number o f p a r t i c l e s k i s Boltzmann's For r a d i a t i n g  constant.  p a r t i c l e s t h i s same f r a c t i o n w i l l  f r e q u e n c i e s b e t w e e n j) and A  dP  have  where c ° y  Substituting f o r v : g  v  N  2kT  l  J  For an o p t i c a l l y t h i n i n c o h e r e n t s o u r c e t h e i n t e n s i t y i s p r o p o r t i o n a l t o t h e number o f r a d i a t i n g  ^  It  "  N  i s thet o t a l l i n e  The h a l f  intensity.  width of this d i s t r i b u t i o n t { f u l l width at half-  maximum) i s :  A  „  „,  AV  K ^ - v M  where l{P-2i) frequency  -  i/  = o -)?( 2 k T l n 2 V2  The n o r m a l i z e d i n t e n s i t y  unit  particles:  2 / I n ?  distribution i s : f  -[2  y-y ) Vln?^-^)] . e  i  2  a t frequency  1? p e r  frequency s h i f t s a r i s i n g from thermal  motions  i s here t h e i n t e n s i t y  interval.  The D o p p l e r  -12-  thus g i v e the l i n e a G a u s s i a n shape.  T h i s i s the  major  b r o a d e n i n g m e c h a n i s m f o r G e i s s l e r t u b e and g l o w d i s c h a r g e plasmas line  s u c h as e m p l o y e d i n t h i s  o f N e l ( i s o t o p e 20)  experiment.  a t T = 350  °K  :  A  ^  C.  The  surrounding p a r t i c l e s  = 49  mK  Effects  p e r t u r b a t i o n s of e m i t t e r s caused  spectral line.  v?  &VD  L i n e Broadening: P r e s s u r e Dependent  'X6074.3A°  For the  by e n c o u n t e r s w i t h  r e s u l t i n a f u r t h e r b r o a d e n i n g of the  As p r e s s u r e and d e n s i t y a r e i n c r e a s e d t h e  rate  of s u c h e n c o u n t e r s i n c r e a s e s , w i t h c o n s e q u e n t l y g r e a t e r broadening.  I n t h i s way  the broadening i s pressure  dependent.  (1) S t a r k B r o a d e n i n g : D u r i n g encounters w i t h charged p a r t i c l e s the energy o f an e m i t t e r a r e p e r t u r b e d ( S t a r k e f f e c t ) . shifted  spectral lines,  This .results i n  broadened  and  profile.  Compared t o i o n - b r o a d e n i n g , b r o a d e n i n g by  i s g e n e r a l l y the g r e a t e r e f f e c t . s u c h as a r e e n c o u n t e r e d  impact' broadening. directly To  For low e l e c t r o n  referred  The w i d t h s and  t o as  Lorentzian electrons densities, the  effect  'electron-  s h i f t s t h e r e b y produced  p r o p o r t i o n a l to the e l e c t r o n  are  density.  e s t i m a t e t h e s i g n i f i c a n c e of t h i s b r o a d e n i n g mechanism  f o r the present experiment required.  an e s t i m a t e o f e l e c t r o n d e n s i t y i s  E c k e r and Z o l l e r  h e l i u m plasma density  g e n e r a l l y of  i n a glow d i s c h a r g e plasma,  of t h e e l e c t r o n s i s s p e c i f i c a l l y  levels  n  e  ^  column. 10  11  cm  (8) have c a l c u l a t e d v a l u e s f o r a  Their calculations yield 3  an  for pressures, currents,  electron and  dimensions  -13-  s u c h as e m p l o y e d i n t h i s  experiment.  Assuming  that  similar  v a l u e s c a n be e x p e c t e d f o r a n e o n d i s c h a r g e - , i t s h o u l d be to  consider  n  ^  g  10  1 2 - 3 cm  C a l c u l a t i o n s of the S t a r k broadening parameters and  other l i g h t  safe  elements  have b e e n p e r f o r m e d  for Nel  by G r i e m ( 9 ) .  From t h e s e c a l c u l a t i o n s X6074.3 A  0  line  A^ The  the e l e c t r o n - i m p a c t h a l f w i d t h of the 12 -3 o f N e l f o r n- <; 10 cm is:  < 0.017  mK  corresponding s h i f t  is:  A%  < 0.009  mK.  For  to  t h e s e c a l c u l a t i o n s t h e e l e c t r o n t e m p e r a t u r e was c h o s e n o . . • be 25,000 K , t h e v a l u e f o u n d by I r w i n (10) f o r a s i m i l a r  neon glow p l a s m a .  • '  S t a r k b r o a d e n i n g of t h i s magnitude w i t h t h e m e a s u r e d w i d t h and resolved  such a s m a l l s h i f t  energy  levels  o f an e m i t t e r may  g e n e r a l l y r e s u l t s a broadened Lorentzian  and  shifted  a l s o be p e r t u r b e d Here a l s o t h e r e spectral  line  pure gases t h e m a j o r i t y of n e u t r a l p a r t i c l e s  the absence  will  be  of  profile.  by t h e e m i t t e r w i l l In  can not  Shift:  during encounters w i t h n e u t r a l p a r t i c l e s .  In  compared  by t h e e x p e r i m e n t a l s e t up.  (2) Van d e r W a a l s B r o a d e n i n g and The  i s negligible  be g r o u n d  o f any  s t a t e atoms o f t h e same  resonance  encountered species.  e f f e c t s the i n t e r a c t i o n  be p r i m a r i l y t h e Van d e r W a a l s a t t r a c t i o n .  For  forces  this  -14-  the  level  k  ^ the r  i s perturbed  i s t h e v a n d e r Waals c o n s t a n t particular perturber  f o r t h e l e v e l k and  i n question.  l o w d e n s i t y g a s e s s u c h as a g l o w d i s c h a r g e  impact theory  the  ^6,k  i s t h e d i s t a n c e b e t w e e n t h e r a d i a t o r and t h e p e r t u r b e r .  For  be  hOJ^_ - -  by:  used.  o f L i n d h o l m and F o l e y  In t h i s theory  (11)  can q u i t e g e n e r a l l y  i t i s assumed t h a t t h e d u r a t i o n o f  e n c o u n t e r I s n e g l i g i b l e ' compared t o t h e t i m e  between such e n c o u n t e r s . valid  This  f o r low perturber  discharge This  plasma the  interval  impact approximation  i s generally  d e n s i t i e s s u c h as i n t y p i c a l  glow  plasmas. impact theory,  i n c o n j u n c t i o n w i t h t h e van d e r Waals  i n t e r a c t i o n assumed, p r e d i c t s a L o r e n t z i a n i n t e n s i t y  distribution  whose h a l f w i d t h i s : = 1.3v*  t±9  v  n sec  v i s t h e mean r e l a t i v e v e l o c i t y and ^  between  emitter  perturber. =  -  •and f i n a l n  VII  1  ^  where k  and k d e s i g n a t e  the i n i t i a l  levels.  i s t h e number d e n s i t y o f t h e p e r t u r b e r s .  In a d d i t i o n t o t h e broadening t h e impact theory predicts  a shift  of t h e s p e c t r a l l i n e t o the red.  broadening to s h i f t constant  C5  also  The r a t i o o f  i s independent of both the i n t e r a c t i o n  and t h e mean r e l a t i v e v e l o c i t y  v.  For a width  -15-  the  shift  The  L\/  is:  = - i±£±. 2.76  0  v a n d e r W a a l s c o n s t a n t s may be e s t i m a t e d u s i n g t h e  following approximation  by U n s o l d  2 6  '  2  I T  k  P  e i s the electronic 'fi a  i s Planck's o  n* i  The  1)  -1  rad  sec  VIII  charge. f o rangular  momentum.  quantum number o f t h e l e v e l  k,  i s t h e a n g u l a r momentum quantum number f o r t h e e l e c t r o n i n l e v e l k.  i s the p o l a r i z a b i l i t y validity  of t h i s  of the p e r t u r b i n g p a r t i c l e s .  approximation  r e s t s on t h e a s s u m p t i o n  t h a t t h e e n e r g y s e p a r a t i o n b e t w e e n t h e i n i t i a l and f i n a l  levels  o f t h e e m i t t e r i s much s m a l l e r t h a n t h e e n e r g y s e p a r a t i o n o f t h e g r o u n d s t a t e and l o w e r  e x c i t e d s t a t e s of the p e r t u r b e r ( f o r  ground s t a t e p e r t u r b e r s ) .  This i s a reasonable  a noble  gas p e r t u r b e r s i n c e t h e r e t h e f i r s t  comparatively  approximation  assumption f o r  excited states l i e  h i g h as a r e s u l t o f t h e i n c r e a s e i n p r i n c i p a l  quantum number o f t h e o p t i c a l V I I I should  electron.  be v a l i d  Hence  Unsold's  f o r neon i n a glow  discharge  plasma. The  a p p l i c a t i o n of Unsold's  approximation  r e q u i r e s an  (•  cm  Bohr r a d i u s ,  i s the effective  optical o<p  2 5 n * + 1 - 3J{/+  2  ~  constant  i s the f i r s t  (12) :  -16-  e s t i m a t e of the p o l a r i z a b i l i t y this  have been u t i l i z e d .  cX^  of neon.  Two  v a l u e s of  The f i r s t , a ^ t h e o r e t i c a l v a l u e , has -25  been t a k e n f r o m A l l e n Using the Unsold C  ( 1 3 ) . who  approximation VIII t h i s  6(Ne6074/ )  = 5.82-10  N e  Hence  c><  gives  from the impact Mn  VII :  1 . 2 4 - l O " ^ mK  cm  (14) on t h e p r e s s u r e  of  Smith's quoted  Ca 2\6573 A °  by n e o n . mK  cm  6(Ca6573/ )  Ca A 6 5 7 3  A  v a l u e of  and r e l a t i o n V I I y i e l d : = 2.27-10"  N e  This  broadening  3  -18 = 11.0-10 C  3  an e x p e r i m e n t a l l y b a s e d v a l u e has b e e n d e r i v e d  from t h e r e s u l t s of Smith  n  cm°  1  n  Secondly,  A T*7  3 2  rad s e c "  l i n e i s a 4s4p - 4s  energy s e p a r a t i o n of the i n i t i a l  1  cm  transition  and f i n a l  e q u a l t o t h a t o f t h e Ne "X6074.3 A ° l i n e .  from  and t h e  Hence t h e U n s o l d case.  Using  V I I I t h e n , t h e p o l a r i z a b i l i t y o f neon was d e r i v e d and  this: C  6(Ne6074/ ) N e  With  6  states i s roughly  a p p r o x i m a t i o n V I I I s h o u l d be e q u a l l y v a l i d i n t h i s relation  cm  yields:  rad s e c "  theory r e l a t i o n  ^ ^ A 2 L = c  = 3.96*10  3  relation  =  1  '  2 6  '  VII again t h i s  A y n  = 1.69*10"  For a plasma w i t h T ^  1 0  '  3 1  rad s e c "  1  cm  6  yields: 1 7  mK  325  o  cm  3  .  K and P = 10 T o r r ( t y p i c a l f o r  -17-  glow d i s c h a r g e s ) Under s u c h  the n e u t r a l p a r t i c l e d e n s i t y  f o r t h e NeA6074.3 A  A?J Since this c o n d i t i o n s , van line  results  mK  (theory)  ~ 5.1  mK  (from Smith  predicts a corresponding  However a s h i f t  the l a r g e r  ~1.8  The observed  broadening  easily  line mK  shift to the  expected  (14) was  not  This f a i l u r e  H i n d m a r s h , P e t f o r d , and  o b t a i n f o r the  the a c t u a l s h i f t s  w i t h the  experimental  also  of: red.  apparatus  experimental  employed.  at the higher  line  However  pressures  b r o a d e n e d by  t h e o r y b u t was  of t h e t h e o r y was  Smith  shift  neon  attributed of  Similar  of t h e N e \ 6 0 7 4 . 3 A°  line  by any  results i n which  p r o d u c e d w o u l d be b e y o n d d e t e c t i o n apparatus.  15  in addition  (15) t o t h e o m i s s i o n  r e p u l s i v e . f o r c e i n t h e i n t e r a c t i o n assumed.  case  substantially  o n l y s m a l l e r by a f a c t o r o f  than the p r e d i c t i o n of the impact  should  could  same  detected.  o f t h e Ca A 6 5 7 3 A°  by S m i t h  to the b l u e .  The  f o r the  der Waals i n t e r a c t i o n  experimental  s h i f t s t o be  shift  width  o f t h i s m a g n i t u d e w o u l d be b a r e l y d e t e c t a b l e ,  w i t h the  u s e d s h o u l d be  Waals  expectation.  t h e o r y w i t h van  A#  der  (14) )  i s 8 - 10 % of t h e D o p p l e r der Waals p r e s s u r e  cm  of:  * 3.7  confirm this  at a l l ,  line  0  shapes i n a glow d i s c h a r g e .  The. i m p a c t  if  3-10  c o n d i t i o n s t h e above r e s u l t s p r e d i c t v a n  half widths  affect  n ^  -18-  D. S e l f A b s o r p t i o n  Broadening  The b r o a d e n i n g m e c h a n i s m s d i s c u s s e d C a c t t o broaden a s p e c t r a l l i n e result  i n Sections  'as i t i s e m i t t e d '  These mechanisms a p p l y  absorption  processes.  t o both the emission  S u b s e q u e n t t r a n s m i s s i o n t h r o u g h an a b s o r b i n g  Since  any p r a c t i c a l  many e m i t t i n g p a r t i c l e s ,  light  source  as a w h o l e may d i f f e r  emitting particles Consider  absorption  may  be  a homogenous  y  0  constant  from  partially source.  distribution  of i n t e n s i t y  from t h a t of t h e  per se.  of o b s e r v a t i o n . where  must be composed o f  emerging from t h e volume of t h e  Consequently the r e s u l t a n t frequency from the source  emitted  some o f t h e l i g h t o r i g i n a t i n g  r e g i o n s most d i s t a n t f r o m an o b s e r v e r absorbed before  and  medium  f u r t h e r a f f e c t the i n t e n s i t y d i s t r i b u t i o n of the  light.  line  and  from the immediate p h y s i c a l environment of the e m i t t i n g  particles.  may  B and  source  of d i m e n s i o n  \l i n t h e  L e t t h e e m i s s i v i t y p e r u n i t l e n g t h be  i s the s p e c t r a l l i n e (as d e f i n e d  centre,  and l e t t h e  i n S e c t i o n A) be  line  k(^  of  -j£).  observation  -19-  In at  t h e a b s e n c e o f any  The is  V  frequency  intensity  similarly  at £  would  :  a b s o r p t i o n t h e emergent  be  j{?-£)J.  =  e m i t t e d by t h e e l e m e n t  j(^-j^)dx.  The  intensity  dx  at frequency  amount o f t h i s w h i c h  1?  emerges  i s g i v e n by I I I :  d l  The  s  ( y - ^ )  =  net i n t e n s i t y  j ( y - ^ ) e x p { -  i s found  k ( y - ^ )  by i n t e g r a t i n g  x]}  over  dx  the  J  source:  1 - exp {The depth  \l-  q u a n t i t y i n t h e e x p o n e n t i s d e f i n e d as t h e  T(V-X)  :  =  optically thin  optical  k{?-X)J -  1  An  k(y-^)Jj  s o u r c e i s one  IX  expf  i n which  any  photon  e m i t t e d has a h i g h p r o b a b i l i t y o f e s c a p i n g (i,e. a v o i d i n g \ absorption). The c r i t e r i o n f o r o p t i c a l t h i n n e s s a t f r e q u e n c y n  is  :  «  T ( W )  F o r an o p t i c a l l y t h i n  i iv-rt)  ~  1. source :  hW-X)  i -  (i  -TkV-ti)  -20-  From t h i s  i t can be s e e n t h a t i n t h e o p t i c a l l y  case the l i n e p r o f i l e F o r an o p t i c a l l y T ( V - t i )  1 still  *  thin  of the e m i t t e d l i g h t i s u n a f f e c t e d . thick  source  ( b u t one  i n which  ) : i _ ( i _ 7V-^)  XW-V.  + 2  i -  + 2  Since line  i s g r e a t e s t f o r t h e c e n t r e of  ( i ^ — ]A0) 7  the l i n e  than the wings. line  ••••  As  core i s s e l f  a result  the  a b s o r b e d -more s t r o n g l y  the apparent  half  w i d t h of  the  increases:  true l i n e  true half  width  apparent half width  self  shape  absorbed  profile  -21-  E. V o i q t  Profiles  Where two d i f f e r e n t  mechanisms a c t i n d e p e n d e n t l y  broaden a l i n e the r e s u l t a n t l i n e p r o f i l e of t h e i r  two s h a p e s .  m e c h a n i s m and ^2^2^-Pa) one c o n s i d e r s  I f S-^{)?-2l)  i s the convolution  i s the p r o f i l e  i s the p r o f i l e  The r e s u l t a n t i n t e n s i t y  1  t o be  then  broadened  a t any f r e q u e n c y "Ps  i s t h e sum o f a l l t h e c o n t r i b u t i o n s f r o m e a c h element of S,.  due t o one  due t o t h e o t h e r ,  e a c h e l e m e n t o f t h e Sj_ p r o f i l e  w i t h an S2 s h a p e .  to  broadened  -22-  If  S^  i s G a u s s i a n and  Lorentzian  (or v i c e v e r s a )  c o n v o l u t i o n i s d e f i n e d as a V o i g t p r o f i l e . that i f  and  are themselves  convolution S w i l l S-^ be of  a l s o be  I t c a n be  Voigt profiles  a Voigt p r o f i l e .  then  w i d t h &%  z  and  Voigt profile  , while  resulting  G a u s s i a n and  and  AV  >S  L2  L  such t h a t :  Lorentzian half  i s then  the  Consequently,  m e c h a n i s m s , e a c h of w h i c h  produces  + £$  are themselves  i f two  F o r e x a m p l e , s h o u l d v a n d e r W a a l s b r o a d e n i n g and their  joint  D Z  broadening  shape w i l l  be  act  Lorentzian.  Stark  result w i l l  be a  Lorentzian p r o f i l e w i t h a half width of:  S u b s t i t u t i n g i n e q u a t i o n X t h e G a u s s i a n o f V I f o r S^ the  L o r e n t z i a n o f V f o r S^  respectively): S(*  -7i)  I  ( w i t h h a l f w i d t h s A1?  D  2 yTnT  and  and  i/TZT(y'-X  2  -, 2  AX  x  fe N-  /)2  + (  ^-  )2  a  extreme  a Lorentzian p r o f i l e ,  independently then the r e s u l t a n t l i n e  significant,  and  =  Lorentzian profiles  c a s e s of V o i g t p r o f i l e s .  b r o a d e n i n g b o t h be  a  should  from a G a u s s i a n of h a l f w i d t h AV  (16)  their  from a G a u s s i a n of  a L o r e n t z i a n of h a l f w i d t h  L o r e n t z i a n of h a l f w i d t h  The  results  shown  Furthermore,  formed from a G a u s s i a n of h a l f w i d t h  h a l f w i d t h AT^j  their  -1 d.  -23-  )  2  Setting x =  dx =  stf-}/) =  =  F ( / - # )  Fd/  All  f  e x  PI ' ) y2  *  -oo  J  27r/e  Setting  FA)£  ( HK-X) s  2 Vln2  =  =  2Ay  2  2  o  dx  2  -x) (M)2 2  +  "  2  =  A V l n T  Y  D  OO  S ( ^ )  =  _ Y  / y -oo  exp{-x } 2  ( F (s ^ )- ^ ) (F(7i-y - xx ) 0  -—dx 2  + Y  2  Al)  The  ratio  of L o r e n t z i a n t o Gaussian h a l f w i d t h : A =  Ay is  termed the V o i g t A-parameter.  the V o i g t p r o f i l e .  I t s p e c i f i e s t h e shape o f  A = 0  - pure Gaussian  A  - pure  o0  V a l u e s of the V o i g t i n t e g r a l  D  Lorentzian  of e q u a t i o n X I r e q u i r e d f o r  t r a n s m i s s i o n curve* c a l c u l a t i o n s w e r e computed  using a Fortran  subprogramme d e v e l o p e d a t t h e U n i v e r s i t y o f M i c h i g a n ( 1 7 ) .  -24-  F. Zeeman S c a n n i n g and I n h o m o q e n e i t y The from  major group of v i s i b l e neon s p e c t r a l l i n e s 5 5  2p 3p —*• 2p 3s  exhibit field,  Broadening  complex  transitions.  results  W h i l e most o f t h e s e  lines  ( a n o m a l o u s ) Zeeman p a t t e r n s i n a m a g n e t i c  s e v e r a l show t h e n o r m a l Zeeman p a t t e r n r e q u i r e d f o r  Zeeman s c a n n i n g . The X 6 0 7 4 . 3 A° l i n e , w h i c h r e s u l t s f r o m 3 3 , ' a P —*• P t r a n s i t i o n , i s one o f t h e s e ( s e e F i q u r e 2 ) . 0 1 1 The s p l i t t i n g i s g i v e n ( 1 8 ) by: N  & where  = ± gHB  XII  B i s the a p p l i e d magnetic f i e l d (gauss). -5 -1 -1 H = 4.695"10 cm g a u s s ( t h e Zeeman c o n s t a n t ) . . g i s the s p l i t t i n g  f a c t o r f o r the l i n e .  (g = 1.45 f o r N e X 6 0 7 4 . 3 A° ( 1 8 ) ) Zeeman s c a n n i n g  i s e f f e c t e d by p l a c i n g t h e s o u r c e i n  a v a r i a b l e magnetic f i e l d . of t h e f i e l d two  A beam i s t a k e n  (longitudinally).  i n the d i r e c t i o n  T h i s beam c o n t a i n s o n l y t h e  cr - c o m p o n e n t s o f t h e n o r m a l Zeeman t r i p l e t ,  r i g h t - and l e f t  - hand c i r c u l a r l y  A q u a r t e r wave p l a t e c o n v e r t s linearly  p o l a r i z e d beams.  suppresses varies  one o f t h e s e  t h e Zeeman s h i f t ,  remaining  beam v a r i e s .  these  which are  polarizedrespectively. to mutually  perpendicular  An a n a l y z i n g N i c o l p r i s m  two beams.  As t h e m a g n e t i c  and hence t h e f r e q u e n c y  then field , of t h e  -25-  LS notation  Paschen notation  2.P,  2 9 S I s 2s 2p 3p  Q  Is  2 2 5 I s 2s 2p 3s  T  J  P0  P,  77-  Fig. 2  S p e c t r o s c o p i c D e s i g n a t i o n and for  Ne 'X6074.3 A°  Zeeman E f f e c t  -26-  9  B  i  This technique variable  frequency,  provides this  i  a single  frequency  -9  spectral line  of  being determined  by  e q u a t i o n X I I i n c o n j u n c t i o n w i t h t h e o r i e n t a t i o n of N i c o l prism If of t h e  and  the  sense of the magnetic  the magnetic f i e l d source  then  the  i s not  source  field.  homogeneous o v e r  line  s h a p e may  be  The  resultant line prdfile  b r o a d e n e d and  frequency  appear  p o s s i b l y asymmetric.  This f i e l d magnetic f i e l d  would thus  volume  magnetic  s t r e n g t h s w o u l d have c o r r e s p o n d i n g l y d i f f e r e n t  shifts.  for  the  distorted.  C o n t r i b u t i o n s from regions w i t h s l i g h t l y d i f f e r e n t field  the  inhomogeneity broadening strength.  The  will  increase with  e f f e c t would thus  measurements of the wings of t h e  absorption  be  greatest  line.  -27-  CHAPTER I I I APPARATUS  A. S o u r c e A neon G e i s s l e r t u b e f i l l e d as t h e s o u r c e .  pressure  served  The gas was i s o t o p i c a l l y p u r e Ne20 w i t h  a 0.6 M o l . % h y d r o g e n The  t o 2 Torr  outer  surface  impurity. of the c a p i l l a r y  s e c t i o n was  w i t h b l a c k enamel p a i n t e x c e p t f o r a s m a l l a p e r t u r e diameter.  The c a p i l l a r y i t s e l f  t h a t t h e source The  a t a c u r r e n t o f 4 ma. p e n t o d e and b a l l a s t with a Tesla  B. S c a n n i n g The the  supply  resistor.  The d i s c h a r g e  was  initiated  coil.  Electromagnet  o f an e l e c t r o m a g n e t .  was c e n t r a l l y p o s i t i o n e d b e t w e e n The p o l e  p i e c e s were  t a p e r i n g t o 3 mm  hollow  diameter  the source.  Magnetic f i e l d calibration using:a  regulated  The c u r r e n t was c o n t r o l l e d by a s e r i e s  centred with the c e n t r a l hole nearest  one c u b i c m i l l i m e t r e .  f r o m a 1000 v o l t  G e i s s l e r tube source  poles  o f 1 mm  had a d i a m e t e r o f 1 mm so  v o l u m e was a p p r o x i m a t e l y  t u b e was o p e r a t e d  coated  strength versus  f o r the f i e l d  a t the source  B e l l M o d e l .240 g a u s s m e t e r  Measurements of f i e l d  electromagnet  current  p o s i t i o n was  (a H a l l p r o b e  obtained  instrument).  i n h o m o g e n e i t y i n d i c a t e no  field  -28-  g r e a t e r t h a n 3% p e r cm i n t h e c e n t r a l r e g i o n .  gradients 1 mm  (the c h a r a c t e r i s t i c  t h a n 0.3%  variation.  l e n g t h of the source) t h e r e  The maximum Zeeman s h i f t  0,4 cm"-'- , i n w h i c h c a s e t h i s  t h a n 3% o f t h e s o u r c e  half width,  was u s u a l l y much l o w e r was n o t c o n s i d e r e d  C. A b s o r p t i o n The  than t h i s ,  significant  Since  i s less  r e q u i r e d was  inhomogeneity r e s u l t s  d i f f e r e n c e s o f n o t more t h a n 1.2 mK.  Over  this  i n shift  i s less  and s i n c e t h e f i e l d  strength  field  broadening  i n this  inhomogeneity experiment.  Tubes  absorber  was a h o l l o w  cathode glow d i s c h a r g e i n  i s o t o p i c a l l y p u r e Ne20 ( a l s o w i t h t h e 0.6 M o l . % h y d r o g e n impurity).  The s o u r c e  beam was p a s s e d t h r o u g h t h e h o l l o w  cathode. Absorption  tubes of t h r e e d i f f e r e n t  2 T o r r , 50 T o r r , in  and 100 T o r r , were e m p l o y e d .  a l l t h r e e t u b e s was m a i n t a i n e d  supply w i t h the current ballast in  order  resistor.  The  by a 1400 v o l t  discharge  regulated  The b a l l a s t was made as l a r g e as p o s s i b l e fluctuations.  u s u a l l y had t o be i n i t i a t e d w i t h a T e s l a  the  pressures,  c o n t r o l l e d by a s e r i e s p e n t o d e and  t o reduce c u r r e n t  Different  filling  absorption  The  discharge  coil.  s t r e n g t h s were o b t a i n e d  c u r r e n t b e t w e e n 0.3 ma and 16 ma.  by v a r y i n g  26  Fig.  3  cm  Absorption  Tube  Construction  -30-  D.  Optical The  beam e m e r g e n t f r o m t h e magnet was  by l e n s 990 Hz  System  (see F i g . 4 ) .  rendered  parallel  After amplitude modulation  by t h e c h o p p i n g w h e e l  through the h o l l o w cathode. 5 mm  I D ) , a l o n g w i t h a 3 mm  exit  end  i t passed The  i n t o the  s m a l l cathode  diameter  absorber bore  (3 t o  s t o p p l a c e d on  of t h e a b s o r p t i o n t u b e , e n s u r e d  at  the  that only a small  r e l a t i v e l y homogeneous r e g i o n i n t h e c e n t r e of t h e a b s o r p t i o n t u b e a t t e n u a t e d t h e beam. N e x t f o l l o w e d t h e q u a r t e r wave p l a t e and Nicol  prism.  they also from the The slit  the a n a l y z i n g  These were p l a c e d a f t e r t h e a b s o r b e r  s e r v e d t o s u p p r e s s p a r t of t h e  second  'noise' emission  l e n s L.2 f o c u s s e d t h e beam o n t o t h e  o f a 500 mm  entire  The  entrance s l i t  and  s t o p s w e r e opened  e x c l u d e any n e a r b y  150  volts  CVP  and  but y e t kept narrow  spectral lines.  t h e m o n o c h r o m a t o r was  1500  The  opened s u f f i c i e n t l y w i d e t o e a s i l y a c c e p t  spectral line  Phillips  entrance  B a u s c h and Lomb g r a t i n g m o n o c h r o m a t o r o f  j u s t w i d e enough t o a c c e p t a l l t h e s o u r c e beam. was  that  absorber.  low d i s p e r s i o n .  slit  so  The  enough t o light  converted to e l e c t r i c a l  exit  the still  emerging  from  c u r r e n t by a  P h o t o m u l t i p l i e r operated at approximately  c o o l e d by d r y i c e .  Electromagnet  Stop Nicol Prism  Absorption Tube  Hollow Cathode  -Geissler Tube (Source) Light  |  Phototransistor  '— Chopping Wheel ( f = 990 Hz) c  Quarter Wave Plate Lock-In Amplifier Narrow Band Amplifier Phase Sens. Detector Integrator  Chart Recorder  'Fig. 4  Experimental Arrangement  L2  Monochramator  Photomultiplier  -32-  E.  Electronic  Detection  C o n d i t i o n s i n the fluctuations strength.  The  both i n the  In order to  noise ratio detection  absorption tubes f l u c t u a t e d ,  i t was  and  radiation  employ phase  s i g n a l was  sent to  Applied Research Lock-In A m p l i f i e r  A  Hz  followed  s i g n a l , p r o d u c e d by  the  network  d.c.  upon t h e  by  sensitive  (incorporated sec  i n the  supplied  Princeton Essentially  tuned to the  noise encountered.  the  chopper  detector.  fed  to  The  and  phase  reference.  an  integrating  RC  Lock-Kin A m p l i f i e r ) .  t o 3 sec  a Heathkit Chart Recorder  a  a phase s e n s i t i v e  s i g n a l p r o d u c e d was  c o n s t a n t s f r o m 0.3  to  chopping wheel w i t h a l i g h t  a photo-sensitive transitor The  signal  (Model 120).  t h i s d e v i c e i s a n a r r o w band a m p l i f i e r 990  absorption  integration.  photomultiplier  f r e q u e n c y of  the  achieve a s a t i s f a c t o r y  necessary to  signal  e m i t t e d and  causing  Time  were employed d e p e n d i n g o u t p u t was  ( M o d e l EUW  -  20A).  monitored  on  -33-  CHAPTER  IV  EXPERIMENTAL  The  PROCEDURE  o p t i c a l _ s y s t e m was i n i t i a l l y  of a c o n t i n u o u s  He-Ne l a s e r  the monochromator.  a l i g n e d on t h e beam  shone i n t o t h e e x i t s l i t o f  F i n a l a l i g n m e n t was a c c o m p l i s h e d by  minor adjustments t o the source  position,  tube p o s i t i o n ,  o f t h e l e n s L2 s u c h t h a t a  and t h e p o s i t i o n  maximum s i g n a l was The equation  obtained.  d i r e c t i o n of t h e frequency  of t h e s h i f t  could  each c u r r e n t v a l u e ,  transmitted line  and i n d i s c r e t e  and h e n c e e a c h s o u r c e  switched  intensities yields  current value  by v a r y i n g t h e  frequency,  on and o f f .  The r a t i o n  was o b t a i n e d  the  The  by c o n v e r t i n g t h e e l e c t r o m a g n e t  to the corresponding  magnetic f i e l d  strength into  XII.  W i t h each a b s o r p t i o n obtained  the  of these  the f r a c t i o n a l transmission t . o  u s i n g t h e magnet c a l i b r a t i o n and t h e n s u b s t i t u t i n g equation  steps.  i n t e n s i t y was m e a s u r e d b o t h w i t h t h e  discharge  frequency  from which the d i r e c t i o n  was o b t a i n e d  electromagnet current monotonically  source  a s o u r c e of  be d e d u c e d .  Each t r a n s m i s s i o n curve  two  (the sign i n  The p r e s e n c e o f t h e Ne22 i s o t o p e c a u s e d an  asymmetry i n t h e t r a n s m i s s i o n curve  absorbing  shift  X I I ) was d e t e r m i n e d by s u b s t i t u t i n g  n a t u r a l neon.  For  the absorption  tube the t r a n s m i s s i o n curves  f o r a range of a b s o r p t i o n  absorption  strengths  were  by v a r y i n g  tube c u r r e n t from experiment t o experiment.  -34-  CHAPTER METHOD  V OF  ANALYSIS  A. C h o i c e o f M o d e l The shape o f t h e a b s o r p t i o n l i n e c a n n o t obtained  from a t r a n s m i s s i o n c u r v e .  consider- models i n which  be d i r e c t l y  I t i s necessary to  t h e e x a c t p r o f i l e s of t h e source  and t h e a b s o r b e r a r e s p e c i f i e d  and f r o m t h e s e t o compute  theoretical  transmission curves.  The m o d e l w h i c h  produces  the c l o s e s t  approximation to the experimental r e s u l t  i s then  considered to describe the absorption l i n e . U n f o r t u n a t e l y t h i s p r o c e d u r e may result.  not y i e l d a  unique  However, i f i t be assumed t h a t t h e shape o f t h e  a b s o r p t i o n l i n e d o e s n o t change as t h e a b s o r p t i o n s t r e n g t h k  Q  i s varied., (by a l t e r i n g t h e a b s o r b e r  variation  current),  then the  of t h e t r a n s m i s s i o n p r o f i l e s w i t h a b s o r p t i o n  strength offers  an a d d i t i o n a l  constraint  on t h e m o d e l .  e n a b l e s a c h o i c e t o be made f r o m an i n i t i a l The s p e c t r a l  This  s e t of models.  l i n e s o f s o u r c e and a b s o r b e r w e r e  both  c o n s i d e r e d t o be d e s c r i b e d by V o i g t p r o f i l e s .  Their Gaussian  h a l f w i d t h s w e r e assumed t o r e s u l t  Doppler  broadening.  Since the Geissler  s o l e l y from  tube  c a p i l l a r y was s l i g h t l y  warmer t h a n t h e a b s o r p t i o n t u b e and s i n c e b o t h w e r e warmer t h a n room t e m p e r a t u r e ,  (b)  T  >  i t c o u l d be assumed:  300  °K  -35-  where T  s  temperatures  a n d T a r e t h e s o u r c e and a b s o r b e r a respectively.  The L o r e n t z i a n h a l f w i d t h s w e r e assumed t o r e s u l t from p r e s s u r e broadening.. pressure absorber ( A3^  half width  Consequently  absorbed  of the 2 Torr  c o u l d be assumed t o have t h e same L o r e n t z i a n ) as t h e s o u r c e .  s  The s o u r c e was c o n s i d e r e d f u r t h e r absorptian.  the l i n e s  entirely  F o r an i n t r i n s i c  b r o a d e n e d by s e l f  V o i g t shape S ( / -7{ ) t h e s e l f  shape was t a k e n a s : I i O  This r e s u l t s jitf-tl)  - ^ )  7  o<  K-S(^-Ti)}  1 - ex.p{ -  from e q u a t i o n IX under t h e assumption  and k(P-%)  that  have t h e same f r e q u e n c y d e p e n d e n c e .  The h i g h e r p r e s s u r e a b s o r b e r s w e r e assumed t o have t h e same t e m p e r a t u r e  as t h e 2 T o r r p r e s s u r e a b s o r b e r  since their  t u b e s w e r e n o t n o t i c e a b l y warmer d u r i n g o p e r a t i o n t h a n t h e 2 Torr tube.  The t r a n s m i s s i o n c u r v e s f o r t h e s e  provide a further test  B. S p e c i f i c  f o r the models.  Procedure  (1) An a s s i g n m e n t  of T , T , A ^ s  g  (2) The a b s o r p t i o n s t r e n g t h a line  centre transmission t  (3) The f u l l and  then  absorbers  0  s  , and K was made.  k(O)./  was v a r i e d  o f 0.33 was o b t a i n e d .  t r a n s m i s s i o n c u r v e was c a l c u l a t e d ,  compared w i t h t h e e x p e r i m e n t a l r e s u l t s  2 Torr absorber  i n which  (4) The p a r a m e t e r s  t  0  until  plotted,  f o r the  e q u a l l e d 0.33.  (T , T , A ^ a  s  , K) were v a r i e d  until  -36-  an a c c e p t a b l e f i t was  obtained.  (5) T r a n s m i s s i o n c u r v e s were t h e n c a l c u l a t e d the corresponding  for t  = 0.16  computed  half width. results  experimental results  Lorentzian half widths  Lorentzian  (see F i g u r e 10).  = 0.33  experimental results  By r e p e a t e d  assigned  ( A t ) versus t  trial  and e r r o r  pressure  and compared t o t h e  a s e t of parameters a l l these  a L o r e n t z i a n h a l f w i d t h was  f o r each absorber  absorber  (see F i g u r e 9 ) .  obtained which s a t i s f i e d  In a d d i t i o n  f o r the i n d i c a t e d  o f t h e 50 T o r r and 100 T o r r  a b s o r b e r s were computed f o r t  tests.  0.53  T h e s e w e r e t h e n compared w i t h t h e e x p e r i m e n t a l  (7) F i n a l l y t r a n s m i s s i o n c u r v e s  AJ>is , K) was '  =  (see F i g u r e 8 ) .  f o r a range of v a l u e s of t h e absorber  f o r a l l three pressures  corresponding  Q  f o r t h e s e p a r a m e t e r s and compared t o  (6) A g r a p h o f t r a n s m i s s i o n h a l f w i d t h was  and t  pressure.  (T_, T ,  c h e c k s and thereby  -37-  CHAPTER  VI  RESULTS  A. D e t e c t i o n o f  Broadening  Broadening curves  c a n be d e t e c t e d  f o r a b s o r p t i o n tubes  In cases where t h e l i n e  by c o m p a r i n g t h e t r a n s m i s s i o n  of d i f f e r e n t  filling  centre transmissions t  pressures. are equal  o comparisons c l e a r l y demonstrate the pressure  broadening  absorption l i n e .  F i g u r e s 5, 6, and 7 on t h e n e x t  show e x p e r i m e n t a l  results  respectively. these  fort  0  a r e summarized  three  of t h e pages  = 0.16, 0.33, and 0.53  I n terms of t r a n s m i s s i o n curve  results  such  n  half widths  ( At)  below: At(mK)  to 2 Torr  50 T o r r  100  Torr  0.16  106  123  144  0.33  91  109  132  0.53  87  Width v a r i a t i o n s  98  l e s s than those  observed  still  be d e t e c t e d .  fifth  of such w i d t h d i f f e r e n c e s c o u l d s t i l l  distinguished.  Experience  121  here  could  i n d i c a t e d t h a t curves w i t h a  In section C following  be u n a m b i g u o u s l y  i t will  be s e e n t h a t  f r o m 2 T o r r t o 100 T o r r t h e r e was an i n c r e a s e i n t h e L o r e n t z i a n h a l f w i d t h of the absorbers study  of a p p r o x i m a t e l y  of t h e t r a n s m i s s i o n curves would enable  the absorber  h a l f w i d t h o f as l i t t l e  45 mK.  Hence  an i n c r e a s e i n  as 5 mK t o be d e t e c t e d .  1.0 o  b  o. o b' g X  v  o  ^  X  °  0.9 t  0  o  ~e>—sr  9 *  •  x  X  *  O  G  O  X  o °  °  o  0.8 -h o  X  0.7  c o  X  0.6  •H  tn w  •H  £  0.5'  X  fO  u  H  0.4  03 C O •H -p  0.3  1—1  o  b  03  6  0.2  f  0.1  0  a  P = 2 Torr  x  P = 50 T o r r  o P = 100 T o r r -250 Fig.  -200  -150  5 Transmission  -100 -50 •% +50 +100 S o u r c e S h i f t f r o m L i n e Centre- (mK) C u r v e s f o r D i f f e r e n t P r e s s u r e s ( t = 0.16) 0  -150  +200  +250  1.0 o  a  o  o  "  °  X  X  • • I ft x x .X o 9  '  X  i  0.8  o  X  A  >; o  °  o  o  •  •  0.6  *  0  <»  *  o  + Q X  X  0.44-  o  X o  0.3f  0.2  +  -250 Fig.  6  -200  -150  Transmission  -100 -50 14 +50 +100 ' Source S h i f t from L i n e C e n t r e (mK) Curves f o r D i f f e r e n t P r e s s u r e s ( t = 0.33) Q  •  P = 2  x  p = 50  o  p = 100  +150  Torr Torr Torr  -280  +250  X  Fractional Transmission O  o ro  o  o -+-  o  o  o o  4-  o  o  o co  —J  o  vO  ro  CJi 0  H n  4-  e oo  ro o  CO  D  01  3  0 ej  H01  OX  W  H-  O  H-  o>»  1  cn • o  O  C  o Xo  fi  0  <  CD  in O H  a  H-  ox©  1  H  H-,  00  crr  fi o  o  I  o'  fD D rf  CO ZT Ht-h c+  TJ fi  fi  CD  fi  CD O)  cn  O  O CJl OJ  X »  X  »  X  o  0*  3  OX ©  fi  O  ©  O £c  C  CD O)  X  o  c CD  l-h  i-h  O  o  o  Xo  3  CD  O  O  +  CH  CD  •  o  O.  X  o  CD  c+ fi  X  O  +  X O  O  3  o X  0  » X  >c©  o —  + 1—  1  CJl +  o + ro o o  + ro  e  0  X© 0 X©  TJ  oy  TJ  II  II  II  O 9  t—  CJl  ro  0X  H o  o ©  1  o o  H O fi fi  O H  O fi fi  fi fi  Cv-  CJl  o "0t7-  -41-  B. D e t e c t i o n o f  Shift  T h e r e i s a s l i g h t b u t u b i q u i t o u s asymmetry of  the  t r a n s m i s s i o n curves w i t h respect to the designated field  - zero  more o r l e s s was  no  shift position.  s y m m e t r i c a b o u t an o r d i n a t e of  discernable variation  a r e s u l t i t must be shift  However t h e c u r v e s  has Any  are a l l  + 4 mK.  There  of t h i s o f f s e t w i t h p r e s s u r e .  concluded  t h a t no  significant  As  pressure  been d e t e c t e d . real  t h a n 4 mK  s h i f t due  f o r t h e 100  t o p r e s s u r e must have been a t most  T o r r absorber..  i n disagreement w i t h the impact interaction, The  zero  Such minimal  t h e o r y f o r a van  i s c o n s i s t e n t w i t h the r e s u l t s  l i n e centre transmission, t  , was  pressure  der  Waals  of S m i t h  (14).  taken  less  on t h e  shift,  axis  o of symmetry/in each  C.  L i n e Shape As  Determination  a result  i n Chapter  case.  of t h e a n a l y s i s by m o d e l l i n g  V s e c t i o n B ) , t h e p a r a m e t e r s o f t h e m o d e l of  best f i t are:  Source = 50 (=f>  T  Absorber(s) mK  = 360  A^„  °K)  s  (=• T  = 48  mK  = 325  °K).  ' = 6  mK  (source Voigt A = K = 1.5 The  (as d e s c r i b e d  Lorentzian half  widths  0.12)  of t h e a b s o r b e r s ,  as  concluded  -42-  from t h e t  versus  A t curves  (see Figure 10), are t a b l e d  below: Pressure  The curves  L\V * (mK)  (Torr)  2  7  0.14  50  23  0.48  100  48  1.00  comparison  of t h e o r e t i c a l  and e x p e r i m e n t a l t r a n s m i s s i o n  f o r p r e s s u r e s o f 2 T o r r and 100 T o r r a r e d i s p l a y e d i n  F i g u r e s 8 and 9 r e s p e c t i v e l y . curves  Voigt A  L  F i g u r e 10 shows t h e t h e o r e t i c a l  f o r l i n e centre transmission versus half width f o r the  model of b e s t f i t , I t was p r i m a r i l y  with the experimental results  from  Lorentzian half widths  also displayed.  t h i s curve t h a t t h e assignment of f o r the higher pressure  absorbers  was made.  D. R a t e o f P r e s s u r e B r o a d e n i n g The  -•Comparison w i t h Theory  r e s u l t s t a b u l a t e d a b o v e may most e a s i l y be compared  w i t h , t h e o r y by means o f a ' r a t e o f p r e s s u r e graph  - s e e F i g u r e 11 - i n w h i c h  half width i s plotted The  against pressure  relationship  passing through  Lorentzian  (and d e n s i t y ) .  data are i n s u f f i c i e n t to permit  the l i n e a r i t y of t h i s curve.  impact  the absorber  broadening'  conclusions regarding  However, a s s u m i n g a l i n e a r the o r i g i n  theory) then the best s t r a i g h t  ( a s p r e d i c t e d by t h e  l i n e has a s l o p e :  Fractional  Transmission  o  i ro otH  1  OJ D CD  ro o Cr  if) (Si PO  h-•  3  O C  1  CJl  O"  M  <  fD  1  F r a c t i o n a l Transmission o o ' o o  1.0 — Theory(model of best f i t )  0.9 +  0.8 +  Voigt A = 0 (absorber)  »  P = 2 Torr  x  P = 50  o  P = 100  Torr Torr  0.7  0.6  o.4 +  0.3  0.2  0.1 +  10 Fig.  70  80  10 T r a n s m i s s i o n  90 100110 120 130 T r a n s m i s s i o n C u r v e H a l f W i d t h (mK) Half Width versus Transmission  ( T h e o r y and  140  150  Experiment)  160  -46=  1.6-10  mK  cm  3  n Both estimates s e c t i o n C ) are experimental nearly there  c a l c u l a t e d i n the  displayed  as w e l l .  I t can  than that predicted  i s c l o s e agreement w i t h  derived* from the  of  the  by  (Chapter I I ,  be  r e s u l t s show a r a t e o f p r e s s u r e  50 % g r e a t e r  E. V a l i d i t y  theory  seen t h a t broadening  theory.  semi-empirical  r e s u l t s of S m i t h  the  However rate  (14).  Results  (1)Reliability: Since of p r o f i l e are  the  a n a l y s i s and  difficult  shown a r e  r e s u l t s are  and  derived  parameter v a r i a t i o n , e r r o r  somewhat u n c e r t a i n .  p r i m a r i l y b a s e d on  In matching experimental curves the are  so  fitting  similar.  t h r o u g h a complex  e r r o r s are  curve s u f f i c i e n t l y  error  and  theoretical  quite  d i s t o r t e d the  small  2 mK  independently,  assigned  A  curves parameter  shape of t h e t h e o r e t i c a l fit.  Similarly,  to the  absorber  a l t e r e d t h e w i d t h of t h e t h e o r e t i c a l  two  l a c k of f i t a p p a r e n t . parameters could  f o r decreases i n the  would e v e n t u a l l y  transmission  absorber Voigt  t o c a u s e r e j e c t i o n of t h e  c u r v e enough t o make t h e v a r i a t i o n s of'these  estimates  since the  v a r i a t i o n of t h e D o p p l e r h a l f w i d t h a s s i g n e d by more t h a n t  estimates  self-consistency.  V a r i a t i o n of the  by more t h a n - 0.05  The  process  necessitate  Moreover  not  be made  altogether  assigned  Doppler  width  concurrent increases  Voigt A parameter, e t c .  As  a r e s u l t the  in  the  uncertainty  -47-  Pressure Density Pig.  11  Rate of P r e s s u r e  Broadening  -48-  i n the assigned probably  absorber  no more t h a n  Lorentzian half width i s thereby  i 4  mK.  From t h e t r a n s m i s s i o n v e r s u s F i g u r e 10) upon w h i c h t h e f i n a l is  a range of V o i g t A parameters  widths)  half width  r e l a t i o n (see  e s t i m a t e s were b a s e d  there  ( a n d hence L o r e n t z i a n h a l f  s p a n n e d by t h e e x p e r i m e n t a l p o i n t s .  Pressure  (Torr)  2  (maximum)  (mK>  (mK)  (mK)  7  2.5  10.5  50  23  20.5  26.0  100  48  46.0  49.5  These v a r i a t i o n s , described  (minimum)  A ^  i n conjunction with the f i t t i n g  errors  a b o v e , were u s e d as t h e b a s i s f o r a s s i g n i n g t h e  confidence  limits  d i s p l a y e d i n F i g u r e 11.  (2) S y s t e m a t i c E r r o r s : Since a l l the t r a n s m i s s i o n curves shift  of approximately  4 mK, w h i c h was m o r e o v e r  o f p r e s s u r e , an a p p a r a t u s o f f s e t i s thought scanning  e r r o r i s suspected.  T h i s + 4 mK of the  to follow perfectly i t s calibration  This condition results  r e s i s t a n c e due t o h e a t i n g .  curve.  from i m p e r f e c t r e g u l a t i o n of t h e  c u r r e n t i n t h e face of v a r i a t i o n s  (the t r a n s i t i o n  slight  independent  t o have o r i g i n a t e d i n a f a i l u r e  electromagnet  electromagnet  showed t h e same  of t h e c o i l  A f t e r t h e c u r r e n t was  from n e g a t i v e t o p o s i t i v e  shift)  reversed i t was t o  -49-  have been m o n o t o n i c a l l y calibration (0.2 amp)  curve.  the  increased. decrease i n the  However a f t e r  each c u r r e n t  c o i l s warmed f u r t h e r and  T h e r e was  very  i n c r e a s e d i n .order t o f o l l o w t h e increment  their resistance  a tendency f o r the c u r r e n t to  slightly,  electromagnet  then  i n s p i t e of t h e , r e g u l a t i o n p r o v i d e d  c u r r e n t power  supply.  T h i s w o u l d have t a k e n t h e magnet o f f t h e assumed curve The  and  slightly  a c t u a l magnetic  would half  result  i n an  i n t o the  'interior'  f i e l d w o u l d be expansion  Zeeman s h i f t )  of t h e h y s t e r i s i s  l e s s than  of t h e f r e q u e n c y  of the t r a n s m i s s i o n c u r v e  calibration loop.  t h a t assumed. scale for  this  i n t h a t the a c t u a l f i e l d  (and  are l e s s than those  assigned.  As  a result  This  the  c e n t r e of g r a v i t y of t h e t r a n s m i s s i o n c u r v e w o u l d be d i s p l a c e d to the high frequency  s i d e (see F i g u r e  In a d d i t i o n to producing  the apparent  must a l s o h a v e c a u s e d a p p a r e n t l y w i d e r No  attempt,  error of  and  h o w e v e r , was  theoretical  shift,  this  effect  transmission curves.  made t o c o r r e c t f o r t h i s p o s s i b l e  p r o f i l e s were f i t t e d  to the  centre  symmetry. The  r a t e of b r o a d e n i n g  p o s s i b l y the The  12).  effect  g r a p h ( F i g u r e 11)  of a s e c o n d s o u r c e  Lorentzian width assigned  of s y s t e m a t i c  to the 2 Torr absorber  a p p a r e n t l y too great s i n c e a l l pressure predict half widths density).. width  broadening  of z e r o p r e s s u r e  error. is  theories  d i r e c t l y p r o p o r t i o n a l to pressure  In the l i m i t  should  r e v e a l s what i s  (and  the L o r e n t z i a n h a l f  approach the n a t u r a l l i n e width  ( h e r e o n l y — 0.6  mK).  1.0  --  /,'  ': / •  i: i: it • •  ' >  i•  I •  i»: • actual  curve  apparent curve to i m p e r f e c t regulation  F i g . 12  E f f e c t of C u r r e n t R e g u l a t i o n F a i l u r e  due  -51-  S i n c e t h i s i s n e g l i g i b l e t h e n f o r the expected of  ^  L o r e n t z i a n w i d t h s h o u l d be t h e v a n d e r W a a l s  1 mK  only.- outside the confidence l i m i t s  The o r i g i n o f . t h i s is  2 Torr absorber  i n a l l probability  S e v e r a l minor broadening  assigned!  of the source.  e f f e c t s which.were n e g l e c t e d a r e :  1. m a g n e t i c f i e l d  inhomogeneities  of t h e source  magnetic , f i e l d  line  (see Chapter shape as t h e  c o n t r a s t t o t h e homogeneous,  It that tends  assumed  to yield  of t h e s o u r c e ,  plane-parallel  i n the theory)  o f many i n d e p e n d e n t  a Voigtprofile".  have had ' a V o i g t t y p e p r o f i l e , Lorentzian  component  broadening  The s o u r c e as was  line  assumed.  effects thus  However  the  s h o u l d p r o p e r l y have been g r e a t e r t h a n t h e  the a n a l y s i s the source  alone.  and' t h e 2 T o r r a b s o r b e r  t o have had e q u a l L o r e n t z i a n h a l f w i d t h s  p r e s s u r e s were e q u a l .  (16)  should  Lorentzian h a l f width a s c r i b e d to pressure broadening  assumed  from  has .been p o i n t e d o u t by v a n de H u l s t and R e e s i n c k  "the combination  In  scanning  absorption resulting  the inhomogeneous'cylinderical nature  source  I I ).'  i s varied.  3. v a r i a t i o n s i n t h e s e l f  (in  width  apparently excessive Lorentzian width  unaccounted broadening  2. a l t e r a t i o n  the  were  since their  Thus an e x a g g e r a t e d . L o r e n t z i a n h a l f  w i d t h must h a v e b e e n a s c r i b e d t o t h e 2 T o r r a b s o r b e r i n order to f i t the t r a n s m i s s i o n curves. S u c h an e r r o r i n t h e s o u r c e e r r o r s in':the r e s u l t s  line  shape w i l l  also create  f o r the higher pressure absorbers.  However  -52-  for  t h e s e i t was  derived  line  found t h a t the L o r e n t z i a n w i d t h s of  profiles  were l e s s a f f e c t e d by c h a n g e s i n t h e  assumed s o u r c e shape t h a n w e r e t h o s e o f t h e 2 T o r r H e n c e , as m i g h t be a n t i c i p a t e d the r e s u l t s less  the  absorber.  f r o m t h e t h e o r y (see. e q u a t i o n I V A ) ,  f o r t h e h i g h e r p r e s s u r e a b s o r b e r s w o u l d have been  affected  by s u c h an e r r o r i n t h e s o u r c e l i n e  shape.  -53-  CHAPTER V I I CONCLUDING  The suited The  Zeeman s c a n n i n g  DISCUSSION  technique  h a s shown i t s e l f  t o t h e d e t e r m i n a t i o n of narrow s p e c t r a l l i n e  ability  —  r e s o l u t i o n of otherwise By  except  with sophisticated spectrographic  broadening  glow d i s c h a r g e  at d i f f e r e n t pressures  conditions.  I t i s apparent  polated  determined  from t h e r e s u l t s will  A t 10 T o r r and 325 °K t h e  shows a V o i g t A p a r a m e t e r o f A = 0.1  (inter-  from F i g u r e 1 1 ) .  The theory.  line  the extent  as l o w a s a f e w T o r r t h i s l i n e  e x h i b i t a non-Gaussian p r o f i l e . 0  techniques.  f o r Ne"\6074.3 A° has been  t h a t even a t p r e s s u r e s  Ne'X6074.3 A  to represent a  3*10^, w h i c h i s d i f f i c u l t t o o b t a i n  comparing absorbers  of p r e s s u r e  profiles.  t o d e t e c t d i f f e r e n c e s as l o w as 5 mK ( o r 2 mA° ) i n  a b s o r p t i o n l i n e w i d t h may be c o n s i d e r e d  for  well  pressure  broadening  This i s probably  neon t r i p l e t  c o u l d be c a l c u l a t e d q u i t e w e l l  true also f o rother l i n e s  of t h e  s y s t e m w h i c h a r e u n a f f e c t e d by r e s o n a n c e  T h o s e neon l i n e s a f f e c t e d by r e s o n a n c e b r o a d e n i n g Voigt A values  even g r e a t e r t h a n Ne'X6074.3 A  0  effects.  likely  under  from  exhibit  similar  conditions. Thus, t h e c a s u a l a s s u m p t i o n o f G a u s s i a n glow d i s c h a r g e  lines  i s i n error.  profiles  Where s u c h an a s s u m p t i o n •  i s t o be made the^consequences o f t h e p r e s s u r e should  f i r s t be c h e c k e d .  f o r neon  broadening  -54-  Close  agreement  f o r t h e r a t e of p r e s s u r e  been o b t a i n e d w i t h v a l u e s with  a v a n d e r Waals i n t e r a c t i o n  value  of  derived the is  calculated  =  from  1.6*10  the r e s u l t s  assigned  confidence  limits.  approximation The of S m i t h  cm  agrees  The with  experimental the value  The more t h e o r e t i c a l  c l o s e - t o w i t h i n 50 % . t h e use o f  within value  Such  VIII).  l a c k of observed  shift,  consistent with the r e s u l t s  ( 1 4 ) , confirms the f a i l u r e  o f t h e v a n d e r Waals  to p r o p e r l y describe the emitter - perturber  interaction  i n this  as a d v o c a t e d  evidently  instance.  The i n c l u s i o n  Such a c o n s i d e r a t i o n f a l l s  s c o p e o f t h e p r e s e n t work and would accurate  study  This argon  by t h i s  interesting.  Zeeman  Of c o u r s e  discharges  for similar  previously  noted  check argon Smith  interaction.  likely  (15),  is  beyond t h e  r e q u i r e a more  line  an i n v e s t i g a t i o n scanning  argon  t e c h n i q u e would  has a l s o  experiments  of. one o r two  been used  be most  i n glow  (19, 20) t o t h o s e  ( 1 , 2) so t h e r e f o r e i t i s d e s i r e a b l e t o s h a p e s as w e l l .  (14) i n d i c a t e  predictions  repulsive  of t h e s h i f t .  i s one r e a s o n why  lines  of a  by H i n d m a r s h , P e t f o r d , and S m i t h  required.  good  Unsold's  interaction  term,  has  theory  (14) t o more o r l e s s  appear t o j u s t i f y  (equation  u s i n g the impact  postulated.  of Smith  likewise encouragingly  agreement would  mK  broadening  t h a t argon  of the impact  In a d d i t i o n  behaves  theory with  In p a r t i c u l a r  the s h i f t  closely  the r e s u l t s of to the  a van der Waals to width  ratio  i s close  -55-  t o t h e 1:2.76 v a l u e p r e d i c t e d . s u c h as '50 o r 100 T o r r t h e s h i f t An  Thus f o r h i g h e r p r e s s u r e s s h o u l d be e a s i l y d e t e c t e d .  i n v e s t i g a t i o n i n argon, t h e n , o f f e r s an e x c e l l e n t o p p o r t u n i t y  not o n l y t o check  these l i n e  shapes but t o a l s o f u r t h e r  test  t h e Zeeman s c a n n i n g t e c h n i q u e and c o n f i r m S m i t h ' s  findings  i n t h e case of argon  shift.  s e l f - p r e s s u r e broadening  and  F o r f u t u r e w o r k s e v e r a l i m p r o v e m e n t s i n t h e Zeeman s c a n n i n g apparatus  c a n be s u g g e s t e d .  i s analogous  The w i d t h o f t h e s o u r c e  line  t o t h e apparatus w i d t h of a s p e c t r o g r a p h or  interferometric  system  i n t h a t the source p r o f i l e  i s folded  w i t h t h a t of t h e absorber t o produce t h e e x p e r i m e n t a l r e s u l t . I d e a l l y t h e s o u r c e l i n e w i d t h s h o u l d be s i g n i f i c a n t l y t h a t of the absorber.  T h e n , as s u g g e s t e d  solely  on t h e a b s o r b e r ' s l i n e  was n o t a c h i e v e d i n t h i s  experiment  shape.  depends  Such a  b u t where i t was  w i t h t h e 100 T o r r a b s o r b e r t h e r e s u l t s  than  by t h e t h e o r y ( s e e  e q u a t i o n IVA)., t h e shape o f t h e t r a n s m i s s i o n c u r v e almost  less  a r e more  situation approached  reliable.  A t l o w e r p r e s s u r e s t h e l i n e w i d t h s o f b o t h s o u r c e and a b s o r b e r are p r i m a r i l y determined comparable.  by D o p p l e r  Unless d r a s t i c  employed t o reduce  b r o a d e n i n g and a r e t h u s  c o o l i n g o r some o t h e r means i s  t h e Doppler w i d t h of the source the i d e a l  narrow - source s i t u a t i o n i s u n r e a l i z a b l e . Alternately, source l i n e  however, a p r e c i s e d e t e r m i n a t i o n of t h e  shape w i l l  absorber l i n e  shape.  p e r m i t an a c c u r a t e measurement o f t h e T h i s c o u l d be a c c o m p l i s h e d  t h e s o u r c e p r e s s u r e and o p t i c a l t h i c k n e s s so t h a t  by r e d u c i n g pressure  -56-  b r o a d e n i n g and s e l f  absorption are e f f e c t i v e l y  Then D o p p l e r . b r o a d e n i n g a l o n e w o u l d line  shape.  These measures would  low i n t e n s i t y , very l i k e l y  i m p l y a l s o a source of  n e c e s s i t a t i n g a more e f f i c i e n t  inhomogeneity would  guarantee  determine the source  r e d u c i n g t h e s i g n a l - t o - n o i s e r a t i o and  t h a n t h a t employed i n t h i s field  eliminated.  t h e absence  experiment.  detection  In addition  have t o be f u r t h e r  be s a t i s f i e d  o f any b r o a d e n i n g r e s u l t i n g t h e r e f r o m .  i n t h e a n a l y s i s would  parameters  be r e d u c e d and t h e  r e s u l t s n o t o n l y more e a s i l y o b t a i n e d b u t a l s o more •In  reliable.  view of the encouraging r e s u l t s o b t a i n e d i n t h i s  experiment further  magnetic  reduced to-  W i t h s u c h i m p r o v e m e n t s t h e number o f " f r e e " to  system  i t i s hoped t h a t f u t u r e w o r k , w i t h t h e a p p a r a t u s  refined, w i l l  be c a r r i e d o u t .  -57BIBLIOGRAPHY (1) N o d w e l l , R., v a n A n d e l , H., & R o b i n s o n ,  A. :  JQSRT 8 , p. 859 ( 1 9 6 8 ) . 2) S e k a ,  W.,  & Curzon,  3) S t a n s f i e l d ,  B. :  JQSRT 8 , p. 1 1 4 7 ( 1 9 6 8 ) .  M.A.Sc. T h e s i s  4) B i t t e r , P l o t k i n , Phys.  F.':  Tichter,  (U.B.C. - 1 9 6 7 ) .  Teviotdale,  Rev. 91 , p . 4 2 1 ( 1 9 5 3 ) .  5) H e i t l e r , W.  : The Quantum T h e o r y o f R a d i a t i o n ,  O.U.P. ( 3  r  d  E d . - 1959) S e c t i o n I ,  6) H e i t l e r , W. : i b i d  S e c t i o n V,  18(pp.  7) N o d w e l , R., v a n A n d e l , H., & R o b i n s o n , 8) E c k e r , G. & Z o l l e r . 9) G r i e m ,  & Young :  0. :  Phys.  181 - 1 8 5 ) . A. : i b i d  , McGraw-Hill  10  I r w i n , J . C . : Ph.D. T h e s i s  11  F o l e y , H. : P h y s .  12  U n s o l d , A. : P h v s i k d e r S t e r n a t m o s p h a r e n  13  Allen,  C.W.  Athlone  p. 8 7 2 .  F I . 7 , p. 1996 ( 1 9 6 4 ) .  H. : P l a s m a S p e c t r o s c o p y  Springer  4 ( p p . 25 - 3 4 ) .  (1964) T a b l e 4-5  (U.B.C. - 1 9 6 5 ) .  R e v . 69 , p. 616 ( 1 9 4 6 ) .  ( 2  n  d  ,  Ed. - 1955).  : Astrophysical Quantities , ( 2  n  d  Ed. - 1963).  14  S m i t h , G. : . P r o c . R o y . S o c . A 2 9 7 , p. 288 ( 1 9 6 7 ) .  15  Hindmarsh. P e t f o r d ,  16  Van  17  Y o u n g , C. : JQSRT 5 , p. 549 ( 1 9 6 5 ) .  18  I n t e r n a t i o n a l C r i t i c a l Tables V :  19  Jacobson,  20  S t o c k m a y e r , P. : M.Sc. T h e s i s  & S m i t h ' : P r o c .Roy .Soc. A 2 9 7 , p.296  de H u l s t & R e e s i n c k  (1967).  : App. J . 106 , p. 121 ( 1 9 4 7 ) .  T. : Ph.D. T h e s i s  McGraw-Hill  , (U.B.C. - 1 9 6 9 ) . (U.B.C. - 1 9 6 9 ) .  (1929) p . 4 1 8 f f .  -58APPENDIX  I  F l o w c h a r t : Computer C a l c u l a t i o n o f T r a n s m i s s i o n C u r v e s * ( a ) START Read  , AVM  I  , &T? , K, A, t L%  *(c)  C a l c u l a t e and s t o r e t h e s o u r c e p r o f i l e f o r an o r d i n a t e s p a c i n g o f 2.5  *(c)  k i Q  Compute  Q  by  *(b)  C a l c u l a t e and s t o r e t h e absorber p r o f i l e (VGA(J)) f o r an o r d i n a t e s p a c i n g o f 2.5 mK  mK  Integrate the source t o compute S{JZ)  Vary k ^ iterative halving  (  NO  *(a)  = 10.0  0{2i)  and t  *(d)  -59-  r Compute and s t o r e t h e absorber f u n c t i o n :  ex.p{  -kJ(VGA{j))}  Compute t h e t r a n s m i s s i o n f o r a l l source f r e q u e n c i e s  r  Write  and p l o t t h e  transmission  curve.  ^STOP  *Notes:  ( a ) The c a l c u l a t i o n s w e r e p e r f o r m e d on an IBM 7044 computer * (b) A i s t h e V o i g t A p a r a m e t e r f o r t h e a b s o r b e r ; o t h e r s y m b o l s a r e as d e f i n e d i n C h a p t e r s I I and V. ( c ) The p r o f i l e i s c a l c u l a t e d u s i n g t h e VOIGT s u b r o u t i n e (17) f o r each s p e c i f i c f r e q u e n c y . '(d) The i n t e g r a t i o n was p e r f o r m e d by u s e o f a c o m p o s i t e Newton - C o t e s f o r m u l a o f o r d e r 4 ( c l o s e d ) i n 100 s t e p s f r o m - 10 t o + 10 h a l f w i d t h s .  

Cite

Citation Scheme:

    

Usage Statistics

Country Views Downloads
United States 4 0
China 3 22
France 1 0
City Views Downloads
Ashburn 3 0
Shenzhen 2 22
Redmond 1 0
Unknown 1 1
Beijing 1 0

{[{ mDataHeader[type] }]} {[{ month[type] }]} {[{ tData[type] }]}
Download Stats

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0084802/manifest

Comment

Related Items