UBC Theses and Dissertations

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UBC Theses and Dissertations

Investigation of the selfpressure broadening of the Ne [Lambda] 6074.3 A° line profile by Zeeman scanning 1969

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AN INVESTIGATION OF THE SELF- PRESSURE ' BROADENING OF THE Ne\6074.3 A 0 LINE PROFILE BY •- ZEEMAN SCANNING by JOHN C. BURNETT B.Sc, U n i v e r s i t y of B r i t i s h Columbia, 1959 A THESIS SUBMITTED IN PARTIAL FULFILMENT THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n the Department of PHYSICS We ac c e p t t h i s t h e s i s as co n f o r m i n g t o the r e q u i r e d s t a n d a r d : THE UNIVERSITY OF BRITISH COLUMBIA November, 1969 In presenting th is thesis in p a r t i a l f u l f i lment of the requirements for an advanced degree at the Un iver s i t y of B r i t i s h Columbia, I agree that the L ibrary sha l l make i t f r e e l y ava i l ab le for reference and Study. I further agree that permission for extensive copying of this thesis for s cho la r l y purposes may be granted by the Head of my Department or by his representat ives . It is understood that copying or pub l i ca t i on of this thes,is for f i n a n c i a l gain sha l l not be allowed without my wr i t ten permission. John C. Burnett) Department of Physics The Un ivers i ty of B r i t i s h Columbia Vancouver 8, Canada Date 1 0 N O V , 1 9 6 9 - i i - A b s t r a c t The- shape of the Ne.X6074.3 A° a b s o r p t i o n l i n e p r o f i l e has been i n v e s t i g a t e d u s i n g the Zeeman sc a n n i n g t e c h n i q u e . Neon glow d i s c h a r g e s a t t h r e e p r e s s u r e s , 2 T o r r , 50 T o r r , and 100 T o r r , were used as a b s o r b e r s w h i l e a 2 T o r r G e i s s l e r tube was used as the s o u r c e . The s e l f - p r e s s u r e b r o a d e n i n g of the observed l i n e was c l e a r l y observed and the r a t e of b r o a d e n i n g compares w e l l w i t h t h e o r e t i c a l e s t i m a t e s made from the impact t h e o r y w i t h a van der Waals i n t e r a c t i o n assumed. No s h i f t was d e t e c t e d , i n c o n t r a d i c t i o n t o the t h e o r y . T h i s l a c k of s h i f t , and the r a t e of p r e s s u r e b r o a d e n i n g o b s e r v e d , were i n agreement w i t h the r e s u l t s of Smi t h (14) r e g a r d i n g t h e s h i f t and br o a d e n i n g of the Ca. X6573 A° l i n e by neon. - i i i - TABLE OF CONTENTS Chapter Page A b s t r a c t i i T a b l e of C o n t e n t s i i i L i s t of F i g u r e s i v L i s t of R e f e r e n c e d E q u a t i o n s v Acknowledgements v i I I n t r o d u c t i o n 1 I I Theory . 4 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 4 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 9 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 12 D. S e l f A b s o r p t i o n Broadening 18 E. V o i g t P r o f i l e s 21 F. Zeeman Sc a n n i n g and Inhomogeneity Broadening 24 I I I A p p a r a t u s 27 A. Source 27 B. S c a n n i n g E l e c t r o m a g n e t 27 C. A b s o r p t i o n Tubes , 28 D. O p t i c a l System 30 E. E l e c t r o n i c D e t e c t i o n 32 IV E x p e r i m e n t a l P r o c e d u r e . 33 V Method of A n a l y s i s 34 A. C h o i c e of Model 34 B. S p e c i f i c P r o c e d u r e 35 VI R e s u l t s 37 A. D e t e c t i o n of Broadening 37 B. D e t e c t i o n of S h i f t 41 C. L i n e Shape D e t e r m i n a t i o n 41 D-. Rate of P r e s s u r e B r o a d e n i n g - Comparison w i t h Theory 42 E. V a l i d i t y of R e s u l t s 46 V I I C o n c l u d i n g D i s c u s s i o n . 53 B i b l i o g r a p h y 57 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 Curves 58 - i v - LIST OF FIGURES F i g u r e Page 1. T r a n s m i s s i o n Curve P a r a m e t e r s . 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 25 E f f e c t f o r NeX6074.3 A 0. 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. E x p e r i m e n t a l Arrangement. 31 5. T r a n s m i s s i o n Curves f o r D i f f e r e n t P r e s s u r e s ( t Q = 0.16). 38 6. T r a n s m i s s i o n Curves f o r D i f f e r e n t P r e s s u r e s ( t Q .= 0.33). 39 7. T r a n s m i s s i o n Curves f o r D i f f e r e n t P r e s s u r e s ( t 0 = 0.53). 40 8. T r a n s m i s s i o n Curve: Theory and Experiment (P = 2 Torr). 43 9. T r a n s m i s s i o n Curve: Theory and Experiment (P = 100 T o r r ) . 44 10. T r a n s m i s s i o n H a l f Width v e r s u s T r a n s m i s s i o n (Theory and E x p e r i m e n t ) . 45 11. Rate of P r e s s u r e Broadening. 47 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 . 50 -v- LIST OF REFERENCED EQUATIONS E q u a t i o n s Page I , I I 4 I I I 5 I V 6 l V ( a ) 8 V 9 VI 11 V I I 14 V I I I 15 IX 19 X 21 X I 23 X I I 24 - v i - 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 Dr. R. No d w e l l f o r h i s encouragement and s u p p o r t , both of my graduate work i n g e n e r a l and t h i s e x p e r i m e n t . I a l s o w i s h t o thank Dr. J . Meyer f o r h i s guidance and a d v i c e i n the p r e p a r a t i o n of t h i s t h e s i s . A d d i t i o n a l thanks are due t o : - Mr. B a r r y S t a n s f i e l d f o r h i s i n i t i a l work s e t t i n g up the Zeeman s c a n n i n g system 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 Dr. W. Seka f o r much h e l p f u l d i s c u s s i o n and a d v i c e . - Mr. J . Lees 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 of the source and a b s o r b e r t u b e s . F i n a l l y I w i s h t o exp 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 her 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 S p e c t r a l l i n e s , 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 , are c h a r a c t e r i z e d 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 or s t r e n g t h . The shape of a s p e c t r a l l i n e i s p r i m a r i l y d e t e r m i n e d by the p h y s i c a l environment of i t s s o u r c e , i n p a r t i c u l a r t he t e m p e r a t u r e , n e u t r a l p a r t i c l e d e n s i t y , e l e c t r o n d e n s i t y , and e l e c t r i c or magnetic f i e l d s p r e s e n t . For most h i g h t e m p e r a t u r e plasmas i n t h e absence of s t r o n g e l e c t r o m a g n e t i c f i e l d s t he shape of the l i n e i s d e t e r m i n e d by t h e temp e r a t u r e and e l e c t r o n d e n s i t y . A t lower t e m p e r a t u r e s i t i s the te m p e r a t u r e and n e u t r a l p a r t i c l e d e n s i t y w h i c h are u s u a l l y most s i g n i f i c a n t . G e i s s l e r tube and glow d i s c h a r g e plasmas, w h i c h b e l o n g t o the l a t t e r c l a s s of lo w e r t e m p e r a t u r e plasmas, are f r e q u e n t l y employed i n s p e c t r o s c o p i c work as so u r c e s or a b s o r b e r s of s p e c t r a l l i n e s . For example i n two r e c e n t experiments a t the U n i v e r s i t y of B r i t i s h Columbia the 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 tubes has been used t o measure r e l a t i v e t r a n s i t i o n p r o b a b i l i t i e s i n neon. One experiment compared t h e a b s o r p t i o n s t r e n g t h s of v a r i o u s s p e c t r a l l i n e s ( l ) w h i l e the second u t i l i z e d Faraday r o t a t i o n i n a. glow d i s c h a r g e t u b e ( 2 ) . I n b o t h experiments i t was assumed t h a t the 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 from the Gaussian shapes assumed could a f f e c t the v a l i d i t y of these r e s u l t s . Estimates of pressure broadening, made ac c o r d i n g to the impact theory under the assumption of a van der Waals i n t e r a c t i o n , i n d i c a t e t h a t under glow d i s c h a r g e c o n d i t i o n s there may indeed be s u f f i c i e n t p r essure broadening to a l t e r the l i n e shapes s i g n i f i c a n t l y . In a d d i t i o n t h i s theory p r e d i c t s a s l i g h t , p r e ssure dependent, decrease i n the frequency of the s p e c t r a l l i n e . I t was thus d e s i r ^ a b l e to examine at l e a s t one such neon glow d i s c h a r g e l i n e not only to check the v a l i d i t y of the assumption of Gaussian l i n e shapes but a l s o to t e s t the t h e o r e t i c a l p r e d i c t i o n s . However the s p e c t r a l l i n e s i n glow d i s c h a r g e and G e i s s l e r tube plasmas are too narrow to be c o n v e n i e n t l y s t u d i e d by c o n v e n t i o n a l s p e c t r o g r a p h i c techniques unless equipment of very high r e s o l u t i o n (—£10 ) i s employed. I t had been demonstrated by S t a n s f i e l d ( 3 ) t h a t with the Zeeman scanning technique of B i t t e r et a l (4) I t should be p o s s i b l e to d i s c e r n the exact shape of such narrow s p e c t r a l l i n e s . With t h i s technique a s i n g l e cr-component of a normal Zeeman t r i p l e t i s i s o l a t e d and employed as a v a r i a b l e frequency source. I t i s passed through an absorber t o . scan the a b s o r p t i o n l i n e under examination. 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 obtained f o r a range of source f r e q u e n c i e s s u f f i c i e n t to span the a b s o r p t i o n l i n e . The r e s u l t a n t t r a n s m i s s i o n curves g e n e r a l l y r e f l e c t the shapes of both the -3- source and the a b s o r b e r and are s e n s i t i v e t o v a r i a t i o n s i n e i t h e r ; , By comparing t h e s e r e s u l t s t o the p r e d i c t i o n s of a s i m p l e model the l i n e shapes of so u r c e and a b s o r b e r may be e x t r a c t e d . As employed 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 of d e t e c t i n g changes i n the w i d t h of an a b s o r p t i o n l i n e as s m a l l as 2 mA° (which f o r the l i n e s t u d i e d c o r r e s p o n d s to 10% or l e s s of t h e h a l f w i d t h ) . I t a l s o seemed c a p a b l e of 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 shape. Because the Zeeman s c a n n i n g a p p a r a t u s i s composed of equipment u s u a l l y 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 a t 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 , economic means of s t u d y i n g t h e shape of a narrow l i n e from a neon glow d i s c h a r g e . -4- CHAPTER I I 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 As r a d i a t i o n p a s s e s t h r o u g h an element of a b s o r b i n g medium the f r a c t i o n of t h i s r a d i a t i o n absorbed i s d i r e c t l y p r o p o r t i o n a l t o the a b s o r b i n g ' s t r e n g t h ' of the medium and the l e n g t h of the a b s o r b e r t r a v e r s e d . d l J j L l = - k(?> )dx I ) l ( y ) i s the i n t e n s i t y of the r a d i a t i o n a t f r e q u e n c y ~P . k ( ^ ) i s t h e a b s o r p t i o n c o n s t a n t ( ' s t r e n g t h ' of the a b s o r b e r ) : a t f r e q u e n c y 7^ . dx i s the e l e m e n t a l l e n g t h of a b s o r b e r t r a v e r s e d . I n t e g r a t i n g f o r a homogeneous ab s o r b e r of l e n g t h J. and d e n o t i n g the i n c i d e n t i n t e n s i t y by l^(j? ) and the t r a n s m i t t e d i n t e n s i t y by Ij(7?): = I.(>>)exp{ - k{f)J] I I The a b s o r b e r w i l l i t s e l f emit- l i g h t a t f r e q u e n c y j). T h i s l i g h t w i l l have an i n t e n s i t y comparable t o 1̂  (1?) . However the s o u r c e i s i n t e n s i t y modulated and a l o c k - i n a m p l i f i e r i s employed t o d e t e r m i n e the t r a n s m i t t e d i n t e n s i t y . The unmodul- ated l i g h t e m i t t e d by the a b s o r b e r i s r e j e c t e d as n o i s e by the phase s e n s i t i v e d e t e c t i o n system. S i n c e t h e l o c k - i n a m p l i f i e r - 5 - used improved the s i g n a l - t o - n o i s e r a t i o by a f a c t o r of 100 or more, the l i g h t emitted by the absorber may be omitted from c o n s i d e r a t i o n . Hence Equation I I giv e s e x a c t l y the i n t e n s i t y emergent from an absorber of l e n g t h i . In the r e g i o n of an a b s o r p t i o n l i n e k ( ^ ) w i l l have a frequency dependence peaking at the l i n e centre ^ as i n d i c a t e d below. k( )\ 2 o.- A u s e f u l measure of the width of an a b s o r p t i o n l i n e i s the h a l f width which i s here d e f i n e d as the f u l l width at the half-maximum of ) - see above. I f a band of r a d i a t i o n w i t h frequency mean c h a r a c t e r i z e d by the shape I ^ ( ^ - ̂  ) i s passed through a l e n g t h 1 of absorber s p e c i f i e d by k ( ^ ) s k ( y - % ) where i s the c e n t r a l frequency of the absorber, then the r e s u l t a n t i n t e n s i t y at frequency i s : I f (/) = I^Z-^s )exp { - k ( / - ^ I I I - 6 - i i l . o - ^- exp{-k( iJ-tiU} ; < \ \ 1 \ 1 • \ 1 • \ ' • \ 1 \ 1 • \ 1 ''• \ 1 \ 1 • \ i \ i i \ i >—~ — i V The inc ident or source f lux i s : s(^) = y , I i ( > ? - ^ ) d y , o oO while the t o t a l f lux transmitted i s : 0 o The f r a c t i o n a l transmission i s the r a t i o of these two f luxes : tit) = ^ M 1 s(i ) IV Considering the absorber frequency j)0 as a constant the transmission w i l l vary with % , the mean frequency of the source, This i s depicted schematically i n F i g . 1. The width of t h i s transmission curve w i l l be defined as the f u l l width at ' half-minimum' - At- as indicated i n F i g . 1. Several s a l i e n t features of such transmission curves are: - 7 - -*» A t *• : t Q = l i n e c e n t r e (minimum) t r a n s m i s s i o n : At = t r a n s m i s s i o n h a l f width F i g . 1 T r a n s m i s s i o n Curve Parameters -8- (a) For f i x e d t , A t w i l l i n c r e a s e as t h e source w i d t h and the a b s o r b e r w i d t h i n c r e a s e , (b) For f i x e d source and a b s o r b e r w i d t h s , A t w i l l i n c r e a s e as i s i n c r e a s e d ( i . e . as t Q d e c r e a s e s ) . (c) For an i n f i n i t e l y narrow source r e p r e s e n t e d by lA?'-%) = then: 0{?t,?.) = I o e x p { - k(/>,- t ( ii) = exp{ - k ( ^ s - ^ )£} IVa Hence: Thus f o r a s u f f i c i e n t l y narrow source t ( ^ ) and A t depend on t h e shape of the a b s o r p t i o n l i n e o n l y . - 9 - B. L i n e B roadening: P r e s s u r e Independent E f f e c t s (1) N a t u r a l B r o a d e n i n g : No s p e c t r a l l i n e can be p e r f e c t l y monochromatic. Even an i s o l a t e d o s c i l l a t o r i s s t i l l p e r t u r b e d by the r e a c t i o n of i t s own r a d i a t i o n . C l a s s i c a l l y t h i s can be shown (5) t o r e s u l t i n the s p e c t r a l d i s t r i b u t i o n of i n t e n s i t y : i ( y - & ) • i where T i s the l i f e t i m e of the o s c i l l a t o r . The h a l f w i d t h of t h i s d i s t r i b u t i o n , r e f e r r e d t o as t h e n a t u r a l l i n e w i d t h , i s : _ l * ~ T The n o r m a l i z e d i n t e n s i t y i s : 27T (1?-%) 2 + (ML)2 V T h i s i n v e r s e square form of f r e q u e n c y dependence was o r i g i n a l l y d e r i v e d by H. A. L o r e n t z i n 1906 and has s i n c e been named the ' L o r e n t z i a n ' p r o f i l e . The quantum m e c h a n i c a l t r e a t m e n t of t h i s problem y i e l d s t h e same form of i n t e n s i t y d i s t r i b u t i o n and f u r t h e r m o r e shows, t h a t L\tfv e q u a l s the sum of the spontaneous t r a n s i t i o n p r o b a b i l i t i e s f o r a l l t r a n s i t i o n s from both the i n i t i a l and f i n a l s t a t e s . Thus f o r a l i n e r e s u l t i n g from a t r a n s i t i o n between s t a t e s m and n: M = LA^ + z A n n, n' 1 + 1 T n -10- where: and A n n, are the a p p r o p r i a t e E i n s t e i n A - c o e f f i c i e n t s . T and T are the ' l i f e t i m e s ' of the two s t a t e s . ° m n I n the o p t i c a l r e g i o n t h e n a t u r a l l i n e w idth, i s u s u a l l y n e g l i g i b l e compared t o the e f f e c t s of o t h e r b r a o d e n i n g mechanisms. F or the X6074.3 A 0 l i n e of N e l the l i f e t i m e has been measured t o be: 5*10" sec ( 7 ) . T h i s y i e l d s a n a t u r a l width, of A^ ^ 6*10 ^ cm ^ =0.06 mK. _ By comparison the D o p p l e r w i d t h (see below) i s : ~ 50 mK. (2) D o p p l e r B r o a d e n i n g : R e l a t i v e m otion between a source of r a d i a t i o n and an o b s e r v e r w i l l cause a f r e q u e n c y s h i f t of the observed r a d i a t i o n # (Doppler e f f e c t ) . The random t h e r m a l motions of an assemblage of r a d i a t i o n p a r t i c l e s w i l l r e s u l t i n a b r o a d e n i n g of the s p e c t r a l l i n e b e i n g o b s e r v e d . F o r a v e l o c i t y component a l o n g the l i n e of s i g h t v , the D o p p l e r f r e q u e n c y s h i f t i s : where )l i s the u n s h i f t e d f r e q u e n c y . I n an assemblage of p a r t i c l e s of mass M w i t h a M a x w e l l i a n v e l o c i t y d i s t r i b u t i o n c h a r a c t e r i z e d by a temperature T, the f r a c t i o n w i t h a l i n e of s i g h t v e l o c i t y component between v and v + dv i s : s s s -11- N i s t h e t o t a l number of p a r t i c l e s k i s Boltzmann's c o n s t a n t . For r a d i a t i n g 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 have f r e q u e n c i e s between j) and A dP where c y° S u b s t i t u t i n g f o r v g : v l 2kT J N 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 source the 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 of r a d i a t i n g p a r t i c l e s : ^ " N I t i s the t o t a l l i n e i n t e n s i t y . The h a l f w i d t h of t h i s d i s t r i b u t i o n t { f u l l w i d t h a t h a l f - maximum) i s : A „ , „ i / AV = 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 d i s t r i b u t i o n i s : y-ye) i 2 K ^ - v M - 2 / I n ? f - [ 2 Vln?̂ -̂ )] . where l{P-2i) i s here the i n t e n s i t y a t f r e q u e n c y 1? per u n i t f r e q u e n c y i n t e r v a l . The D o p p l e r f r e q u e n c y s h i f t s a r i s i n g from t h e r m a l motions -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 mechanism f o r G e i s s l e r tube and glow d i s c h a r g e plasmas such as employed i n t h i s e x p e r i m e n t . For the 'X6074.3A° l i n e of N e l ( i s o t o p e 20) a t T = 350 °K : A v ? ^ &VD = 49 mK C. L i n e Broadening: P r e s s u r e Dependent E f f e c t s The p e r t u r b a t i o n s of e m i t t e r s caused by e n c o u n t e r s w i t h s u r r o u n d i n g p a r t i c l e s 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 s p e c t r a l l i n e . As p r e s s u r e and d e n s i t y are i n c r e a s e d the r a t e of such encounters 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 b r o a d e n i n g . I n t h i s way the b r o a d e n i n g i s p r e s s u r e dependent. (1) S t a r k B r o a d e n i n g : D u r i n g e n c o u n t e r s w i t h charged p a r t i c l e s the energy l e v e l s of an e m i t t e r are p e r t u r b e d ( S t a r k e f f e c t ) . T h i s . r e s u l t s i n broadened and s h i f t e d s p e c t r a l l i n e s , g e n e r a l l y of L o r e n t z i a n p r o f i l e . 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 e l e c t r o n s 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 . For low e l e c t r o n d e n s i t i e s , such as are encountered i n a glow d i s c h a r g e plasma, the e f f e c t 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 r e f e r r e d t o as ' e l e c t r o n - i m pact' b r o a d e n i n g . The w i d t h s and s h i f t s t h e r e b y produced are d i r e c t l y p r o p o r t i o n a l t o t h e e l e c t r o n d e n s i t y . To e s t i m a t e the 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 t h e p r e s e n t experiment an e s t i m a t e of e l e c t r o n d e n s i t y i s r e q u i r e d . E c k e r and Z o l l e r (8) have c a l c u l a t e d v a l u e s f o r a h e l i u m plasma column. T h e i r c a l c u l a t i o n s y i e l d an e l e c t r o n 11 3 d e n s i t y n e ^ 10 cm f o r p r e s s u r e s , c u r r e n t s , and dimensions -13- such as employed i n t h i s e x p e r i m e n t . Assuming t h a t s i m i l a r v a l u e s can be expected f o r a neon discharge-, i t s h o u l d be s a f e 1 2 - 3 t o c o n s i d e r n g ^ 10 cm C a l c u l a t i o n s of the S t a r k b r o a d e n i n g parameters f o r N e l and o t h e r l i g h t elements have been performed by Griem ( 9 ) . From t h e s e c a l c u l a t i o n s 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 X6074.3 A 0 l i n e of N e l f o r n- <; 10 cm i s : A ^ < 0.017 mK The c o r r e s p o n d i n g s h i f t i s : A% < 0.009 mK. For t h e s e c a l c u l a t i o n s the e l e c t r o n t e m p e r a t u r e was chosen o . . • to be 25,000 K , t h e v a l u e found by I r w i n (10) f o r a s i m i l a r neon glow plasma. • ' S t a r k b r o a d e n i n g of t h i s magnitude i s n e g l i g i b l e compared w i t h t h e measured w i d t h and such a s m a l l s h i f t can not be r e s o l v e d by the e x p e r i m e n t a l s e t up. (2) Van der Waals Broadening and S h i f t : The energy l e v e l s of an e m i t t e r may a l s o be p e r t u r b e d d u r i n g e n c o u n t e r s w i t h n e u t r a l p a r t i c l e s . Here a l s o t h e r e g e n e r a l l y r e s u l t s a broadened and s h i f t e d s p e c t r a l l i n e of L o r e n t z i a n p r o f i l e . I n 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 encountered by t h e e m i t t e r w i l l be ground s t a t e atoms of the same s p e c i e s . In t h e absence of any resonance e f f e c t s the i n t e r a c t i o n f o r c e s w i l l be p r i m a r i l y t h e Van der Waals a t t r a c t i o n . For t h i s -14- t h e l e v e l k i s p e r t u r b e d by: hOJ^_ - - ^6,k ^ i s the van der Waals c o n s t a n t f o r the l e v e l k and the p a r t i c u l a r p e r t u r b e r i n q u e s t i o n . r i s the d i s t a n c e between 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 low d e n s i t y gases such as a glow d i s c h a r g e plasma the impact t h e o r y of L i n d h o l m and F o l e y (11) can q u i t e g e n e r a l l y be used. I n t h i s t h e o r y i t i s assumed t h a t the d u r a t i o n of the encounter I s n e g l i g i b l e ' compared t o the time i n t e r v a l between such e n c o u n t e r s . T h i s impact a p p r o x i m a t i o n i s g e n e r a l l y v a l i d f o r low p e r t u r b e r d e n s i t i e s such as i n t y p i c a l glow d i s c h a r g e plasmas. T h i s impact t h e o r y , i n c o n j u n c t i o n w i t h the van der 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 d i s t r i b u t i o n whose h a l f w i d t h i s : t±9v = 1.3v* n sec 1 V I I ^ = - ^ where k and k d e s i g n a t e the i n i t i a l v i s the mean r e l a t i v e v e l o c i t y between e m i t t e r and p e r t u r b e r . •and f i n a l l e v e l s . n i s the number d e n s i t y of the p e r t u r b e r s . In a d d i t i o n t o t h e b r o a d e n i n g t h e impact t h e o r y a l s o p r e d i c t s a s h i f t of t h e s p e c t r a l l i n e t o the r e d . The r a t i o of b r o a d e n i n g t o s h i f t i s independent of both the i n t e r a c t i o n c o n s t a n t C5 and the mean r e l a t i v e v e l o c i t y v. For a w i d t h -15- the s h i f t i s : L\/0 = - i±£±. 2.76 The van der Waals 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 the f o l l o w i n g a p p r o x i m a t i o n by Un s o l d (12) : 2 2 2 6 ' k I T P ~ 2 5n* + 1 - 3J{/+ 1) -1 (• r a d sec cm V I I I e i s the e l e c t r o n i c c h a rge. 'fi i s P l a n c k ' s c o n s t a n t f o r a n g u l a r momentum. a i s the f i r s t Bohr r a d i u s , o n* i s t h e e f f e c t i v e quantum number of the l e v e l k, i i s the a n g u l a r momentum quantum number f o r the o p t i c a l e l e c t r o n i n l e v e l k. o<p i s the p o l a r i z a b i l i t y of the p e r t u r b i n g p a r t i c l e s . The v a l i d i t y of t h i s a p p r o x i m a t i o n r e s t s on the assumption t h a t the energy s e p a r a t i o n between t h e i n i t i a l and f i n a l l e v e l s of the e m i t t e r i s much s m a l l e r t h a n the energy s e p a r a t i o n of the ground s t a t e and lower 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 ) . T h i s i s a r e a s o n a b l e assumption f o r a n o b l e gas p e r t u r b e r s i n c e t h e r e the f i r s t e x c i t e d s t a t e s l i e c o m p a r a t i v e l y h i g h as a r e s u l t of t h e i n c r e a s e i n p r i n c i p a l quantum number of the o p t i c a l e l e c t r o n . Hence Un s o l d ' s a p p r o x i m a t i o n V I I I s h o u l d be v a l i d f o r neon i n a glow d i s c h a r g e p lasma. The a p p l i c a t i o n of Uns o l d ' s a p p r o x i m a t i o n r e q u i r e s an -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 cX^ of neon. Two v a l u e s of t h i s have been u t i l i z e d . 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 3 been t a k e n from A l l e n (13). who g i v e s c>< = 3.96*10 cm U s i n g t h e U n s o l d a p p r o x i m a t i o n V I I I t h i s y i e l d s : C 6 ( N e 6 0 7 4 / N e ) = 5.82-10 rad s e c " 1 cm° Hence from the impact t h e o r y r e l a t i o n VII : M - ^ ^ A 2 L = 1.24-lO"^ mK cm 3 n c n S e c o n d l y , an e x p e r i m e n t a l l y based v a l u e has been d e r i v e d from t h e r e s u l t s of Sm i t h (14) on t h e p r e s s u r e b r o a d e n i n g of Ca 2\6573 A° by neon. Smith's quoted v a l u e of A T*7 -18 3 = 11.0-10 mK cm and r e l a t i o n VII y i e l d : n C 6 ( C a 6 5 7 3 / N e ) = 2 . 2 7 - 1 0 " 3 2 r a d s e c " 1 cm 6 T h i s Ca A6573 A l i n e i s a 4s4p - 4s t r a n s i t i o n and the energy s e p a r a t i o n of the i n i t i a l and f i n a l s t a t e s i s r o u g h l y e q u a l to t h a t of the Ne "X6074.3 A° l i n e . Hence the U n s o l d 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 c a s e . U s i n g r e l a t i o n 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 of neon was d e r i v e d and from t h i s : C 6 ( N e 6 0 7 4 / N e ) = 1 ' 2 6 ' 1 0 ' 3 1 r a d s e c " 1 cm 6 W i t h r e l a t i o n VII a g a i n t h i s y i e l d s : A y = 1.69*10" 1 7 mK cm 3 . n o For a plasma w i t h T ^ 325 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 ) the n e u t r a l p a r t i c l e d e n s i t y n ^ 3-10 cm Under such 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 van der Waals h a l f w i d t h s f o r the NeA6074.3 A 0 l i n e o f : * 3.7 mK ( t h e o r y ) A?J ~ 5.1 mK (from S m i t h (14) ) S i n c e t h i s i s 8 - 10 % of the D o p p l e r w i d t h f o r the same c o n d i t i o n s , van der Waals p r e s s u r e b r o a d e n i n g c o u l d s u b s t a n t i a l l y a f f e c t l i n e shapes i n a glow d i s c h a r g e . The e x p e r i m e n t a l r e s u l t s c o n f i r m t h i s e x p e c t a t i o n . The. impact t h e o r y w i t h van der Waals i n t e r a c t i o n a l s o p r e d i c t s a c o r r e s p o n d i n g l i n e s h i f t o f : A # ~1.8 mK t o the r e d . However a s h i f t of t h i s magnitude would be b a r e l y d e t e c t a b l e , i f a t a l l , w i t h the e x p e r i m e n t a l a p p a r a t u s employed. However the l a r g e r s h i f t s t o be expected a t the h i g h e r p r e s s u r e s used s h o u l d be e a s i l y d e t e c t e d . The s h i f t of t h e Ca A6573 A° l i n e broadened by neon observed by Smith (14) was not o n l y s m a l l e r by a f a c t o r of 15 t h a n t h e p r e d i c t i o n of the impact t h e o r y but was i n a d d i t i o n t o the b l u e . T h i s f a i l u r e of the t h e o r y was a t t r i b u t e d by Hindmarsh, P e t f o r d , and S m i t h (15) t o the o m i s s i o n of any 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. S i m i l a r r e s u l t s s h o u l d o b t a i n f o r the s h i f t of the Ne\6074.3 A° l i n e i n which case t h e a c t u a l s h i f t s produced would be beyond d e t e c t i o n w i t h t h e e x p e r i m e n t a l a p p a r a t u s . -18- D. S e l f A b s o r p t i o n B r o a dening The b r o a d e n i n g mechanisms d i s c u s s e d i n S e c t i o n s B and C a c t t o broaden a s p e c t r a l l i n e 'as i t i s e m i t t e d ' and r e s u l t from the immediate p h y s i c a l environment of the e m i t t i n g p a r t i c l e s . These mechanisms a p p l y t o both the e m i s s i o n and a b s o r p t i o n p r o c e s s e s . Subsequent 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 medium may 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 e m i t t e d l i g h t . S i n c e any p r a c t i c a l l i g h t source must be composed of many e m i t t i n g p a r t i c l e s , some of the l i g h t o r i g i n a t i n g from r e g i o n s most d i s t a n t from an o b s e r v e r may be p a r t i a l l y absorbed b e f o r e emerging from the volume of the s o u r c e . C o n s e q u e n t l y the r e s u l t a n t f r e q u e n c y d i s t r i b u t i o n of i n t e n s i t y from t h e source as a whole may d i f f e r from t h a t of t h e e m i t t i n g p a r t i c l e s per se. C o n s i d e r a homogenous source of d i m e n s i o n \l i n the l i n e of o b s e r v a t i o n . L e t the e m i s s i v i t y per u n i t l e n g t h be where y0 i s the s p e c t r a l l i n e c e n t r e , and l e t the a b s o r p t i o n c o n s t a n t (as d e f i n e d i n S e c t i o n A) be k(^ -j£). l i n e of o b s e r v a t i o n -19- I n t h e absence of any a b s o r p t i o n the emergent i n t e n s i t y a t f r e q u e n c y V would be = j{?-£)J. The i n t e n s i t y e m i t t e d by the element dx a t f r e q u e n c y 1? i s s i m i l a r l y : j ( ^ - j ^ ) d x . The amount of t h i s w h i c h emerges a t £ i s g i v e n by I I I : d l s ( y - ^ ) = j ( y - ^ ) e x p { - k ( y - ^ ) \l- x]} dx The net i n t e n s i t y i s found by i n t e g r a t i n g over the J s o u r c e : 1 - exp {- k(y-^)Jj The q u a n t i t y i n the exponent i s d e f i n e d as the o p t i c a l d epth : T(V-X) = k{?-X)J 1 - e x p f IX An o p t i c a l l y t h i n source i s one 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 of e s c a p i n g (i,e. a v o i d i n g \ n a b s o r p t i o n ) . The c r i t e r i o n f o r o p t i c a l thinness a t f r e q u e n c y i s : T ( W ) « 1. For an o p t i c a l l y t h i n s ource : i iv-rt) ~ hW-X) i - ( i -TkV-ti) -20- From t h i s i t can be seen t h a t i n the o p t i c a l l y t h i n case t h e l i n e p r o f i l e 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 . For an o p t i c a l l y t h i c k source ( but one i n w h i c h T ( V - t i ) * 1 s t i l l ) : i _ ( i _ 7 V - ^ ) + XW-V. 2 i - + 2 • • • • S i n c e i s g r e a t e s t f o r the c e n t r e of the l i n e ( i^ 7 — ]A0) t h e l i n e c o r e i s s e l f absorbed -more s t r o n g l y t han t h e w i n g s . As a r e s u l t the apparent h a l f w i d t h of the l i n e i n c r e a s e s : t r u e h a l f w i d t h apparent h a l f w i d t h t r u e l i n e shape s e l f absorbed p r o f i l e -21- E. V o i q t P r o f i l e s 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 t o 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 i s the c o n v o l u t i o n of t h e i r two shapes. I f S-^{)?-2l) i s t h e p r o f i l e due t o one mechanism and ^2^2^-Pa) i s the p r o f i l e due t o the o t h e r , t h e n one c o n s i d e r s each element of the Sj_ p r o f i l e t o be broadened w i t h an S2 shape. The r e s u l t a n t i n t e n s i t y a t any f r e q u e n c y "Ps i s t h e sum of a l l t h e c o n t r i b u t i o n s from each broadened element of S , . 1 -22- I f S^ i s G a u s s i a n and L o r e n t z i a n (or v i c e v e r s a ) t h e i r 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 . I t can be shown (16) t h a t i f and are themselves V o i g t p r o f i l e s then t h e i r c o n v o l u t i o n S w i l l a l s o be a V o i g t p r o f i l e . F u r t h e r m o r e , s h o u l d S-̂  be formed from a G a u s s i a n of h a l f w i d t h and a L o r e n t z i a n of h a l f w i d t h AT^j , w h i l e r e s u l t s from a G a u s s i a n of h a l f w i d t h &%z and a L o r e n t z i a n of h a l f w i d t h AVL2 > S i s then the V o i g t p r o f i l e r e s u l t i n g from a G a u s s i a n of h a l f w i d t h and a L o r e n t z i a n of h a l f w i d t h AVL such t h a t : = + £ $ D Z The G a u s s i a n and L o r e n t z i a n p r o f i l e s are themselves extreme cases of V o i g t p r o f i l e s . C o n s e q u e n t l y , i f two b r o a d e n i n g mechanisms, each of w h i c h produces a L o r e n t z i a n p r o f i l e , a c t i n d e p e n d e n t l y t h e n the r e s u l t a n t l i n e shape w i l l be L o r e n t z i a n . For example, s h o u l d van der Waals b r o a d e n i n g and S t a r k b r o a d e n i n g both be s i g n i f i c a n t , t h e i r j o i n t r e s u l t w i l l be a L o r e n t z i a n p r o f i l e w i t h a h a l f w i d t h o f : S u b s t i t u t i n g i n e q u a t i o n X the G a u s s i a n of V I f o r S^ and the L o r e n t z i a n of V f o r S^ ( w i t h h a l f w i d t h s A1?D and r e s p e c t i v e l y ) : S ( * -7i) I 2 y T n T 2 i/TZT(y'-X AX -, 2 x fe N-/)2 + (^-)2 -1 d. - 2 3 - S e t t i n g x = 2 ) = F ( / - # ) dx = F d / stf-}/) = All f e x P I ' y2) dx o2 -oo * 2 27r/e J ( H K - X ) -x) 2 +(M)2 s " 2 S e t t i n g FA)£ = 2 V l n 2 = A V l n T = Y 2 2 A y D OO S ( ^ ) = _ Y / e x p { - x 2 } y ( F ( ^ - ^ ) - x - — d x (F(7i-y0) - x) 2 + Y 2 s -oo Al) The r a t i o of L o r e n t z i a n t o G a u s s i a n h a l f w i d t h : A = Ay D i s termed the V o i g t A-parameter. I t s p e c i f i e s the shape of the V o i g t p r o f i l e . A = 0 - pure G a u s s i a n A o0 - pure L o r e n t z i a n V a l u e s of the V o i g t i n t e g r a l 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 were computed u s i n g a F o r t r a n subprogramme d e v e l o p e d a t the U n i v e r s i t y of M i c h i g a n (17). -24- F. Zeeman S c a n n i n g and Inhomoqeneity Broadening The major group of v i s i b l e neon s p e c t r a l l i n e s r e s u l t s 5 5 from 2p 3p —*• 2p 3s t r a n s i t i o n s . W h i l e most of t h e s e l i n e s e x h i b i t complex (anomalous) Zeeman p a t t e r n s i n a magnetic f i e l d , s e v e r a l show t h e normal 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 X6074.3 A° l i n e , w h i c h r e s u l t s from 3 3 , ' N a P —*• P t r a n s i t i o n , i s one of t h e s e (see 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 (18) by: & = ± gHB X I I where B i s the a p p l i e d magnetic f i e l d ( g a u s s ) . -5 -1 -1 H = 4.695"10 cm gauss (the 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 NeX6074.3 A° (18)) 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 the source i n a v a r i a b l e magnetic f i e l d . A beam i s t a k e n i n the d i r e c t i o n of the f i e l d ( l o n g i t u d i n a l l y ) . T h i s beam c o n t a i n s o n l y the two cr - components of the normal Zeeman t r i p l e t , w h i c h are r i g h t - and l e f t - hand c i r c u l a r l y p o l a r i z e d r e s p e c t i v e l y . A q u a r t e r wave p l a t e c o n v e r t s t h e s e t o m u t u a l l y p e r p e n d i c u l a r l i n e a r l y p o l a r i z e d beams. An a n a l y z i n g N i c o l p r i s m t h e n s u p p r e s s e s one of t h e s e two beams. As the magnetic f i e l d v a r i e s the Zeeman s h i f t , and hence the f r e q u e n c y , of the r e m a i n i n g beam v a r i e s . -25- Paschen n o t a t i o n LS n o t a t i o n 2.P, I s 2 9 S Q I s 2s 2p 3p J P 0 2 2 5 T I s 2s 2p 3s P, 77- F i g . 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 Ne 'X6074.3 A° -26- 9 B i i -9 T h i s t e c h n i q u e p r o v i d e s a s i n g l e s p e c t r a l l i n e of v a r i a b l e f r e q u e n c y , t h i s f r e q u e n c y b e i n g 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 the N i c o l p r i s m and the sense of the magnetic f i e l d . I f the magnetic f i e l d i s not homogeneous over the volume of the source t h e n t h e source l i n e shape may be d i s t o r t e d . C o n t r i b u t i o n s from r e g i o n s w i t h s l i g h t l y d i f f e r e n t magnetic f i e l d s t r e n g t h s would 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 f r e q u e n c y s h i f t s . The r e s u l t a n t l i n e p r d f i l e would thus appear broadened and p o s s i b l y asymmetric. T h i s f i e l d i nhomogeneity b r o a d e n i n g w i l l i n c r e a s e w i t h magnetic f i e l d s t r e n g t h . The e f f e c t would thus be g r e a t e s t f o r measurements of the wings of t h e a b s o r p t i o n l i n e . -27- CHAPTER I I I APPARATUS A. Source A neon G e i s s l e r tube f i l l e d t o 2 T o r r p r e s s u r e s e r v e d as the s o u r c e . The gas was i s o t o p i c a l l y pure Ne20 w i t h a 0.6 M o l . % hydrogen i m p u r i t y . The o u t e r s u r f a c e of the c a p i l l a r y s e c t i o n was c o a t e d w i t h b l a c k enamel p a i n t except f o r a s m a l l a p e r t u r e of 1 mm d i a m e t e r . The c a p i l l a r y i t s e l f had a d i a m e t e r of 1 mm so t h a t the source volume was a p p r o x i m a t e l y one c u b i c m i l l i m e t r e . The tube was o p e r a t e d from a 1000 v o l t r e g u l a t e d s u p p l y a t a c u r r e n t of 4 ma. 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 pentode and b a l l a s t r e s i s t o r . The d i s c h a r g e was i n i t i a t e d w i t h a T e s l a c o i l . B. S c a n n i n g E l e c t r o m a g n e t The G e i s s l e r tube source was c e n t r a l l y p o s i t i o n e d between the p o l e s of an e l e c t r o m a g n e t . The p o l e p i e c e s were h o l l o w c e n t r e d w i t h the c e n t r a l h o l e t a p e r i n g t o 3 mm d i a m e t e r n e a r e s t the s o u r c e . M a gnetic f i e l d s t r e n g t h v e r s u s e l e c t r o m a g n e t c u r r e n t c a l i b r a t i o n f o r the f i e l d a t the source p o s i t i o n was o b t a i n e d u s i n g : a B e l l Model .240 gaussmeter (a H a l l probe i n s t r u m e n t ) . Measurements of f i e l d i nhomogeneity i n d i c a t e no f i e l d -28- g r a d i e n t s g r e a t e r t h a n 3% per cm i n t h e c e n t r a l r e g i o n . Over 1 mm (the c h a r a c t e r i s t i c l e n g t h of the source) t h e r e i s l e s s than 0.3% v a r i a t i o n . The maximum Zeeman s h i f t r e q u i r e d was 0,4 cm"-'- , i n which case t h i s i nhomogeneity r e s u l t s i n s h i f t d i f f e r e n c e s of not more than 1.2 mK. S i n c e t h i s i s l e s s t h a n 3% of the source h a l f w i d t h , and s i n c e the f i e l d s t r e n g t h was u s u a l l y much lower than t h i s , f i e l d i nhomogeneity br o a d e n i n g was not c o n s i d e r e d s i g n i f i c a n t i n t h i s e x periment. C. A b s o r p t i o n Tubes The a b s o r b e r 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 pure Ne20 ( a l s o w i t h t h e 0.6 M o l . % hydrogen i m p u r i t y ) . The source beam was passed t h r o u g h the h o l l o w c athode. A b s o r p t i o n tubes of t h r e e d i f f e r e n t f i l l i n g p r e s s u r e s , 2 T o r r , 50 T o r r , and 100 T o r r , were employed. The d i s c h a r g e i n a l l t h r e e tubes was m a i n t a i n e d by a 1400 v o l t r e g u l a t e d s u p p l y w i t h t h e c u r r e n t c o n t r o l l e d by a s e r i e s pentode and b a l l a s t r e s i s t o r . 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 i n o r d e r t o reduce c u r r e n t f l u c t u a t i o n s . The d i s c h a r g e 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 c o i l . D i f f e r e n t a b s o r p t i o n s t r e n g t h s were o b t a i n e d by v a r y i n g the c u r r e n t between 0.3 ma and 16 ma. 26 cm F i g . 3 A b s o r p t i o n Tube C o n s t r u c t i o n -30- D. O p t i c a l System The beam emergent from the magnet was rendered p a r a l l e l by l e n s (see F i g . 4 ) . A f t e r a m p l i t u d e m o d u l a t i o n a t 990 Hz by the chopping wheel i t passed i n t o the a b s o r b e r t h r o u g h the h o l l o w cathode. The s m a l l cathode bore (3 t o 5 mm I D ) , a l o n g w i t h a 3 mm d i a m e t e r stop p l a c e d on the e x i t end of the a b s o r p t i o n t u b e , ensured t h a t o n l y a s m a l l r e l a t i v e l y homogeneous r e g i o n i n the c e n t r e of the a b s o r p t i o n tube a t t e n u a t e d the beam. Next f o l l o w e d the q u a r t e r wave p l a t e and the a n a l y z i n g N i c o l p r i s m . These were p l a c e d a f t e r the a b s o r b e r so t h a t t h e y a l s o s e r v e d t o suppress p a r t of the ' n o i s e ' e m i s s i o n from t h e a b s o r b e r . The second l e n s L.2 f o c u s s e d the beam onto the e n t r a n c e s l i t of a 500 mm Bausch and Lomb g r a t i n g monochromator of low d i s p e r s i o n . The e n t r a n c e s l i t and s t o p s were opened j u s t wide enough t o a c c e p t a l l the source beam. The e x i t s l i t was opened s u f f i c i e n t l y wide t o e a s i l y a c c e p t the e n t i r e s p e c t r a l l i n e but y e t kept narrow enough t o s t i l l e x c l u d e any nearby s p e c t r a l l i n e s . The l i g h t emerging from the monochromator was c o n v e r t e d t o e l e c t r i c a l c u r r e n t by a P h i l l i p s 150 CVP P h o t o m u l t i p l i e r o p e r a t e d a t a p p r o x i m a t e l y 1500 v o l t s and c o o l e d by d r y i c e . Electromagnet Stop Absorption Tube -Geissler Tube (Source) Hollow Cathode Light | Photo-t r a n s i s t o r '— Chopping Wheel ( f c = 990 Hz) N i c o l L2 Monochramator Prism Quarter Wave Plate Lock-In A m p l i f i e r Narrow Band A m p l i f i e r Phase Sens. Detector Integrator Chart Recorder Photo- m u l t i p l i e r ' F i g . 4 Experimental Arrangement -32- E. E l e c t r o n i c D e t e c t i o n C o n d i t i o n s i n t h e a b s o r p t i o n tubes f l u c t u a t e d , c a u s i n g f l u c t u a t i o n s both i n the r a d i a t i o n e m i t t e d and the a b s o r p t i o n s t r e n g t h . I n o r d e r t o a c h i e v e a s a t i s f a c t o r y s i g n a l t o n o i s e r a t i o i t was n e c e s s a r y t o employ phase s e n s i t i v e d e t e c t i o n and s i g n a l i n t e g r a t i o n . The p h o t o m u l t i p l i e r s i g n a l was sent t o a P r i n c e t o n A p p l i e d R esearch L o c k - I n A m p l i f i e r (Model 120). E s s e n t i a l l y t h i s d e v i c e i s a narrow band a m p l i f i e r tuned t o the chopper f r e q u e n c y of 990 Hz f o l l o w e d by a phase s e n s i t i v e d e t e c t o r . A s i g n a l , produced by the chopping wheel w i t h a l i g h t and a p h o t o - s e n s i t i v e t r a n s i t o r s u p p l i e d t h e phase r e f e r e n c e . The d.c. s i g n a l produced was f e d t o an RC i n t e g r a t i n g network ( i n c o r p o r a t e d i n the Lock-Kin A m p l i f i e r ) . Time c o n s t a n t s from 0.3 sec t o 3 sec were employed depending - upon the n o i s e e n c o u n t e r e d . The o u t p u t was m o n i t o r e d on a H e a t h k i t C h a r t Recorder (Model EUW - 20A). -33- CHAPTER IV EXPERIMENTAL PROCEDURE The o p t i c a l _ s y s t e m was i n i t i a l l y a l i g n e d on the beam of a c o n t i n u o u s He-Ne l a s e r shone i n t o the e x i t s l i t of the monochromator. 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 adj u s t m e n t s t o the source p o s i t i o n , the a b s o r p t i o n tube p o s i t i o n , and t h e p o s i t i o n of the l e n s L2 such t h a t a maximum s i g n a l was o b t a i n e d . The d i r e c t i o n of the f r e q u e n c y s h i f t ( the s i g n i n e q u a t i o n X I I ) was determined by s u b s t i t u t i n g a source of n a t u r a l neon. The presence of the Ne22 i s o t o p e caused an asymmetry i n the t r a n s m i s s i o n curve from which the d i r e c t i o n of the s h i f t c o u l d be deduced. Each t r a n s m i s s i o n curve was o b t a i n e d by v a r y i n g the e l e c t r o m a g n e t c u r r e n t m o n o t o n i c a l l y and i n d i s c r e t e s t e p s . For each c u r r e n t v a l u e , and hence each source f r e q u e n c y , the t r a n s m i t t e d l i n e i n t e n s i t y was measured both w i t h the a b s o r b i n g d i s c h a r g e s w i t c h e d on and o f f . The r a t i o n of t h e s e two i n t e n s i t i e s y i e l d s the f r a c t i o n a l t r a n s m i s s i o n t . The o source f r e q u e n c y was o b t a i n e d by c o n v e r t i n g the e l e c t r o m a g n e t c u r r e n t v a l u e t o t h e c o r r e s p o n d i n g magnetic f i e l d s t r e n g t h u s i n g the magnet c a l i b r a t i o n and th e n s u b s t i t u t i n g i n t o e q u a t i o n X I I . W i t h each a b s o r p t i o n tube the t r a n s m i s s i o n c u r v e s were o b t a i n e d f o r a range of a b s o r p t i o n s t r e n g t h s by v a r y i n g the a b s o r p t i o n tube c u r r e n t from experiment t o ex p e r i m e n t . - 3 4 - CHAPTER V METHOD OF ANALYSIS A. C h o i c e of Model The shape of the a b s o r p t i o n l i n e cannot be d i r e c t l y o b t a i n e d from a t r a n s m i s s i o n c u r v e . I t i s n e c e s s a r y t o con s i d e r - models i n wh i c h the e x a c t p r o f i l e s of the source and the a b s o r b e r are s p e c i f i e d and from t h e s e t o compute t h e o r e t i c a l t r a n s m i s s i o n c u r v e s . The model wh i c h produces the c l o s e s t a p p r o x i m a t i o n t o the e x p e r i m e n t a l r e s u l t i s t h e n c o n s i d e r e d t o d e s c r i b e the a b s o r p t i o n l i n e . U n f o r t u n a t e l y t h i s p rocedure may not y i e l d a unique r e s u l t . However, i f i t be assumed t h a t the shape of the a b s o r p t i o n l i n e does not change as the 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 the a b s o r b e r c u r r e n t ) , t h e n the v a r i a t i o n of the 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 s t r e n g t h o f f e r s an a d d i t i o n a l c o n s t r a i n t on the model. T h i s e n a b l e s a c h o i c e t o be made from an i n i t i a l s e t of models. The s p e c t r a l l i n e s of source and abs o r b e r were b o t h 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 . T h e i r G a u s s i a n h a l f w i d t h s were assumed t o r e s u l t s o l e l y from D o p p l e r b r o a d e n i n g . S i n c e t h e G e i s s l e r tube c a p i l l a r y was s l i g h t l y warmer than the a b s o r p t i o n tube and s i n c e b oth were warmer than room t e m p e r a t u r e , i t c o u l d be assumed: (b) T > 300 ° K -35- where T and T are t h e source and a b s o r b e r s a tem p e r a t u r e s r e s p e c t i v e l y . The L o r e n t z i a n h a l f w i d t h s were assumed t o r e s u l t e n t i r e l y from p r e s s u r e broadening.. C o n s e q u e n t l y the l i n e s of the 2 T o r r p r e s s u r e a b s o r b e r c o u l d be assumed t o have the same L o r e n t z i a n h a l f w i d t h ( A3^s ) as t h e s o u r c e . The source was c o n s i d e r e d f u r t h e r broadened by s e l f a b s o r p t i a n . For an i n t r i n s i c V o i g t shape S ( / -7{ ) the s e l f absorbed shape was t a k e n as : I i O 7 - ^ ) o< 1 - ex.p{ - K-S(^-Ti)} T h i s r e s u l t s from e q u a t i o n IX under t h e assumption t h a t jitf-tl) and k(P-%) have the same f r e q u e n c y dependence. The h i g h e r p r e s s u r e a b s o r b e r s were assumed t o have the same te m p e r a t u r e as the 2 T o r r p r e s s u r e a b s o r b e r s i n c e t h e i r t ubes were not 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 the 2 T o r r t u b e . 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 a b s o r b e r s p r o v i d e a f u r t h e r t e s t f o r t h e models. B. S p e c i f i c P r o c e d u r e (1) An assignment of T s, T g, A ^ s , and K was made. (2) The a b s o r p t i o n s t r e n g t h k(O)./ was v a r i e d u n t i l a l i n e c e n t r e t r a n s m i s s i o n t 0 of 0.33 was o b t a i n e d . (3) The f u l l t r a n s m i s s i o n curve was c a l c u l a t e d , p l o t t e d , and t h e n compared w i t h the e x p e r i m e n t a l r e s u l t s f o r the 2 T o r r a b s o r b e r i n which t 0 e q u a l l e d 0.33. (4) The parameters (T , T a, A ^ s , K) were v a r i e d u n t i l -36- an a c c e p t a b l e f i t was o b t a i n e d . (5) T r a n s m i s s i o n c u r v e s f o r t = 0.16 and t Q = 0.53 were th e n c a l c u l a t e d f o r t h e s e parameters and compared t o the c o r r e s p o n d i n g e x p e r i m e n t a l r e s u l t s (see F i g u r e 8 ) . (6) A graph of t r a n s m i s s i o n h a l f w i d t h ( A t ) v e r s u s t was computed f o r a range of v a l u e s of the abs o r b e r L o r e n t z i a n h a l f w i d t h . These were th e n compared w i t h the e x p e r i m e n t a l r e s u l t s f o r a l l t h r e e p r e s s u r e s (see F i g u r e 1 0 ) . (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 f o r the i n d i c a t e d a b s o r b e r L o r e n t z i a n h a l f w i d t h s of the 50 T o r r and 100 T o r r p r e s s u r e a b s o r b e r s were computed f o r t = 0.33 and compared t o the c o r r e s p o n d i n g e x p e r i m e n t a l r e s u l t s (see F i g u r e 9 ) . By r e p e a t e d t r i a l and e r r o r a s e t of parameters (T_, T , AJ> , K) was o b t a i n e d which s a t i s f i e d a l l t h e s e checks and is ' t e s t s . In a d d i t i o n a L o r e n t z i a n h a l f w i d t h was t h e r e b y a s s i g n e d f o r each a b s o r b e r p r e s s u r e . -37- CHAPTER VI RESULTS A. D e t e c t i o n of Broadening Broadening can be d e t e c t e d by comparing the t r a n s m i s s i o n c u r v e s f o r a b s o r p t i o n tubes of d i f f e r e n t f i l l i n g p r e s s u r e s . In cases where the l i n e c e n t r e t r a n s m i s s i o n s t are e q u a l such o n comparisons c l e a r l y demonstrate the p r e s s u r e b r o a d e n i n g of the a b s o r p t i o n l i n e . F i g u r e s 5, 6, and 7 on the next t h r e e pages show e x p e r i m e n t a l r e s u l t s f o r t 0 = 0.16, 0.33, and 0.53 r e s p e c t i v e l y . I n terms of t r a n s m i s s i o n curve h a l f w i d t h s ( A t ) t h e s e r e s u l t s are summarized below: t o At(mK) 2 T o r r 50 T o r r 100 T o r r 0.16 106 123 144 0.33 91 109 132 0.53 87 98 121 Width v a r i a t i o n s l e s s than t h o s e observed here c o u l d s t i l l be d e t e c t e d . E x p e r i e n c e i n d i c a t e d t h a t c u r v e s w i t h a f i f t h 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 be unambiguously d i s t i n g u i s h e d . I n s e c t i o n C f o l l o w i n g i t w i l l be seen t h a t from 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 a b s o r b e r s of a p p r o x i m a t e l y 45 mK. Hence stu d y of the t r a n s m i s s i o n c u r v e s would enable an i n c r e a s e i n the a b s o r b e r h a l f w i d t h of as l i t t l e as 5 mK t o be d e t e c t e d . c o •H tn w •H £ fO u H 1—1 03 C O •H -p b 03 1.0 0.9 t 0.8 -h 0.7 0.6 0.5' 0.4 0.3 0.2 f 0.1 0 o b o. o b' g X v o ^ X ° x o o X X X o 6 ~e>—sr 9 0 * G O ° • X * O ° o X o a P = 2 T o r r x P = 50 T o r r o P = 100 T o r r -250 -200 -150 -100 -50 • % +50 +100 Source S h i f t from L i n e Centre- (mK) F i g . 5 T r a n s m i s s i o n Curves f o r D i f f e r e n t P r e s s u r e s ( t 0 = 0.16) -150 +200 +250 1 . 0 o a o 0.8 i 0.6 + 0.44- 0 . 3 f 0.2 + -250 o " X <» ° X X o • Q X X o • • I ft x x * A X .X o 0 >; o o 9 ' ° X o • * o X o • P = 2 T o r r x p = 50 T o r r o p = 100 T o r r -200 -150 -100 -50 14 +50 +100 +150 ' Source S h i f t from L i n e C e n t r e (mK) F i g . 6 T r a n s m i s s i o n Curves f o r D i f f e r e n t P r e s s u r e s ( t Q = 0.33) -280 +250 F r a c t i o n a l T r a n s m i s s i o n H n CO D 01 3 H- 01 W H- O O C fi < CD in H - , O H a H- l-h i-h CD fi fD D r f TJ fi CD O) cn C fi CD O) O O CJl OJ O ro CJi 0 4 - ro o o H - 1 cn • o 1 H crr 00 o o c fi o CD I CO o' ZT H- t-h c+ fi O 3 3 + CD CH O. O CD c+ fi CD + 3 O + 1—1 CJl + o + ro o o + ro CJl o o ro o -+- o 4 - o o o o —J o co o vO o TJ TJ II II II t—1 CJl ro o O o H H o H O fi O fi fi fi fi fi o e oo 0 ej O X o > » o Xo 0 X o o x © O X © o X » X » O £c 0 * O X © O X • o X o X o O X o O X » 0 X e o >c© — 0 X© 0 X© oy O 9 0X o © Cv- "0t7- -41- B. D e t e c t i o n of S h i f t There i s a s l i g h t but 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 c u r v e s w i t h r e s p e c t t o the d e s i g n a t e d z e r o f i e l d - z e r o s h i f t p o s i t i o n . However the c u r v e s are a l l more or l e s s symmetric about an o r d i n a t e of + 4 mK. There was no d i s c e r n a b l e v a r i a t i o n of t h i s o f f s e t w i t h p r e s s u r e . As a r e s u l t i t must be c o n c l u d e d t h a t no s i g n i f i c a n t p r e s s u r e s h i f t has been d e t e c t e d . Any r e a l s h i f t due t o p r e s s u r e must have been a t most l e s s t h a n 4 mK f o r the 100 T o r r absorber.. Such m i n i m a l p r e s s u r e s h i f t , i n d i sagreement w i t h the impact t h e o r y f o r a van der Waals i n t e r a c t i o n , i s c o n s i s t e n t w i t h the r e s u l t s of S m i t h ( 1 4 ) . The l i n e c e n t r e t r a n s m i s s i o n , t , was t a k e n on the a x i s o of symmetry/in each c a s e . C. L i n e Shape D e t e r m i n a t i o n As a r e s u l t of the a n a l y s i s by m o d e l l i n g (as d e s c r i b e d i n C h apter V s e c t i o n B ) , the parameters of the model of b e s t f i t a r e : Source A b s o r b e r ( s ) = 50 mK (=f> T = 360 °K) s ' = 6 mK ( s o u r c e V o i g t A = 0.12) A ^ „ = 48 mK (=• T = 325 °K). K = 1.5 The L o r e n t z i a n h a l f w i d t h s of the a b s o r b e r s , as c o n c l u d e d -42- from t h e t v e r s u s A t curves (see F i g u r e 1 0 ) , are t a b l e d below: P r e s s u r e ( T o r r ) L\VL* (mK) V o i g t A 2 7 0.14 50 23 0.48 100 48 1.00 The 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 c u r v e s f o r p r e s s u r e s of 2 T o r r and 100 T o r r are 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 . F i g u r e 10 shows the t h e o r e t i c a l c u r v e s f o r l i n e c e n t r e t r a n s m i s s i o n v e r s u s h a l f w i d t h f o r the model of b e s t f i t , w i t h the e x p e r i m e n t a l r e s u l t s a l s o d i s p l a y e d . I t was p r i m a r i l y from t h i s curve t h a t the assignment of L o r e n t z i a n h a l f w i d t h s f o r the h i g h e r p r e s s u r e a b s o r b e r s was made. D. Rate of P r e s s u r e Broadening -•Comparison w i t h Theory The r e s u l t s t a b u l a t e d above may most e a s i l y be compared with, t h e o r y by means of a ' r a t e of p r e s s u r e b r o a d e n i n g ' graph - see F i g u r e 11 - i n which the a b s o r b e r L o r e n t z i a n h a l f w i d t h i s p l o t t e d a g a i n s t p r e s s u r e (and d e n s i t y ) . The d a t a are i n s u f f i c i e n t t o p e r m i t c o n c l u s i o n s r e g a r d i n g the l i n e a r i t y of t h i s c u r v e . However, assuming a l i n e a r r e l a t i o n s h i p p a s s i n g t h r o u g h the o r i g i n (as p r e d i c t e d by the impact t h e o r y ) then the b e s t s t r a i g h t l i n e has a s l o p e : F r a c t i o n a l T r a n s m i s s i o n F r a c t i o n a l Transmission o o o ' o o i ro ot- H 1 OJ ro D o CD Cr 3 if) (Si P- 1 O h-• CJl O" O C M < fD 1 1.0 0.9 + 0.8 + 0.7 0.6 o.4 + 0.3 0.2 0.1 + V o i g t A = 0 ( a b s o r b e r ) — Theory(model of b e s t f i t ) » P = 2 T o r r x P = 50 T o r r o P = 100 T o r r 10 70 80 90 100- 110 120 130 140 150 T r a n s m i s s i o n Curve H a l f Width (mK) F i g . 10 T r a n s m i s s i o n H a l f Width v e r s u s T r a n s m i s s i o n (Theory and E x p e r i m e n t ) 160 -46- = 1.6-10 mK cm 3 n B o t h e s t i m a t e s c a l c u l a t e d i n the t h e o r y (Chapter I I , s e c t i o n C ) are d i s p l a y e d as w e l l . I t can be seen t h a t the e x p e r i m e n t a l r e s u l t s show a r a t e of p r e s s u r e b r o a d e n i n g n e a r l y 50 % g r e a t e r t h a n t h a t p r e d i c t e d by t h e o r y . However t h e r e i s c l o s e agreement w i t h the s e m i - e m p i r i c a l r a t e d e r i v e d * from the r e s u l t s of S m i t h ( 1 4 ) . E. V a l i d i t y of R e s u l t s ( 1 ) R e l i a b i l i t y : S i n c e the r e s u l t s are d e r i v e d t h r o u g h a complex p r o c e s s of p r o f i l e a n a l y s i s and parameter v a r i a t i o n , e r r o r e s t i m a t e s are d i f f i c u l t and somewhat u n c e r t a i n . The e r r o r e s t i m a t e s shown are p r i m a r i l y based on s e l f - c o n s i s t e n c y . I n matching e x p e r i m e n t a l and t h e o r e t i c a l t r a n s m i s s i o n c u r v e s the f i t t i n g e r r o r s are q u i t e s m a l l s i n c e t h e c u r v e s are so s i m i l a r . V a r i a t i o n of the a b s o r b e r V o i g t A parameter by more t h a n - 0.05 d i s t o r t e d t h e shape of the t h e o r e t i c a l c urve s u f f i c i e n t l y t o cause r e j e c t i o n of the f i t . S i m i l a r l y , v a r i a t i o n of the D o p p l e r h a l f w i d t h a s s i g n e d t o the a b s o r b e r by more t h a n t 2 mK a l t e r e d the w i d t h of the t h e o r e t i c a l c urve enough t o make the l a c k of f i t a p p a r e n t . Moreover v a r i a t i o n s o f ' t h e s e two parameters c o u l d not be made a l t o g e t h e r i n d e p e n d e n t l y , f o r d e c r e a s e s i n the a s s i g n e d D o p p l e r w i d t h would e v e n t u a l l y n e c e s s i t a t e c o n c u r r e n t i n c r e a s e s i n the a s s i g n e d V o i g t A parameter, e t c . As a r e s u l t the u n c e r t a i n t y -47- P r e s s u r e D e n s i t y P i g . 11 Rate of P r e s s u r e B r o a d e n i n g -48- i n t h e a s s i g n e d a b s o r b e r L o r e n t z i a n h a l f w i d t h i s t h e r e b y p r o b a b l y no more tha n i 4 mK. From the t r a n s m i s s i o n v e r s u s h a l f w i d t h r e l a t i o n (see F i g u r e 10) upon which the f i n a l e s t i m a t e s were based t h e r e i s a range of V o i g t A parameters (and hence L o r e n t z i a n h a l f w i d t h s ) spanned by the e x p e r i m e n t a l p o i n t s . P r e s s u r e ( T o r r ) A ^ (mK> (minimum) (mK) (maximum) (mK) 2 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 , i n c o n j u n c t i o n w i t h the f i t t i n g e r r o r s d e s c r i b e d above, were used as the b a s i s f o r a s s i g n i n g the c o n f i d e n c e l i m i t s 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 : S i n c e a l l the t r a n s m i s s i o n c u r v e s showed the same s l i g h t s h i f t of a p p r o x i m a t e l y 4 mK, which was moreover independent of p r e s s u r e , an ap p a r a t u s e r r o r i s s u s p e c t e d . T h i s + 4 mK o f f s e t i s thought t o have o r i g i n a t e d i n a f a i l u r e of the s c a n n i n g e l e c t r o m a g n e t t o f o l l o w p e r f e c t l y i t s c a l i b r a t i o n c u r v e . T h i s c o n d i t i o n r e s u l t s from i m p e r f e c t r e g u l a t i o n of the e l e c t r o m a g n e t c u r r e n t i n the f a c e of v a r i a t i o n s of the c o i l r e s i s t a n c e due t o h e a t i n g . A f t e r the c u r r e n t was r e v e r s e d (the t r a n s i t i o n from n e g a t i v e t o p o s i t i v e s h i f t ) i t was t o -49- have been m o n o t o n i c a l l y i n c r e a s e d i n .order t o f o l l o w the c a l i b r a t i o n c u r v e . However a f t e r each c u r r e n t i n c r e m e n t (0.2 amp) the c o i l s warmed f u r t h e r and t h e i r r e s i s t a n c e i n c r e a s e d . There was a tendency f o r the c u r r e n t t o then d e c r e a s e v e r y s l i g h t l y , i n s p i t e of the , r e g u l a t i o n p r o v i d e d i n the e l e c t r o m a g n e t c u r r e n t power s u p p l y . T h i s would have t a k e n the magnet o f f the assumed c a l i b r a t i o n c u rve and s l i g h t l y i n t o the ' i n t e r i o r ' of the h y s t e r i s i s l o o p . The a c t u a l magnetic f i e l d would be l e s s than t h a t assumed. T h i s would r e s u l t i n an e x p a n s i o n of the f r e q u e n c y s c a l e f o r t h i s h a l f of the t r a n s m i s s i o n c u r v e i n t h a t the a c t u a l f i e l d (and Zeeman s h i f t ) are l e s s t h a n t h o s e a s s i g n e d . As a r e s u l t the c e n t r e of g r a v i t y of the t r a n s m i s s i o n curve would be d i s p l a c e d t o t h e h i g h f r e q u e n c y s i d e (see F i g u r e 12). I n a d d i t i o n t o p r o d u c i n g the apparent s h i f t , t h i s e f f e c t must a l s o have caused a p p a r e n t l y w i d e r t r a n s m i s s i o n c u r v e s . No a t t e m p t , however, was 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 e r r o r and t h e o r e t i c a l p r o f i l e s were f i t t e d t o the c e n t r e of symmetry. The r a t e of b r o a d e n i n g graph ( F i g u r e 11) r e v e a l s what i s p o s s i b l y the e f f e c t of a second source of s y s t e m a t i c e r r o r . The L o r e n t z i a n w i d t h a s s i g n e d t o the 2 T o r r a b s o r b e r i s a p p a r e n t l y too g r e a t s i n c e a l l p r e s s u r e b r o a d e n i n g t h e o r i e s p r e d i c t h a l f w i d t h s d i r e c t l y p r o p o r t i o n a l t o p r e s s u r e (and d e n s i t y ) . . In the l i m i t of z e r o p r e s s u r e the L o r e n t z i a n h a l f w i d t h s h o u l d approach th e n a t u r a l l i n e w i d t h (here o n l y — 0.6 mK). 1 . 0 - - / , ' ': / • i: i: t • i • ' > i • I • »: i • a c t u a l c u r v e apparent curve due t o i m p e r f e c t r e g u l a t i o n 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 -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 2 T o r r a b s o r b e r the expected L o r e n t z i a n w i d t h s h o u l d be the van der Waals w i d t h of ^ 1 mK o n l y . - o u t s i d e the c o n f i d e n c e l i m i t s a s s i g n e d ! The o r i g i n o f . t h i s a p p a r e n t l y e x c e s s i v e L o r e n t z i a n w i d t h i s i n a l l p r o b a b i l i t y unaccounted b r o a d e n i n g of the s o u r c e . S e v e r a l minor b r o a d e n i n g e f f e c t s which.were n e g l e c t e d a r e : 1. magnetic f i e l d i n h o m o g e n e i t i e s (see Chapter I I ).' 2. a l t e r a t i o n of the source l i n e shape as t h e s c a n n i n g magnetic , f i e l d i s v a r i e d . 3. v a r i a t i o n s i n the s e l f a b s o r p t i o n r e s u l t i n g from t h e i n h o m o g e n e o u s ' c y l i n d e r i c a l n a t u r e of t h e s o u r c e , ( i n c o n t r a s t t o the homogeneous, p l a n e - p a r a l l e l source assumed i n the t h e o r y ) I t has .been p o i n t e d out by van de H u l s t and R e e s i n c k (16) t h a t "the c o m b i n a t i o n of many independent b r o a d e n i n g e f f e c t s tends t o y i e l d a V o i g t p r o f i l e " . The source l i n e s h o u l d t h u s have had ' a V o i g t type p r o f i l e , as was assumed. However the L o r e n t z i a n component 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 the L o r e n t z i a n h a l f w i d t h a s c r i b e d t o p r e s s u r e b r o a d e n i n g a l o n e . I n t h e a n a l y s i s the source and' t h e 2 T o r r a b s o r b e r were assumed 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 s i n c e t h e i r p r e s s u r e s were e q u a l . Thus an exaggerated. L o r e n t z i a n h a l f w i d t h must have been 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 o r d e r t o f i t the t r a n s m i s s i o n c u r v e s . Such an e r r o r i n t h e source l i n e shape w i l l a l s o c r e a t e e r r o r s in':the r e s u l t s f o r the h i g h e r p r e s s u r e a b s o r b e r s . However -52- f o r t h e s e i t was found t h a t the L o r e n t z i a n w i d t h s of the d e r i v e d l i n e p r o f i l e s were l e s s a f f e c t e d by changes i n the assumed source shape t h a n were th o s e of the 2 T o r r a b s o r b e r . Hence, as might be a n t i c i p a t e d from the t h e o r y (see. e q u a t i o n IVA), the r e s u l t s f o r the h i g h e r p r e s s u r e a b s o r b e r s would have been l e s s a f f e c t e d by such an e r r o r i n t h e source l i n e shape. -53- CHAPTER V I I CONCLUDING DISCUSSION The Zeeman s c a n n i n g t e c h n i q u e has shown i t s e l f w e l l s u i t e d t o the 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 p r o f i l e s . The a b i l i t y t o d e t e c t d i f f e r e n c e s as low as 5 mK (or 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 t o r e p r e s e n t a r e s o l u t i o n of — 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 o t h e r w i s e except w i t h s o p h i s t i c a t e d s p e c t r o g r a p h i c t e c h n i q u e s . By comparing a b s o r b e r s a t d i f f e r e n t p r e s s u r e s the e x t e n t of p r e s s u r e b r o a d e n i n g f o r Ne"\6074.3 A° has been determined f o r glow d i s c h a r g e c o n d i t i o n s . I t i s apparent from t h e r e s u l t s t h a t even a t p r e s s u r e s as low as a few T o r r t h i s l i n e w i l l e x h i b i t a non-Gaussian p r o f i l e . A t 10 T o r r and 325 °K the Ne 'X6074.3 A 0 l i n e shows a V o i g t A parameter of A = 0.1 ( i n t e r - p o l a t e d from F i g u r e 1 1 ) . The p r e s s u r e b r o a d e n i n g 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 from t h e o r y . T h i s i s p r o b a b l y t r u e a l s o f o r o t h e r l i n e s of the neon t r i p l e t system w h i c h are u n a f f e c t e d by resonance e f f e c t s . Those neon l i n e s a f f e c t e d by resonance broa d e n i n g l i k e l y e x h i b i t V o i g t A v a l u e s even g r e a t e r than Ne'X6074.3 A 0 under s i m i l a r c o n d i t i o n s . Thus, th e c a s u a l assumption of G a u s s i a n p r o f i l e s f o r neon glow d i s c h a r g e l i n e s i s i n e r r o r . Where such an assumption • i s t o be made the^consequences of the p r e s s u r e b r o a d e n i n g s h o u l d f i r s t be checked. -54- Close agreement f o r the r a t e of pressure broadening has been obtained w i t h values c a l c u l a t e d u s i n g the impact theory w i t h a van der Waals i n t e r a c t i o n p o s t u l a t e d . The experimental value of = 1.6*10 mK cm agrees w i t h the value d e r i v e d from the r e s u l t s of Smith (14) to more or l e s s w i t h i n the assigned confidence l i m i t s . The more t h e o r e t i c a l value i s l i k e w i s e e n c o u r a g i n g l y c l o s e - to w i t h i n 50 %. Such good agreement would appear to j u s t i f y the use of Unsold's approximation (equation V I I I ) . The l a c k of observed s h i f t , c o n s i s t e n t w i t h the r e s u l t s of Smith (14), confirms the f a i l u r e of the van der Waals i n t e r a c t i o n to p r o p e r l y d e s c r i b e the em i t t e r - p e r t u r b e r i n t e r a c t i o n i n t h i s i n s t a n c e . The i n c l u s i o n of a r e p u l s i v e term, as advocated by Hindmarsh, P e t f o r d , and Smith (15), i s e v i d e n t l y r e q u i r e d . Such a c o n s i d e r a t i o n f a l l s beyond the scope of the present work and would l i k e l y r e q u i r e a more accurate study of the s h i f t . T h i s i s one reason why an i n v e s t i g a t i o n of. one or two argon l i n e s by t h i s Zeeman scanning technique would be most i n t e r e s t i n g . Of course argon has a l s o been used i n glow d i s c h a r g e s f o r s i m i l a r experiments (19, 20) to those p r e v i o u s l y noted (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 to check argon l i n e shapes as w e l l . In a d d i t i o n the r e s u l t s of Smith (14) i n d i c a t e t h a t argon behaves c l o s e l y to the p r e d i c t i o n s of the impact theory w i t h a van der Waals i n t e r a c t i o n . In p a r t i c u l a r the s h i f t to width r a t i o i s c l o s e -55- t o t h e 1:2.76 v a l u e p r e d i c t e d . Thus f o r h i g h e r p r e s s u r e s such as '50 or 100 T o r r the s h i f t s h o u l d be e a s i l y d e t e c t e d . An 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 t h e s e l i n e shapes but t o a l s o f u r t h e r t e s t the 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 Smith's f i n d i n g s i n t h e case of argon s e l f - p r e s s u r e b r o a d e n i n g and s h i f t . For f u t u r e work s e v e r a l improvements i n the Zeeman s c a n n i n g a p p a r a t u s can be s u g g e s t e d . The w i d t h of the sour c e l i n e i s analogous t o the a p p a r a t u s w i d t h of a s p e c t r o g r a p h or i n t e r f e r o m e t r i c system i n t h a t the source p r o f i l e i s f o l d e d w i t h t h a t of the a b s o r b e r t o produce the 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 the source 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 l e s s than t h a t of the a b s o r b e r . Then, as suggested by the t h e o r y (see e q u a t i o n IVA)., the shape of the t r a n s m i s s i o n curve depends almost s o l e l y on t h e a b s o r b e r ' s l i n e shape. Such a s i t u a t i o n was not a c h i e v e d i n t h i s experiment but where i t was approached w i t h the 100 T o r r a b s o r b e r the r e s u l t s are more r e l i a b l e . At lower p r e s s u r e s the l i n e w i d t h s of both source and a b s o r b e r are p r i m a r i l y d e t e r m i n e d by D o p p l e r b r o a d e n i n g and are thus comparable. U n l e s s d r a s t i c c o o l i n g or some o t h e r means i s employed t o reduce t h e D o p p l e r 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 . A l t e r n a t e l y , however, a p r e c i s e d e t e r m i n a t i o n of the source l i n e shape w i l l p e r m i t an a c c u r a t e measurement of the a b s o r b e r l i n e shape. T h i s c o u l d be a c c o m p l i s h e d by r e d u c i n g the source 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 p r e s s u r e -56- b r o a d e n i n g and s e l f a b s o r p t i o n are e f f e c t i v e l y e l i m i n a t e d . Then D o p p l e r .broadening a l o n e would determine the source l i n e shape. These measures would i m p l y a l s o a source of low i n t e n s i t y , r e d u c i n g the s i g n a l - t o - n o i s e r a t i o and v e r y l i k e l y n e c e s s i t a t i n g a more e f f i c i e n t d e t e c t i o n system t h a n t h a t employed i n t h i s e x p e r i m e n t . In a d d i t i o n magnetic f i e l d inhomogeneity would have t o be f u r t h e r reduced to- guarantee the absence of 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 . W i t h such improvements the number of " f r e e " parameters t o be s a t i s f i e d i n t h e a n a l y s i s would be reduced and the r e s u l t s not o n l y more e a s i l y o b t a i n e d but a l s o more r e l i a b l e . •In v i e w of the e n c o u r a g i n g r e s u l t s o b t a i n e d i n t h i s experiment i t i s hoped t h a t f u t u r e work, w i t h the ap p a r a t u s f u r t h e r r e f i n e d , w i l l be c a r r i e d o u t . -57- BIBLIOGRAPHY (1) N o d w e l l , R., van A n d e l , H., & Robinson, A. : JQSRT 8 , p. 859 (1968). 2) Seka, W., & Curzon, F.': JQSRT 8 , p. 1147 (1968). 3) S t a n s f i e l d , B. : M.A.Sc. T h e s i s (U.B.C. - 1967). 4) B i t t e r , P l o t k i n , T i c h t e r , T e v i o t d a l e , & Young : Phys. Rev. 91 , p. 421 (1953). 5) H e i t l e r , W. : The Quantum Theory of R a d i a t i o n , O.U.P. ( 3 r d Ed. - 1959) S e c t i o n I , 4(pp. 25 - 3 4 ) . 6) H e i t l e r , W. : i b i d S e c t i o n V, 18(pp. 181 - 185). 7) Nodwel, R., van A n d e l , H., & Robin s o n , A. : i b i d p. 872. 8) E c k e r , G. & Z o l l e r . 0. : Phys. F I . 7 , p. 1996 (1964). 9) Griem, H. : Plasma S p e c t r o s c o p y , M c G r a w - H i l l (1964) T a b l e 4-5 10 11 12 13 14 15 16 17 18 19 20 I r w i n , J.C. : Ph.D. T h e s i s (U.B.C. - 1965). F o l e y , H. : Phys. Rev. 69 , p. 616 (1946). U n s o l d , A. : P h v s i k der Sternatmospharen , S p r i n g e r ( 2 n d Ed. - 1955). A l l e n , C.W. : A s t r o p h y s i c a l Q u a n t i t i e s , A t h l o n e ( 2 n d Ed. - 1963). S m i t h , G. : . P r o c . Roy. Soc. A297 , p. 288 (1967). Hindmarsh. P e t f o r d , & Smith' : P r o c .Roy .Soc. A297, p.296 (1967). Van de H u l s t & R e e s i n c k : App. J . 106 , p. 121 (1947). Young, C. : JQSRT 5 , p. 549 (1965). I n t e r n a t i o n a l C r i t i c a l T a b l e s V : M c G r a w - H i l l (1929) p . 4 1 8 f f . J a c o b s o n , T. : Ph.D. T h e s i s , (U.B.C. - 1969). Stockmayer, P. : M.Sc. T h e s i s (U.B.C. - 1969). -58- 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 Curves * ( a ) START I Read , AVM , &T?L% , K, A, t ( C a l c u l a t e and s t o r e the a b s o r b e r 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 of 2.5 mK C a l c u l a t e and s t o r e the source 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 of 2.5 mK I n t e g r a t e the source t o compute S{JZ) k Q i = 10.0 Compute 0{2i) and t V a r y k Q^ by i t e r a t i v e h a l v i n g NO * ( b ) * ( c ) * ( c ) *(a) *(d) -59- r Compute and s t o r e the ab s o r b e r f u n c t i o n : ex.p{ -kJ(VGA{j))} Compute the 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 W r i t e and p l o t the t r a n s m i s s i o n c u r v e . ^STOP *Notes: (a) The c a l c u l a t i o n s were performed on an IBM 7044 computer * (b) A i s the V o i g t A parameter f o r the a b s o r b e r ; o t h e r symbols are as d e f i n e d i n Cha 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 the 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 performed by use of a composite Newton - Cotes f o r m u l a of o r d e r 4 ( c l o s e d ) i n 100 s t e p s from - 10 t o + 10 h a l f w i d t h s .

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