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Far-infrared absorption by liquid nitrogen and liquid oxygen Wishnow, Edward Hyman 1985

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FAR-INFRARED ABSORPTION BY LIQUID NITROGEN AND LIQUID OXYGEN by EDWARD H. WISHNOW B.A., Reed C o l l e g e , 1980 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n THE FACULTY OF GRADUATE STUDIES -Department Of P h y s i c s We ac c e p t t h i s t h e s i s as c o 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 October 1985 © Edward H. Wishnow, 1985 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the r e q u i r e m e n t s f o r an advanced degree a t the U n i v e r s i t y of B r i t i s h C o l u m b i a , I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i l e c o p y i n g of t h i s t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by the Head of my Department or by h i s or her r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department of P h y s i c s The U n i v e r s i t y of B r i t i s h Columbia 2075 Wesbrook P l a c e Vancouver, Canada V6T 1W5 Date: October 15, 1985 A b s t r a c t T h i s t h e s i s examines the c o l l i s i o n i n d u c e d , f a r - i n f r a r e d a b s o r p t i o n of homonuclear d i a t o m i c m o l e c u l e s . These m o l e c u l a r p r o c e s s e s a r e r e l e v a n t i n the a s t r o p h y s i c a l environments of p l a n e t a r y atmospheres and g a l a c t i c m o l e c u l a r c l o u d s , and a b r i e f s u r v ey of f a r - i n f r a r e d measurements of thes e r e g i o n s i s p r e s e n t e d . The t h e o r y of c o l l i s i o n i n d u c e d a b s o r p t i o n by m o l e c u l a r r o t a t i o n a l t r a n s i t i o n s i s re v i e w e d and a c a l c u l a t i o n i s made of the q u a d r u p o l a r i n d u c e d , s i n g l e r o t a t i o n a l t r a n s i t i o n a b s o r p t i o n l i n e i n t e n s i t i e s of the n i t r o g e n and oxygen m o l e c u l e s . The f a r - i n f r a r e d a b s o r p t i o n s p e c t r a of l i q u i d n i t r o g e n and l i q u i d oxygen a t 77K, over the fre q u e n c y range 5 t o 70 cm 1 , have been measured. The f a r -i n f r a r e d spectrum of l i q u i d oxygen has not p r e v i o u s l y been r e p o r t e d . The p r e s e n t work i n c l u d e s t h e d e s i g n of a low te m p e r a t u r e , m u l t i p l e pass, f a r - i n f r a r e d a b s o r p t i o n c e l l i n t e n d e d f o r low t e m p e r a t u r e , low d e n s i t y gas measurements. The e f f e c t of d i f f r a c t i o n on the c e l l ' s maximum a t t a i n a b l e o p t i c a l p a t h l e n g t h , and a model used t o e s t i m a t e the a n t i c i p a t e d l i q u i d h e l i u m consumption a r e d i s c u s s e d . T a b l e of C o n t e n t s A b s t r a c t . i L i s t of T a b l e s i L i s t of F i g u r e s Acknowledgement v Chapter I INTRODUCTION 1 1.1 M o l e c u l e s And R a d i a t i o n 2 1.2 A s t r o p h y s i c a l A p p l i c a t i o n s Of M o l e c u l a r S p e c t r o s c o p y 5 Chapter I I THE THEORY OF COLLISION INDUCED ABSORPTION 10 2.1 Review Of The Theory 10 2.2 C a l c u l a t i o n Of A b s o r p t i o n I n t e n s i t i e s 19 Chapter I I I EXPERIMENTAL APPARATUS AND RESULTS 27 3.1 E x p e r i m e n t a l A p p a r a t u s And P r o c e d u r e s 27 3.2 E x p e r i m e n t a l R e s u l t s 46 Chapter IV LOW TEMPERATURE MULTIPLE PASS FAR-INFRARED ABSORPTION CELL 64 Chapter V CONCLUSION 77 REFERENCES 79 i v L i s t of T a b l e s 1. Quadrupole moment, p o l a r i z a b i l i t y , and a n i s o t r o p y of the p o l a r i z a b i l i t y f o r the n i t r o g e n and oxygen m o l e c u l e s 20 2. R o t a t i o n a l c o n s t a n t s of the n i t r o g e n and oxygen m o l e c u l e s 23 3. F r e q u e n c i e s and a b s o r p t i o n i n t e n s i t i e s of q u a d r u p o l a r induced s i n g l e r o t a t i o n a l t r a n s i t i o n s i n n i t r o g e n and oxygen m o l e c u l e s 26 4. I n t e r f e r o m e t e r p a r a m e t e r s , as s p e c i f i e d i n the d e s i g n and as measured 31 5. D i e l e c t r i c c o n s t a n t , index of r e f r a c t i o n , and t r a n s m i s s i o n of c e l l f o r l i q u i d n i t r o g e n and l i q u i d oxygen 54 6. D i f f r a c t i o n spot s i z e and maximum p a t h l e n g t h f o r low o p t i c a l f r e q u e n c i e s 66 V L i s t of F i g u r e s 1. I n t e r f e r o m e t e r o p t i c a l p a t h 29 2. I n t e r f e r o g r a m , modulus spectrum and phase a n g l e as a f u n c t i o n of f r e q u e n c y 37 3. P o l y n o m i a l f i t t o the phase and the spectrum V^'(0") 38 4. L i q u i f i e d gas sample c e l l 43 5. Diagram of the o p t i c a l system 44 6. Hi g h f r e q u e n c y c u t o f f of o p t i c a l system 51 7. A b s o r p t i o n c o e f f i c i e n t of l i q u i d n i t r o g e n 56 8. A b s o r p t i o n c o e f f i c i e n t of l i q u i d oxygen 57 9. L i n e shape f u n c t i o n of l i q u i d n i t r o g e n 61 10. L i n e shape f u n c t i o n of l i q u i d oxygen 62 11. Diagram of the low temperature m u l t i p a s s a b s o r p t i o n c e l l 68 v i Acknowledgement I would l i k e t o thank my f a m i l y and f r i e n d s f o r t h e i r encouragement of my s t u d i e s . Among them, I r a B l e v i s and e s p e c i a l l y C a r o l y n Coons have been v e r y s u p p o r t i v e , p a r t i c u l a r l y d u r i n g my e a r l y y e a r s of graduate s c h o o l , and I s i n c e r e l y thank them. I am v e r y t h a n k f u l of t h e generous u n d e r s t a n d i n g which Anna F r i t z has shown towards me over the c o u r s e of t h i s work. The members and a s s o c i a t e s of our l a b o r a t o r y d e s e r v e r e c o g n i t i o n and my t h a n k s f o r t h e i r c o n t r i b u t i o n s t o t h i s work. I r v i n g O z i e r has c o n t r i b u t e d h i s s u p p o r t and s u g g e s t i o n s t o the d e s i g n of the low temperature c e l l , as has Sucha Parmar. V i t t o r i o DeCosmo's comments and company have been much a p p r e c i a t e d . A l e x Leung has made v e r y i m p r e s s i v e , not t o mention i n v a l u a b l e , d e s i g n c o n t r i b u t i o n s t o the low temperature c e l l . I have l e a r n e d a g r e a t d e a l of p h y s i c s from Mark H a l p e r n and I thank him f o r t h i s and f o r h i s h e l p throughout t h i s work. F i n a l l y , I would l i k e t o thank P r o f . H e r b e r t Gush f o r h i s c o n f i d e n c e i n me, and h i s s u p p o r t , and f o r i n c l u d i n g me i n h i s c h a l l e n g i n g r e s e a r c h work, f o r which I f e e l v e r y f o r t u n a t e . I would l i k e t o d e d i c a t e t h i s work t o my mom and dad. 1 I . INTRODUCTION The u n i v e r s e i s composed p r i m a r i l y of hydrogen and i n our g a l a x y a l a r g e p o r t i o n of i t e x i s t s i n c o l d , s p a r s e m o l e c u l a r c l o u d s . S i n c e the m o l e c u l e s w i t h i n t h e s e gas c l o u d s a r e c o l d , o n l y the low energy r o t a t i o n a l o r t r a n s l a t i o n a l m o l e c u l a r s t a t e s a re h i g h l y p o p u l a t e d . M o l e c u l a r t r a n s i t i o n s between t h e s e s t a t e s c o r r e s p o n d i n energy t o the f a r - i n f r a r e d f r e q u e n c y r e g i o n of e l e c t r o m a g n e t i c r a d i a t i o n . I s o l a t e d m o l e c u l e s l i k e hydrogen a b s o r b i n f r a r e d r a d i a t i o n v e r y weakly because of t h e i r symmetry, y e t a g g r e g a t e s of the s e m o l e c u l e s , v i a c o l l i s i o n s or c l u s t e r i n g , can absorb more s t r o n g l y . Other d i a t o m i c m o l e c u l e s , i n p a r t i c u l a r n i t r o g e n and oxygen, a l s o a b s o r b r a d i a t i o n by the s e mechanisms, where n i t r o g e n has an importance i n a s t r o p h y s i c s due t o i t s p r e v a l e n c e i n p l a n e t a r y atmospheres. The m o t i v a t i o n f o r the p r e s e n t work i s t o g a i n an u n d e r s t a n d i n g of the a b s o r p t i o n of f a r - i n f r a r e d r a d i a t i o n by homonuclear d i a t o m i c m o l e c u l e s . S e v e r a l a s p e c t s of c o l l i s i o n i n d u ced a b s o r p t i o n by the s e m o l e c u l e s have been i n v e s t i g a t e d : the t h e o r y , the a b s o r p t i o n of f a r - i n f r a r e d r a d i a t i o n by l i q u i d n i t r o g e n and l i q u i d oxygen, and t h e d e s i g n of a low temperature o p t i c a l a b s o r p t i o n c e l l . The f i r s t p a r t of t h i s c h a p t e r i n t r o d u c e s the t o p i c s of c o l l i s i o n i n d u c e d a b s o r p t i o n and dimer a b s o r p t i o n by homonuclear d i a t o m i c m o l e c u l e s . The second p a r t r e v i e w s t h e a s t r o p h y s i c a l measurements t o which t h e s e s p e c t r o s c o p i c r e s u l t s may be a p p l i e d . 2 1.1 M o l e c u l e s And R a d i a t i o n When r a d i a t i o n i s absorbed by any system, t h e f r e q u e n c y i s r e l a t e d t o the energy change of the system by Bohr's f r e q u e n c y c o n d i t i o n : - Et' = h i> = he C Here, Et* and Ey a r e the i n i t i a l and f i n a l energy s t a t e s , h i s P l a n c k ' s c o n s t a n t , )) i s the f r e q u e n c y , c i s t h e speed of l i g h t , and <J i s the f r e q u e n c y i n wave numbers, where CT = \/\ ( i n cm ' ) , and ?\ i s the w a v e l e n g t h . S p e c t r o s c o p y t h e r e f o r e i n d i c a t e s the n a t u r e of o p t i c a l l y a c t i v e energy t r a n s i t i o n s w i t h i n m a t t e r . In the c a s e of m o l e c u l e s , the t y p e s of t r a n s i t i o n s t h a t may be examined a r e : ( g e n e r a l l y d e c r e a s i n g i n energy) E l e c t r o n i c , v i b r a t i o n a l , and r o t a t i o n a l . The a b s o r p t i o n of i n f r a r e d r a d i a t i o n a t f r e q u e n c i e s a s s o c i a t e d w i t h v i b r a t i o n a l or r o t a t i o n a l t r a n s i t i o n s , by i s o l a t e d homonuclear d i a t o m i c m o l e c u l e s , i s however q u i t e weak. T h i s i s a consequence of t h e symmetry of t h e ground s t a t e of t h e s e m o l e c u l e s , whereby they do not p o s s e s s a permanent e l e c t r i c d i p o l e moment, or i t s d e r i v a t i v e s . A b s o r p t i o n of r a d i a t i o n by t h i s s p e c i e s of m o l e c u l e s o c c u r s o n l y as a r e s u l t of q u a d r u p o l e or h i g h e r o r d e r m u l t i p o l e moments, and i s much weaker than t h a t of a m o l e c u l e w i t h a s t r o n g d i p o l e moment, such as H C 1 . However, when two or more m o l e c u l e s c o l l i d e , t h e i r 3 c h a r g e d i s t r i b u t i o n s may be d i s t o r t e d s u c h t h a t a ( t r a n s i e n t ) d i p o l e moment a r i s e s . S i n c e t h e m a g n i t u d e a n d d i r e c t i o n o f t h i s d i p o l e moment d e p e n d s on t h e c o l l i d i n g m o l e c u l e s ' i n t e r n u c l e a r s e p a r a t i o n , a n d o r i e n t a t i o n s , t h e v i b r a t i o n a l a n d r o t a t i o n a l t r a n s i t i o n s o f t h e m o l e c u l e s become i n f r a r e d a c t i v e . The d i p o l e moment a l s o d e p e n d s on t h e i n t e r m o l e c u l a r d i s t a n c e , a n d t h e r e f o r e t r a n s i t i o n s b e t w e e n t r a n s l a t i o n a l e n e r g y s t a t e s c a n a b s o r b r a d i a t i o n . C o l l i s i o n i n d u c e d a b s o r p t i o n may be o b s e r v e d i n d e n s e s y s t e m s w h e r e c o l l i s i o n s a r e f r e q u e n t s u c h a s t h e c o m p r e s s e d g a s o r t h e l i q u i d p h a s e . The s p e c t r u m due t o c o l l i s i o n i n d u c e d a b s o r p t i o n i s d i f f e r e n t t h a n t h a t o f e i t h e r a n o r m a l d i p o l e o r q u a d r u p o l e s p e c t r u m . The r e a s o n i s t h a t t h e d i p o l e moment i n d u c e d by — 12. c o l l i s i o n i s o f b r i e f d u r a t i o n , s a y At ( on t h e o r d e r o f 10 s e c o n d s ) , a n d due t o t h e u n c e r t a i n t y p r i n c i p l e A E At >-fa , t h e w i d t h o f t h e e n e r g y s t a t e s i n v o l v e d , AE, i s l a r g e . I n t h e c a s e o f o x y g e n a n d n i t r o g e n , t h i s e n e r g y s p r e a d e x c e e d s t h e s p a c i n g b e t w e e n l i n e s i n t h e r o t a t i o n a l s p e c t r u m a n d t h u s t h e a b s o r p t i o n s p e c t r u m o f b o t h v i b r a t i o n a l a n d r o t a t i o n a l b a n d s i s d e v o i d o f s t r u c t u r e . The s h a p e o f t h e c o l l i s i o n i n d u c e d s p e c t r u m r e s e m b l e s t h e e n v e l o p e o f t h e n o r m a l d i p o l e a b s o r p t i o n l i n e s p e c t r u m . I n t h e c a s e o f h y d r o g e n , w h e r e t h e s p a c i n g b e t w e e n t h e r o t a t i o n a l e n e r g y l e v e l s i s w i d e , t h e c o l l i s i o n i n d u c e d a b s o r p t i o n s p e c t r u m s h o w s b r o a d b u t d i s t i n c t r o t a t i o n a l t r a n s i t i o n s . A c o n s i d e r a b l e b o d y o f l i t e r a t u r e now e x i s t s on t h e t o p i c o f c o l l i s i o n i n d u c e d a b s o r p t i o n b o t h o f an e x p e r i m e n t a l a n d t h e o r e t i c a l n a t u r e . 4 At c e r t a i n i n t e r m o l e c u l a r d i s t a n c e s , the f o r c e between two m o l e c u l e s i s a t t r a c t i v e and they may be bound t o g e t h e r t o form a dimer, or Van der Waals m o l e c u l e . The dimer can p o s s e s s an e l e c t r i c d i p o l e moment, j u s t as a c o l l i d i n g p a i r does, w i t h the d i s t i n c t i o n t h a t i t i s "permanent" p r o v i d e d t h e dimer i s not d i s s o c i a t e d . The hydrogen dimer spectrum has r e l a t i v e l y s harp a b s o r p t i o n l i n e s a t the v i b r a t i o n a l and r o t a t i o n a l f r e q u e n c i e s of the i n d i v i d u a l m o l e c u l e s , accompanied by s a t e l l i t e l i n e s due t o the energy l e v e l s t r u c t u r e of the dimer i t s e l f . The d i s s o c i a t i o n energy of dimers i s low, r o u g h l y e q u a l t o the depth of the i n t e r m o l e c u l a r p o t e n t i a l : f o r ( H ^ ) z i t i s 2.5 cm ' , f o r ( 0 ^ ) ^ i t i s 87 cm ' ( 1 ) . Dimers have a l o n g l i f e t i m e o n l y a t low te m p e r a t u r e s and low d e n s i t i e s where the, k i n e t i c energy of t h e m o l e c u l e s i s low and c o l l i s i o n s a r e i n f r e q u e n t . Dimer a b s o r p t i o n has been o b s e r v e d i n the l a b o r a t o r y i n the fundamental r o t a t i o n - v i b r a t i o n band of hydrogen ( 2 ) ( 3 ) a t low te m p e r a t u r e s (~20K), and low d e n s i t i e s (~2 Amagat), and r e c e n t l y (H^)^ f e a t u r e s have been i d e n t i f i e d i n the r o t a t i o n a l band of the f a r - i n f r a r e d s p e c t r a of J u p i t e r and S a t u r n ( 4 ) ( 5 ) . In t h i s t h e s i s p r e l i m i n a r y measurements a r e r e p o r t e d of the f a r - i n f r a r e d a b s o r p t i o n spectrum of l i q u i d n i t r o g e n and l i q u i d oxygen. These measurements have been made over the f r e q u e n c y range 5 t o 70 cm 1 u s i n g a F o u r i e r t r a n s f o r m s p e c t r o m e t e r d e s i g n e d t o measure t h e spectrum of the s u b m i l l i m e t e r cosmic background r a d i a t i o n . A l t h o u g h l i q u i d 5 n i t r o g e n has a l r e a d y been s t u d i e d , t h e r e a r e not i n f a c t good measurements of the a b s o r p t i o n c o e f f i c i e n t , p a r t i c u l a r l y a t low f r e q u e n c i e s . The f a r - i n f r a r e d a b s o r p t i o n spectrum of l i q u i d oxygen has not been p r e v i o u s l y been r e p o r t e d . A r e v i e w of the t h e o r y of c o l l i s i o n i n d u ced a b s o r p t i o n , and a c a l c u l a t i o n of the e x p e c t e d a b s o r p t i o n i n t e n s i t i e s of oxygen and n i t r o g e n by q u a d r u p o l a r i n d u c e d d i p o l e moments a r e p r e s e n t e d i n Ch a p t e r I I . The e x p e r i m e n t a l p r o c e d u r e s and r e s u l t s a r e d e s c r i b e d i n Chapter I I I . The o r i g i n a l i n t e n t of t h i s work was t o examine the f a r -i n f r a r e d s p e c t r u m of low t e m p e r a t u r e , low p r e s s u r e , hydrogen gas over t h e f r e q u e n c y range 20 - 200 cm f o r the presence of d i m e r s . In o r d e r t o do t h i s a low temp e r a t u r e m u l t i p l e pass o p t i c a l a b s o r p t i o n c e l l was d e s i g n e d . T h i s c e l l p r o v e d t o be q u i t e complex and c o n s t r u c t i o n has o n l y now s t a r t e d . The c e l l d e s i g n i s p r e s e n t e d i n Chapter IV. 1.2 A s t r o p h y s i c a l A p p l i c a t i o n s Of M o l e c u l a r S p e c t r o s c o p y The r e m a i n d e r of t h i s c h a p t e r i s a survey of a r e a s i n a s t r o p h y s i c s where a b s o r p t i o n of r a d i a t i o n by homonuclear d i a t o m i c m o l e c u l e s v i a c o l l i s i o n i n d u c e d d i p o l e moments or dimers i s an i m p o r t a n t p h y s i c a l mechanism. Both t h e s e mechanisms a s e x h i b i t e d by hydrogen, n i t r o g e n and r a r e gas m i x t u r e s , a r e p a r t i c u l a r l y r e l e v a n t t o the s t u d y of i n f r a r e d s p e c t r a of t h e o u t e r p l a n e t s and t h e i r s a t e l l i t e s which have atmospheres. These moons a r e not massive enough t o r e t a i n 6 hydrogen, so t h e i r atmospheres are composed p r i m a r i l y of n i t r o g e n and methane, and i n t e r p r e t a t i o n of t h e i r i n f r a r e d s p e c t r a i n v o l v e s c o l l i s i o n i n d u ced a b s o r p t i o n by gaseous and l i q u i d n i t r o g e n . A b r i e f d i s c u s s i o n of work i n t h e s e a r e a s f o l l o w s . Hydrogen i s the dominant c o n s t i t u e n t element of the p l a n e t s J u p i t e r , S a t u r n , Uranus, and Neptune, and c o l l i s i o n i nduced a b s o r p t i o n has been observed i n the m i d - i n f r a r e d s p e c t r a of Uranus and J u p i t e r ( 6 ) . The f a r - i n f r a r e d spectrum of J u p i t e r (7) shows d i s c r e t e a b s o r p t i o n l i n e s due t o r o t a t i o n a l t r a n s i t i o n s of ammonia from 100 - 250 cm ' and then a b r o a d a b s o r p t i o n from 300 - 450 cm ' due t o c o l l i s i o n i n d u c ed a b s o r p t i o n c e n t r e d on the S o ( 0 ) hydrogen l i n e a t 354 -7 cm . The a ssumption u n d e r l y i n g the f a r - i n f r a r e d r e s u l t s i s t h a t the p l a n e t i s a c t i n g as a b l a c k b o d y s o u r c e a t Te^f = 125K, and the a b s o r b i n g gas l i e s i n an a t m o s p h e r i c t e m p e r a t u r e i n v e r s i o n l a y e r above the p l a n e t . These p l a n e t a r y s p e c t r a , i n c o n j u n c t i o n w i t h l a b o r a t o r y measurements of c o l l i s i o n induced a b s o r p t i o n by gases, y i e l d i n f o r m a t i o n about the c o m p o s i t i o n , p r e s s u r e , and t e m p e r a t u r e of the p l a n e t ' s atmospheres. The r e c e n t Voyager i n t e r p l a n e t a r y probes have measured i n f r a r e d s p e c t r a over the range 180 - 1800 cm ' , of J u p i t e r , S a t u r n , and t h e i r moons a t v e r y c l o s e range, f r e e of the s t r o n g i n f r a r e d a b s o r p t i o n of the e a r t h ' s atmosphere ( 8 ) ( 9 ) ( 1 0 ) ( 1 1 ) . These s p e c t r a show d i s c r e t e r o t a t i o n a l l i n e s of ammonia (180-250 cm ' ) , v i b r a t i o n a l l i n e s of methane (1100-7 1300 cm ), and a broad c o l l i s i o n i nduced a b s o r p t i o n band of hydrogen from 300 - 700 cm '. Hydrogen dimers have been i d e n t i f i e d i n the s p e c t r a of J u p i t e r and S a t u r n a t the S o ( 0 ) l i n e a t 354 cm ' and a t the S 0 ( 1 ) l i n e a t 587 cm 1 . The low t e m p e r a t u r e s , low p r e s s u r e s and v e r y l o n g p a t h l e n g t h s p r e s e n t i n t h e s e p l a n e t ' s atmospheres p r o v i d e an i d e a l environment f o r the o b s e r v a t i o n of dimer a b s o r p t i o n . Another r e g i o n of space i n which d i m e r s might be e x p e c t e d t o form i s w i t h i n m o l e c u l a r c l o u d s i n our g a l a x y . Here the d e n s i t y i s low, the temperature i s 20 - 60K, and hydrogen dimers can be e x p e c t e d t o have a l o n g l i f e t i m e . A l t h o u g h the d e n s i t y of a m o l e c u l a r c l o u d i s q u i t e low, an o p t i c a l p a t h l e n g t h t h r o u g h i t can be e x t r e m e l y l o n g . R a d i a t i o n p a s s i n g t h r o u g h such a c l o u d might be absorbed by d i m e r s , but t h i s remains unobserved. I t has been suggested t h a t a s u b m i l l i m e t e r measurement of the cosmic background r a d i a t i o n spectrum i n the d i r e c t i o n of a m o l e c u l a r c l o u d might be d i s t o r t e d by dimer or c o l l i s i o n i n d u ced e f f e c t s . S a t u r n ' s moon T i t a n ( s u r f a c e temperature ~95K) i s w e l l known as a s a t e l l i t e w i t h an atmosphere. The Voyager space probe has a l s o t a k e n f a r - i n f r a r e d s p e c t r a of T i t a n and i n t e r p r e t a t i o n of t h e s e s p e c t r a has l e d t o the f o l l o w i n g p i c t u r e of T i t a n ' s atmosphere. The p r i m a r y a t m o s p h e r i c c o n s t i t u e n t i s n i t r o g e n w i t h methane perhaps p l a y i n g the r o l e of water i n our atmosphere, t h a t i s , methane forms c l o u d s i n the t r o p o s p h e r e , p r e c i p i t a t e s , and may form l i q u i d s or i c e on the s u r f a c e ( 1 2 ) . There i s an a t m o s p h e r i c c o l d t r a p (~70K) 8 i n the t r o p o s p h e r e i n which condensed n i t r o g e n d r o p l e t s might be found. Computer models r e q u i r e such d r o p l e t s of n i t r o g e n or methane t o account f o r the measured spectrum, as c o l l i s i o n i n d u c ed a b s o r p t i o n a l o n e i s not s u f f i c i e n t ( 1 3 ) . Neptune's moon T r i t o n ( s u r f a c e temperature ~73K) may a l s o have an atmosphere, s i n c e methane a b s o r p t i o n l i n e s have been d e t e c t e d i n i t s n e a r - i n f r a r e d spectrum ( 1 4 ) . In a d d i t i o n , a s t r o n g a b s o r p t i o n f e a t u r e has been d e t e c t e d a t 4628 cm ' , e x a c t l y a t the maximum of the n i t r o g e n f i r s t o v e r t o n e band ( 1 5 ) . To produce such a s t r o n g f e a t u r e , the n i t r o g e n must be dense and g i v e n T r i t o n ' s low te m p e r a t u r e , i t i s s uggested t h a t T r i t o n may be co v e r e d w i t h an ocean of l i q u i d n i t r o g e n . I t i s u n f o r t u n a t e t h a t the frequ e n c y range of the p r e s e n t l i q u i d N z spectrum (5 - 70 cm"') does not o v e r l a p w i t h the Voyager s p e c t r o m e t e r (180 - 1800 cm"'), as on August 24, 1989, i t w i l l pass w i t h i n 10,000 km of T r i t o n and may r e c o r d the f a r - i n f r a r e d c o l l i s i o n induced spectrum of l i q u i d n i t r o g e n . In any c a s e , i t w i l l be e x c i t i n g t o see i f the p r e s e n t i n v e s t i g a t i o n s w i l l be a p p l i c a b l e t o the Voyager r e s u l t s . The f o l l o w i n g s e c t i o n p r e s e n t s an o u t l i n e of the r e s t of t h i s work. Chapter I I d i s c u s s e s i n d e t a i l the t h e o r y of c o l l i s i o n i n d u c e d a b s o r p t i o n and a c a l c u l a t i o n i s made of the a b s o r p t i o n i n t e n s i t i e s due t o q u a d r u p o l a r i n d u c e d d i p o l e moments i n n i t r o g e n and oxygen. Chapter I I I d e s c r i b e s the e x p e r i m e n t a l a p p a r a t u s , a f a r - i n f r a r e d F o u r i e r t r a n s f o r m s p e c t r o m e t e r , w i t h p a r t i c u l a r a t t e n t i o n t o s p e c i a l f e a t u r e s 9 of the i n t e r f e r o m e t e r and the d a t a a n a l y s i s . R e p o r t e d here a r e new o b s e r v a t i o n s of the f a r - i n f r a r e d a b s o r p t i o n of l i q u i d n i t r o g e n and l i q u i d oxygen, where the f a r - i n f r a r e d oxygen spectrum has not p r e v i o u s l y been p u b l i s h e d . F i n a l l y , Chapter •IV d i s c u s s e s the d e s i g n of a low t e m p e r a t u r e m u l t i p l e pass a b s o r p t i o n c e l l i n t e n d e d f o r f a r - i n f r a r e d o b s e r v a t i o n s of hydrogen d i m e r s . 10 I I . THE THEORY OF COLLISION INDUCED ABSORPTION 2.1 Review Of The Theory The f o l l o w i n g i s a review of the t h e o r y of c o l l i s i o n i n d u c ed a b s o r p t i o n i n a gas. I t i s ta k e n p r i m a r i l y from Van Kranendonk and K i s s ( 1 6 ) , and a l s o from r e f e r e n c e s ( 1 7 ) ( 1 8 ) ( 1 9 ) . Elements of the t h e o r y which a r e p e r t i n e n t t o l i q u i d s a r e emphasized, but an a n a l y s i s of c o l l i s i o n induced a b s o r p t i o n i n l i q u i d s per se does not c u r r e n t l y e x i s t . T h i s d i s c u s s i o n c o n c l u d e s w i t h a d e s c r i p t i o n of the c a l c u l a t i o n of the r e l a t i v e s t r e n g t h s of unbroadened r o t a t i o n a l a b s o r p t i o n l i n e s of n i t r o g e n and oxygen. L a t e r i n Chapter I I I , these c a l c u l a t e d l i n e i n t e n s i t i e s a r e compared t o the e x p e r i m e n t a l r e s u l t s . S t a r t i n g from an e x p e r i m e n t a l p e r s p e c t i v e , the a b s o r p t i o n c o e f f i c i e n t measured i s A(cT) which i s d e f i n e d as: where 0* i s the f r e q u e n c y , i n cm" , 1 i s the l e n g t h of the sample c e l l , I a ( c r ) i s the background spectrum, and I$( cr) i s the sample spectrum. The i n t e g r a t e d a b s o r p t i o n c o e f f i c i e n t ex i s : /. where t h i s i n t e g r a l i s taken over the e n t i r e a b s o r p t i o n band. The i n t e g r a t e d a b s o r p t i o n c o e f f i c i e n t per wav e l e n g t h °< i s : A(cr) = J - in L Is«r) (2.1 ) (2.2) (2.3) 11 where A ( ^ ) i s the a b s o r p t i o n c o e f f i c i e n t per wav e l e n g t h , A ( t T ) = Xk{Cf). The i n t e g r a t e d a b s o r p t i o n c o e f f i c i e n t per wave l e n g t h i s a l s o c a l l e d the i n t e g r a t e d i n t e n s i t y . The a b s o r p t i o n c o e f f i c i e n t a s s o c i a t e d w i t h a s p e c i f i c d i p o l e t r a n s i t i o n i s g i v e n by: (19) A if (cr) = i l l cr^ in-tf) l ^ t f ( c r - * / ) . ( 2 . 4 ) 3nC ]/ if-Here Cr i s the f r e q u e n c y , V i s the volume, P i and Py the Boltzmann f a c t o r s ( d i s c u s s e d l a t e r ) f o r the i n i t i a l and f i n a l s t a t e s , /A i s the m a t r i x element of the d i p o l e moment of the system between the s t a t e s i and f , and ® = (E^ > -)/he where E-L and Ep a r e the e n e r g i e s of the i n i t i a l and f i n a l s t a t e s r e s p e c t i v e l y . The i n t e g r a t e d i n t e n s i t y i n the gas f o r a s p e c i f i c r o t a t i o n a l t r a n s i t i o n i s : Z(r,r') - C < (PrPt-Pr'Pt-) «rt'u I rt>T where C =4 77"2/3hc, and r and r ' a r e the i n i t i a l and f i n a l r o t a t i o n a l s t a t e s , t and t ' a r e the i n i t i a l and f i n a l t r a n s l a t i o n a l s t a t e s , P i s the Boltzmann f a c t o r , and /4 i s the d i p o l e moment which i s a f u n c t i o n of the m o l e c u l e ' s o r i e n t a t i o n s and p o s i t i o n s . The summation t a k e s p l a c e over p a i r s of s t a t e s f o r which E r + Et< E r'+ Et', and i f the r o t a t i o n a l l i n e r -» r ' i s g r e a t e r than z e r o f r e q u e n c y , t h i s sum can be extended over a l l s t a t e s t , t ' . The t r a n s l a t i o n a l a s p e c t of the i n t e n s i t y i s t a k e n i n t o account by c o n s i d e r i n g 1 2 rotational transitions in a fixed configuration of molecules, and then averaging over a l l configurations, by the inclusion of a configurational distribution function. The c o l l i s i o n induced integrated intensity can be written in powers of the density n = N/V , where N is the number of molecules and V is the volume. C< - cX, n + <*». Y\ -r . . . C*i is the binary absorption coefficient, ocx is the ternary absorption coefficient etc. For low density gases, only binary collisions need to be considered, however for liquids, interactions are probably taking place between many molecules and this assumption is not correct. The binary absorption- coefficient for a specific rotational line B is then: £,05) = ± C (Pr-Pr')J iMrr' ( j O f ^ o f i ? ) cfX (2.5) The expectation value of the total dipole moment in eqn. (2.5) is now written as an integral over the matrix elements of the pair dipole moment times the pair distribution function. A r r ' ( R ) = < r - / | / M f w I y 3 » / ? ) | r > (2.6) is the matrix element of the pair dipole moment which is a function of the molecules orientations t^>\ , u)^ , and separation R. g0(R) is the low density pair distribution 13 f u n c t i o n of the m o l e c u l e s . At h i g h t e m p e r a t u r e s i t i s e q u a l t o : exp(-V(R/d)/kT) , where V(R/d) i s the i n t e r m o l e c u l a r p o t e n t i a l , f o r i n s t a n c e the Lennard-Jones p o t e n t i a l , where d here i s the Lennard-Jones m o l e c u l a r d i a m e t e r . Now examine the m a t r i x element of the d i p o l e moment M r r / ( R ) . The s i t u a t i o n i s d e p i c t e d i n the f o l l o w i n g d r a w i n g . t 1 z The i n d uced d i p o l e of the p a i r i s a f u n c t i o n of t h e i r d i s t a n c e a p a r t and t h e i r r e l a t i v e o r i e n t a t i o n s t o an a x i s between t h e i r c e n t r e s of mass, where. CO, = (©,,$) , and = The p a i r d i p o l e moment /T(tO|,i*L*) can be w r i t t e n i n terms of the s p h e r i c a l harmonics. K = 0,±1 r e f e r s t o components of i n a s p h e r i c a l c o o r d i n a t e system where 0 c o r r e s p o n d s t o the z a x i s which l i e s a l o n g R, i l r e f e r t o bases c o r r e s p o n d i n g t o the d i r e c t i o n s ( X - ' / ) . The (X,/*, ^t/it) are the c o e f f i c i e n t s of the d i p o l e moment i n the b a s i s of the s p h e r i c a l h a rmonics. The r o t a t i o n a l p a r t of the w a v e f u n c t i o n of a two m o l e c u l e system i s : 14 ^ ~ (fii)y£''(i5>) t h u s I r> = ) J,m,Ta Wx> i n eqn. ( 2 . 6 ) , >^zm2. r e f e r t o the a n g u l a r momentum and the p r o j e c t i o n of of the a n g u l a r momentum p e r p e n d i c u l a r t o "R f o r m o l e c u l e s 1 and 2. Eqn. (2.6) f o r the d i p o l e moment m a t r i x elements i s now: A V r ' (X) = < J", I n t e g r a t i n g over the i n i t i a l and f i n a l s t a t e s of a n g u l a r momentum u s i n g the e x p a n s i o n of /X i n t o s p h e r i c a l harmonics y i e l d s the d i p o l e moment m a t r i x e lements. From t h i s i n t e g r a t i o n and the p r o p e r t i e s of the s p h e r i c a l harmonics, the s e l e c t i o n r u l e s f o r the a l l o w e d - a n g u l a r momentum t r a n s i t i o n s a r e o b t a i n e d . These s e l e c t i o n r u l e s y i e l d non-z e r o d i p o l e m a t r i x elements o n l y when \ and hz. have the v a l u e s : 0, 2, 4, w i t h the r e s t r i c t i o n t h a t X ; and X 2 cannot s i m u l t a n e o u s l y e q u a l z e r o . A l l o w e d r o t a t i o n a l t r a n s i t i o n s a r e t h e r e f o r e from J-*J+2, J+4,...,. U s i n g t h e s e d i p o l e m a t r i x e lements, and o n l y t a k i n g the e x p a n s i o n i n the s p h e r i c a l harmonics t o the Xt , X* = 2 terms, the b i n a r y a b s o r p t i o n c o e f f i c i e n t i s o b t a i n e d from eqn. (2.5) The b i n a r y a b s o r p t i o n c o e f f i c i e n t oZt (B) i s a sum of s i n g l e r o t a t i o n a l t r a n s i t i o n s and double r o t a t i o n a l t r a n s i t i o n s . S i n g l e t r a n s i t i o n s a r e when one m o l e c u l e of the c o l l i d i n g p a i r goes from J-*J+2 and the o t h e r makes no t r a n s i t i o n . Double t r a n s i t i o n s a r e when b o t h m o l e c u l e s make t r a n s i t i o n s : J,-*J,+2, J^-^J^+2. For s i n g l e t r a n s i t i o n s the 15 b i n a r y a b s o r p t i o n c o e f f i c i e n t i s : O f . f j - j = C L(J)[lo(Z0) + L'I*(Z2)] ( 2 - 8 ) The J dependent f u n c t i o n s L ( J ) and L' a r i s e from the i n t e g r a t i o n over the w a v e f u n c t i o n s and the d i p o l e moment i n the s p h e r i c a l b a s i s . L(J) - i 2 (J,J+i) [ ?{j) - P(j+z)] l' = £ L a ( J J ) PC J ) J=o Uhtre. Lx CJ,J*-±) = 3(3"H)(J>iJ & L 2(J,J) = J{J+\){2T+\) I C (X ( X^) i s the r e m a i n i n g i n t e g r a l over the r a d i a l dependence of the c o e f f i c i e n t s of the d i p o l e moment and the p a i r d i s t r i b u t i o n f u n c t i o n . where X,, A i a re 0 or 2 . The b i n a r y a b s o r p t i o n c o e f f i c i e n t f o r double t r a n s i t i o n s i s : Z,(J-,jJI) = C [ I - £ < f ( j , , J 4 ) L ( J , , J * ) 7 o f i 2 j ( 2 . 9 ) W h e r e U j , , j J = 1* (J,j J,+2) LX(JZLJX*2) X [P(J,)P(JJ - P(T,*2)P(Jx+lj} The d i p o l e moment c o e f f i c i e n t s DK(X(//<,Xz/^) a r e o b t a i n e d from the d i p o l e i n d u c e d i n one m o l e c u l e due t o t h e q u a d r u p o l a r f i e l d of the o t h e r m o l e c u l e a c t i n g upon the 16 p o l a r i z a b i l i t y of the f i r s t m o l e c u l e . The f o l l o w i n g i s an a s i d e which d i s c u s s e s the p h e n o m e n o l o g i c a l b a s i s f o r the s e c o e f f i c i e n t s . The d i p o l e moment /A i n a p o l a r i z a b l e d i e l e c t r i c medium i s o b t a i n e d from: where o<l i s the p o l a r i z a b i l i t y t e n s o r and E t h e e l e c t r i c f i e l d . The e l e c t r i c f i e l d at a p o i n t i n space i s g i v e n by: The p o t e n t i a l a t m o l e c u l e 2 due t o the charge d i s t r i b u t i o n of m o l e c u l e 1 which i s a t . a d i s t a n c e R can be w r i t t e n as a m u l t i p o l e e x p a n s i o n : (20) The d r a w i n g below e x p l a i n s the p h y s i c a l s i t u a t i o n . R i s the d i s t a n c e between the m o l e c u l e s , f i s the charge d e n s i t y of m o l e c u l e 1, r i s the d i s t a n c e from an o r i g i n a t the c e n t r e of mass of m o l e c u l e 1 t o a volume element d T , i s the a n g l e between R and r", and Pn a r e the Legendre p o l y n o m i a l s . The i n t e g r a l i s over the volume of m o l e c u l e 1. 17 As p r e v i o u s l y s t a t e d t h e r e i s no d i p o l e a s s o c i a t e d w i t h homonuclear d i a t o m i c m o l e c u l e s , so the f i r s t s i g n i f i c a n t term i s t h i s e x p a n s i o n i s the q u a d r u p o l a r term, V(i) = JLj rzPz(cose)^zr = _I_ f rl ( I cos*e-±)p For d i s c r e t e c h a r g e s , the quadr u p o l e moment becomes an e x p e c t a t i o n v a l u e . (19) Q = < $L ei n z Fz (cose;)} i where e'L , r t*, Ol , are the magnitude, and p o l a r c o o r d i n a t e s of the i t h charge from an o r i g i n a t the c e n t r e of mass of mol e c u l e 1. The magnitude of the e l e c t r i c f i e l d a t m o l e c u l e 2 due t o the q u a d r u p o l a r p o t e n t i a l of m o l e c u l e 1 i s : \EU)1 - - L - a The magnitude of the induced d i p o l e moment of m o l e c u l e 2 i s the n : where CX i s the average p o l a r i z a b i l i t y CX = -I (2.<*1 + <*u ). S i n c e the p o l a r i z a b i l i t y i s a t e n s o r , the d i p o l e moment a l s o depends on the a n i s o t r o p y of the p o l a r i z a b i l i t y 2 . I f the q u a d r u p o l a r f i e l d of each m o l e c u l e of the p a i r i n d u c e s a d i p o l e i n the o t h e r , the net d i p o l e moment of the p a i r i s /A =/U,+ /u i. S i n c e the e l e c t r i c f i e l d of a quadr u p o l e 18 r o t a t e s t w i c e as f a s t as t h e m o l e c u l e , t h e i n d u c e d d i p o l e moment w i l l o s c i l l a t e a t t w i c e the r o t a t i o n a l f r e q u e n c y . T h i s demonstrates h e u r i s t i c a l l y , the s e l e c t i o n r u l e s t h a t l i g h t w i l l be absorbed by d i p o l e moment t r a n s i t i o n s of A J = 2 . The c o e f f i c i e n t s a r e g i v e n by VanKranendonk and K i s s a s : Do (2000) - i o<Q. Z>, (ZIOO) - ~3 <* Q D, inzo) = -±/T VQ D, (i2z-i) =-TT la /*- IS R* and 10 o t h e r c o e f f i c i e n t s from the symmetry p r o p e r t i e s of the D K c o e f f i c i e n t s . The 1/R+ , , and Q dependence of the d i p o l e moment m a t r i x e l e m e n t s i s c l e a r . $ i s the a n i s o t r o p y of the p o l a r i z a b i l i t y of the m o l e c u l e , X = ~ <X± . I n s e r t i n g these c o e f f i c i e n t s i n t o eqns. (2 .8) and (2.9) y i e l d s b i n a r y a b s o r p t i o n c o e f f i c i e n t s . T h i s d i s c u s s i o n o n l y c o v e r s the d i p o l e moment induced by the l o n g range q u a d r u p o l a r i n t e r a c t i o n . T h i s i s the dominant i n t e r a c t i o n f o r r o t a t i o n a l t r a n s i t i o n s of t h e m o l e c u l e s , but t h i s i s not the case f o r t h e t r a n s l a t i o n a l band, where the i s o t r o p i c o v e r l a p i n t e r a c t i o n induced d i p o l e moments a r e i m p o r t a n t ( 1 9 ) . To i n c l u d e s h o r t range o v e r l a p i n t e r a c t i o n s , the e l e c t r o n i c p a r t of t h e wave f u n c t i o n must be i n c l u d e d i n the c a l c u l a t i o n of the d i p o l e moment m a t r i x e l e m e n t s . The 19 c o e f f i c i e n t s o b t a i n e d v i a t h i s c a l c u l a t i o n have an e x p ( -R) dependence. A complete account of the c o l l i s i o n induced a b s o r p t i o n adds t h e s e c o e f f i c i e n t s t o the q u a d r u p o l a r c o e f f i c i e n t s i n the c a l c u l a t i o n of the r a d i a l dependent i n t e g r a l I 0 ( X, Az). 2.2 C a l c u l a t i o n Of A b s o r p t i o n I n t e n s i t i e s To compare the measured a b s o r p t i o n c o e f f i c i e n t s t o the c o l l i s i o n i n d u ced a b s o r p t i o n t h e o r y a c a l c u l a t i o n was made of the unbroadened r o t a t i o n a l a b s o r p t i o n l i n e s ( s t i c k spectrum) based on eqns. (2.8) and ( 2 . 9 ) . The p a i r d i s t r i b u t i o n f u n c t i o n g 0 ( R ) i s not known f o r the l i q u i d case so the r a d i a l •dependent i n t e g r a l s were not e v a l u a t e d i n t h i s c a l c u l a t i o n . The a b s o l u t e i n t e n s i t i e s of a b s o r p t i o n from t h i s c a l c u l a t i o n a re t h e r e f o r e not known, but the r e l a t i v e s t r e n g t h of a b s o r p t i o n i s p r o p o r t i o n a l t o the J dependence of the b i n a r y a b s o r p t i o n c o e f f i c i e n t . E q u a t i o n s (2.8) and (2.9) can be s i m p l i f i e d c o n s i d e r a b l y i f a b s o l u t e i n t e n s i t i e s a r e not r e q u i r e d . In p a r t i c u l a r the r a d i a l dependence of the b i n a r y a b s o r p t i o n c o e f f i c i e n t i s c o n s i d e r e d a c o n s t a n t . The s i m p l i f i e d form of the b i n a r y a b s o r p t i o n c o e f f i c i e n t i n terms of J f o r s i n g l e t r a n s i t i o n s i s : - [ ("af f L' s i ota)*] (2-10) where C< i s the average p o l a r i z a b i l i t y , Q i s the q u a d r u p o l e 20 moment, 6 i s the a n i s o t r o p y of the p o l a r i z a b i l i t y and L ( J ) and L' a r e d e f i n e d p r e v i o u s l y . The s i m p l i f i e d form of the b i n a r y a b s o r p t i o n c o e f f i c i e n t f o r double t r a n s i t i o n s i s : « , ( J . j J j - f / - i S ( l > , J j ] L(J.,JJ 1 1 (*Q)Z ( 2 ' n ) 2 ZZS where L ( J / , J ^ ) i s g i v e n above. Note t h a t the double t r a n s i t i o n s depend on o n l y the a n i s o t r o p y of the p o l a r i z a b i l i t y . For n i t r o g e n , the s i n g l e t r a n s i t i o n c o e f f i c i e n t s a r e about 1000 ti m e s l a r g e r than the double t r a n s i t i o n s c o e f f i c i e n t s f o r a temperature of 77K and f r e q u e n c i e s below about 60 cm '. The c o n s t a n t s which a re i m p o r t a n t f o r the c a l c u l a t i o n a r e t a b u l a t e d below: Q £X 2f N 2 1.46 * 10~ esu 1.74*10* cm 3 0 . 696 *1 0"" cm' -lb (ZZ) -31 -24 (2?) Ox 0 . 4 x 1 0 esu 1.59 x 10 cm' 1.1*10 cm 5 Table 1 - Quadrupole moment, p o l a r i z a b i l i t y , and a n i s o t r o p y of the p o l a r i z a b i l i t y f o r the n i t r o g e n and oxygen m o l e c u l e s A b s o r p t i o n l i n e i n t e n s i t i e s can be o b t a i n e d from the b i n a r y a b s o r p t i o n c o e f f i c i e n t s f o r comparison t o the measured a b s o r p t i o n c o e f f i c i e n t s . To o b t a i n a r e l a t i v e a b s o r p t i o n i n t e n s i t y , f o r a s p e c i f i c r o t a t i o n a l l i n e , t he b i n a r y a b s o r p t i o n c o e f f i c i e n t s a r e m u l t i p l i e d by the fr e q u e n c y 21 a s s o c i a t e d w i t h the r o t a t i o n a l t r a n s i t i o n . a(j") s, ex) + o - ( j , , j ; ) 5, (j,,^) (2.12) where cT(J) a r e the f r e q u e n c i e s of s i n g l e t r a n s i t i o n s and ^" ( J , ,JZ) a r e the f r e q u e n c i e s of double t r a n s i t i o n s . To complete the c a l c u l a t i o n of the s t i c k spectrum, the f r e q u e n c i e s of the v a r i o u s t r a n s i t i o n s must be o b t a i n e d . The energy s t a t e s of a d i a t o m i c v i b r a t i n g - r o t a t o r are d e s c r i b e d by a r o t a t i o n a l c o n s t a n t B, and a c e n t r i f u g a l d i s t o r t i o n c o n s t a n t D. B i s i n v e r s e l y p r o p o r t i o n a l t o the moment of i n e r t i a of the m o l e c u l e . The energy spectrum of a r i g i d r o t a t o r i s o b t a i n e d by m u l t i p l y i n g the e i g e n v a l u e s of the a n g u l a r momentum squared, J(J+1) by B. The spectrum of the v i b r a t i n g - r o t a t o r " d e v i a t e s from t h e r i g i d r o t a t o r spectrum because of the c e n t r i f u g a l d i s t o r t i o n of the m o l e c u l e and the a d d i t i o n a l f e a t u r e t h a t the i n t e r n u c l e a r s e p a r a t i o n i s not f i x e d but i s d e s c r i b e d by a p r o b a b i l i t y d i s t r i b u t i o n . The i n d e t e r m i n a n c y of the i n t e r n u c l e a r d i s t a n c e i s r e f e r r e d t o as the " z e r o p o i n t " energy of the m o l e c u l e . Both B and D a r e m o d i f i e d by the v i b r a t i o n a l s t a t e of t he m o l e c u l e . T h i s i s because the i n t e r n u c l e a r s e p a r a t i o n i s c h a n g i n g and t h e r e f o r e so i s t h e moment of i n e r t i a and c e n t r i f u g a l d i s t o r t i o n of the m o l e c u l e . The " r o t a t i o n a l terms" of the v i b r a t i n g - r o t a t o r i n the v i b r a t i o n a l ground s t a t e a r e : (24) F(J) Ac = Bo T<T+i) ~ D*J'<**')X ( 2 ' 1 3 ) 22 B Q i s the r o t a t i o n a l c o n s t a n t i n the v i b r a t i o n a l ground s t a t e . To f i r s t a p p r o x i m a t i o n , Bo = Be - <*e ( 0 + £ ) J u)htrt 0 = O . Be i s the r o t a t i o n a l c o n s t a n t of the m o l e c u l e c o r r e s p o n d i n g t o the e q u i l i b r i u m i n t e r n u c l e a r d i s t a n c e % . B e = h / B ^ d g , where I e i s the e q u i l i b r i u m moment of i n e r t i a . o(e. i s a c o n s t a n t r e p r e s e n t i n g the change i n i n t e r n u c l e a r s e p a r a t i o n . D D i s the c e n t r i f u g a l d i s t o r t i o n c o n s t a n t i n the v i b r a t i o n a l ground s t a t e . D e i s the e q u i l i b r i u m c e n t r i f u g a l c o n s t a n t , De = 4Be /cde • i s g i v e n a s : where the c o n s t a n t s (Ae , td«?(e, <*e r and B e a r e o b t a i n e d from t a b l e s of s p e c t r o s c o p i c m o l e c u l a r c o n s t a n t s . These c o n s t a n t s f o r n i t r o g e n and oxygen are t a b u l a t e d below ( 2 5 ) . ( a l l i n cm ) 23 B « e ^ e ^ e y f c B< -6 N- 1.9987 0.01781 2358.07 14.188 1.990 5.743*10 O z 1.44567 0.01579 1580.36 12.073 1.438 4.843«10"6 T a b l e 2 - R o t a t i o n a l c o n s t a n t s of the n i t r o g e n and oxygen m o l e c u l e s The f r e q u e n c y of l i g h t a bsorbed by a r o t a t i o n a l t r a n s i t i o n i s g i v e n by: The f r e q u e n c y of a double t r a n s i t i o n J / - * J , + 2 , J^-* J A+2, i s g i v e n by Cr = C, + cx where 0",, a r e c a l c u l a t e d from the above. F i n a l l y , the Boltzmann f a c t o r s P ( J ) i n t h i s c a l c u l a t i o n a re g i v e n by: - FIT) hc/kT PW « S ( T ) e (2.15) -F(T)hc/kT e J»0 D i v i d i n g by the sum of a l l Boltzmann f a c t o r s n o r m a l i z e s the temperature dependent p o p u l a t i o n d i s t r i b u t i o n . Here S ( J ) i s the degeneracy of a g i v e n r o t a t i o n a l s t a t e due t o t h e n u c l e a r s p i n s t a t i s t i c s of the m o l e c u l e s , t h i s i s d i s c u s s e d below. One l a s t f e a t u r e of the s t i c k spectrum i s t h e i n f l u e n c e of the n u c l e a r s p i n on t h e m o l e c u l a r a b s o r p t i o n spectrum. The t o t a l w a v e f u n c t i o n of a d i a t o m i c m o l e c u l e a l s o i n v o l v e s a 24 n u c l e a r s p i n p a r t . For a homonuclear m o l e c u l e , the t o t a l w a v e f u n c t i o n i s : ^ = ^ A/, Total electronic rotational nuc/tar I t must be symmetric w i t h r e s p e c t t o i n t e r c h a n g e of the n u c l e i i f the n u c l e i are bosons, and a n t i s y m m e t r i c i f the n u c l e i a r e f e r m i o n s . There a r e (21 + 1)2" p o s s i b l e n u c l e a r s p i n s t a t e s , (21 + 1 ) ( I + 1) of t h e s e s t a t e s a r e symmetric and (21 + 1)1 are a n t i s y m m e t r i c , where I i s the s p i n of the n u c l e u s . The n u c l e u s of n i t r o g e n has 14 p a r t i c l e s , the net n u c l e a r s p i n i n the ground s t a t e i s I = l . The n u c l e u s of oxygen has 16 p a r t i c l e s , the net n u c l e a r s p i n i n the ground s t a t e i s I = 0. Both n i t r o g e n and oxygen n u c l e i a r e bosons. The e l e c t r o n i c ground s t a t e of n i t r o g e n i s t h i s i s a symmetric w a v e f u n c t i o n (26) . The n u c l e u s of n i t r o g e n i s a boson which i s symmetric and i t i s r e q u i r e d t h a t the t o t a l w a v e f u n c t i o n be symmetric. S i n c e the even r o t a t i o n a l J s t a t e s a r e symmetric they combine w i t h the (21 + 1 ) ( I + 1) symmetric n u c l e a r s p i n s t a t e s and have a s t a t i s t i c a l weight of 6. The odd r o t a t i o n a l s t a t e s a r e a n t i s y m m e t r i c and combine w i t h the (21 + 1)1 a n t i s y m m e t r i c n u c l e a r s p i n s t a t e s and have a s t a t i s t i c a l weight of 3. T h e r e f o r e f o r n i t r o g e n , the l i n e i n t e n s i t i e s c a l c u l a t e d above a r e m u l t i p l i e d by 2 f o r even r o t a t i o n a l t r a n s i t i o n s . The e l e c t r o n i c ground s t a t e of oxygen i s which has an a n t i s y m m e t r i c w a v e f u n c t i o n (26 ) . The n u c l e u s of oxygen i s a boson which has a symmetric w a v e f u n c t i o n . T h e r e f o r e , t o 25 o b t a i n a symmetric t o t a l w a v e f u n c t i o n , the a n t i s y m m e t r i c n u c l e a r s p i n s t a t e s must be combined w i t h th e even J r o t a t i o n a l s t a t e s . The symmetric n u c l e a r s p i n s t a t e s a r e then combined w i t h the odd r o t a t i o n a l s t a t e s . The even r o t a t i o n a l l e v e l s have a s t a t i s t i c a l weight of (21 + 1 ) 1 or z e r o . The odd r o t a t i o n a l l e v e l s have a s t a t i s t i c a l w e i g h t of (21 + 1 ) ( I + 1) or 1. Hence, m o l e c u l a r oxygen, i n the e l e c t r o n i c ground s t a t e , o n l y e x i s t s i n odd r o t a t i o n a l energy l e v e l s , and the a b s o r p t i o n spectrum i s l i m i t e d t o f r e q u e n c i e s which c o r r e s p o n d t o odd r o t a t i o n a l t r a n s i t i o n s . The r e s u l t s of the r e l a t i v e i n t e n s i t i e s of the q u a d r u p o l a r induced s i n g l e t r a n s i t i o n a b s o r p t i o n l i n e s , a t a t e m p e r a t u r e of 77K, are d i s p l a y e d below. These r e s u l t s a r e a l s o d i s p l a y e d on the p l o t s of the measured a b s o r p t i o n c o e f f i c i e n t s , f i g s . 7 and 8. 26 NITROGEN SINGLE TRANSITIONS:FREQS, LINE INTENSITIES J FREQS. INTENTS. 0 11.9398 0.502182E- 01 1 19.8992 0.108585 2 27.8579 0.489118 3 35.8157 0.392025 4 43.7722 1.00000 5 51.7272 0.535227 6 59.6803 0.990866 7 67.6314 0.403938 8 75.5802 0.587287 9 83.5262 0.191948 10 91.4694 0.227040 1 1 99.4099 0.610225E- 01 12 107.346 0.598390E- 01 13 115.280 0.134175E- 01 14 123.208 0.110314E- 01 15 131.133 0.208214E- 02 16 139.053 0.144573E- 02 17 146.968 0.231081E- 03 18 154.878 0.136181E- 03 19 162.784 0.185100E- 04 20 170.683 0.929140E- 05 OXYGEN SINGLE TRANSITIONS:FREQS, LINE INTENSITIES J FREQS. INTENTS. 1 14.3793 0. 140019 3 25.8803 0.580474 5 37.3772 0.984951 7 48.8680 1.00000 9 60.3508 0.692051 1 1 71.8234 0.346924 13 83.2859 0.130268 15 94.7332 0.373910E- 01 17 106.166 0.831551E- 02 19 117.581 0.144622E- 02 T a b l e 3 - F r e q u e n c i e s and a b s o r p t i o n i n t e n s i t i e s of q u a d r u p o l a r i n d u c e d s i n g l e r o t a t i o n a l t r a n s i t i o n s i n n i t r o g e n and oxygen m o l e c u l e s , at 77K. 27 I I I . EXPERIMENTAL APPARATUS AND RESULTS The e x p e r i m e n t s d e s c r i b e d i n t h i s t h e s i s were performed i n c o n j u n c t i o n w i t h the i n i t i a l t e s t i n g of a r o c k e t borne, h e l i u m c o o l e d i n t e r f e r o m e t e r , d e s i g n e d t o measure the s u b i m i l l i m e t e r cosmic background r a d i a t i o n spectrum ( 2 7 ) . These t e s t s demonstrated t h a t the i n t e r f e r o m e t e r ' s o p t i c s , scan mechanism, and d a t a c o l l e c t i o n scheme worked a c c o r d i n g t o d e s i g n . In a d d i t i o n t o c o n f i r m i n g the i n t e r f e r o m e t e r o p e r a t i o n , e x p e r i m e n t s were undertaken t o measure the a b s o r p t i o n of room t e m p e r a t u r e and c o l d f a r - i n f r a r e d o p t i c a l m a t e r i a l s f o r use as f a r i n f r a - r e d d e t e c t o r f i l t e r s ( 2 8 ) . In the c o u r s e of these e x p e r i m e n t s , the a b s o r p t i o n c o e f f i c i e n t s of l i q u i d n i t r o g e n a n d ' l i q u i d oxygen were a l s o measured. . The f i r s t p a r t of t h i s c h a p t e r d e s c r i b e s the e x p e r i m e n t a l a p p a r a t u s and p r o c e d u r e . The second p a r t d i s c u s s e s the l i q u i d N^ and 0^ s p e c t r a . 3.1 E x p e r i m e n t a l A p p a r a t u s And P r o c e d u r e s The measurements were o b t a i n e d u s i n g the i n t e r f e r o m e t e r mentioned above as a l a b o r a t o r y F o u r i e r t r a n s f o r m s p e c t r o m e t e r . In g e n e r a l , a F o u r i e r t r a n s f o r m s p e c t r o m e t e r i s an i n s t r u m e n t which in d u c e s a v a r i a b l e p a t h d i f f e r e n c e between two o p t i c a l p a t h s , where the two l i g h t beams a r e then combined a t a d e t e c t o r . The s i g n a l g e n e r a t e d by the d e t e c t o r i s c a l l e d the i n t e r f e r o g r a m and i s p r o p o r t i o n a l t o the a u t o c o r r e l a t i o n f u n c t i o n of the i n t e n s i t y of the 28 e l e c t r o m a g n e t i c r a d i a t i o n i n c i d e n t on the i n t e r f e r o m e t e r . The power spectrum of the i n c i d e n t r a d i a t i o n i s o b t a i n e d from the F o u r i e r t r a n s f o r m of the i n t e r f e r o g r a m . The d e s i g n of an i n t e r f e r o m e t e r depends on what i s the most i m p o r t a n t parameter of the d e s i r e d spectrum: r e s o l u t i o n , s p e c t r a l bandwidth, a b s o l u t e i n t e n s i t y , e t c . The most i m p o r t a n t a s p e c t s of the cosmic background measurement are i n t e n s i t y c a l i b r a t i o n and wide s p e c t r a l range. Hence, the r o c k e t i n s t r u m e n t i s a p o l a r i z i n g d u a l i n p u t - d u a l o u t p u t i n t e r f e r o m e t e r , w i t h an ar e a s o l i d a n g l e product of about 0.1 cm 1 s t e r a d i a n . The advantage of t h i s d e s i g n i s t h a t the s i g n a l measured a t each d e t e c t o r i s p r o p o r t i o n a l t o the d i f f e r e n c e i n b r i g h t n e s s between the two i n p u t s . In the cosmic background e x p e r i m e n t , t h i s p e r m i t s the spectrum of the sky t o be compared d i r e c t l y w i t h t h a t of a bl a c k b o d y c a l i b r a t o r whose temp e r a t u r e can be set near 2.IK. The o p t i c a l p a th of the p o l a r i z i n g i n t e r f e r o m e t e r used i n t h i s work i s shown i n f i g . 1. L i g h t from a 600 C bl a c k b o d y so u r c e i s c o l l i m a t e d by a TPX l e n s , which p r o j e c t s a q u a s i - p a r a l l e l beam i n t o the i n t e r f e r o m e t e r . The beam e n c o u n t e r s a v e r t i c a l (out of the p i c t u r e p l a n e ) w i r e g r i d p o l a r i z e r A; a p p r o x i m a t e l y h a l f the beam i s t r a n s m i t t e d 1 ( p o l a r i z e d h o r i z o n t a l l y ) , and h a l f r e f l e c t e d 2 ( p o l a r i z e d v e r t i c a l l y ) . Beam 2 i s r e f l e c t e d o f f m i r r o r B and proceeds t o t h e w i r e g r i d b e a m s p l i t t e r C, whose w i r e s a r e i n c l i n e d o about 45 t o the p l a n e of the diagram. For each i n i t i a l beam 29 VARIABLE F i g u r e 1 - I n t e r f e r o m e t e r o p t i c a l p a t h Text t r a c e s l i g h t p a t h from blackbody s o u r c e t h r o u g h system. O p t i c a l components a r e : i n i t i a l p o l a r i z e r A, m i r r o r B, p o l a r i z i n g b e a m s p l i t t e r C, s c a n n i n g m i r r o r s D, m i r r o r E, f i n a l p o l a r i z e r F, and d e t e c t o r . 30 (1 or 2 ) , h a l f the beam i s t r a n s m i t t e d and h a l f r e f l e c t e d . The beam now r e f l e c t s o f f the t w i n 60 m i r r o r s D, which may be moved back and f o r t h , i n d i c a t e d by the a r r o w s . The o p o l a r i z a t i o n of the beam i s r o t a t e d 90 w i t h r e s p e c t t o the b e a m s p l i t t e r by r e f l e c t i o n o f f the t w i n m i r r o r s . A beam which was i n i t i a l l y r e f l e c t e d by the b e a m s p l i t t e r i s now t r a n s m i t t e d , l i k e w i s e a beam which was i n i t i a l l y t r a n s m i t t e d by the b e a m s p l i t t e r i s now r e f l e c t e d . The combined beams now r e f l e c t from m i r r o r E, and then e n c o u n t e r a n o t h e r v e r t i c a l w i r e g r i d , the a n a l y z i n g p o l a r i z e r F. A p p r o x i m a t e l y h a l f of the " t r a n s m i t t e d - r e f l e c t e d " beam i s t r a n s m i t t e d t h r o u g h t h i s p o l a r i z e r and combined w i t h h a l f of the " r e f l e c t e d -t r a n s m i t t e d " beam, which i s r e f l e c t e d by t h i s p o l a r i z e r . T h i s beam i s now composed of l i g h t from two d i f f e r e n t o p t i c a l p a t h s of d i f f e r e n t l e n g t h s , due t o the p o s i t i o n of the moving m i r r o r s . The l i g h t beam i s u n p o l a r i z e d , i t i s f o c u s s e d t o a d e t e c t o r and an i n t e r f e r o g r a m i s measured. T h i s d i s c u s s i o n t r a c e s t h e p a t h of o n l y h a l f the l i g h t from a s i n g l e i n p u t . I f b o t h i n p u t s a r e c o n s i d e r e d , the l i g h t a t each d e t e c t o r i s then a c o m b i n a t i o n of " r e f l e c t e d - t r a n s m i t t e d " and " t r a n s m i t t e d - r e f l e c t e d " l i g h t , from each i n p u t . The b e a m s p l i t t e r s were d e s i g n e d and c o n s t r u c t e d a t U.B.C., they a r e o p t i m i z e d f o r o p e r a t i o n i n the f r e q u e n c y range 0 - 200 cm . Each b e a m s p l i t t e r c o n s i s t s of 18/um g o l d p l a t e d t u n g s t e n w i r e spaced e v e r y 36/<m, t o form a w i r e g r i d . The r e s o l u t i o n of a F o u r i e r t r a n s f o r m i n t e r f e r o m e t e r i s p r o p o r t i o n a l t o the maximum p a t h l e n g t h d i f f e r e n c e between 31 the two o p t i c a l p a t h s . I f the i n t e r f e r o g r a m s a r e not a p o d i z e d b e f o r e F o u r i e r t r a n s f o r m i n g , the r e s o l u t i o n of the spectrum i s ACT = , where AC i s i n cm ' , and L i s the maximum p a t h l e n g t h d i f f e r e n c e i n cm. For t h i s i n t e r f e r o m e t e r , double s i d e d i n t e r f e r o g r a m s of 1024 p o i n t s were t r a n s f o r m e d y i e l d i n g a spectrum of 512 p o i n t s spanning a fre q u e n c y range of 0 - 235 cm 1 . The frequ e n c y s c a l e was c a l i b r a t e d by matching l i n e s i n the measured s p e c t r a t o known water vapor a b s o r p t i o n l i n e s . The r e s o l u t i o n of the s p e c t r a from d i g i t a l s ampling i s O - f 6 cm 1 . The f o l l o w i n g t a b l e c o n t a i n s i n f o r m a t i o n p e r t i n e n t t o the r e s o l u t i o n of t h i s i n t e r f e r o m e t e r . E x p e c t e d A c t u a l Max. p a t h d i f f e r e n c e Ah 1.16 cm 1109 x _ f _ /024 Z*.4$9 = 1,/Jcm # samples / scan 1067 1 1 09 ^}L per sample 21.8 yum 21.1 /<m Max. f r e q u e n c y 229 cm 235.0 cm -/ L i n e r e s o l u t i o n -i 0.54 cm 0.51 cm Ta b l e 4 - I n t e r f e r o m e t e r p a r a m e t e r s , as s p e c i f i e d i n the d e s i g n and as measured where t h e l i n e r e s o l u t i o n above i s d e s c r i b e d by the w i d t h of 32 a s i n e f u n c t i o n a t h a l f maximum (A^TuL ^* T h i s i s d i f f e r e n t from the r e s o l u t i o n as d e s c r i b e d by the f i r s t z e r o s of t h e s i n e f u n c t i o n o c c u r i n g a t A Cr = -L , as mentioned 2.L-above. The d e t e c t o r f o r the l a b o r a t o r y e x p e r i m e n t s was a s i l i c o n m o n o l i t h i c bolometer brought by Dr. Mark H a l p e r n from MIT ( 2 9 ) . T h i s d e t e c t o r c o n s i s t s b a s i c a l l y of a 5 mm square i o n i m p l a n t e d s i l i c o n wafer connected t o the l i q u i d h e l i u m r e s e r v o i r by t h i n t h e r m a l l y r e s i s t i v e l e g s . In o r d e r t o a b s o r b r a d i a t i o n i t has been c o a t e d w i t h a f i l m of bismuth t h e r e b y impedance matching the bolometer and f r e e space. S i n c e the d e t e c t o r i s p o o r l y c o u p l e d t o the h e l i u m bath i t s t e m p e r a t u r e i s s e n s i t i v e t o t h e r a d i a t i o n l o a d on i t . The e l e c t r i c a l r e s i s t a n c e of the bo l o m e t e r , n o m i n a l l y 1 M i l at 4.2K, i s v e r y t e m p e r a t u r e dependent and t h e r e f o r e , changes i n r a d i a t i v e power can be measured as v o l t a g e f l u c t a t i o n s , i f a c o n s t a n t c u r r e n t (~-10"^  amp.) i s passed through the d e v i c e . T h i s i s done here u s i n g a s p e c i a l c o o l e d p r e a m p l i f i e r . The b o l o m e t e r , b i a s r e s i s t o r , p r e a m p l i f i e r , and a f i l t e r wheel f o r c o l d o p t i c a l f i l t e r measurements, are a l l a t t a c h e d t o t he c o l d p l a t e of a m o d i f i e d I n f r a r e d L a b o r a t o r y h e l i u m dewar. L i g h t i s c o n c e n t r a t e d on the bolometer by a p o l y e t h y l e n e l e n s f o l l o w e d by a copper c o n d e n s i n g cone. C o l d o p t i c a l f i l t e r s were p l a c e d j u s t b e h i n d the l e n s t o l e s s e n the change i n t o t a l power absorbed by the bolometer upon i n s e r t i o n of the sample. These f i l t e r s d e f i n e the h i g h f r e q u e n c y c u t o f f of the e x p e r i m e n t s . The low frequ e n c y 33 c u t o f f i s 2.4 cm and i s d e f i n e d by the e x i t a p e r t u r e of the c o n d e n s i n g cone. The o p t i c a l f i l t e r s f o r the May 17, 1985 e x p e r i m e n t s ( h e r e a f t e r c a l l e d the low f r e q u e n c y e x p e r i m e n t s ) gave a h i g h f r e q u e n c y c u t o f f of 40 cm"' (chosen f o r d i e l e c t r i c f i l t e r measurements ( 2 8 ) ) . These f i l t e r s were: a p o l y e t h y l e n e l e n s , 1.05 mm t h i c k f l u o r o g o l d , 0.014" b l a c k p o l y e t h y l e n e , and a 1.94 t o 2.01 mm p l e x i g l a s s wedge. The o p t i c a l f i l t e r s f o r the May 30 e x p e r i m e n t s ( t h e h i g h f r e q u e n c y e x p e r i m e n t s ) gave a h i g h f r e q u e n c y c u t o f f of 80 cm ' . These f i l t e r s were: a p o l y e t h y l e n e l e n s , 0.005" b l a c k p o l y e t h y l e n e , 4 s h e e t s of 0.002" m y l a r , and 1.01 mm N a C l . The d a t a a q u i s i t i o n scheme f o r the l a b o r a t o r y i s c o n t r o l l e d by a PDP Micro-11 computer system. V o l t a g e s from the experiment are measured by an a n a l o g - d i g i t a l c o n v e r t e r (Analog D e v i c e s RT1-1250 1 2 - b i t , 32 c h a n n e l d e v i c e ) c o n t r o l l e d from an assembly language program run by the computer. The computer responds t o e x t e r n a l t r i g g e r s g e n e r a t e d by t h e moving m i r r o r system, and each i n t e r f e r o g r a m i s sampled about 1110 t i m e s . F o r the h i g h f r e q u e n c y e x p e r i m e n t s , a c a p a c i t a n c e gauge mounted d i r e c t l y on the moving m i r r o r c a r r i a g e measures the m i r r o r d i s p l a c e m e n t . The s i g n a l from t h i s gauge i s sampled i m m e d i a t e l y a f t e r the d e t e c t o r s i g n a l . Once the e x p e r i m e n t s a r e completed and the d a t a has been w r i t t e n t o t a p e , the d a t a a n a l y s i s i s done on the U.B.C. main computer, an Amdahl V8. The i n t e r f e r o g r a m s a r e F o u r i e r 34 t r a n s f o r m e d and the r e s u l t i n g s p e c t r a a r e averaged. P r o c e d u r e s used i n the F o u r i e r t r a n s f o r m p r o c e s s may d i f f e r , and i t i s w o r t h w h i l e t o f o l l o w i n d e t a i l the proced u r e f o r t h i s work. The raw d a t a c o n s i s t s of i n t e r f e r o g r a m s of 1110 samples, and t h e r e were u s u a l l y 28 i n t e r f e r o g r a m s per d a t a s e t . The f i r s t s t e p i n the a n a l y s i s i s t o f i n d t he 28 maxima of- the d a t a s e t , near t h e z e r o p a t h d i f f e r e n c e of each i n t e r f e r o g r a m . 1024 p o i n t i n t e r f e r o g r a m s a r e o b t a i n e d by s e l e c t i n g 512 p o i n t s on e i t h e r s i d e of each maximum. Each i n t e r f e r o g r a m i s complex F o u r i e r t r a n s f o r m e d , r e s u l t i n g i n 512 p a i r s of r e a l ( c o s ) and i m a g i n a r y ( s i n e ) F o u r i e r c o e f f i c i e n t s . These a r e used t o c a l c u l a t e a modulus and a phase. F i g . 2 below, t a k e n from the a n a l y s i s of a t y p i c a l background r u n , shows t h e i n t e r f e r o g r a m , and the modulus and the phase a n g l e as a f u n c t i o n of f r e q u e n c y . I f t he i n t e r f e r o g r a m were p e r f e c t l y symmetric, and i f the maximum -sample c o i n c i d e d e x a c t l y w i t h the z e r o p a t h d i f f e r e n c e , the s i n e c o e f f i c i e n t s would be z e r o and the spectrum would e q u a l s i m p l y the c o s i n e t r a n s f o r m c o e f f i c i e n t s . In r e a l i t y n e i t h e r of t h e s e c o n d i t i o n s a r e f u l f i l l e d . Phase s h i f t s i n t r o d u c e d by the d e t e c t o r - a m p l i f i e r c o m b i n a t i o n cause an asymmetry i n the i n t e r f e r o g r a m , and the sa m p l i n g i s not e x a c t l y s y n c h r o n i z e d w i t h the z e r o p o i n t of the moving m i r r o r system. To o b t a i n a spectrum c o r r e c t e d f o r t h e s a m p l i n g e r r o r , the c o s i n e c o e f f i c i e n t s a r e mapped onto the x a x i s i n a two 35 d i m e n s i o n a l C a r t e s i a n system, and the s i n e c o e f f i c i e n t s a r e mapped mapped on the y a x i s . These axes a r e o r t h o g o n a l t o the fr e q u e n c y a x i s . The i n t e n s i t y of the spectrum a t a g i v e n f r e q u e n c y i s a v e c t o r V i n t h i s x-y p l a n e . T h i s i s p i c t u r e d below, where the sa m p l i n g e r r o r i s c o n s i d e r e d t o be a "phase a n g l e " $f t h a t V makes w i t h the x a x i s . \ v v y • V \ X \ ^ Yx where $f = a r c t a n / _ ^ V ) , d e f i n e d over 0 27T. \ Vx I To reduce the phase a n g l e t o z e r o , the components of V a r e found i n a r o t a t e d c o o r d i n a t e system. The components of a v e c t o r i n a r o t a t e d c o o r d i n a t e system a r e : x' = x c o s 0 + y s i n 0 y' = -x s i n c ^ + y cos $ The new c o o r d i n a t e system i s o b t a i n e d by r o t a t i n g t h rough the phase a n g l e <Pf so t h a t the x' a x i s l i e s a l o n g the s p e c t r a l i n t e n s i t y V. In t h i s new c o o r d i n a t e system V has a non-zero component o n l y a l o n g the x' a x i s . 36 y x / = v x c o s ^ + v ^ s i n ^ (3.1) In the computer a n a l y s i s , the phase a n g l e s 0f a r e f i t t e d w i t h p o l y n o m i a l i n the f r e q u e n c y over the s p e c t r a l range where the s e c o e f f i c i e n t s a r e not f l u c t u a t i n g w i l d l y , t h a t i s where t h e r e i s a p p r e c i a b l e i n t e n s i t y . V^' i s found from eqn. ( 3 . 1 ) , where 0f i s o b t a i n e d from the p o l y n o m i a l f i t t o the measured phase. T h i s p r o c e d u r e i s e q u i v a l e n t t o s y m m e t r i z i n g the i n t e r f e r o g r a m , but i s more r a p i d from a c o m p u t a t i o n a l p o i n t of view, as i t does not i n v o l v e a c o n v o l u t i o n . U s i n g the a c t u a l phase ang l e fif. would e x a c t l y symmetrize the i n t e r f e r o g r a m , but u s i n g the f i t t e d phase p r o v i d e s a low r e s o l u t i o n phase c o r r e c t i o n t o the i n t e r f e r o g r a m . F i g . 3 shows the p o l y n o m i a l f i t t o the phase and the spectrum V y / ( C ) . May 30/85 F i g u r e 2 - I n t e r f e r o g r a m , modulus spectrum and phase ang le as a f u n c t i o n of f requency 39 The spectrum o b t a i n e d Vx'(CT) can be e i t h e r p o s i t i v e or n e g a t i v e . T h i s d i f f e r s from the modulus spectrum which i s the magnitude of j v / = JVx* + Vy3' and i s always p o s i t i v e . The n o i s e i n V ^ ' ( (X ) i s the l i n e a r sum of the n o i s e i n Vx and Vy , whereas the n o i s e i n the modulus i s added i n q u a d r a t u r e . When s p e c t r a Vy'iC) a r e ave r a g e d the s i g n a l t o n o i s e r a t i o improves; when s p e c t r a ) v | a r e averaged the base l e v e l i n c r e a s e s because the n o i s e i s always p o s i t i v e and t h e r e f o r e the i n t e n s i t i e s o b t a i n e d a r e not c o r r e c t . A problem i n the performance of the i n t e r f e r o m e t e r was d i s c o v e r e d d u r i n g t h e s e t e s t s . E x p e r i m e n t s were conducted w i t h an o p t i c a l h i g h f r e q u e n c y c u t o f f of about 40 cm ' , and ye t s p e c t r a appeared a t 90, 150, and 200 cm ' . The peak i n t e n s i t i e s of the " a l i a s " s p e c t r a were about one or two p e r c e n t of. the peak of the t r u e spectrum i n t e n s i t y . Moreover, t h e s e " a l i a s " s p e c t r a were images or m i r r o r images of the spectrum measured between 2 and 40 cm '. Dr. Gush demonstrated t h a t t h i s a l i a s i n g was due t o uneven s a m p l i n g of the i n t e r f e r o g r a m . The f o u r f o l d r e p e a t i n g of the r e a l , low freq u e n c y spectrum i n d i c a t e d a f o u r f o l d p e r i o d i c i t y w i t h r e s p e c t t o the sa m p l i n g e r r o r . To e l i m i n a t e t h e s a m p l i n g e r r o r , d i r e c t measurement of the m i r r o r c a r r i a g e p o s i t i o n i s made by a c a p a c i t a n c e gauge. The p o s i t i o n of the m i r r o r s i s a l i n e a r f u n c t i o n of a measured v o l t a g e . However, t h e 12 b i t A-D c o n v e r s i o n i s not s e n s i t i v e enough t o d e t e c t d e v i a t i o n s from even s a m p l i n g . The data from the c a p a c i t a n c e gauge i s d i v i d e d up i n t o f o u r 40 s e t s of d a t a . Each s e t c o r r e s p o n d s t o the f i r s t , second, t h i r d , or f o u r t h sample i n a r e p e a t i n g c y c l e of f o u r samples. Each s e t i s then f i t w i t h a l i n e of v o l t a g e as a f u n c t i o n of sample number. The d a t a i s recomposed i n t o a more a c c u r a t e s e t of f i t t e d v o l t a g e s per sample number, where the d i g i t i z a t i o n n o i s e of the measurements i s now removed. The i n t e r f e r o g r a m s a r e now a f u n c t i o n of v o l t a g e , where the s a m p l i n g i n t e r v a l s between p o i n t s a r e uneven, but known. Computer i n t e r p o l a t i o n of the- i n t e r f e r o g r a m y i e l d s a new i n t e r f e r o g r a m which i s a f u n c t i o n of even i n t e r v a l s a m p l i n g . T h i s new i n t e r f e r o g r a m i s F o u r i e r t r a n s f o r m e d a c c o r d i n g t o t h e above proc e d u r e and the a l i a s i n g observed p r i o r t o the c a p a c i t a n c e measurement i s e f f e c t i v e l y e l i m i n a t e d . The peak i n t e n s i t y now of the " a l i a s " spectrum i s a p p r o x i m a t e l y 0.3 p e r c e n t of the r e a l spectrum peak i n t e n s i t y . T h i s i s comparable t o the n o i s e l e v e l of the spectrum. The a b s o r p t i o n measurements of l i q u i d n i t r o g e n and oxygen u t i l i z e d not o n l y the i n t e r f e r o m e t e r and a s s o c i a t e d d a t a a q u i s i t i o n and a n a l y s i s schemes, but a l s o r e q u i r e d a s p e c i a l l y d e s i g n e d sample c e l l . E s s e n t i a l l y , the c e l l i s a sample space between two vacuum s p a c e s . I t s b a s i c purpose i s t o c o n t a i n a 1 cm s l a b of a l i q u i f i e d gas a t l i q u i d n i t r o g e n t e m p e r a t u r e s , and t o p r e v e n t c o n d e n s a t i o n on the sample chamber windows. The t h i c k n e s s i s chosen so t h a t a l i q u i d n i t r o g e n sample absorbs about 50% of the i n c i d e n t l i g h t a t a f r e q u e n c y of 50 cm ', based on the work of Buontempo et a l ( 3 1 ) . The a p e r t u r e of the c e l l i s l a r g e i n o r d e r t o pass as 41 much of the i n t e r f e r o m e t e r beam th r o u g h t h e sample as p o s s i b l e . The window m a t e r i a l i s TPX which i s r e l a t i v e l y t r a n s m i s s i v e i n the f a r - i n f r a r e d , and the o p t i c a l r e g i o n s ( 2 8 ) . N y l o n i s chosen f o r the c e l l body because i t i s e a s i l y machined, i s r e l a t i v e l y s t r o n g , and has a t h e r m a l c o e f f i c i e n t of e x p a n s i o n s i m i l a r t o the windows. The c e l l c o o l i n g system i s e x t r e m e l y s i m p l e . The c e l l i s b u i l t i n t o a s t y r o f o a m box which i s f i l l e d w i t h l i q u i d n i t r o g e n . In p r a c t i c e , f i l l i n g the box i s done g r a d u a l l y t o a v o i d c r a c k i n g the windows or gl u e j o i n t s . C o n s t r u c t i o n of the vacuum windows i s a l s o s i m p l e , but i t i s not p a r t i c u l a r l y rugged. Low t e m p e r a t u r e vacuum windows a r e i n g e n e r a l r a t h e r t r i c k y and the s o l u t i o n here was t o epoxy the TPX windows t o the n y l o n c e l l body. The c e l l body was t u r n e d down on a l a t h e t o an a n n u l u s 2 i n c h e s i n d i a m e t e r and 0.025" t h i c k . T h i s t h i n r i n g e x t e n d s 0.5" from e i t h e r end of the window c y l i n d e r s . I t accomodates d i f f e r e n c e s i n c o n t r a c t i o n between TPX and n y l o n . A s l o t i n the windows of 0.030" t h i c k n e s s and h a l f the window d e p t h i s cu t t o e x a c t l y f i t the t h i n r i n g of the window c y l i n d e r . Armstrong A-271 epoxy i s then used t o f i x the windows t o the n y l o n c e l l . T h i s system works p r e t t y w e l l i f t h e c e l l i s c o o l e d s l o w l y , however sudden c o o l i n g w i l l break the windows or the j o i n t (see accompanying c e l l d r a wing f i g . 4 ) . The two vacuum window s e c t i o n s a r e j o i n e d t o a c e n t r a l s e c t i o n which i s the sample space. Indium O - r i n g s s e a l these window s e c t i o n s t o the c e n t r a l s e c t i o n . A s t a i n l e s s s t e e l 42 tube i s i n s e r t e d i n t o the c e n t r a l s e c t i o n t o f i l l the sample chamber. The c e n t r a l s e c t i o n i s wrapped i n aluminum tape t o i n s u r e t h a t the temperature of the sample chamber i s u n i f o r m . The gas h a n d l i n g system c o n s i s t s of the sample c e l l , a p r e s s u r e gauge, the sample gas c y l i n d e r , and a vacuum pump. I n i t i a l l y the vacuum spaces a r e pumped out w i t h a d i f f u s i o n pump and then c l o s e d o f f . The sample chamber and gas l i n e s ar e then e v a c u a t e d . A f t e r the s t y r o f o a m box i s f i l l e d w i t h l i q u i d n i t r o g e n and the c e l l i s c o l d , gas i s a d m i t t e d i n t o the sample chamber. The gas condenses and s l o w l y f i l l s the chamber. The sample chamber i s c l e a r e d by s l o w l y e v a c u a t i n g i t w i t h the r o u g h i n g pump. The placement of t h e sample c e l l i n t h e i n t e r f e r o m e t e r o p t i c a l p a t h i s d e p i c t e d i n f i g . 5. The c e l l e n t r a n c e window i s p l a c e d a p p r o x i m a t e l y 15 cm from t h e a n a l y z i n g p o l a r i z e r . T h i s p u t s t h e c e l l e x i t window about 32 cm from the TPX c o n d e n s i n g l e n s . The i n t e r f e r o m e t e r beam co n v e r g e s 43 F i g u r e 4 - L i q u i f i e d gas sample c e l l Components a r e : vacuum spaces V, sample chamber S, l i q u i d N 2 b a t h N, s t y r o f o a m box B, f i l l tube F, indium O - r i n g s I. 44 F i g u r e 5 - Diagram of t h e o p t i c a l system P, the i n t e r f e r o m e t e r ( t h e d o t t e d l i n e s r e p r e s e n t the w i r e g r i d p o l a r i z e r s , the arrows i n d i c a t e the m i r r o r movement); L, TPX l e n s ; S, a 600 C b l a c k b o d y s o u r c e ; R the room a t 23 C, a second b l a c k b o d y s o u r c e ; B, t h e l i q u i d h e l i u m c o o l e d b o l o m e t e r ; C, the sample c e l l . 45 w i t h i n the c e l l , the beam d i a m e t e r a t the c e l l e x i t window i s about 7 cm. The c e l l window d i a m e t e r of 5 cm t h e r e f o r e p a s s e s h a l f t h e l i g h t from the i n t e r f e r m e t e r assuming a beam of u n i f o r m i n t e n s i t y . The t r a n s m i s s i o n of a l l the TPX windows at 30 cm ( r o u g h l y midrange i n the spectrum) i s about 50%. T h e r e f o r e , the t o t a l l i g h t t r a n s m i t t e d by an empty c e l l i s about 1/4 of t h e l i g h t t r a n s m i t t e d by the i n t e r f e r o m e t e r system w i t h no c e l l p r e s e n t . T h i s i s g e n e r a l l y c o n f i r m e d by comparing the t o t a l i n t e n s i t y f a l l i n g on the d e t e c t o r w i t h the c e l l ' i n the p a t h t o the t o t a l i n t e n s i t y w i t h no c e l l i n the o p t i c a l p a t h . One f i n a l f e a t u r e of the e x p e r i m e n t a l p r o c e d u r e i s the p u r g i n g of t h e o p t i c a l p a t h . Water vapor i s a v e r y s t r o n g a b s o r b e r i n t h e f a r - i n f r a r e d f r e q u e n c y r e g i o n and i t i s d e s i r a b l e t o remove i t as much as p o s s i b l e . The o p t i c a l system was e n c l o s e d by a p o l y e t h y l e n e t e n t purged w i t h n i t r o g e n vapor by p o u r i n g l i q u i d n i t r o g e n i n t o an u n i n s u l a t e d c o n t a i n e r w i t h i n the t e n t . For the h i g h f r e q u e n c y measurements, a d d i t i o n a l n i t r o g e n gas was blown i n t o the t e n t from a gas c y l i n d e r and t h i s was more e f f e c t i v e a t e l i m i n a t i n g t h e water vapor l i n e s than u s i n g l i q u i d a l o n e . One problem w i t h p u r g i n g i s t h a t the water vapor c o n t e n t w i t h i n the t e n t v a r i e s from measurement t o measurement. S i n c e the a b s o r p t i o n c o e f f i c i e n t i s based on a r a t i o of background t o sample s p e c t r a , t h e v a r i a t i o n i n p u r g i n g can produce s t r o n g f e a t u r e s i n the a b s o r p t i o n c u r v e s a t the f r e q u e n c i e s o f water vapor a b s o r p t i o n l i n e s . 46 3.2 E x p e r i m e n t a l R e s u l t s A p o r t i o n of the e x p e r i m e n t a l work of t h i s t h e s i s i s a measurement of the a b s o r p t i o n of f a r - i n f r a r e d l i g h t by l i q u i d n i t r o g e n and l i q u i d oxygen. As p r e v i o u s l y d i s c u s s e d t h i s a b s o r p t i o n i s p r e d o m i n a n t l y due t o A J = 2 r o t a t i o n a l m o l e c u l a r t r a n s i t i o n s a r i s i n g from c o l l i s i o n i n d u c e d d i p o l e moments. A c o n s i d e r a b l e amount of i n v e s t i g a t i o n has been c a r r i e d out on c o l l i s i o n induced a b s o r p t i o n i n g a s e s , both t h e o r e t i c a l and e x p e r i m e n t a l , e s p e c i a l l y on , N^ ., and r a r e gas m i x t u r e s . However, not much f a r - i n f r a r e d work has been done on l i q u i d s i n g e n e r a l , or on oxygen i n p a r t i c u l a r . A r e v i e w of p r e v i o u s e x p e r i m e n t s which a r e p e r t i n e n t t o the p r e s e n t s t u d i e s f o l l o w s . There have been numerous measurements of the spectrum of gaseous n i t r o g e n s i n c e the d i s c o v e r y of c o l l i s i o n i n d u ced a b s o r p t i o n . The e x p e r i m e n t s of Bosomworth and Gush (30) u s i n g a F o u r i e r , t r a n s f o r m s p e c t r o m e t e r a r e w i d e l y q u o t e d and compared t o more r e c e n t measurements under d i f f e r e n t c o n d i t i o n s . They measured the a b s o r p t i o n c o e f f i c i e n t of gaseous n i t r o g e n 300 K, from 40 t o 350 cm ' i n t h e d e n s i t y range 20.9 t o 33.6 Amagat. Measurements i n the gas have a l s o been made by Buontempo e t a l (31) a t 124K, and Dagg e t a l (32) and Stone e t a l (21) over a wide temperature range. I n a d d i t i o n , t h e r e a r e two p u b l i s h e d measurements of the f a r IR a b s o r p t i o n of l i q u i d n i t r o g e n : an e a r l y e xperiment of Stone and W i l l i a m s (33) and a l a t e r experiment by Buontempo e t a l ( 3 1 ) . 47 The Stone paper d e s c r i b e s the t r a n s m i s s i o n of l i q u i d n i t r o g e n over the f r e q u e n c y band 30 - 200 cm"' . These measurements use a g r a t i n g s p e c t r o m e t e r purged w i t h n i t r o g e n gas. The l i q u i d n i t r o g e n was c o n t a i n e d by two c e l l s , one 12.5 mm t h i c k , the o t h e r 2.5 mm t h i c k . The r a t i o Of the s p e c t r a o b t a i n e d through each c e l l i s t h e r e f o r e the t r a n s m i s s i o n of a 10 mm s l a b of l i q u i d . An a b s o r p t i o n peak near 75 cm ' was o b s e r v e d . A major problem w i t h t h i s measurement i s t h a t i c e c r y s t a l s were observed i n some of t h e i r l i q u i d samples. S i n c e water i s s t r o n g l y a b s o r b i n g i n the f a r - i n f r a r e d , the r e l i a b i l i t y of these r e s u l t s i s q u e s t i o n a b l e . Buontempo e t a l (31) have measured the t r a n s m i s s i o n of l i q u i d n i t r o g e n a t a temperature of 66K, u s i n g a M i c h e l s o n i n t e r f e r o m e t e r i n the fr e q u e n c y r e g i o n 25 t o 250 cm '. In a d d i t i o n they measured the a b s o r p t i o n c o e f f i c i e n t of the gas a t 300K and 124K. The c e l l f o r the l i q u i d experiment was r o u g h l y 10 mm l o n g and had mylar windows. T h e i r c e l l l e n g t h was u n c e r t a i n s i n c e the windows b u l g e d outwards when the c e l l was f u l l . C o n s e q u e n t l y they were unable t o c a l c u l a t e an a c c u r a t e a b s o r p t i o n c o e f f i c i e n t . In s p i t e of t h i s s e r i o u s d e f i c i e n c y , i t remains the best a v a i l a b l e measurement of l i q u i d n i t r o g e n . Background s p e c t r a were o b t a i n e d w i t h an ev a c u a t e d c e l l or w i t h a c e l l f i l l e d w i t h l i q u i d a r g o n . F i l l i n g t he c e l l w i t h l i q u i d argon compensates f o r the change i n index of r e f r a c t i o n between an empty c e l l and one t h a t i s f u l l of l i q u i d . . They s t a t e t h a t the l i q u i d n i t r o g e n 48 t r a n s m i s s i o n r e s u l t s were the same u s i n g e i t h e r background. T h e i r work shows t h a t i n g e n e r a l , the a b s o r p t i o n i n the l i q u i d i s s i m i l a r t o t h a t i n the gas. The peak a b s o r p t i o n i n the l i q u i d phase a t 66K o c c u r s a t 60 cm ' , whereas i n the gas a t 124K, i t o c c u r s a t 70 cm-' . A d i f f e r e n c e between the gas and l i q u i d s p e c t r a i s t h a t the i n t e g r a t e d a b s o r p t i o n c o e f f i c i e n t d i v i d e d by the square of the d e n s i t y i s l e s s f o r the l i q u i d t han t h a t e s t i m a t e d f o r a gas a t the same tempe r a t u r e . A l s o the l i q u i d spectrum shows a s t r o n g e r a b s o r p t i o n a t h i g h f r e q u e n c i e s than the gas spectrum. These f e a t u r e s may be a c c o u n t e d f o r i n p a r t by c o n s i d e r i n g t h a t i n the l i q u i d i n t e r a c t i o n s a r e t a k i n g p l a c e between more than j u s t i s o l a t e d p a i r s of m o l e c u l e s ( u n l i k e the low d e n s i t y g a s ) . The q u a d r u p o l e f i e l d s of many n e i g h b o r i n g m o l e c u l e s w i l l be superimposed on the s i t e of the m o l e c u l e i n which a d i p o l e i s i n d u c e d . T h i s s u p e r p o s i t i o n d e c r e a s e s on average the magnitude of the e l e c t r i c f i e l d a t t h i s s i t e as the m o l e c u l e s a r e c o n s i d e r e d t o be randomly o r i e n t e d . The l i q u i d ' s h i g h e r a b s o r p t i o n i n the h i g h f r e q u e n c y r e g i o n may be a s c r i b e d t o double t r a n s i t i o n s , where each of a p a i r of m o l e c u l e s undergoes a r o t a t i o n a l t r a n s i t i o n . In t h i s c a s e , the d i p o l e moment i s not c a n c e l l e d , as i t i s f o r s i n g l e t r a n s i t i o n s , by the p r o x i m i t y of n e i g h b o r i n g m o l e c u l e s . The microwave a b s o r p t i o n a t 2.3 cm ' , of l i q u i d n i t r o g e n has been measured by U r b a n i a k e t a l ( 3 4 ) . T h i s measurement i s a t a f r e q u e n c y where f a r - i n f r a r e d t e c h n i q u e s become i n a c c u r a t e and hence i s i m p o r t a n t i n d e f i n i n g the spectrum i n 49 the low wavenumber r e g i o n . In t h e case of l i q u i d oxygen, no p r e v i o u s work i n the f a r - i n f r a r e d has been p u b l i s h e d . Even f o r gaseous oxygen t h e r e a r e few f a r - i n f r a r e d e x p e r i m e n t s e x c e p t t h a t of Bosomworth and Gush ( 3 0 ) . The c o l l i s i o n i n d u c e d r o t a t i o n a l spectrum of gaseous oxygen a t 300K and d e n s i t i e s between 35 and 75 Amagat was measured over the f r e q u e n c y r e g i o n 20 -400 cm ' . T h e i r work shows an oxygen a b s o r p t i o n peak at a p p r o x i m a t e l y 110 cm ^ , about the same as t h e i r n i t r o g e n a b s o r p t i o n peak. The f a r - i n f r a r e d a b s o r p t i o n of gaseous oxygen i s about 10 t i m e s l e s s than gaseous n i t r o g e n . The c o l l i s i o n i n d u c e d fundamental v i b r a t i o n - r o t a t i o n band of oxygen was measured over the range 1300 - 1800 cm 1 by S h a p i r o and Gush ( 3 5 ) . The gas t e m p e r a t u r e was 300K and the d e n s i t y was i n the range 40 - 60 Amagat. In t h e i r measurement, the r o t a t i o n a l t r a n s i t i o n s a r e o b s e r v e d as s i d e bands on t h e fundamental v i b r a t i o n a l t r a n s i t i o n a t 1553 cm ' . Measurements of the f a r - i n f r a r e d a b s o r p t i o n of l i q u i d n i t r o g e n and oxygen were performed u s i n g the a f o r e m e n t i o n e d i n t e r f e r o m e t e r and sample c e l l . Two s e t s of measurements c o v e r e d the f r e q u e n c y r e g i o n s , 2 - 40 cm ' and 2 - 80 cm ' . The h i g h f r e q u e n c y c u t o f f i n the f i r s t case i s d e t e r m i n e d by the o p t i c a l f i l t e r s i n f r o n t of the d e t e c t o r (see S e c t i o n 3.1). The c u t o f f i n the second c a s e i s d e t e r m i n e d p r i m a r i l y by the a b s o r p t i o n of TPX, the m a t e r i a l used t o make the c e l l windows and c o n d e n s i n g l e n s e s . Measurements of the a b s o r p t i o n of TPX (28) show t h a t t h e t r a n s m i s s i o n i s : 50 - O.OI i) t e where t i s the t h i c k n e s s of the TPX and ^ i s the f r e q u e n c y . The t h i c k n e s s i n the o p t i c a l p a t h here was •~5 cm, so the t r a n s m i s s i o n t h r o u g h the o p t i c a l system at 80 cm ' i s l e s s than 2%. In f i g . 6 a background spectrum d i v i d e d by t7 ( i n o r d e r t o n o r m a l i z e the i n t e n s i t y of the b l a c k b o d y s o u r c e , i s p l o t t e d w i t h the t r a n s m i s s i o n of the v a r i o u s f i l t e r s and TPX of the o p t i c a l system. The h i g h f r e q u e n c y c u t o f f of the spectrum i s w e l l matched by the t r a n s m i s s i o n of the combined elements of the o p t i c a l system. The g o a l of t h e s e e x p e r i m e n t s i s t o measure the a b s o r p t i o n c o e f f i c i e n t A( o" ) of the two l i q u i f i e d gases (eqn. 2.1). To do t h i s the f o l l o w i n g e x p e r i m e n t a l p r o c e d u r e was adopted. F i r s t , background s p e c t r a were measured w i t h the sample c e l l empty. Next, the c e l l was f i l l e d w i t h l i q u i d by c o n d e n s a t i o n from the gas and s p e c t r a were t a k e n . F i n a l l y , the c e l l was emptied and the background s p e c t r a were r e p e a t e d . Each s p e c t r a l measurement s e t c o n s i s t s of about 2 or 3 s e t s of 28 i n t e r f e r o g r a m s . Each i n t e r f e r o g r a m was t r a n s f o r m e d and phase c o r r e c t e d and then a l l 56 or 84 s p e c t r a were averaged. The background s p e c t r a used i n c a l c u l a t i n g h{CT) a r e a v e r a g e s of about 112 or 140 background s p e c t r a , h a l f taken b e f o r e and h a l f a f t e r the sample s p e c t r a . I t took a p p r o x i m a t e l y one hour t o condense gas i n the c e l l and one hour t o evacuate the c e l l w i t h the r o u g h i n g pump. J I 1 200 FREQUENCY (cm-') Figure 6 - High frequency cutoff of optical system Plotted are: a background spectrum/ ; transmission of: 1 mm NaCl, mylar and polyethelene combined f i l t e r s , 4.5 cm TPX; and a composite transmission spectrum of a l l these elements combined 52 T h i s l o n g p e r i o d between background and sample s p e c t r a l e d t o two s e r i o u s problems. F i r s t , t h e t e m p e r a t u r e of the bolometer d r i f t e d s l i g h t l y d u r i n g t h i s p e r i o d l e a d i n g t o changes i n the measured s p e c t r a l i n t e n s i t y . I n a d d i t i o n , the p u r g i n g of the o p t i c a l p a t h w i t h n i t r o g e n vapor was not e x a c t l y the same from one measurement t o the n e x t . T h i s d e f e c t i s p a r t i c u l a r l y n o t i c e a b l e i n t h e oxygen s p e c t r a where the a b s o r p t i o n i s low, and pronounced w a t e r vapor l i n e s may be observed a t 18, 25, 36, and 40 cm ' . These l i n e s a r e due t o i m p e r f e c t c a n c e l l a t i o n of a t m o s p h e r i c f e a t u r e s i n the r a t i o i 5 ( CT ) / i 5 ( cr ). An a c c i d e n t happened d u r i n g t h e h i g h f r e q u e n c y e x p e r i m e n t s i n which the vacuum windows on t h e c e l l were c r a c k e d by a s p i l l of l i q u i d N^ . However, the c e l l worked i n s p i t e of t h i s and no f r o s t was o b s e r v e d on the windows as the o p t i c a l p a t h t e n t was b e i n g w e l l purged w i t h not o n l y e v a p o r a t i n g l i q u i d n i t r o g e n , but a l s o w i t h f l o w i n g n i t r o g e n gas. The r a t i o of background t o sample spectrum needs t o be tak e n t o o b t a i n the a b s o r p t i o n c o e f f i c i e n t . However, the t r a n s m i s s i o n of the sample c e l l when i t c o n t a i n s a non-a b s o r b i n g f l u i d i s g r e a t e r than when i t i s empty, s i n c e r e f l e c t i o n l o s s e s a t the boundary between t h e TPX windows and the sample a r e a a r e l e s s . I f i n t e r f e r e n c e of l i g h t p a t h s r e f l e c t i n g back and f o r t h i n the sample r e g i o n i s n e g l e c t e d , the t r a n s m i s s i o n of l i g h t a t normal i n c i d e n c e , from a medium of index n, , through a medium of in d e x , and i n t o a 53 med ium o f n T- [ 4 n,nx H e r e n / . i s t h e i n d e x o f r e f r a c t i o n o f T P X , a n d nz i s t h e i n d e x o f o f t h e v a c u u m o r a l i q u i d s a m p l e . The i n d e x o f r e f r a c t i o n n c a n be o b t a i n e d f r o m t h e p e r m i t t i v i t y o f a d i e l e c t r i c m e d i u m . w h e r e c i s t h e s p e e d o f l i g h t i n v a c u u m , v i s t h e s p e e d o f l i g h t i n t h e d i e l e c t r i c , t: a n d /A a r e t h e p e r m i t t i v i t y a n d p e r m e a b i l i t y o f t h e m e d i u m , a n d 6 0 a n d /Ao a r e t h e p e r m i t t i v i t y a n d p e r m e a b i l i t y o f f r e e s p a c e . F o r m o s t d i e l e c t r i c m a t e r i a l s , /A =/40 . The i n d e x o f r e f r a c t i o n o f T P X i s : n = 1 .42 ( 2 8 ) , t h e r e f o r e t h e t r a n s m i s s i o n o f t h e e m p t y c e l l , T e = 0 . 9 4 1 . The t a b l e b e l o w g i v e s 6 , n , Tf t h e t r a n s m i s s i o n o f t h e f u l l c e l l , a n d T ^ / T e t h e r a t i o o f t r a n s m i s s i o n o f t h e f u l l c e l l d i v i d e d by e m p t y c e l l , f o r l i q u i d s a n d Oz . The v a l u e s o f 6 a r e g i v e n i n ( 3 6 ) a n d h a v e b e e n m e a s u r e d i n t h e l i q u i d p h a s e i n t h e m i c r o w a v e f r e q u e n c y r e g i o n . C. V 54 6 n Ty Tj/ T e N 2 1.454 1.21 0.987 1.049 O z 1.507 1.23 0.990 1.052 T a b l e 5 - D i e l e c t r i c c o n s t a n t , index of r e f r a c t i o n , and t r a n s m i s s i o n of c e l l f o r l i q u i d n i t r o g e n and l i q u i d oxygen To compensate f o r the change i n c e l l t r a n s m i s s i o n , the sample s p e c t r a are d i v i d e d by Tf /T e , o t h e r w i s e a t r a n s m i s s i o n i n excess of u n i t y would be o b s e r v e d i n the f r e q u e n c y r e g i o n of low a b s o r p t i o n . The r e s u l t s of the low f r e q u e n c y measurements a r e a c c u r a t e l y compensated by the above c o n s t a n t s and t r a n s m i s s i o n a t low f r e q u e n c y i s s h i f t e d t o u n i t y . The compensation of the h i g h f r e q u e n c y measurements i s not so a c c u r a t e , but i t s h o u l d be noted t h a t i n the low wavenumber r e g i o n , the low f r e q u e n c y measurements a r e p r o b a b l y more a c c u r a t e than the h i g h frequency measurements. The o p t i c a l f i l t e r i n g used f o r the low f r e q u e n c y measurements produced w e l l t e s t e d and r e l i a b l e low f r e q u e n c y s p e c t r a i n the c o u r s e of measuring the o p t i c a l p r o p e r t i e s of c o l d d i e l e c t r i c s ( H a l p e r n e t . a l . 1985). The a b s o r p t i o n c o e f f i c i e n t i s o b t a i n e d from measurements of background s p e c t r a and sample s p e c t r a . The background measured i s : I f l = I 0 ( 1 - Re ) = Io T e where Io i s the i n i t i a l i n t e n s i t y , R e i s the r e f l e c t i o n of t h e empty c e l l , and T e t h e t r a n s m i s s i o n of the empty c e l l . 55 The sample s p e c t r a measured i s : -ex C i s = i c ( 1 - )e = i 0 Tys e where Ryr i s the r e f l e c t i o n of the f u l l c e l l , Ty the t r a n s m i s s i o n of the f u l l c e l l , cx the a b s o r p t i o n c o e f f i c i e n t , and t the sample t h i c k n e s s . The r a t i o of 1$ / I 6 then i s : = i f . e T / / Te i s c a l c u l a t e d above f o r 0^ and l i q u i d s i n s i d e a TPX c e l l . The a b s o r p t i o n c o e f f i c i e n t i s t h e n : ©< = _L In Tfj , tohtrc Is = Zs t n' Mi The a b s o r p t i o n c o e f f i c i e n t of l i q u i d n i t r o g e n i s d i s p l a y e d i n f i g . 7. The heavy l i n e i s from the s e t of low f r e q u e n c y measurements, and the l i g h t l i n e i s from the h i g h f r e q u e n c y measurements. For both s e t s of measurements the d a t a p l o t t e d e x t e n d s about 10 cm ' h i g h e r i n f r e q u e n c y than the r e g i o n of r e l i a b l e r e s u l t s . A l s o p l o t t e d on t h i s graph a r e the a b s o r p t i o n c o e f f i c i e n t s of l i q u i d found by Stone e t a l , and Buontempo et a l , which were o b t a i n e d from t h e i r t r a n s m i s s i o n d a t a assuming a known c e l l l e n g t h . The v e r t i c a l b a r s a r e p r o p o r t i o n a l t o the unbroadened i n t e n s i t i e s of a b s o r p t i o n by r o t a t i o n a l t r a n s i t i o n s i n a p a i r of n i t r o g e n m o l e c u l e s . These a r e s i n g l e t r a n s i t i o n s which a r e due o n l y t o q u a d r u p o l a r i n d u c t i o n and t h e i r i n t e n s i t y s c a l e i s a r b i t r a r y (see t a b l e 3). 2D 1 — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — r May 17 & 30/85 Absorption coefficient o u o NITROGEN liquid N2 C 0 0 0 O C M - > » - c O 0 0 O t N - > » - < £ > 0 0 O < N - ' * " < O a 0 C CM-1 tn F i g u r e 7 - A b s o r p t i o n c o e f f i c i e n t of l i q u i d n i t r o g e n Heavy l i n e , low frequency measurements; l i g h t l i n e , h i g h f r e q u e n c y measurements. A l s o p l o t t e d are r e s u l t s from ( 3 1 ) , d o t s ; and ( 3 3 ) , open c i r c l e s ; and c a l c u l a t e d q u a d r u p o l a r induced s i n g l e t r a n s i t i o n l i n e i n t e n s i t i e s , b a rs (see t a b l e 3 ) . 1 — i — i — i — i — i — i — i — i — i — i — i — i — i — i — r " i — i — i — i i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — r May 17 & 30/85 Absorption coefficient OXYGEN liquid 02 o Q5\ 00 j e i o 1 \ _ t_ J 1 _ i _ I li I _ i _ I l CO IT) o CM T f IO <o C O O <N •* to CO r-~ r~- o oc F i g u r e 8 - A b s o r p t i o n c o e f f i c i e n t of l i q u i d oxygen Heavy l i n e , low frequency measurements; l i g h t l i n e , h i g h f r e q u e n c y measurements. V e r t i c a l b a r s are c a l c u l a t e d q u a d r u p o l a r i n d u c e d s i n g l e t r a n s i t i o n l i n e i n t e n s i t i e s , (see t a b l e 3 ) . CJ1 58 F i g u r e 7 shows t h a t the a b s o r p t i o n c o e f f i c i e n t measured i n t h i s work i s l e s s than t h a t measured by e i t h e r of the p r e v i o u s e x p e r i m e n t s . In the case of Stone, t h i s d i s c r e p a n c y may be a c c o u n t e d f o r by the p r e s ence of i c e p a r t i c l e s i n the l i q u i d n i t r o g e n samples which would l e a d t o l a r g e r a b s o r p t i o n . In the case of Buontempo, i f t h e i r c e l l t h i c k n e s s was l a r g e r than r e p o r t e d , the a b s o r p t i o n c o e f f i c i e n t c a l c u l a t e d from t h e i r d ata would be reduced. The d i s c r e p a n c y i n the shape of the a b s o r p t i o n c u r v e s remains u n e x p l a i n e d . T h e i r a b s o r p t i o n curve shows a r o l l - o f f s t a r t i n g a t 60 cm , and a peak near 70 cm . The a b s o r p t i o n c u r v e f i g . 7, c l e a r l y does not f o l l o w the i n t e n s i t i e s f o r b i n a r y c o l l i s i o n s r e p r e s e n t e d by the v e r t i c a l b a r s . The reason f o r t h i s c o u l d be the r e s u l t of double t r a n s i t i o n s , as mentioned e a r l i e r , or h i g h e r o r d e r m u l t i p o l e i n d u c t i o n p r o c e s s e s ( 3 7 ) . The f i r s t r e p o r t e d measurement of the f a r - i n f r a r e d a b s o r p t i o n c o e f f i c i e n t of l i q u i d oxygen i s d i s p l a y e d i n f i g . 8. The heavy l i n e i s from the low f r e q u e n c y measurements, the l i g h t l i n e i s from the h i g h f r e q u e n c y measurements. A l s o shown i s a t h e o r e t i c a l r o t a t i o n a l s t i c k spectrum t a k i n g i n t o account o n l y q u a d r u p o l a r i n d u c t i o n and s i n g l e m o l e c u l e t r a n s i t i o n s (see t a b l e 3 ) . The agreement between the low frequency measurements and the h i g h f r e q u e n c y measurements f o r oxygen i s not as good as the n i t r o g e n r e s u l t s . The s i g n a l t o n o i s e r a t i o i n the oxygen d a t a i s a l s o not as good as the n i t r o g e n c a s e , because 59 oxygen a b s o r b s c o n s i d e r a b l y l e s s than n i t r o g e n f o r the same pa t h l e n g t h . Major d e v i a t i o n s between s p e c t r a and background i n the case where a b s o r p t i o n i s s m a l l (and the s i g n a l i s s m a l l ) a r e r e l a t e d t o i n c o n s i s t e n c i e s w i t h the p u r g i n g of the o p t i c a l p a t h . The a b s o r p t i o n c o e f f i c i e n t of l i q u i d oxygen i s about h a l f t h a t of l i q u i d n i t r o g e n , whereas the a b s o r p t i o n c o e f f i c i e n t of gaseous oxygen i s about one t e n t h t h a t of gaseous n i t r o g e n ( 3 0 ) . The h i g h f r e q u e n c y spectrum does not c l e a r l y show a peak, a l t h o u g h t h e r e appears t o be a r o l l - o f f a t about 60 cm 1. I t i s c l e a r however, t h a t the observed spectrum does not f o l l o w the envelope of the t h e o r e t i c a l s t i c k spectrum. For both n i t r o g e n and oxygen, h i g h e r f r e q u e n c y measurements encompassing the e n t i r e a b s o r p t i o n band a r e d e s i r a b l e . I n c r e a s i n g the. c e l l l e n g t h "to o b t a i n l a r g e r a b s o r p t i o n would improve the s i g n a l t o n o i s e r a t i o a t low f r e q u e n c i e s , e s p e c i a l l y f o r oxygen. I n f o r m a t i o n on the t r a n s i t i o n p r o b a b i l i t y between r o t a t i o n a l s t a t e s of the m o l e c u l e s i n the l i q u i d can be o b t a i n e d from t h e a b s o r p t i o n c u r v e s by t a k i n g i n t o account a fr e q u e n c y f a c t o r and the e f f e c t of s t i m u l a t e d e m i s s i o n . The p r o b a b i l i t i e s of s t i m u l a t e d e m i s s i o n and s t i m u l a t e d a b s o r p t i o n of l i g h t due t o m o l e c u l a r energy t r a n s i t i o n s a re e q u a l , however s i n c e the p o p u l a t i o n of lower energy s t a t e s i s g r e a t e r than h i g h e r energy s t a t e s f o r a system i n t h e r m a l e q u i l i b r i u m , t h e r e w i l l be a net a b s o r p t i o n of r a d i a t i o n . At l i q u i d n i t r o g e n t e m p e r a t u r e s , the i n t e n s i t y of e m i s s i o n i s about t h e same as a b s o r p t i o n f o r energy t r a n s i t i o n s l e s s than 60 50 cm . The l i n e shape f u n c t i o n i s p r o p o r t i o n a l t o the p r o b a b i l i t y of m o l e c u l a r t r a n s i t i o n s between s t a t e s s e p a r a t e d i n energy by E = hccT, and i s r e l a t e d t o the a b s o r p t i o n c o e f f i c i e n t by: Cr(a) = * < * J Here d i v i d i n g by & a c c o u n t s f o r the c o n t r i b u t i o n of f r e q u e n c y t o the i n t e n s i t y of a b s o r p t i o n and d i v i d i n g by (1 -exp(-he c / k T ) ) a c c o u n t s f o r the measured l i g h t i n t e n s i t y due t o s t i m u l a t e d e m i s s i o n . The f o l l o w i n g graphs, f i g s . 9 and 10, show the l i n e shape f u n c t i o n f o r l i q u i d and l i q u i d Oz . The microwave p o i n t from (34) i s a l s o p l o t t e d , and seems r e l a t i v e l y c o n s i s t e n t w i t h the p r e s e n t measurement i f the h i g h e r f r e q u e n c y p a r t of the c u r v e i s c o n t i n u e d t o z e r o wavenumbers. Both c u r v e s show t h a t a t lower f r e q u e n c i e s t h e r e i s a h i g h e r t r a n s i t i o n p r o b a b i l i t y than a t h i g h e r f r e q u e n c i e s . There i s a l a r g e i n c r e a s e i n the l i n e shape f u n c t i o n of n i t r o g e n gas a t the low f r e q u e n c i e s due t o c o l l i s i o n i nduced t r a n s l a t i o n a l a b s o r p t i o n (31) (32) . The absence of any l a r g e i n c r e a s e i n the l i q u i d l i n e shape f u n c t i o n might i n d i c a t e t h a t t r a n s l a t i o n a l motion i s i n h i b i t e d by the d e n s i t y or m o l e c u l a r c l u s t e r i n g . F i g u r e 9 - L i n e shape f u n c t i o n of l i q u i d n i t r o g e n Heavy l i n e , low f requency measurements; l i g h t l i n e , h i g h f requency measurements; microwave p o i n t from (34) i s a l s o p l o t t e d . CX025 F i g u r e 10 - L i n e shape f u n c t i o n of l i q u i d oxyqen Heavy l i n e , low frequency measurements; l i g h t l i n e , h i g h f r e q u e n c y measurements. ' y c y u c " ^ cn to 63 The 5 - 8 cm d i p i n the n i t r o g e n low f r e q u e n c y l i n e shape c u r v e (heavy l i n e ) may be s i m i l a r t o a d i p o b s e r v e d a t low f r e q u e n c i e s i n the t r a n s l a t i o n a l a b s o r p t i o n of hydrogen gas ( 3 8 ) . For hydrogen gas, t h i s d i p i s a t t r i b u t e d t o a change i n s i g n of the d i p o l e moment between s u c c e s s i v e m o l e c u l a r c o l l i s i o n s . In the p r e s e n t c a s e , s i n c e the a b s o r p t i o n i s q u i t e low, t h i s r e g i o n of the l i n e shape f u n c t i o n i s v e r y s e n s i t i v e t o s m a l l e r r o r s i n the background spectrum. By i n c r e a s i n g the background by 2% ( w i t h i n the e r r o r of t h e s e measurements) t h i s d i p i s e l i m i n a t e d and t h e r e f o r e i t w i l l be n e c e s s a r y t o improve the a c c u r a c y of t h e s e measurements t o demonstrate the v a l i d i t y of t h i s f e a t u r e of the l i n e shape f u n c t i o n . 64 IV. LOW TEMPERATURE MULTIPLE PASS FAR-INFRARED ABSORPTION CELL In o r d e r t o i n v e s t i g a t e H-j. i n a s i t u a t i o n s i m i l a r t o a s t r o p h y s i c a l e n v i r o n m e n t s , a low t e m p e r a t u r e , m u l t i p l e p a s s , o p t i c a l a b s o r p t i o n c e l l was d e s i g n e d . The d e s i g n concept i s b e i n g augmented and t r a n s l a t e d i n t o d e t a i l e d m e c h a n i c a l drawings by A l e x Leung. I t i s a n t i c i p a t e d t h a t the c e l l c o n s t r u c t i o n w i l l b e g i n s h o r t l y . The f i r s t use of the a b s o r p t i o n c e l l w i l l be t o measure the f a r - i n f r a r e d spectrum of hydrogen dimers ( H z ) a a t h i g h r e s o l u t i o n . The e x i s t e n c e of t h e s e dimers has been c o n f i r m e d by o b s e r v a t i o n s of the c o l l i s i o n i nduced a b s o r p t i o n i n the fundamental band ( 2 ) ( 3 ) , but no p r e v i o u s f a r - i n f r a r e d measurements have been made. Experiments a r e p l a n n e d t o examine th e t r a n s l a t i o n a l spectrum of hydrogen from a p p r o x i m a t e l y 20 - 200 cm"' u s i n g a F o u r i e r t r a n s f o r m M i c h e l s o n i n t e r f e r o m e t e r as w e l l as the dimer a b s o r p t i o n a t the S e ( 0 ) hydrogen l i n e a t 354.4 cm' u s i n g a l a s e r d i o d e s p e c t r o m e t e r . The b i n d i n g energy of % d i m e r s i s of t h e o r d e r of a -/ few cm and they a r e e a s i l y d i s s o c i a t e d by c o l l i s i o n . To observe dimers the gas p r e s s u r e must be l e s s than a few atmospheres, and t h e t e m p e r a t u r e must be l e s s than about 50K. S i n c e the a b s o r p t i o n i s e x p e c t e d t o be weak, i t i s d e s i r a b l e t o have as l o n g an o p t i c a l p a t h l e n g t h as i s p r a c t i c a l . T h i s c e l l d e s i g n , a low t e m p e r a t u r e m u l t i p a s s "White c e l l " (39) f u l f i l l s b o t h t h e s e r e q u i r e m e n t s . 65 A White c e l l e s s e n t i a l l y c o n s i s t s of a f i e l d m i r r o r and 2 f o l d i n g m i r r o r s , ( t w i n m i r r o r s ) a l l of the same r a d i u s of c u r v a t u r e . The d i s t a n c e between t h e m i r r o r s i s e q u a l t o the r a d i u s of c u r v a t u r e , and the p a t h l e n g t h can be a d j u s t e d by ch a n g i n g the angl e between the t w i n f o l d i n g m i r r o r s . The p a t h l e n g t h o b t a i n e d i s : L = (zx * n ) +2. where 1 i s the l e n g t h of the c e l l and n i s the t o t a l number of s p o t s on the f i e l d m i r r o r . To o b t a i n t h e l o n g e s t path l e n g t h , the f o l d i n g m i r r o r s a r e a d j u s t e d u n t i l t h e s p o t s on the f i e l d m i r r o r a r e as c l o s e as- p o s s i b l e w i t h o u t o v e r l a p p i n g . A n o t a b l e f e a t u r e of t h i s new c e l l i s t h a t i t has an f/10 o p t i c a l system, t h i s i s a " f a s t e r " beam th a n o t h e r low temperature White c e l l s d e s c r i b e d i n t h e l i t e r a t u r e ( 4 0 ) ( 4 1 ) ( 2 ) . Because v e r y low o p t i c a l f r e q u e n c i e s w i l l be used i n thes e e x p e r i m e n t s , the l i g h t beam w i l l be s i g n i f i c a n t l y d i f f r a c t e d by the f o l d i n g m i r r o r s , and t h i s w i l l l i m i t the maximum a t t a i n a b l e p a t h l e n g t h . D i f f r a c t i o n from th e s e m i r r o r s i s m i n i m i z e d by d e s i g n i n g them t o be as l a r g e as p o s s i b l e . To o b t a i n l o n g p a t h l e n g t h s , f o r a g i v e n c e l l l e n g t h , the f i e l d m i r r o r must a l s o have a l a r g e d iameter i n o r d e r t o s t a c k up as many s p o t s as p o s s i b l e . An o p t i c a l system has been d e s i g n e d where the f i e l d m i r r o r has a di a m e t e r of 20 cm and each f o l d i n g m i r r o r a d i a m e t e r of 10 cm. A l l m i r r o r s have a r a d i u s of c u r v a t u r e of 1 meter. 66 A l t h o u g h a l o n g e r p a t h l e n g t h would be p o s s i b l e i f the c e l l were l a r g e r , d i f f i c u l t i e s w i t h a p r e v i o u s l y c o n s t r u c t e d 3 meter c e l l i n d i c a t e d t h a t i t i s more p r a c t i c a l t o b u i l d and o p e r a t e a 1 meter c e l l . The maximum p a t h l e n g t h a t t a i n a b l e w i t h t h i s c e l l i s d e t e r m i n e d by the s i z e of the d i f f r a c t i o n spot and the number of t h e s e s p o t s t h a t can be p l a c e d onto the upper row of images on t h e f i e l d m i r r o r . The w i d t h of the f i e l d m i r r o r between t h e e n t r a n c e and e x i t s l o t s i s 16.8 cm. The t a b l e below g i v e s the w a v e l e n g t h , the d i f f r a c t i o n spot s i z e d i a m e t e r , t h e number of s p o t s on the t o p row, the t o t a l number of s p o t s , and the t o t a l p a t h l e n g t h of the c e l l f o r low f r e q u e n c i e s of l i g h t . 0" X d #top # t o t a l p a t h l e n g t h 20 cm' 0.5 mm 1.22 cm 13 27 56 m 30 cm"' 0.33 mm 0.85 cm 19 39 80 m T a b l e 6 - D i f f r a c t i o n spot s i z e and maximum p a t h l e n g t h f o r low o p t i c a l f r e q u e n c i e s The d i f f r a c t i o n spot s i z e c a l c u l a t e d above assumes t h a t the i n p u t t o t h e c e l l i s a p o i n t s o u r c e . T h i s i s not the c a s e , as the t r a n s f e r o p t i c s magnify the i n t e r f e r o m e t e r output a p e r t u r e by a f a c t o r of 2. The i n p u t spot s i z e i s 0.6 cm, and the maximum p a t h l e n g t h u s i n g t h i s i n t e r f e r o m e t e r , d i s c o u n t i n g d i f f r a c t i o n , i s 116 mete r s . 67 The p h o t o g r a p h , f i g . 11 i n d i c a t e s the major components of the c e l l system. I t c o n s i s t s of a 1 meter l o n g low tem p e r a t u r e o p t i c a l c e l l , which i s made of s t a i n l e s s s t e e l and i s e l e c t r o p l a t e d w i t h copper. The m i r r o r s a r e mounted on i n v a r beams w i t h i n the c e l l . I n v a r has a low t h e r m a l c o n t r a c t i o n , so the d i s t a n c e between the m i r r o r s s t a y s c o n s t a n t as the c e l l c o o l s . S u r r o u n d i n g the c e l l a r e two p o l i s h e d copper r a d i a t i o n s h i e l d s . The c e l l , s h i e l d s , and t r a n s f e r o p t i c s a r e a l l c o n t a i n e d i n a vacuum tank . H e l i u m vapor c i r c u l a t e s t h r o u g h copper tubes s o l d e r e d t o the c e l l t o c o o l the sample gas. The h e l i u m vapor then c i r c u l a t e s around the copper s h i e l d s t o e x t r a c t the heat i n p u t t o the s h i e l d s from t h e r m a l r a d i a t i o n . A s o p h i s t i c a t e d m e c h a n i c a l f e e d t h r o u g h scheme a l l o w s f o r adjustment of the c e l l o p t i c s even when the c e l l i s c o l d . The i n p u t t r a n s f e r o p t i c s have been d e s i g n e d t o match the f/10 o p t i c a l c e l l t o an f/5 i n t e r f e r o m e t e r and a l s o t o an f /11 l a s e r d i o d e s p e c t r o m e t e r . The output t r a n s f e r o p t i c s match the c e l l l i g h t beam t o a l i q u i d h e l i u m c o o l e d bolometer w h i c h a c c e p t s a l i g h t cone of about f / 4 . 5 . The vacuum windows of the o p t i c a l c e l l a r e c r y s t a l q u a r t z l e n s e s ( f o r 2 0 _ 200 cm ' , C s l f o r 200 cm ' and up) and a r e d e s i g n e d t o image the t r a n s f e r o p t i c s m i r r o r s onto the c e l l f o l d i n g m i r r o r s . By d o i n g t h i s extreme r a y s , due t o an i n t e r f e r o m e t e r a p e r t u r e of f i n i t e s i z e , a r e prop a g a t e d t h r o u g h the o p t i c a l system w i t h o u t v i g n e t t i n g . COLD C E L L FIELD I TRANSFER RADIATION SHIELDS MIRROR! OPTICS VACUUM V E S S E L FOLDING MIRROR VACUUM WINDOW/LENS Figure 11 - Diagram of the low temperature multipass absorption c e l l Mirrors have 1 m radius of curvature and are spaced 1 m apart, low temperature c e l l i s 1.2 m long and 20 cm in diameter, Vacuum tank i s 1.75 m long and 35 cm in diameter. Drawing shows minimum o p t i c a l path of 4 m. L i q u i d helium cooled bolometer s i t s above transfer optic area (out of the plane of the diagram). cn 69 A computer c a l c u l a t i o n has demonstrated t h a t t h i s c e l l d e s i g n i s p r a c t i c a l from a c r y o g e n i c s t a n d p o i n t . The c e l l w i l l be c o o l e d by h e l i u m vapor o b t a i n e d from the e v a p o r a t i o n of l i q u i d h e l i u m . The c a l c u l a t i o n p r o v i d e s an e s t i m a t e of the r a t e of h e l i u m consumption, and i s based b a l a n c i n g the heat i n p u t s from r a d i a t i o n and c o n d u c t i o n w i t h the heat o u t p u t due t o i n c r e a s i n g the e n t h a l p y of the h e l i u m vapor c o o l a n t . T h i s c a l c u l a t i o n i s based on a s i m i l a r one used by P r o f . Gush t o e s t i m a t e the h e l i u m consumption of the r o c k e t borne, l i q u i d h e l i u m c o o l e d i n t e r f e r o m e t e r . A s i m p l i f i e d p r e s e n t a t i o n of t h i s c a l c u l a t i o n i s g i v e n by the f o l l o w i n g d r a wing and d i s c u s s i o n . Here T c ,T, ,T2 ,T3 ,TC a r e the t e m p e r a t u r e s of the c e l l , s h i e l d 1, s h i e l d 2, the vacuum t a n k , and the l i q u i d h e l i u m r e s e r v o i r , r e s p e c t i v e l y . Q( , Qz , Q 3 are the heat f l o w s by c o n d u c t i o n , from s h i e l d 1 t o the c e l l , from s h i e l d 2 t o s h i e l d 1, and from the tank w a l l t o s h i e l d 2, r e s p e c t i v e l y . R i ' R 2 ' R 3 a r e t h e r a d i a n t heat i n p u t s , a g a i n from s h i e l d 70 1 t o the c e l l , from s h i e l d 2 t o s h i e l d 1, and from the tank w a l l t o s h i e l d 2. , Q s , Q 6 a r e heat f l o w s a b s o r b e d by the changes i n e n t h a l p y of the c o o l i n g v apor, from the c e l l t o s h i e l d 1, from s h i e l d 1 t o 2, and from s h i e l d 2 t o room t e m p e r a t u r e . The heat b a l a n c e e q u a t i o n s f o r t h i s model f o l l o w . At the c e l l : Q + R, = Q*, At s h i e l d 1 : Q 2 + Rx + Q4 = Q r At s h i e l d 2: Q 3 + R 3 + Q r = Q 6 Ql2 3 a r e heat f l o w r a t e s , i n W a t t s , i n t o the c e l l and s h i e l d s due t o c o n d u c t i o n . For. example, Q/ i s g i v e n by: Q , = x / c f r , - r c ) where K ( c i s the t h e r m a l c o n d u c t i v i t y of the s u p p o r t s t r u c t u r e of the o p t i c a l c e l l and (T/ - Tc) i s the t e m p e r a t u r e d i f f e r e n c e between s h i e l d 1 and the c e l l . The heat f l o w s e x t r a c t e d from the c e l l and s h i e l d s by t h e h e l i u m vapor a r e Q^y^- For example, Q 4 i s g i v e n by: Q4 = m (L tCP (Tc-To)) where m i s the mass f l o w r a t e of the c o o l i n g g a s , L i s the l a t e n t heat of e v a p o r a t i o n of h e l i u m and Cp i s t h e s p e c i f i c heat of h e l i u m . The r a d i a n t heat i n p u t s , R / y i / 5 , a r e due t o b l a c k b o d y r a d i a t i o n from s t r u c t u r e s a t h i g h e r t e m p e r a t u r e s t o s t r u c t u r e s a t lower t e m p e r a t u r e s . For example R/ i s g i v e n 71 by: (42) where 0* i s the S t e f a n - B o l t z m a n n c o n s t a n t , A c i s the s u r f a c e a r e a of the c e l l , and E/ c i s the e m i s s i v i t y which t a k e s i n t o a c count the e m i s s i v i t i e s of the c e l l w a l l and s h i e l d 1, and t h e i r geometry. The computer c a l c u l a t i o n s o l v e s s i m u l t a n e o u s l y f o r the t h r e e unknowns of t h i s system: T/ , T^ _ , m, g i v e n i n p u t s of the e m i s s i v i t i e s , t h e r m a l c o n d u c t i v i t i e s , and d e s i r e d c e l l o p e r a t i n g t e m p e r a t u r e . The r e s u l t s f o r the c e l l o p e r a t i n g a t a temperature of 20K a r e : T/ = 144K, T^ = 243K, m = 0.435* 10 gms/sec, t h i s i s a l i q u i d h e l i u m l o s s r a t e of 3.08 l i t e r s per day. T h i s i s the e x p e c t e d h e l i u m consumption once the c e l l has reached the o p e r a t i n g t e m p e r a t u r e ; a d d i t i o n a l h e l i u m w i l l be n e c e s s a r y t o c o o l i t down i n i t i a l l y . The c e l l c r y o g e n i c d e s i g n a t t e m p t s t o m i n i m i z e t h e r m a l c o n d u c t i o n from room temperature t o the c e l l by u s i n g low t h e r m a l c o n d u c t i v i t y m a t e r i a l s and l o n g p a t h l e n g t h s i n the c e l l s u s p e n s i o n system. The r a d i a n t h e a t i n g i s a l s o m i n i m i z e d by d e s i g n i n g the c e l l and s h i e l d s t o be as r e f l e c t i v e as p o s s i b l e . The s t a i n l e s s s t e e l o p t i c a l c e l l i s e l e c t r o p l a t e d w i t h copper t o i n c r e a s e the t h e r m a l c o n d u c t i v i t y . T h i s w i l l i n s u r e temperature u n i f o r m i t y a c r o s s the c e l l and w i l l conduct heat more e f f i c i e n t l y t o the c o o l i n g v a p o r . 72 The problem of d i f f r a c t i o n as mentioned above i s c r u c i a l t o t he performance of t h i s c e l l i n the f a r - i n f r a r e d . A c a l c u l a t i o n of the s p h e r i c a l a b e r r a t i o n and a s t i g m a t i s m (41) of the l i g h t beam a t maximum p a t h l e n g t h shows t h a t these a b e r r a t i o n s a r e n e g l i g i b l e compared t o d i f f r a c t i o n . In o r d e r t o u n d e r s t a n d t o what e x t e n t d i f f r a c t i o n d i s t o r t s the o p t i c a l beam an e x p e r i m e n t a l i n v e s t i g a t i o n was undertaken. The problem s i m p l y s t a t e d i s : Does the beam spot s i z e i n c r e a s e w i t h s u c c e s s i v e r e f l e c t i o n s i n the m i r r o r c e l l ? T h i s d i s c u s s i o n b e g i n s by f o l l o w i n g the l i g h t beam th r o u g h the c e l l . The t r a n s f e r o p t i c s i n j e c t an f/10 beam i n t o the c e l l so t h a t the beam i s f o c u s s e d a t the f i e l d m i r r o r edge and then f i l l s one of the t w i n m i r r o r s . The t w i n m i r r o r f o c u s s e s the beam back t o a s m a l l spot on the s u r f a c e of the f i e l d m i r r o r . The l i g h t beam c o n t i n u e s t o d i v e r g e back t o the t w i n m i r r o r s and then f o c u s a g a i n onto the f i e l d m i r r o r , r e p e a t e d l y . F i n a l l y , the beam e x i t s the c e l l at the edge of the f i e l d m i r r o r o p p o s i t e t o the p o i n t a t which i t was i n j e c t e d . Every time the l i g h t beam r e f l e c t s o f f the t w i n m i r r o r s i t e n c o u n t e r s an e f f e c t i v e a p e r t u r e and d i f f r a c t s . The d i f f r a c t i o n ( F r a u n h o f e r ) of a p l a n e wave by a c i r c u l a r a p e r t u r e may be e x p r e s s e d i n terms of an A i r y r a d i u s : (43) r ~ i.xz R_X 0 which i s the r a d i u s of the d i f f r a c t i o n p a t t e r n from the c e n t r a l maximum t o the c e n t r e of the f i r s t dark r i n g , R i s 73 the d i s t a n c e from the a p e r t u r e , D i s the a p e r t u r e d i a m e t e r , and X i s the wav e l e n g t h . As the beam r e f l e c t s back and f o r t h i n the c e l l i t might be e x p e c t e d t h a t the beam spot on the f i e l d m i r r o r would grow i n s i z e , as the r e s u l t of s u c c e s s i v e d i f f r a c t i o n s . C o n v e r s e l y , i t might be argued t h a t the d i f f r a c t e d beam i s r e f o c u s s e d t o a spot on a l t e r n a t i n g t w i n m i r r o r r e f l e c t i o n s . T h i s argument r e l i e s on a F o u r i e r o p t i c s analogue t o the m i r r o r system ( 43 ) . The l i g h t beam f i l l s the t w i n m i r r o r and d i f f r a c t s , where the t w i n m i r r o r can be c o n s i d e r e d the t r a n s f o r m l e n s . The t w i n m i r r o r converges the d i f f r a c t i o n spot onto the f i e l d m i r r o r . T h i s i s i n the F o u r i e r t r a n s f o r m p l a n e of the t w i n m i r r o r and the A i r y p a t t e r n formed i s the.two d i m e n s i o n a l ' F o u r i e r t r a n s f o r m of the c i r c u l a r a p e r t u r e . The d i f f r a c t i o n spot now r e f l e c t s t o f i l l the o t h e r t w i n m i r r o r , which can be c o n s i d e r e d the i n v e r s e t r a n s f o r m l e n s . The i n v e r s e F o u r i e r t r a n s f o r m of the p a t t e r n a t the f i e l d m i r r o r ( the A i r y p a t t e r n ) appears at the image p l a n e of the i n v e r s e t r a n s f o r m l e n s . Thus, the d i f f r a c t i o n spot i s reimaged t o a p o i n t , and the beam i s s u c c e s s i v e l y d i f f r a c t e d and reimaged every 4 t r a n s i t s of the c e l l . To r e s o l v e t h i s problem t h e o r e t i c a l l y would be d i f f i c u l t , s i n c e r i g o r o u s d i f f r a c t i o n c a l c u l a t i o n s can be e x t r e m e l y complex. There i s no f o r m a l t r e a t m e n t i n the l i t e r a t u r e of a m u l t i p l e pass system of t h i s t y p e . Born and Wolf (44) t r e a t the r e l a t e d s i m p l e r problem of the 74 d i f f r a c t i o n of a s p h e r i c a l w a v e front by a c i r c u l a r a p e r t u r e . The s o l u t i o n y i e l d s a d i f f r a c t i o n p a t t e r n a t the f o c a l p l a n e of the s p h e r i c a l l y c o n v e r g i n g beam t h a t i s the same as t h a t f o r p l a n e p a r a l l e l w a v e f r o n t s . However, t h e i n t e n s i t y of the c e n t r a l spot goes t o z e r o on e i t h e r s i d e of the f o c a l p l a n e , a l o n g t he o p t i c a x i s . The d i s t a n c e a l o n g the o p t i c a l a x i s between the n u l l p o i n t s of the c e n t r a l spot i s c a l l e d the f o c a l t o l e r a n c e . I t i s g i v e n by: where f i s the f o c a l l e n g t h of the beam, 2a i s the diameter of the a p e r t u r e , and i s the wav e l e n g t h . In the White c e l l , t he f i e l d m i r r o r i s i n the f o c a l p l a n e of the t w i n m i r r o r , t h e r e f o r e the d i f f r a c t i o n spot -on the f i e l d m i r r o r s h o u l d be the same as the A i r y p a t t e r n . The f o c a l t o l e r a n c e f o r f a r - i n f r a r e d l i g h t a t 20 cm i n t h i s 1 meter c e l l i s 10 cm. The drawing below from (44) shows the c r o s s s e c t i o n of the i n t e n s i t y d i s t r i b u t i o n of the d i f f r a c - t i o n p a t t e r n due to' a c i r c u l a r a p e r t u r e near the fo c u s of a s p h e r i c a l l y c o n v e r g i n g l i g h t beam. Fig. 8.41. Isophotea [contour lines of the intensity I(u, i>)] in a meridional plane near focus of a converging spherical wave diffracted at a circular aperture. The intensity is normalized to unity at focus. The dotted lines represent the boundary of the geometrical shadow. When the figure is rotated about the u-axis, the m i n i m . o n the e-axis generate the A i r y dark rings. 75 An experiment t o measure the d i f f r a c t i o n spot s i z e on s u c c e s s i v e r e f l e c t i o n s i n the m i r r o r c e l l has been performed. The e x p e r i m e n t ' s d e s i g n i s drawn s c h e m a t i c a l l y below. The HeNe l a s e r A i l l u m i n a t e s the microscope o b j e c t i v e B t o form a d i v e r g i n g beam. The l e n s e s and i r i s c o m b i n a t i o n C d e f i n e a beam which f o c u s s e s a t the edge of the f i e l d m i r r o r and f i l l s the t w i n m i r r o r F. A v a r i a b l e a p e r t u r e or p i n h o l e E i s p l a c e d i n f r o n t of the t w i n m i r r o r . The beam e x i t s the c e l l and the d i f f r a c t i o n p a t t e r n i s f o c u s s e d by the l e n s G onto the scr e e n H. R a d i a t i o n c o r r e s p o n d i n g t o p a t h l e n g t h s of 2 , 6 , 10 , ... a r e t r a n s m i t t e d by the c e l l used i n t h i s e x p e r i m e n t , where i s the l e n g t h of the c e l l ( t h i s i s d i f f e r e n t from the c e l l d e s i g n e d h e r e ) . The a p e r t u r e i s p l a c e d o n l y over one t w i n m i r r o r . T h e r e f o r e , l i g h t c o r r e s p o n d i n g t o a p a t h l e n g t h of 2 passes t h r o u g h the a p e r t u r e once, 6 passes t h r o u g h t w i c e , e t c . U s i n g a 3 mm di a m e t e r a p e r t u r e , the same A i r y p a t t e r n 76 was obser v e d on t h e s c r e e n f o r p a t h l e n g t h s of 2, 6, 10, 14, 18, and 34jf, c o r r e s p o n d i n g t o 1, 2, 3, 4, 5, and 9, passes through the a p e r t u r e . The A i r y d i s k d i a m e t e r measured on the s c r e e n , t a k i n g i n t o account the m a g n i f i c a t i o n by the l e n s G, i s the same as p r e d i c t e d by egn. 4.1 t o b e t t e r than 10%. In a d d i t i o n , an experiment was c o n d u c t e d w i t h an a p e r t u r e diameter of 0.3 mm. A g a i n , the same d i f f r a c t i o n p a t t e r n i s observed f o r p a t h l e n g t h s of 2, 6, 10^. The measured A i r y d i s k d i ameter was the same as the p r e d i c t e d d i a m e t e r , where the e r r o r i n the p r e d i c t i o n and i n the measurement i s l e s s than 10%. These e x p e r i m e n t s demonstrate t h a t the d i f f r a c t i o n spot does not grow w i t h s u c c e s s i v e r e f l e c t i o n s and t h a t n e i t h e r of the proposed arguments i s c o r r e c t . A more s a t i s f a c t o r y e x p l a n a t i o n may l i e i n the f a c t t h a t most of the l i g h t i n t e n s i t y of the d i f f r a c t e d beam l i e s i n the c e n t r a l s p o t . The o b s e r v a t i o n of the d i f f r a c t i o n p a t t e r n from a s i n g l e a p e r t u r e even a f t e r r e p e a t e d r e f l e c t i o n s may j u s t be the most r e c e n t d i f f r a c t i o n of the c e n t r a l s p o t . The o u t e r r i n g s of p r e v i o u s d i f f r a c t i o n s have l i t t l e i n t e n s i t y and are o b s c u r e d by the A i r y p a t t e r n of the l a s t d i f f r a c t i o n . An i n d i c a t i o n of what i s happening here might be f o u n d by making i n t e n s i t y measurements of the c e n t r a l spot on s u c c e s s i v e d i f f r a c t i o n s . I t would be i n t e r e s t i n g and v a l u b l e t o c o n t i n u e t h i s i n v e s t i g a t i o n s i n c e no p r e v i o u s work, e i t h e r e x p e r i m e n t a l or t h e o r e t i c a l , on the d i f f r a c t i o n of l i g h t i n a White c e l l has been found. 77 V. CONCLUSION The p r e s e n t work c o v e r s a s p e c t s of c o l l i s i o n induced a b s o r p t i o n by homonuclear d i a t o m i c m o l e c u l e s . The p r e v a l e n c e of t h i s s p e c i e s of m o l e c u l e s i n the a s t r o p h y s i c a l e n v i r onments of p l a n e t a r y atmospheres and g a l a c t i c m o l e c u l a r c l o u d s makes t h e i r f a r - i n f r a r e d s p e c t r a p a r t i c u l a r l y i n t e r e s t i n g . The s i m u l a t i o n i n the l a b o r a t o r y of c o n d i t i o n s s i m i l a r t o the s e environments has been the major m o t i v a t i o n f o r t h i s work. The r e s e a r c h r e p o r t e d here has i n v o l v e d : an i n v e s t i g a t i o n of the t h e o r y of c o l l i s i o n i n d u c e d a b s o r p t i o n , a measurement of the f a r - i n f r a r e d (5 - 70 cm ') a b s o r p t i o n s p e c t r a of l i q u i d n i t r o g e n and l i q u i d oxygen a t 77K, and the d e s i g n of a low t e m p e r a t u r e , l o n g p a t h l e n g t h , o p t i c a l a b s o r p t i o n c e l l . The f a r - i n f r a r e d spectrum of l i q u i d oxygen measured here has not p r e v i o u s l y been p u b l i s h e d . I t i s d e s i r a b l e t o i n c r e a s e the s p e c t r a l bandwidth of both the n i t r o g e n and oxygen measurements t o encompass the e n t i r e r o t a t i o n a l band, and t h e r e b y o b t a i n the i n t e g r a t e d a b s o r p t i o n c o e f f i c i e n t . T h i s c o u l d p r o v i d e i n f o r m a t i o n on the m o l e c u l a r i n t e r a c t i o n s w i t h i n the l i q u i d , i f a s u i t a b l e t h e o r y of t h e s e l i q u i d s e x i s t e d . Good measurements of the e n t i r e r o t a t i o n a l band of thes e m o l e c u l e s i n the l i q u i d phase might m o t i v a t e the development of such a t h e o r y . In a d d i t i o n , a l i q u i d n i t r o g e n a b s o r p t i o n spectrum extended t o h i g h e r f r e q u e n c i e s might h e l p d e t e r m i n e i f l i q u i d n i t r o g e n i s p r e s e n t on the s u r f a c e of Neptune's moon T r i t o n when the Voyager f a r - i n f r a r e d s p e c t r a a r e examined. 78 Work on the f a r - i n f r a r e d a b s o r p t i o n by c o l d hydrogen gas, w i t h the g o a l of o b s e r v i n g dimer a b s o r p t i o n , i s c o n t i n u i n g . The c o m p l e t i o n of the low t emperature c e l l i s e x p e c t e d i n the near f u t u r e and t h e s e e x p e r i m e n t s w i l l b e g i n s h o r t l y t h e r e a f t e r . F u r t h e r i n v e s t i g a t i o n of d i f f r a c t i o n w i t h i n the c e l l o p t i c a l system would be v a l u a b l e , s i n c e t h i s type of c e l l i s f r e q u e n t l y used i n s p e c t r o s c o p y e x p e r i m e n t s and t h e r e i s p r e s e n t l y no d i s c u s s i o n of t h i s i s s u e i n the l i t e r a t u r e . 79 REFERENCES 1. G. E. Ewing, C. J . P. , 54, 487 (1976) 2. A. Watanabe, H. L. Welsh, C. J . P. ,43, 818 (1965) 3. A. R. W. M c K e l l a r , H. L. Welsh, C. J . P. , 52, 1082 (1974) 4. A. R. W. M c K e l l a r , C. J . P. , 62, 760, (1984) 5. L. Frommhold, R. Samuelson, G. Birnbaum, Ap. J . , 283, L79 (1984) 6. U . F i n k , H. P. L a r s o n , Ap. J . , 233, 1021 (1979) 7. E. F. E r i c k s o n et a l , I c a r u s , 35, 61 (1978) 8. R. Hanel and the Voyager I n f r a r e d Spectrometer Team, Sc i e n c e 204, 972 (1979) 9. R. Hanel e t a l , S c i e n c e , 206, 952 (1979) 10. R. Hanel e t a l , S c i e n c e , 212, 192 (1981) 11. R. Hanel e t a l , S c i e n c e , 215, 544 (1979) 12. R. C o u r t i n , I c a r u s , 5_1_, 466 ( 1 982) 13. D. M o r r i s o n , Ann. Rev. A s t . A s t r o . , 20, 469 (1982) 14. D. P. C r u i c k s h a n k , P. M. S i l v a g g i o , Ap. J . , 233, 1016 (1979) 15. R. H. Brown, D. P. C r u i c k s h a n k , S c i . Am. , 253, 38 ( J u l y 1985) 16. J . Van Kranendonk, Z. J . K i s s , C. J . P. , 3_7, 1187 (1959) 17. J . P. C o l p a , J . A. A. K e t e l a a r , M o l . Phys. , 1, 343 (1958) 18. M. M. S h a p i r o , Ph. D. T h e s i s , U n i v e r s i t y of T o r o n t o , T o r o n t o , O n t a r i o (1965) 19. J . D. P o l l , J . L. Hunt, C. J . P. , 59, 1448 (1981) 20. D. J . G r i f f i t h s , I n t r o d u c t i o n t o E l e c t r o d y n a m i c s , P r e n t i c e - H a l l , Englewood C l i f f s , NJ (1981), pg. 130. 21. N. W. B. Stone e t a l , C. J . P. , 62, 338 (1984) 80 22. A. D. Buckingham, R. L. D i s c h , D. A. Dunmuir, J . Am. Chem. Soc. , 90, 3104 (1968) 23. G. Birnbaum, I n t e r m o l e c u l a r S p e c t r o s c o p y and Dynamical P r o p e r t i e s of Dense Systems, E d i t e d by J . Van Kranendonk, N o r t h - H o l l a n d , Amsterdam, The N e t h e r l a n d s (1980), pg. 132. 24. G. H e r z b e r g , S p e c t r a of D i a t o m i c M o l e c u l e s , D. Van N o s t r a n d , NY, NY (1950), pg. 107 25. A. I . P. Handbook, M c G r a w - H i l l , NY, NY, pg. 7-168. 26. J . I . S t e i n f e l d , M o l e c u l e s and R a d i a t i o n , MIT P r e s s , Cambridge, Mass. (1981), pg. 107 27. H. P.. Gush, P r o c e e d i n g s of 1983 Space Helium Dewar Con f e r e n c e , E d i t e d by, J . B. H e n d r i c k s , G. R. K e r r , U n i v e r s i t y of Alabama i n H u n t s v i l l e (1984), pg. 99. 28. M. H a l p e r n , H. P. Gush, E. Wishnow, V. DeCosmo, su b m i t t e d t o Ap. O p t i c s (1985) 29. M. H a l p e r n , Ph. D. T h e s i s , MIT, Cambridge, Mass. (1983) 30. D. R. Bosomworth, H. P. Gush, C. J . P. , 43, 751 (1965) 31. U. Buontempo, S. C u n s o l o , G. J a c u c c i , J . J . Weis, J . Chem. Phys. , 63, 2570 (1975) 32. I . R. Dagg et a l , C. J . P. , 63, 625 (1985) 33. N. W. B. Stone, D. W i l l i a m s , M o l . Phys. , J_, 85 (1965) 34. J . L. U r b a n i a k , I . R. Dagg, G. E. Reesor, C. J . P. , 55, 496 (1977) 35. M. M. S h a p i r o , H. P. Gush, C. J . P. , 44, 949 (1966) 36. C. R. C. Handbook, C h e m i c a l Rubber Co. , C l e v e l a n d , OH (1971), pg. E-43. 37. M. Evans, M o l . Phys. , 29, 1345 (1975) 38. S. C u n s o l o , H. P. Gush, C. J . P. , 2058 (1972) 39. J . U. White, J . 0. S. A. , 32, 285 (1942) 40. R. P. B l i c k e n s d e r f e r , G. E. Ewing, R. L e o n a r d , Ap. O p t i c s , 7, 2214 (1968) 41. D. Horn, G. C. P i m e n t a l , Ap. O p t i c s , H), 1892 (1971) 42. G. K. White, E x p e r i m e n t a l T e c h n i q u e s i n Low Temperature 81 P h y s i c s , O x f o r d , London, (1968). pg. 220. 43. E. Hecht, A. Z a j a c , O p t i c s , Addison-Wesley, Reading, Mass. (1979) 44. M. B o r n , E. Wolf, P r i n c i p l e s of O p t i c s , Pergammon, London (1959) pg. 439. 

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