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

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NONLINEAR RESONANT PHOTOIONIZATION IN MOLECULAR IODINE by GEORGENA SARAH PETTY SIL B . S c , Un ivers i ty of Saskatchewan, 1973 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES Department of Physics We accept th i s thes i s as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September, 1976 © Georgena Sarah Petty S i l , 1976 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 l m e n t o f 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 o f B r i t i s h C o l u m b i a , I ag ree 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 v e copy 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 an ted by the Head of my D e p a r t -ment or by h i s r e p r e s e n t a t i v e s . I t i s unde r s tood t h a t c opy -i n g or p u b l i c a t i o n o f 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 o f 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 Co lumbia 2075 Wesbrook P l a c e Vancouve r , Canada V6T 1W5 Date - i -ABSTRACT S t r ong p h o t o i o n i z a t i o n s p e c t r a have been obse rved i n m o l e c u l a r I od i ne f o l l o w i n g l a s e r e x c i t a t i o n i n the near u l t r a v i o l e t . The dependence upon l a s e r power, and the s t r u c -t u r e o f the s p e c t r a a re c o n s i s t e n t w i t h t h r e e - p h o t o n i o n i z a -t i o n w i t h resonance i n an i n t e r m e d i a t e s t a t e e x c i t e d by two pho ton s . V i b r a t i o n a l a n a l y s i s i n d i c a t e s an e l e c t r o n i c energy T g o f 53 , 562.75 ± 1 c m - * , a harmonic v i b r a t i o n a l c o n s t a n t coe of 241.4 ± 0.4 c m " * , and an anharmonic v i b r a t i o n a l c o n s t a n t t o e x e o f 0.58 ± 0.06 c m " * . R o t a t i o n a l a n a l y s i s done by the F ranck-Condon method, whereby the r e l a t i v e e x p e r i m e n t a l band i n t e n s i t i e s a re compared w i t h t h e o r e t i c a l v a l u e s , i n d i c a t e s 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 r g i n the r e s onan t e l e c t r o n i c 0 s t a t e i s 2.567 ± 0.002A, c o r r e s p o n d i n g to a r o t a t i o n a l c o n -s t a n t B of 0.04029 ± 0.00007 c m - 1 . The new e l e c t r o n i c s t a t e e has , w i t h h i gh p r o b a b i l i t y , the d e s i g n a t i o n 1 . S e v e r a l im -y p u r i t y l i n e s were ob se rved a t e x c i t i n g e n e r g i e s 26,297.14 ± 1 c m " 1 ( h a l f w i d t h 8.09 c m " 1 ) , a t 26,915.22 ± 1 c m " 1 , and a t -1 2 02 27,343.96 ± 1 cm 1 . The i m p u r i t y s i g n a l v a r i e s as I . The f e a t u r e s l i k e l y a r i s e from complex m o l e c u l a r s p e c i e s formed i n r e a c t i o n s a t h i gh t empe ra tu re w i t h l^, and have not been i d e n t i f i e d . The p h o t o i o n i z a t i o n e f f i c i e n c y of i n n o n l i n e a r a b s o r p t i o n e x h i b i t s an appa ren t re sonance i n the v i c i n i t y of 80,000 c m " 1 i n terms o f t o t a l m o l e c u l a r ene rgy . - i i _ TABLE OF CONTENTS Chapte r p a g e 1. INTRODUCTION ! 2. THEORY AND ANALYTIC TECHNIQUES 2.1 Theory of N o n l i n e a r O p t i c s 7 2.2 Coarse S t r u c t u r e : V i b r a t i o n a l A n a l y s i s . 12 2.3 F i ne S t r u c t u r e : R o t a t i o n a l A n a l y s i s . . 17 2.4 S e l e c t i o n Ru le s f o r R a d i a t i v e A b s o r p t i o n . 21 2.5 The I od i ne M o l e c u l e 25 2.6 V i b r a t i o n a l A n a l y t i c Techn iques 30 2.7 F ranck -Condon R o t a t i o n a l A n a l y t i c Techn iques 30 2.8 E l e c t r o n i c C o n f i g u r a t i o n s and Band Contour 34 3. INSTRUMENTATION AND EXPERIMENTAL DESIGN 3.1 I n t r o d u c t i o n 3 9 3.2 C a l i b r a t i o n and O p e r a t i n g C h a r a c t e r -i s t i c s 42 3.3 S i g n a l P r o c e s s i n g 57 4. DATA ANALYSIS 4.1 I n t r o d u c t i o n 65 4.2 Power-Dependence o f the P h o t o i o n i z a t i o n S i g n a l 69 - i i i -TABLE OF CONTENTS ( c o n t . ) Chapter Page 4.3 V i b r a t i o n a l A n a l y s i s 72 4.4 R o t a t i o n a l A n a l y s i s 85 4.5 Band Contour A n a l y s i s 93 4.6 I m p u r i t y L i n e s 99 5. DISCUSSION 5.1 R e s u l t s and C o n c l u s i o n s 101 5.2 Fu tu re Research 106 Append ix A CALIBRATION OF PHOTOMULTIPLIER FILTERS . . . 108 Append ix B DETAILS OF BRANCH CONTOUR CALCULATIONS . . . I l l REFERENCES , , , - i v -LIST OF TABLES Tab le Page I V i b r a t i o n a l Energy L e v e l s o f the Ground E l e c t r o n i c S t a t e of 2 7 II Power-Dependence of the P h o t o i o n i z a t i o n S i g n a l . . 71 n i I I I F r i n g e S e p a r a t i o n o f the (0-v ) and (v -0) Bands of I 0 77 IV C a l i b r a t i o n o f the F a b r y - P e r o t I n t e r f e r o m e t e r . . 78 n i V Energy S e p a r a t i o n of the (0-v ) and (v -0) Bands of I 2 79 i VI E x p e r i m e n t a l E v a l u a t i o n of co Us ing the i e ( v - 0 ) P r o g r e s s i o n 80 II i VII F r i n g e S e p a r a t i o n of the (1-v ) and (v -1) Bands of ^ 81 II i V I I I Energy S e p a r a t i o n of the (1-v ) and (v -1) Bands o f ^ 82 i IX E x p e r i m e n t a l E v a l u a t i o n of co Us ing the i e (v -1) P r o g r e s s i o n 83 X E n e r g i e s o f the Observed Resonances i n . . . . 84 XI R e l a t i v e E q u i l i b r i u m P o p u l a t i o n of V i b r a t i o n a l S t a t e s i n the Ground E l e c t r o n i c S t a t e of . . . 87 XI I R e l a t i v e I n t e n s i t i e s o f the P h o t o i © n i z a t i o n Bands of I 2 90 X I I I T h e o r e t i c a l F ranck -Condon F a c t o r s f o r S e l e c t e d V i b r a t i o n a l T r a n s i t i o n s Between the Ground and Resonant E l e c t r o n i c S t a t e s o f I „ 91 - v -LIST OF TABLES ( c o n t . ) T a b l e Page XIV Compar ison o f the I 2 E x p e r i m e n t a l I n t e n s i t y R a t i o s Wi th the R a t i o s of the T h e o r e t i c a l 0 Franck-Condon F a c t o r s From 3 = 0.096 to 0.104A . . 92 XV D e n s i t y of ND F i l t e r #3.0 as a F u n c t i o n o f Wavelength 109 XVI T o t a l D e n s i t y , as a F u n c t i o n of Wave leng th , of M a t e r i a l s S h i e l d i n g P h o t o m u l t i p i i e r EMI 6256S . . 110 - v i -LIST OF FIGURES AND ILLUSTRATIONS F i g u r e Page 1. The Appara tu s 40 2. C i r c u i t Diagram of SLO-SYN T r a n s l a t o r DC Power Supp ly 46 3. SLO-SYN Synchronous Motor W i r i n g Diagram 47 4. EMI 6256S P h o t o m u l t i p i i e r Tube C i r c u i t 52 5. L i n e a r i t y o f P h o t o m u l t i p i i e r Tube EMI 6256S . . . 53 6. L i n e a r i t y of Cha r t Reco rde r 56 7. P h o t o e l e c t r o n S i g n a l P u l s e Shape a t T e r m i n a t i n g Impedance 100 Ktt 58 8. V o l t a g e Dependence o f the I od i ne Band Contour I l l u s t r a t e d f o r a T y p i c a l Band a t 100°C 63 9. V o l t a g e Dependence o f the Peak S i g n a l I n t e n s i t y . . 64 10. T y p i c a l P h o t o e l e c t r o n Spectrum o f I od i ne Vapor a t 20°C Accompanied by L a se r Output 66 11. T y p i c a l P h o t o e l e c t r o n Spectrum of I o d i ne Vapor a t 100°C Accompanied by La se r Output 67 12. P o r t i o n o f the P h o t o e l e c t r o n Spectrum at H i ghe r R e s o l u t i o n Accompanied by F a b r y - P e r o t F r i n g e s . . 68 13. Dependence of S i g n a l I n t e n s i t y on La se r Power I l l u s t r a t e d f o r the (1 -0 ) Band 70 14. R a t i o of N o r m a l i z e d I n t e n s i t i e s to T h e o r e t i c a l F ranck -Condon F a c t o r s A g a i n s t F i n a l Energy . . . . 94 15. N o r m a l i z e d Band Contour of the 0* ->- 0 + 9 g E l e c t r o n i c T r a n s i t i o n 96 - v i i -FIGURES AND ILLUSTRATIONS ( c o n t . ) F i g u r e Page 16. N o r m a l i z e d Band Contour o f the 0 + -> 1 9 9 E l e c t r o n i c T r a n s i t i o n 97 17. No rma l i z ed Band Contour of the 0 + + 2 g g E l e c t r o n i c T r a n s i t i o n 98 18. E l e c t r o n i c P o t e n t i a l Diagram I n c l u d i n g the Approx imate P o t e n t i a l o f the New S t a t e Super imposed on the Known V a l e n c e - S h e l l S t a t e s on I 0 104 - v i i i -ACKNOWLEDGEMENT With p l e a s u r e I thank P r o f e s s o r F.W. Dalby f o r h i s s t i m u l a t i n g a d v i c e , a s s i s t a n c e and encouragement d u r i n g t h i s r e s e a r c h p r o j e c t . A l s o c l o s e l y a s s o c i a t e d w i t h the p r o j e c t was P r o f e s s o r M.H.L. P r y c e , who made i n v a l u a b l e t h e o r e t i c a l c o n t r i b u t i o n s . Dr. C. Ta i i s thanked f o r many h e l p f u l d i s c u s s i o n s . The t e c h n i c a l e x p e r t i s e o f John Lees and Herman B l e s s i s a l s o a p p r e c i a t e d . The N a t i o n a l Research C o u n c i l o f Canada p r o v i d e d f i n a n c i a l s uppo r t i n the form of r e s e a r c h g r an t s and s c h o l a r s h i p s . I a l s o thank my husband Ashok f o r what may be the most i m p o r t a n t c o n t r i b u t i o n o f a l l : h i s moral s uppo r t and u n f a i l i n g good humor d u r i n g the c o m p l e t i o n of t h i s t h e s i s . - i x -To my F a t h e r 1. INTRODUCTION A number of n o n l i n e a r phenomena have been i n v e s t i g a t e d s i n c e the i n t r o d u c t i o n o f the l a s e r as a s p e c t r o s c o p i c t o o l . A l l of the e a r l i e s t work was done i n s o l i d s i n which the g e n e r a t i o n of s e c o n d - o r d e r o p t i c a l harmonics and p a r a m e t r i c c o n v e r s i o n was a c h i e v e d , among o t h e r s , by Franken e t a l . (1961) and G io rdma ine (1962 ) . The i n t e n s i t y o f the gene r -a ted n o n l i n e a r component i s l i m i t e d by i n t e r f e r e n c e due to the normal d i s p e r s i o n o f the m a t e r i a l . I t was soon d i s c o v e r e d t h a t the o n l y means of enhanc ing the n o n l i n e a r ou tpu t to p r a c t i c a l magni tudes was to employ s t r o n g l y b i r e f r i n g e n t c r y -s t a l s i n w h i c h , upon r o t a t i o n , match ing of the r e f r a c t i v e i n d i c e s of the i n c i d e n t and gene r a t ed waves i s p o s s i b l e ( B a l d w i n , 1969 and Z e r n i k e , 1973) . The i n e r t gases and a tomic and m o l e c u l a r vapors became m a t e r i a l s o f i n t e r e s t somewhat l a t e r . In a few cases ( M i l e s and H a r r i s , 1973 and Young e t a l . , 1973) enhancement t e c h n i q u e s were pursued s i m -i l a r to those i n s o l i d s , i n wh ich pha se -match i ng was a c h i e v e d th rough p r e c i s e m i x i n g of gases . Most of the work, however, i n v o l v e d enhancement of the n o n l i n e a r re sponse th rough a t l e a s t one resonance w i t h an a tomic or m o l e c u l a r s t a t e , made p r a c t i c a l w i t h the deve lopment o f t u n a b l e , na r r ow-bandw id th l a s e r s c i r c a 1970. Th i s re sonant -enhancement t e c h n i q u e i s becoming not on l y a means of p a r a m e t r i c c o n v e r s i o n and g e n e r a t i o n of c ohe ren t f a r - u l t r a v i o l e t r a d i a t i o n i n gases - 2 -and v a p o r s , but a l s o a means o f g a i n i n g s p e c t r o s c o p i c i n f o r m a -t i o n about atoms and m o l e c u l e s h e r e t o f o r e i n a c c e s s i b l e . Very l i t t l e work has been c a r r i e d out to date i n t h i s f i e l d . Among o t h e r e x p e r i m e n t s , DC- induced second harmonic g e n e r a t i o n i n the i n e r t gases was ob se rved by F inn and Ward ( 1971 ) , and t h i r d - o r d e r o p t i c a l components were gene ra ted i n a tom ic vapors by Hodgson e t a l . (1974) and Leung e t a l . ( 1974 ) . Resonance f l u o r e s c e n c e i n m o l e c u l a r I od i ne f o l l o w i n g two-photon e x c i t a -t i o n o f the l o w - l y i n g E s t a t e has been s t u d i e d by Rousseau and Wi11iams ( 1974 ) . The p a r t i c u l a r n o n l i n e a r i n t e r a c t i o n which i s the s u b j e c t of the p r e s e n t work i s m u l t i p h o t o n a b s o r p t i o n and i o n i z a t i o n of m o l e c u l e s under the i n f l u e n c e o f t u n a b l e l a s e r r a d i a t i o n . As w i t h most n o n l i n e a r phenomena i n gases and v a p o r s , m u l t i p h o t o n i o n i z a t i o n has r e c e i v e d renewed i n t e r e s t o n l y d u r i n g the l a s t f o u r y e a r s or so . T h e o r e t i c a l i n v e s t i -g a t i o n s have been c a r r i e d out by Lambropoulos (1974) and P i n d z o l a and K e l l y ( 1975 ) , and e x p e r i m e n t a l work has been done by Bakos e t a l . ( 1 972 ) , C o l l i n s e t a l . ( 1 973 ) , C o l l i n s e t a l . ( 1 974 ) , Delone et a l . ( 1 972 ) , LuVan and M a i n f r a y ( 1972 ) , and LuVan et a l . (1972) upon the e lements He, K, Na, Cs, Cs2» N^ and W^. The m u l t i p h o t o n i o n i z a t i o n p roce s s i s d e s c r i b e d as f o l l o w s . When a m o l e c u l e i s i o n i z e d i n a s t r o n g e l e c t r o m a g n e t i c f i e l d of o p t i c a l f r e q u e n c y , a s i t u a t i o n may a r i s e whe re i n the energy of s e v e r a l quanta t u r n s out to be - 3 -equa l to the energy of the bound s t a t e of the e l e c t r o n s . In t h i s case the i o n i z a t i o n w i l l p roceed i n two s t a g e s , m u l t i p h o t o n r e s onan t e x c i t a t i o n o f the m o l e c u l e and i o n i z a -t i o n of the e x c i t e d m o l e c u l e . The second s tage can a l s o have the c h a r a c t e r of a m u l t i p h o t o n t r a n s i t i o n (De lone e t a l . , 1972) . When i o n i z a t i o n o c c u r s v i a an i n t e r m e d i a t e r e s o n a n t s t a t e , new and s i g n i f i c a n t s p e c t r o s c o p i c i n f o r m a t i o n may be o b t a i n e d r e g a r d i n g the e l e c t r o n i c s t r u c t u r e and s p e c t r o s c o p i c pa rameter s of m o l e c u l a r s t a t e s wh ich a re i n a c c e s s i b l e , f o r a v a r i e t y of r e a s o n s , u s i n g c o n v e n t i o n a l a b s o r p t i o n s p e c t r o -scopy. T r a n s i t i o n s wh ich are p a r i t y - f o r b i d d e n i n o n e - s t e p p r o ce s s e s may be i n v e s t i g a t e d i n m u l t i p h o t o n s p e c t r o s c o p y i f the r e s onan t e x c i t e d s t a t e l i e s a t an energy above the ground s t a t e c o r r e s p o n d i n g to an even number of quanta o f i n c i d e n t ene rgy . M u l t i p h o t o n s p e c t r o s c o p y has the a d d i t i o n a l advantage of a l l o w i n g d e t a i l e d i n v e s t i g a t i o n o f h i g h - e n e r g y e l e c t r o n i c s t a t e s u s i n g v i s i b l e l i g h t s o u r c e s . In the p a s t , p o p u l a t i o n of both p a r i t y - f o r b i d d e n and h i g h - e n e r g y s t a t e s c o u l d be a c c o m p l i s h e d o n l y by h i g h - e n e r g y e x c i t a t i o n ( f o r example , e l e c t r i c a l d i s c h a r g e s ) i n which many o t h e r e l e c t r o n i c s t a t e s were s i m u l t a n e o u s l y e x c i t e d . The subsequent r e - e m i s s i o n was g e n e r a l l y e x t r e m e l y c o m p l i c a t e d and the a s s i gnment s were at bes t ambiguous. In c o n t r a s t , m u l t i p h o t o n e xpe r imen t s can s e l e c t i v e l y p o p u l a t e such f o r b i d d e n s t a t e s w i t h o u t i n t e r -f e r e n c e from o t h e r e l e c t r o n i c s t a t e s . M u l t i p h o t o n s p e c t r o s c o p y - 4 -a l s o has the advantage a l s o has the advantage of r e d u c i n g Dopp le r b roaden ing i n a p p l i c a t i o n s such as doub le-beam expe r imen t s (B loembergen , 1965 and Cagnac e t a l . , 1973) . M o l e c u l a r I od i ne i s the s u b j e c t of the p r e s e n t m u l t i -photon i n v e s t i g a t i o n s . The n a t u r e and i d e n t i f i c a t i o n o f the h i g h e r v a l e n c e - s h e l l s t a t e s and the Rydberg s t a t e s of remain con fu sed and c o n t r o v e r s i a l , -and even some a s p e c t s of the l ower v a l e n c e - s h e l l s t a t e s a re i n c o n t r o v e r s y . M o l e c u l a r I od i ne has been e x t e n s i v e l y s t u d i e d both i n a b s o r p t i o n and i n e m i s s i o n , and a g r e a t many papers have been devoted to the c o r r e l a t i o n of e x p e r i m e n t a l e v i d e n c e w i t h p r e d i c t i o n s on the p o t e n t i a l c u r ve s and o t h e r f e a t u r e s of the numerous e l e c t r o n i c s t a t e s . N e v e r t h e l e s s , a number of c o n t r a d i c t o r y s t a t emen t s r e g a r d i n g t h i s m o l e c u l e e x i s t even i n the more r e c e n t l i t e r a t u r e . The a n a l y s e s of Haranath and Rao ( 1958 ) , LeRoy (1970a and 1970b) , Math ie son and Rees ( 1956 ) , M u l l i k e n ( 1971 ) , Nobs and W ie l and ( 1966 ) , and V e n k a t e s w a r l u (1970) c o n f l i c t on the p o i n t s : (a) the number of band systems i n c e r t a i n r e g i o n s o f the s p e c t r u m , and the ar rangement o f bands i n t o the se s y s tems , (b) the f i n a l s t a t e s i n the u l t r a v i o l e t re sonance f l u o r e s c e n c e s y s tems , (c ) the b a s i c s p e c t r o s c o p i c c o n s t a n t s ( 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 , e l e c t r o n i c p o t e n t i a l - w e l 1 - 5 -m in ima, and d i s s o c i a t i o n e n e r g i e s ) o f both hi g h-and l ow -ene r g y s t a t e s , (d) e l e c t r o n i c c o n f i g u r a t i o n s and d i s s o c i a t i o n p r oduc t s o f the upper s t a t e s . T h i s amply demons t ra te s t h a t w i t h i t s ve r y complex s p e c -trum i s a good c a n d i d a t e f o r i n v e s t i g a t i o n by m u l t i p h o t o n t e c h n i q u e s . In the p r e s e n t work, the I o d i n e m o l e c u l e i s e x c i t e d i n the near u l t r a v i o l e t w i t h a p u l s e d , c o n t i n u o u s l y t u n a b l e , na r r ow-bandw id th l a s e r . I t i s known t h a t the spect rum of I o d i ne changes i n the p re sence o f f o r e i g n gases such as argon and n i t r o g e n , and thus the e x p e r i m e n t a l work was pe r fo rmed i n pure I od i ne vapor wh ich was d i s t i l l e d i n t o an e vacua ted c e l l . The e x p e r i m e n t a l c o n d i t i o n s are such t h a t we e xpec t t r i p i e - p h o t o n i o n i z a t i o n of the I od i ne m o l e c u l e v i a the r e a c t i o n : I 2 + 3v •* I 2 + + e " , accompanied by a ve ry sma l l pe r cen tage of t r i p l e - p h o t o n d i s -s o c i a t i o n . As d i s c u s s e d i n Chap te r 2, any re sonances which o c c u r s i n w i l l c o r r e s p o n d to an i n t e r m e d i a t e s t a t e e x c i t e d by two photons . The range o f e x c i t i n g energy i s 26,316 -27,397 c m - 1 . Thus the a c c e s s i b l e r e sonan t t r a n s i t i o n s a re those which are p a r i t y - f o r b i d d e n from the ground e l e c t r o n i c s t a t e and whose energy l i e s between 52,632 and 54,794 cm~^. In what f o l l o w s , v i b r a t i o n a l and r o t a t i o n a l a n a l y s i s i s - 6 -c a r r i e d o u t , and the a s s i gnment of the e l e c t r o n i c c o n f i g u r a -t i o n i s a t t e m p t e d , upon a new e l e c t r o n i c s t a t e ob se rved i n I2 v i a r e s onan t enhancement of the n o n l i n e a r p h o t o e l e c t r o n s i g n a l . Th i s r e s e a r c h c o n t r i b u t e s to the s p e c t r o s c o p i c i n f o r m a t i o n of the I od i ne m o l e c u l e , but more i m p o r t a n t , t h i s r e s e a r c h c o n t r i b u t e s to the deve lopment o f a new s p e c t r o -s c o p i c t o o l w h i c h , i n v iew of i t s s e n s i t i v i t y and s i m p l i c i t y , i s e xpec ted to have s i g n i f i c a n t a p p l i c a t i o n s . - 7 -2. THEORY AND ANALYTIC TECHNIQUES 2.1 Theory of N o n l i n e a r O p t i c s The d i e l e c t r i c c o n s t a n t e i n M a x w e l l ' s c o n s t i t u t i v e r e l a t i o n TJ = e t i s i n g e n e r a l a f u n c t i o n o f the f i e l d s t r e n g t h |E|. The n o n l i n e a r terms are ve ry sma l l a t o p t i c a l f r e -q u e n c i e s , however, and thus t h e i r e x p e r i m e n t a l d i s c o v e r y o c c u r r e d o n l y a f t e r the deve lopment o f powe r f u l l a s e r s . For pure e l e c t r i c d i p o l e i n t e r a c t i o n s , wh ich form the s t r o n g e s t o p t i c a l t r a n s i t i o n s i n m o l e c u l e s , we may expand the p o l a r i -z a t i o n P i n a power s e r i e s i n the a p p l i e d e l e c t r i c f i e l d E as f o l l o w s : ? VoX E(I + X + ( X ) * + ( X ) 3 t ... ). ( 2 .V ) For any atom or m o l e c u l e , the parameter s a-j , a 2 , a 3 , e t c . are on the o r d e r of the magnitude of the e l e c t r i c f i e l d E i n s i d e m Q the atom or m o l e c u l e , t y p i c a l l y about 3 x 10 v o l t s / c m (B loembergen , 1965) . Thus we may w r i t e P - 0 x l ( , + X + ( X ) 2 t ( X ) 3 + . . . ) . m v m' x m / S i n ce the r a t i o l ^ l / E < 3 x 1 0 " 3 i n the focus of the most powe r f u l l a s e r s a v a i l a b l e (B loembergen , 1965 ) , the n o n l i n e a r response i s ve ry s m a l l . Each o r d e r o f n o n l i n e a r i t y r e q u i r e s i t s own e x p r e s s i o n for the s u s c e p t i b i l i t y x> and thus x must take the form of - 8 -a t e n s o r when d e s c r i b i n g n o n l i n e a r phenomena. The g e n e r a l e x p r e s s i o n f o r a s u s c e p t i b i l i t y c o e f f i c i e n t o f N o r d e r i n the s t a n d a r d n o t a t i o n of the l i t e r a t u r e i s X ( - D ° ; U> I ,<D2 > • • • > <J where the f r e q u e n c i e s u . o f the a p p l i e d e l e c t r i c f i e l d s s a t i s f y t o 0 .= to i + <JJ2 + * ' " + u>^. S i n c e i n t h i s r e s e a r c h o n l y one l i g h t sou rce i s u sed , a l l w.. are equa l and hence t o 0 = N w . Thus, the e x p r e s s i o n s f o r the s u s c e p t i b i l i t y c o e f f i c i e n t s f o r p o l a r i z a t i o n s l i n e a r , second o r d e r , and t h i r d o r d e r i n the a p p l i e d e l e c t r i c f i e l d £ ( t o ) may be w r i t t e n (Gucc i one-Gush e t a l . , 1967 , Lambropou lo s , 1974 , Leung e t a l . , 1974) : LINEAR . , -<^[«K> X(-w; wj <* TT) 77Y C Q n g w j SECOND ORDER , , < j i « i * x ; i » i O x(- 2" ; - - I < » t g - -) o>ng - 2 . r THIRD ORDER x( -3 - i « . .) ( = £ g - . ) « ! . „ - 2 « ) ( a n 9 - 3.) i s the e l e c t r i c dipo1e-moment o p e r a t o r of s e c t i o n 2.4 The s t a t e |i j; 0 ^>is the ground s t a t e of the s y s t em, and l * £ ^ ' ' ^ m ^ " ' ' ^ n ^ a r e e i 9 e n s t a t e s o f s u c c e e d i n g l y h i g h e r e n e r g i e s , be ing the f i n a l s t a t e i n a b s o r p t i o n p r e ce s s e s When a b s o r p t i o n l ead s to i o n i z a t i o n , the m a t r i c e lement - 9 -<i|j01 ft I ip° > between the f i n a l and i n i t i a l s t a t e s need not be n 1 T g i n c l u d e d i n the s u s c e p t i b i l i t i e s . An upper s t a t e , f o r example has energy h c c o ^ and l i f e t i m e r £ ~ ^ » and ft d e f i n e d by: The form o f the s u s c e p t i b i l i t y c o e f f i c i e n t s i n d i c a t e s t h a t the n o n l i n e a r p o l a r i z a b i l i t y may be enhanced whenever a re sonance i n one o f the f a c t o r s i n the denominato r o f the s u s c e p t i b i l i t y o c c u r s . Such a re sonance o c cu r s whenever the a p p l i e d f i e l d f r e q u e n c y co i s such t h a t the r e a l p a r t of a re sonance f a c t o r i n the denomina to r v a n i s h e s . For t h i r d - o r d e r n o n l i n e a r i t i e s , f o r example , wh ich i s the sub-j e c t o f t h i s r e s e a r c h , we r e q u i r e f o r re sonance enhancement a t l e a s t one of the f o l l o w i n g : R e ( % " w ) = °» ° r R e ( % " 2 w ) = ° ' o r R e ( % " 3 w ) = ° ' These r e l a t i o n s h i p s are e q u i v a l e n t t o : c o 0 - co = co , or Jo g co - co = 2 c o , o r m g co - co = 3co . n g - 10 -n m I ground EIGENSTATES OF THE SYSTEM As w e l l , the a p p r o p r i a t e m a t r i x e lement s must not v a n i s h (see s e c t i o n 2 . 4 ) . In o r d e r t h a t the i n c i d e n t l i g h t energy not be l o s t th rough s c a t t e r i n g or l i n e a r a b s o r p t i o n , we must tune away from re sonance w i t h r ega rd s to the f i r s t e x c i t e d s t a t e . Thus the s t a t e l ^ 0 ^ i s a v i r t u a l s t a t e and |(co„ - co ) - co I >> 0. On the o t h e r hand, both o f the uppermost s t a t e s and |ijj°> may be r e s o n a n t , or r e a l s t a t e s . However, s i n c e the f i n a l s t a t e 1^°^  i s a cont inuum s t a t e i n the p h o t o i o n i z a -t i o n p r o c e s s , no s i g n i f i c a n t s p e c t r o s c o p i c i n f o r m a t i o n would be ga ined i f t h i s were the o n l y r e s onan t s t a t e . Thus, we f ocu s on the d i s c r e t e second e x c i t e d s t a t e |ii)°> as the 1 r m n e c e s s a r y r e s onan t s t a t e , r e s onan t enhancement o c c u r r i n g when t w i c e the energy o f the fundamenta l photon becomes equa l to the energy d i f f e r e n c e between |^^> and the ground s t a t e of the m o l e c u l e : 0 J m - cog = 2co . Two-photon resonance has the advantage of a l l o w i n g d e t a i l e d i n v e s t i g a t i o n o f e l e c t r o n i c s t a t e s which a re symmetry-- 11 -f o r b i d d e n i n l i n e a r ( one -photon ) s p e c t r o s c o p y , as shown i n s e c t i o n 2.4. The o r d e r o f the s t a t e s i s t h e n , f o r two-photon r e s o n a n t , t r i p i e - p h o t o n i o n i z a t i o n of the I od i ne m o l e c u l e : n cont inuum (> 75,814 ± 10 c m - 1 ) m r e s onan t £ v i r t u a l g XOg ground The use o f a t u n a b l e dye l a s e r as the sou rce o f the a p p l i e d e l e c t r i c f i e l d p r o v i d e s an a b s o r p t i o n spect rum as a c o n t i n u o u s f u n c t i o n o f wave leng th over the u s e f u l range of the l a s e r dye , and hence as a f u n c t i o n o f the i d e n t i t y o f the r e s onan t s t a t e s \ t y ^ > • When N photons a re i n v o l v e d i n the t r a n s i t i o n , the p h o t o i o n i z a t i o n s i g n a l i n t e n s i t y S depends upon the N t h power of the i n t e n s i t y I o f the i n c i d e n t l i g h t . T h i s f o l l o w s from e q u a t i o n 2.1 i n wh ich the n o n l i n e a r pol a r i z ab i 1 i t y i n N^*1 o r d e r depends upon the N t h power o f the e l e c t r i c f i e l d v e c t o r . Thus i f C i s a p r o p o r t i o n a l i t y c o n s t a n t we may w r i t e : S = C I N . o 3 The s i g n a l i s e xpec ted to va ry as I q . The power-dependence of our p h o t o i o n i z a t i o n s i g n a l may be measured e x p e r i m e n t a l l y i n the f o l l o w i n g manner. When a number n of c a l i b r a t e d n e u t r a l - 12 -d e n s i t y f i l t e r s , each o f the same d e n s i t y K(>), a re used to a t t e n u a t e the l a s e r beam b e f o r e i t e n t e r s the I od i ne chamber, then the p h o t o i o n i z a t i o n s i g n a l S i s a t t e n u a t e d as f o l l o w s : S = C i o N i 0 " K ( A ) n N , o r , i n a more c o n v e n i e n t f o rm: l o g S = l og (C I Q N ) - K(A)nN = c o n s t a n t s - K ( \ )nN The power dependence N may be de te rm ined from the s l o p e of a p l o t o f the l o g o f the p h o t o i o n i z a t i o n s i g n a l i n t e n s i t y ve r su s the number o f f i l t e r s i n the path o f the i n c i d e n t beam, i f the d e n s i t y K(X) i s known. We have: 2.2 Coarse S t r u c t u r e : V i b r a t i o n a l A n a l y s i s 2.2.1 The an harmonic o s c i l l a t o r The s i m p l e harmonic o s c i l l a t o r model p r o v i d e s o n l y a f i r s t - o r d e r a p p r o x i m a t i o n to any p h y s i c a l o s c i l l a t o r , s i n c e p e r f e c t l y e l a s t i c f o r c e s , wh ich a re l i n e a r l y p r o p o r t i o n a l to the a m p l i t u d e of v i b r a t i o n , do not e x i s t i n n a t u r e . In p a r t i c u l a r , the a t t r a c t i v e f o r c e between any two atoms of a m o l e c u l e tends to z e r o , r a t h e r than i n c r e a s i n g i n d e f i n i t e l y , w i t h i n c r e a s i n g d i s t a n c e from the e q u i l i b r i u m p o s i t i o n . The a c t u a l b i n d i n g f o r c e must be r e p r e s e n t e d by power s e r i e s i n - 13 -powers o f the d i s p l a c e m e n t from e q u i l i b r i u m , and asymmetry r e q u i r e s both even and odd te rms . The o n e - d i m e n s i o n a l b i n d i n g f o r c e o f a d i a t o m i c m o l e c u l e , i n the absence o f e x t e r n a l l y a p p l i e d f i e l d s , i s t h u s : F = Harmonic Term + Anharmonic Terms = - k ^ r - r e ) + k 2 ( r - r g ) 2 - k 3 ( r - r g ) 3 + ••• where r i s the i n t e r n u c l e a r s e p a r a t i o n , r g i s the e q u i l i b r i u m s e p a r a t i o n , and k^, k 2 , k^ a re f o r c e c o n s t a n t s . The c o r r e s -ponding p o t e n t i a l energy f u n c t i o n , which i s e l e c t r o n i c i n n a t u r e , i n wh ich the n u c l e i i move i s : U = k 1 / 2 ( r - r e ) 2 - k 2 / 3 ( r - r g ) 3 + k 3 / 4 ( r - r g ) 4 + ••• For sma l l a n h a r m o n i c i t y of the o s c i l l a t o r (Ik^ l << |k 2 | << | k-| | ) the e i gen e n e r g i e s o f the S c h r o e d i n g e r e q u a t i o n may be d e t e r -mined w i t h a ' p e r t u r b a t i o n c a l c u l a t i o n to be: E v = h cw e ( v + H) - h ca ) e x e ( v + k)2 + h c w e y e ( v + k)3 + ••• where h i s P l a n c k ' s c o n s t a n t , c i s the v e l o c i t y of l i g h t , v i s the v i b r a t i o n a l quantum number , and co , co x , co y , . . . ^ e e e e e are c o n s t a n t s c h a r a c t e r i z i n g the m o l e c u l e , p r o p o r t i o n a l to the f o r c e c o n s t a n t s . The q u a n t i t i e s co x , co y , . . . a re a e e e e measure o f the anharmoni c i t y of the m o l e c u l e , w h i l e cog i s the harmonic a p p r o x i m a t i o n to the o s c i l l a t o r f r e q u e n c y (co g = / k ^ / u , where y i s the reduced mass ) . A more u s e f u l - 14 -e x p r e s s i o n i n s p e c t r o s c o p y i s the " v i b r a t i o n a l t e r m " G(v) i n wavenumber u n i t s g i v en by G(v) = u e ( v + H) - ^ e x e ( v + % ) 2 + ^ e y e ( v + % ) 3 + ••• (2 .3 ) f o r the anharmonic o s c i l l a t o r . A l t hough the v i b r a t i o n a l mot ion i s s t i l l s t r i c t l y p e r i o d i c , the n a t u r a l or r e s onan t f r e q u e n c y i s a m p l i t u d e - d e p e n d e n t , the f r e q u e n c y d e c r e a s i n g w i t h i n c r e a s i n g a m p l i t u d e . F u r t h e r m o r e , due to the asymmetry o f the p o t e n t i a l c u r v e , the t ime average o f the p o s i t i o n o f the o s c i l l a t o r i s no l o n g e r the e q u i l i b r i u m p o s i t i o n , b u t , f o r a lmos t a l l m o l e c u l e s , i s g r e a t e r (<r> > r ). The s e p a r a t i o n o f s u c c e s s i v e v i b r a t i o n a l l e v e l s i s d e s c r i b e d i n wavenumber u n i t s by the f o l l o w i n g FIRST DIFFERENCE A G V j V + 1 = G(v+1) - G(v) = a) - u e x e ( 2 v + 2) + w e y e ( 3 v 2 + 6v+13/4) + ••• (2 .4 ) SECOND DIFFERENCE A 2 G v , V + 2 E A G V , V + 1 " A G v + l , v + 2 = 2 o j e x e - w e y e ( 6 v + 9). + • . . (2 .5 ) where v i s by d e f i n i t i o n the quantum number of the l o w e s t v i b r a t i o n a l s t a t e i n v o l v e d i n the c ompa r i s on . Wh i le " e y e may be p o s i t i v e or n e g a t i v e , co e x e i s p o s i t i v e f o r n e a r l y a l l - 15 -d i a t o m i c m o l e c u l e s ( H e r z b e r g , 1950) . Thus the v i b r a t i o n a l l e v e l s draw t o g e t h e r w i t h i n c r e a s i n g v i b r a t i o n a l quantum number, and e v e n t u a l l y merge i n t o a con t i nuum. In t h i s work, the s t a n d a r d s p e c t r o s c o p i c n o t a t i o n i s adopted whereby v 1 r e p r e s e n t s the uppe r , and v" the l ower s t a t e i n v o l v e d i n a v i b r a t i o n a l t r a n s i t i o n . A s e r i e s o f t r a n s i t i o n s wh ich i n v o l v e s a s i n g l e upper s t a t e and s e v e r a l a d j a c e n t l ower s t a t e s ( o r v i c e v e r s a ) i s termed a p r o g r e s s i o n . See s e c t i o n 2.4 f o r a d i s c u s s i o n of v i b r a t i o n a l s e l e c t i o n r u l e s . 2.2.2 Thermal d i s t r i b u t i o n of the v i b r a t i o n a l s t a t e s A c c o r d i n g to the Maxwel1 -Bo l tzmann d i s t r i b u t i o n law a p p l i e d to quantum mechan ics under c o n d i t i o n s of the rma l e q u i l i b r i u m , the number o f m o l e c u l e s N y i n each o f the v i b r a -- E/ kT t i o n a l s t a t e s i s p r o p o r t i o n a l to the Bo l tzmann f a c t o r e , where k i s the Bo l tzmann c o n s t a n t , T i s the a b s o l u t e t empera -t u r e i n degrees K e l v i n , and E i s the energy o f v i b r a t i o n ( H e r z b e r g , 1950). I f E i s d e f i n e d as the v i b r a t i o n a l energy measured from the f i r s t s t a t e , E = G(v) - G(0) - G 0 ( v ) then the Bo l tzmann f a c t o r e ~Go ( v ) A T g i v e s the r e l a t i v e numbers o f m o l e c u l e s i n the d i f f e r e n t v i b r a t i o n a l l e v e l s r e f e r r e d to the number of m o l e c u l e s i n the l owe s t v i b r a t i o n a l - 16 -l e v e l . When G Q ( v ) i s e xp re s s ed i n wavenumber u n i t s , then s u b s t i t u t i o n of the c o n s t a n t k g i v e s the r e s u l t N v _ - G Q ( v ) / ( 0 . 6 9 5 2 c m * 1 / 0 ^ I f we wi sh t o de te rm ine N y r e l a t i v e to the t o t a l number N of m o l e c u l e s i n the gas sample , the s o - c a l l e d p a r t i t i o n f u n c t i o n Q v i s r e q u i r e d i n which the Bo l tzmann f a c t o r s a re summed over a l l s t a t e s : -G ( v ) / ( 0 . 6952 c m _ 1 / ° K ) T Q v = 2 e 0 v Then the f r a c t i o n a l number o f m o l e c u l e s i n v i b r a t i o n a l s t a t e v i s N -G ( v ) / ( 0 . 6952 cm'VlOT v _ e N Q ^ v In most d i a t o m i c ga se s , o n l y one p r o g r e s s i o n o f a band system n o r m a l l y a p p e a r s , t h a t w i t h v " = 0. For I o d i n e , however, the v i b r a t i o n a l quanta a re sma l l because the m o l e c u l e i s r e l a -t i v e l y heavy, l e a d i n g to an a p p r e c i a b l e p o p u l a t i o n of the upper v i b r a t i o n a l s t a t e s o f the ground e l e c t r o n i c s t a t e a t room tempe ra tu re (see Tab l e X I ) . Thus, i t i s p r e d i c t e d t h a t i n a d d i t i o n to the v " = 0 to v 1 = 0, 1, 2 n a b s o r p t i o n p r o g r e s s i o n , the p r o g r e s s i o n s v" = 1, 2, 3, 4 (and p o s s i b l y higher) to v 1 = 0, n w i l l appear i n our d a t a . - 17 -2.3 F i ne S t r u c t u r e : R o t a t i o n a l A n a l y s i s The s imp le r i g i d r o t a t o r model p r o v i d e s a f i r s t - o r d e r a p p r o x i m a t i o n to the r o t a t i o n a l mot ion o f a d i a t o m i c mo le -c u l e . In t h i s model we c o n s i d e r the two atoms o f reduced mass y to be p o i n t - l i k e and f a s t e n e d a t a d i s t a n c e r a p a r t a t the ends of a w e i g h t l e s s , r i g i d r o d . The s o l u t i o n of the a p p r o p r i a t e S c h r o e d i n g e r e q u a t i o n i s c o m p a r a t i v e l y s i m p l e and y i e l d s the e i g e n e n e r g i e s of r o t a t i o n , i n wavenumber u n i t s : F( J ) = BJ (J +• 1 ) , B E — ^ — j . 4 i T C y r J i s the r o t a t i o n a l quantum number, and r i s the i n t e r n u c l e a r s e p a r a t i o n . The r o t a t i o n a l c o n s t a n t B i s e s s e n t i a l l y the r e c i p r o c a l moment o f i n e r t i a of the n u c l e i i . For a more a c c u r a t e t r e a t m e n t , we must take i n t o c o n s i d e r a t i o n the f a c t t h a t r o t a t i o n and v i b r a t i o n take p l a c e s i m u l t a n e o u s l y . Dur ing a v i b r a t i o n p e r i o d , the i n t e r n u c l e a r d i s t a n c e and c o n s e q u e n t l y the moment o f i n e r t i a and r o t a t i o n a l c o n s t a n t B a re c h a n g i n g . S i n c e the p e r i o d o f v i b r a t i o n i s ve ry sma l l compared to the p e r i o d o f r o t a t i o n , we must use a mean B v a l u e i n the v i b r a -t i o n a l s t a t e c o n s i d e r e d : B = - i -v 4ircy V 2 2 2 where O/r ^ i s the t ime average o f 1/r d u r i n g the v i b r a t i o n p e r i o d . B y i s somewhat s m a l l e r than the c o n s t a n t B g e v a l u a t e d - 18 -a t the e q u i l i b r i u m s e p a r a t i o n r , s i n c e w i t h i n c r e a s i n g v i b r a -t i o n , because o f the a n h a r m o n i c i t y , the mean n u c l e a r s e p a r a -t i o n w i l l be g r e a t e r than r e . To a f i r s t ( u s u a l l y s a t i s f a c -t o r y ) a p p r o x i m a t i o n , the r o t a t i o n a l c o n s t a n t B y i n the v i b r a -t i o n a l s t a t e v i s g i v en by: B v = B e - a e ( v + %) , a e << B g . C o n s i d e r a t i o n o f the datomic m o l e c u l e as a n o n r i g i d r o t a t o r a l s o b r i n g s i n a sma l l c o r r e c t i o n term f o r c e n t r i f u g a l f o r c e , whereby the i n t e r n u c l e a r d i s t a n c e , and c o n s e q u e n t l y the moment o f i n e r t i a , i n c r e a s e s w i t h i n c r e a s i n g energy o f r o t a t i o n . T h e r e f o r e the r o t a t i o n a l c o n s t a n t B i s a f u n c t i o n o f quantum number J , d e c r e a s i n g w i t h i n c r e a s i n g J . A l t hough an e x a c t s o l u t i o n o f the n o n r i g i d r o t a t o r model r e q u i r e s t h a t the energy be e x p r e s s e d i n an i n f i n i t e power s e r i e s i n powers o f J ( J + 1 ) , ve ry good a c c u r a c y i s o b t a i n e d u s i n g o n l y the l i n e a r and quad-r a t i c t e rms . The r o t a t i o n a l term f o r the n o n r i g i d r o t a t o r becomes: F y ( J ) = B v J ( J + 1) - D V J 2 ( J + l ) 2 , 4B 3 D v u 2 (2 .6 ) where oo i s the v i b r a t i o n a l f r e q u e n c y . T y p i c a l l y D y < 1 0 ~ y . In the models of the s i m p l e r o t a t o r s , the atoms were t r e a t e d as p o i n t masses. A c t u a l l y , the mass d i s t r i b u t i o n o f the e l e c t r o n s r e v o l v i n g about the two n u c l e i i must be taken - 19 -i n t o a c c o u n t . The moment o f i n e r t i a o f t he se e l e c t r o n s i s much s m a l l e r than the moment of the two n u c l e i i about the c e n t e r o f mass, owing to the much s m a l l e r mass o f the e l e c t r o n . In s p i t e o f t h i s , the c o r r e s p o n d i n g a n g u l a r momenta are o f the same o r d e r o f magnitude s i n c e the e l e c t r o n s r o t a t e much more r a p i d l y . The model o f a symmetr ic top f i t s the d i a t o m i c m o l e c u l e (two of the t h r e e p r i n c i p a l moments of i n e r t i a a re e q u a l ) . For a g i v en e l e c t r o n i c s t a t e , i n the absence of e x t e r n a l t o r q u e s , the t o t a l a n g u l a r momentum 3 i s c o n s t a n t i n magni tude and d i r e c t i o n , w h i l e the e l e c t r o n i c a n g u l a r momentum ft about the f i g u r e a x i s i s c o n s t a n t i n magni tude but not i n d i r e c t i o n . In f a c t , the f i g u r e a x i s r o t a t e s a t a c o n s t a n t ang l e about J" w i t h the f r e q u e n c y of the v i b r a t i n g n o n r i g i d r o t a t o r . The energy l e v e l s t h a t r e s u l t f rom s o l u t i o n o f the wave e q u a t i o n o f the symmetr i c top ( H e r z b e r g , 1950) a r e : F y ( J ) = B v J ( J + 1) - D V J 2 ( J + l ) 2 + (A - B y ) f t 2 , J * ft (2 .7 ) w i t h A = . T 4 ire I „ where I n i s the moment o f i n e r t i a of the e l e c t r o n s about an a x i s p a r a l l e l to the f i g u r e a x i s . For a g i v en e l e c t r o n i c s t a t e , ft i s c o n s t a n t and has o n l y a sma l l ( i n t e g r a l ) v a l u e . Thus the r o t a t i o n a l l e v e l s o f the symmetr i c top a re the same as those o f the s imp l e r o t a t o r e x cep t f o r a s h i f t i n mag-n i t u d e (A - B y ) f t c h a r a c t e r i s t i c of the e l e c t r o n i c s t a t e , and - 20 -e xcep t t h a t l e v e l s w i t h J < Q, a re a b s e n t . S i n c e r o t a t i o n a l quanta a re much s m a l l e r than v i b r a -t i o n a l q u a n t a , a combined r o t a t i o n - v i b r a t i o n spect rum g i v e s r i s e to more or l e s s broad wave leng th r e g i o n s (bands) which u s u a l l y have a t one end a sharp edge (band head ) . In the e x p r e s s i o n f o r the t o t a l energy o f a t r a n s i t i o n , v = vQ + v v •> the q u a n t i t y v Q = v g + v y i s c o n s t a n t f o r a g i v en band w h i l e v r i s v a r i a b l e . We may w r i t e v = v Q + F v , ( J ' ) - F V „ ( J " ) f o r a b s o r p t i o n , where v Q i s c a l l e d the band o r i g i n . N e g l e c t -i ng the s m a l l c o r r e c t i o n term i n D v and n o t i n g t h a t ti" = 0 f o r the ground e l e c t r o n i c s t a t e o f \^ we then have: v = v Q + (A 1 - B v ' ) f i ' 2 + B v ' J ' ( J , + l ) - B " J " ( . J " + 1) = v + f ( n ' ) + B ' J ' ( J ' + 1 ) - B " J " ( J " + 1 ) . 0 V V In two-photon p r o c e s s e s , we may expec t up to f i v e branches of l i n e s ( s e c t i o n 2.4) whose wavenumbers a re g i v en by the f o l l o w -i n g f o rmu l ae ( J r e p r e s e n t s the r o t a t i o n a l quantum number o f the ground s t a t e ) : AJ = + 2 S(.J) = v Q + f ( f i ' ) + 6 B y ' + ( 5 B v ' - B v " ) J + ( B v ' - B v " ) J 2 (2 . AJ = + 1 R (J ) = V q + f ( f i ' ) + 2 B V ' + ( 3 B V ' - B V " ) J + ( B v ' - B v " ) J 2 (2 . - 21 -A J = 0 Q(J) = v Q + f ( f i ' ) + ( B v ' - B v " ) J + ( B y ' - B y " ) J 2 (2 .10) AJ = -1 P ( J ) = V q + f ( f t ' ) - ( B v « + B y " ) J + ( B / - B v " ) J 2 (2 .11) AJ = -2 0 ( J ) = v Q + f ( n ' ) + 2 B v ' - (3B V' + B v " ) J + ( B y ' - B v " ) J 2 (2 .12) A band head i s formed i n a branch i f the l i n e a r and q u a d r a t i c terms i n J have o p p o s i t e s i g n s . Case I. I f B v ' < B v " (but 3 B v ' > B y " ) i t i s e a s i l y seen from e q u a t i o n s 2.8 to 2.12 t h a t a head i s formed i n each o f the R and S b r a n c h e s , both heads l y i n g to the h i g h - e n e r g y s i d e o f v . In a d d i t i o n , the Q b r a n c h , i f i t e x i s t s , sometimes forms a head ve ry c l o s e to v . A l l b ranches o f the band are degraded to l o w e r - e n e r g y , i . e . to the r e d . Case I I . When B 1 > B v " , heads are formed i n the P and 0 b r a n c h e s , the heads now l y i n g to the l ow -ene r gy s i d e of v Q . The Q branch may a l s o form a head, as i n case I. A l l branches of the band are degraded now toward h i g h e r ene r g y , i . e . to the v i o l e t . 2.4 S e l e c t i o n Ru les f o r R a d i a t i v e A b s o r p t i o n I f a system e x i s t s i n an unpe r t u r bed s t a t e r e p r e -sen ted by one member o f a comp le te o r t hono rma l s e t ii>n°(r,t)} - 22 -of s t a t i o n a r y - s t a t e w a v e f u n c t i o n s , then i n t e r a c t i o n o f t h i s system w i t h an e l e c t r o m a g n e t i c wave 1 c r e a t e s a p e r t u r b a t i o n , and c o n s e q u e n t l y a c h a n g e - o f - s t a t e to the s t a t e ¥ ( r , t ) wh ich may a lways be e x p r e s s e d as a " m i x t u r e " o f the e i g e n s t a t e s : Y ( r , t ) = Z C n ( t ) ^ n ° ( r , t ) The p r o b a b i l i t y t h a t the system w i l l make a t r a n s i t i o n to any new e i g e n s t a t e , say ^ m ° , under the i n f l u e n c e o f the e x t e r n a l r a d i a t i o n f i e l d i s g i v en by C m ( t ) C m ( t ) . D e t e r m i n a -t i o n o f the c o e f f i c i e n t s C „ ( t ) i n v o l v e s a c a l c u l a t i o n o f the m a t r i x e lement s O m ° I HE ' ^ n ° ^ w n e r e » a r e t ' i e ^ 1 " n a ' ' and i n i t i a l s t a t e s of the s y s t em, and i s the H a m i l t o n i a n a s s o c i a t e d w i t h the p e r t u r b a t i o n E ( Penne r , 1959) . In a f i r s t a p p r o x i m a t i o n , the m a t r i x e lements o f the i n t e r a c t i o n o f an e l e c t r o m a g n e t i c wave w i t h a d i a t o m i c m o l e c u l e reduce to the i n t e r a c t i o n o f the wave w i t h the ( v a r i a b l e ) e l e c t r i c d i p o l e moment M of the m o l e c u l e whose components are N M = E e u x b (M » M s i m i l a r ) where the e. a re the charges x |< = 1 K K y z K on the N p a r t i c l e s o f c o o r d i n a t e s x ^ , y ^, z ^ . Then f o r sma l l p e r t u r b a t i o n s , the t r a n s i t i o n p r o b a b i l i t y per u n i t t i m e , P , i s c o n s t a n t and i s g i v en by: n+m 3 J t 3 f i 2 V"m " l^n ' % n The r a d i a t i o n d e n s i t y p i s s t r i c t l y a p r o p e r t y of the v mn - 23 -a p p l i e d f i e l d , w h i l e the d ipo le -moment m a t r i x e lement c h a r a c t e r i z e s the m o l e c u l e . The p r e v i o u s r e s u l t s r e s t upon the a s sumpt ion t h a t t h e r e i s no s p a t i a l v a r i a t i o n i n the e l e c t r i c f i e l d t o ve r the r e g i o n o f the d i a t o m i c m o l e c u l e i n wh ich the d i s t r i b u -t i o n of e l e c t r i c charge i s a p p r e c i a b l e ( t h a t i s , where the e l e c t r o n i c w a v e f u n c t i o n i s l a r g e ) . T h i s a p p r o x i m a t i o n i s v a l i d i n any but e x c e p t i o n a l cases s i n c e i n m o l e c u l a r s p e c t r o s c o p y we a re conce rned w i t h u l t r a v i o l e t , v i s i b l e o and i n f r a r e d r a d i a t i o n (A > 1000A) so the wave leng th s a re o l a r g e compared w i t h m o l e c u l a r d imens ion s (- 2A ) . I f the v a r i a t i o n of the e l e c t r i c f i e l d ove r the d imens ion s of the m o l e c u l e i s not n e g l e c t e d , t h e r e appear i n the e x p r e s s i o n f o r the t r a n s i t i o n p r o b a b i l i t y , m a t r i x e l ement s o f the magnet i c d i p o l e , e l e c t r i c q u a d r u p o l e , and h i g h e r moments. However, the m a t r i x e lement s o f the h i g h e r moments are many powers of ten s m a l l e r than the m a t r i x e lement o f the d i p o l e moment, and hence the c o r r e s p o n d i n g t r a n s i t i o n s a re o b s e r v -a b l e o n l y when the d i p o l e t r a n s i t i o n i s f o r b i d d e n . The r e q u i r e m e n t t h a t the t r a n s i t i o n p r o b a b i l i t y P m g i ven by e q u a t i o n 2.13 be nonzero f o r the comb in ing s t a t e s l e a d s to c e r t a i n s e l e c t i o n r u l e s based on the e v a l u a t i o n o f the d i p o l e m a t r i x e lement between the g i v en s t a t e s . For many wou ld -be t r a n s i t i o n s t h i s d i p o l e m a t r i x e lement v an i s he s i d e n t i c a l l y , and the t r a n s i t i o n i s termed f o r b i d d e n . - 24 -For example , a homonuclear d i a t o m i c m o l e c u l e such as has no permanent e l e c t r i c d i p o l e moment and n e i t h e r i t s v i b r a -t i o n s nor r o t a t i o n s i nduce a d i p o l e (M 5 0 ) . T h e r e f o r e i t does not i n t e r a c t w i t h r a d i a t i o n to produce a pure v i b r a -t i o n a l or r o t a t i o n a l s pec t r um. However, such m o l e c u l e s do e x h i b i t e l e c t r o n i c s p e c t r a w i t h v i b r a t i o n a l and r o t a t i o n a l s t r u c t u r e ( b a n d s ) , because the i n s t a n t a n e o u s d i p o l e moment changes d u r i n g the r e d i s t r i b u t i o n o f e l e c t r i c charge which accompanies the e l e c t r o n i c t r a n s i t i o n ( K i n g , 1964) . conforms to Hund ' s c o u p l i n g case c , i n wh ich the L-S c o u p l i n g of the s e p a r a t e atoms p e r s i s t s when the m o l e c u l e i s fo rmed. The component o f t o t a l a n g u l a r momentum a l ong the i n t e r -n u c l e a r a x i s , ft,-is w e l l - d e f i n e d . For the d i a t o m i c mo le -c u l e ^ 5 the t r a n s i t i o n s which are a l l o w e d may be c a t e g o r -i z e d under the f o l l o w i n g s e l e c t i o n r u l e s f o r the quantum numbers: 1. VIBRATIONAL-ELECTRONIC TRANSITION Av = 0, ± 1 , ± 2 , . . . f o r the anharmonic o s c i l -l a t o r . 2. ROTATIONAL-ELECTRONIC TRANSITION In the s y m m e t r i c - t o p mode l , AJ = ±1 i f ft = 0 i n both upper and l ower s t a t e s , and AJ = 0, ±1 ( e x c l u d i n g J = 0 J = 0) i f a t l e a s t one o f the two s t a t e s has ft f 0. 3. ELECTRONIC TRANSITION Aft = 0, ±1 . - 25 -The p a r i t y of the wavefunction under i n v e r s i o n must change: g (even p a r i t y ) u (odd p a r i t y ) . The p a r i t y of non-degenerate wavefunctions upon r e f l e c t i o n in a plane of symmetry must not change: 0 + +\* 0". Two-photon resonance processes allow the i n v e s t i g a -t i o n of e l e c t r o n i c s t a t e s which are symmetry-forbidden i n one-photon spectroscopy. The s e l e c t i o n r u l e s f o r two-photon resonance may e a s i l y be deduced from the previous r e s u l t s . The allowed change in i s 0, ±1, ±2. Since the ground e l e c t r o n i c s t a t e of has the c o n f i g u r a t i o n 0*, the f i r s t (non-resonant) s t a t e must have symmetry "u" while the second (resonant) s t a t e must be of symmetry "g" and t h e r e f o r e i s i n a c c e s s i b l e v i a conventional one-photon a b s o r p t i o n from the ground s t a t e . S t a r t i n g from the c o n f i g u r a t i o n 0* , the I 2 molecule may t h e r e f o r e go to 0*, 1^, or 2g. The s e l e c t i o n r u l e s f o r J are AJ = 0, ±1, ±2, g i v i n g r i s e to S, R, Q, P and 0 branches. 2.5 The Iodine Molecule 127 Diatomic Iodine, I 2 with reduced mass 63.466 amu, has the e l e c t r o n i c ground-state c o n f i g u r a t i o n Og with v i b r a t i o n a l and r o t a t i o n a l constants as f o l l o w s (Herzberg, 1950): - 26 CO " e = 2 1 4 . 5 7 cm " e X e " 0 . 6 127 cm » . V = - 0 . 0 0 0 8 9 5 cm Ve" = - 0 . 0 0 0 0 1 8 7 cm B e " 0 . 0 3 7 3 5 cm "." 0 . 0 0 0 1 1 7 cm D e " 4 . 5 1 0 "9 cm o 2 .666 A N o t e t h a t D " e i s c a l c u l a t e d u s i n g A c c o r d i n g t o t h e a n h a r m o n i c o s c i l l a t o r m o d e l , t h e q u a n t i z e d v i b r a t i o n a l e n e r g y ( e q u a t i o n 2 . 3 ) o f t h e g r o u n d e l e c t r o n i c s t a t e o f d i a t o m i c I o d i n e i s g i v e n i n wavenumber u n i t s b y : G ( v " ) = 2 1 4 . 5 7 ( v " + \ ) - 0 . 6 1 2 7 ( v ' + \ ) 2 2 ' v " 2 - 0 . 0 0 0 8 9 5 ( v " + J-) 3 + 0 . 0 0 0 0 1 8 7 ( v " + \ ) F o r l a t e r u s e , t h e e n e r g y l e v e l s G ( v " ) p l u s t h e f i r s t and s e c o n d d i f f e r e n c e s , A G ( v " ) and A G ( v " ) , a r e t a b u l a t e d f o r t h e f i r s t s i x v i b r a t i o n a l l e v e l s o f I^ i n T a b l e I. No i s o t o p e e f f e c t s a r e e x p e c t e d i n t h e s p e c t r u m o f I o d i n e , s i n c e t h e 127 i s o t o p e I 2 has a b u n d a n c e b e t t e r t h a n 9 9 . 9 % ( R o b i n s o n , 1 9 7 4 ) . The q u a n t i z e d r o t a t i o n a l e n e r g y ( e q u a t i o n 2 . 7 ) o f V w e(v+k) a) x (v+h) e e w e y e ( v+J§)3 ow e (v+3s ) 4 6(») AG(v) ( c m - 1 ) ( c m - 1 ) ( c m - 1 ) ( c m - 1 ) ( c m - 1 ) ( c m - 1 ) 0 107.29 -0.1532 -0.0001 - 107.14 213.34 1 321.86 -1 .379 -0.0030 0.0001 320.48 212.11 2 536.43 -3 .829 -0.0140 0.0007 532.59 210.87 3 751.00 -7.506 -0.0384 0.0028 743.46 209.63 4 965.57 -12.41 -0.0816 0.0077 953.09 208.39 5 1180.14 -18 .53 -0.1489 0.0171 1161.48 207.13 6 T394.71 -25.89 -0.2458 0.0334 1368.61 A 2 =1.24 c m " 1 Tab l e I . V i b r a t i o n a l Energy L e v e l s of the Ground E l e c t r o n i c S t a t e of I 2. - 28 -the ground e l e c t r o n i c s t a t e i s g i v en i n wavenumber u n i t s by: F V ( . J " ) = - 4.5 x lo"9 J " 2 ( J " + 1 ) 2 . (2 .13) The i o n i z a t i o n p o t e n t i a l o f m o l e c u l a r I od i ne i s 75,814 ± 10 c m " 1 (Myer and Samson, 1970, and V e n k a t e s w a r l u , 1970) . The aim o f t h i s r e s e a r c h i s to o b t a i n m u l t i p l e -photon i o n i z a t i o n of the I 2 m o l e c u l e v i a the r e a c t i o n : I 2 + Nv -> I 2 + + e " , where N i s the number of photons abso rbed s i m u l t a n e o u s l y by I 2 i n the p h o t o i o n i z a t i o n p r o c e s s . The fundamenta l f r equency v of the i n c i d e n t l i g h t must l i e w i t h i n the s p e c t r a l range 3600-7400 A (27,778 - 13,514 c m " 1 ) p r o v i d e d by commerc ia l l a s e r dyes a v a i l a b l e to d a t e . The r e q u i r e m e n t 13,514 c m " 1 x< v.< 27, 778 c m " 1 w i t h Nv > 75,814 ± 10 c m " 1 i s s a t i s f i e d f o r the v a l u e s N = 3, 4, 5 and 6. S i n c e the l o w e s t - o r d e r n o n l i n e a r i t y w i l l be the most i n t e n s e , we choose N = 3. The p h o t o i o n i z a t i o n r e a c t i o n i s then I 2 + 3v -*- I 2 + + e " , where the e x c i t i n g energy r e q u i r e d i s v > 25,271 ± 3 c m " 1 o which co r r e spond s to photons of wave leng th ^ 3957 ± 1 A. 0.03735 - 0.000117 ( v " + i ) J " ( J " + 1) - 29 -In p r i n c i p l e , n o n - l i n e a r p h o t o d i s s o c i a t i o n o f I^  c o n t r i b u t e s to the n o n - l i n e a r p h o t o e l e c t r o n s i g n a l . S i n c e the i o n i z a t i o n and d i s s o c i a t i o n t h r e s h o l d s are s i m i l a r , the on se t o f d i s s o c i a -t i o n o c c u r r i n g a t a p p r o x i m a t e l y 71,300 c m - 1 (Myer and Samson, 1970 ) , both p r o ce s s e s w i l l o ccu r i n the same o r d e r of non-l i n e a r i t y . The r e a c t i o n I 2 + 3v -> I* •* I + + I" w i l l c o n t r i b u t e o n l y a ve r y sma l l p e r c e n t a g e , however, s i n c e the p h o t o d i s s o c i a t i o n y i e l d f a l l s below 10%, compared to a p h o t o i o n i z a t i o n y i e l d o f 80-100% (Myer and Samson, 1970 ) , t h r oughou t the s p e c t r a l range i n v e s t i g a t e d . In o r d e r t h a t the i n c i d e n t l i g h t energy not be l o s t th rough l i n e a r a b s o r p t i o n and s c a t t e r i n g , the wave leng th o f the i n c i d e n t l i g h t must not c o i n c i d e w i t h a r e sonan t s t a t e i n d i a t o m i c I od ine ( s e c t i o n 2 . 1 ) . A c c o r d i n g to p r e v i o u s i n v e s t i g a t i o n s of d i a t o m i c I od i ne (Haranath and Rao, 1958, Ma th ie son and Rees, 1956, M u l l i k e n , 1934 and 1971, Nobs and W i e l a n d , 1 966 , and V e n k a t e s w a r l u , 1 970 ) , t h e r e appear numer-ous band systems i n the v i s i b l e and n e a r - u l t r a v i o l e t a b s o r p -t i o n s p e c t r a ( s i n g 1 e - p h o t o n ) of l^. No bands appea r , however, i n a b s o r p t i o n from the ground s t a t e between the wave leng th s o 3957 A, the l o n g e s t wave leng th p o s s i b l e f o r t r i p l e - p h o t o n o i o n i z a t i o n o f I^ , and 3600 A, the l ower l i m i t o f the dye l a s e r . Thus, i f a l a s e r dye i s chosen which l a s e s below o 3957 A, we expec t to a c h i e v e t r i p l e - p h o t o n i o n i z a t i o n w i t h - 30 -no c o m p l i c a t i o n s f rom s i n g l e - p h o t o n r e s o n a n c e s . When r e s o n -ant enhancement o f the p h o t o i o n i z a t i o n s i g n a l o c c u r s , we expec t two-photon re sonance to an i n t e r m e d i a t e s t a t e of symmetry " g " f o l l o w e d by p h o t o i o n i z a t i o n . 2.6 V i b r a t i o n a l A n a l y t i c Techn iques In the v i s i b l e and n e a r - u l t r a v i o l e t spect rum of m o l -e c u l a r I o d i n e , the band heads a re c l e a r l y deve l oped ( V e n k a t e s w a r l u , 1970, and P e t t y e t a l . , 1975) . S i n c e a m a x i -mum of i n t e n s i t y (band head) w i l l o c c u r i n each v i b r a t i o n a l band a t about the same energy o r J v a l ue ( s e c t i o n 2 . 8 ) , r o t a t i o n a l e n e r g i e s may be i g n o r e d i n the v i b r a t i o n a l a n a l y s i s . Thus, once the v i b r a t i o n a l t r a n s i t i o n s have been a s s i g n e d , a s i m p l e measurement of the s e p a r a t i o n o f the band heads i n a chosen p r o g r e s s i o n w i l l y i e l d v a l u e s f o r the v i b r a t i o n a l c o n s t a n t s to , co x , e t c . f o r the chosen e l e c t r o n i c s t a t e , e e e a c c o r d i n g to e q u a t i o n s 2.4 and 2 .5 . F u r t h e r m o r e , i t w i l l be demons t ra ted t h a t the head o f any band l i e s ve r y c l o s e to the band o r i g i n ( s e c t i o n 4 . 5 ) , and thus the minimum T g o f the p o t e n t i a l w e l l o f the upper e l e c t r o n i c s t a t e may be found w i t h i n a few wavenumbers. 2.7 F ranck-Condon R o t a t i o n a l A n a l y t i c Techn iques D e t e r m i n a t i o n of the r o t a t i o n a l c o n s t a n t s B v ' and r g ' t h rough a n a l y s i s o f r o t a t i o n a l e n e r g i e s i s complex. The o l a s e r ' s bandwidth (- 0.2 A) i s b roader than the l i n e w i d t h o of a s i n g l e resonance l i n e i n I ? (- 0.03 A, e s s e n t i a l l y the - 31 -Dopp le r w i d t h ) so t h a t the band i s not r e s o l v e d . To c a r r y out the r o t a t i o n a l a n a l y s i s , a d i f f e r e n t approach must be found than t h a t o f measur ing the s e p a r a t i o n of the r o t a t i o n a l energy l e v e l s . The measurement o f F ranck -Condon f a c t o r s i s an a l t e r n a t i v e approach w i t h ve ry p r e c i s e r e s u l t s . The r e l a t i v e i n t e n s i t y o f v i b r a t i o n a 1 - e l e c t r o n i c t r a n s i t i o n s i n a b s o r p t i o n i s governed by (a) the r e l a t i v e p o p u l a t i o n o f the i n i t i a l v i b r a t i o n a l s t a t e s of the m o l e c u l e , and (b) the o v e r l a p of the p r o b a b i l i t y d i s t r i b u t i o n f u n c t i o n s o f t he two v i b r a t i o n a l s t a t e s under c o n s i d e r a t i o n . The f i r s t f a c t o r i s e - G G ( v " ) / ( 0 . 6 9 5 2 c m " 1 /°K)T a $ d i s c u s s e ( J i n $ e c t i o n 2 . 2 . 2 . The square o f the second f a c t o r , the o v e r l a p i n t e g r a l , i s termed the F ranck -Condon f a c t o r o f the s t a t e s , and depends upon the r e l a t i v e e q u i l i b r i u m p o s i t i o n s r g 1 and r e " and the r e l a t i v e v i b r a t i o n a l f r e q u e n c i e s co ' and co " o f the e l e c -^ e e t r o n i c s t a t e s . When t h r e e o f t he se m o l e c u l a r c o n s t a n t s are known the f o u r t h may be c a l c u l a t e d from a measurement of the r e l a t i v e band i n t e n s i t i e s . S i n c e the r o t a t i o n a l c o n s t a n t o f the e x c i t e d e l e c t r o n i c s t a t e o b t a i n e d i n I o d i ne was d i f -f i c u l t to measure, the F ranck-Condon f a c t o r s were used to de te rm ine the s i z e o f the m o l e c u l e i n the upper e l e c t r o n i c s t a t e . The one a s sumpt i on o f t h i s approach i s t h a t the i o n i z a t i o n p r o b a b i l i t y from the r e s onan t e x c i t e d s t a t e i s i ndependent o f v ' . We may app rox ima te the l o w e s t - l y i n g v i b r a t i o n a l s t a t e s w i t h the e i g e n f u n c t i o n s of the harmonic o s c i l l a t o r mode l . - 32 -These a re the Hermi te o r t h o g o n a l f u n c t i o n s ( H e r z b e r g , 1950) . The n o r m a l i z e d v i b r a t i o n a l w a v e f u n c t i o n i n the ground e l e c -t r o n i c s t a t e i s t h e n : * v . i ( x ) [* J 2 v " / 2 • a X 2 / 2 AT H v „(/crx) where x. i s the d i s t a n c e from the e q u i l i b r i u m s e p a r a t i o n , o f II the n u c l e i i , a = y u ) g /fi , and H v l l (/cTx) i s a Hermi te p o l y -nomia l of v - t h deg ree . In the e x c i t e d e l e c t r o n i c s t a t e the n o r m a l i z e d v i b r a t i o n a l w a v e f u n c t i o n i s : *. v.ty) ( * ) 9 v 1 •3y2/2 /2 2 ' - /v where y i s the d i s t a n c e from e q u i l i b r i u m and The Hermi te p o l y n o m i a l s a re o b t a i n e d from the g e n e r a t i n g 2 2 f u n c t i o n H n ( u ) = (-1) n e u ( d n / d u n ) e -u The F ranck-Condon f a c t o r between s t a t e s v and v i s F ( v ' , v " ) * V I I ( X ) • i | ; v , ( x - 3 ) dx where 3 r e p r e s e n t s the d i s t a n c e between the e q u i l i b r i u m p o s i t i o n s i n the ground and e x c i t e d e l e c t r o n i c s t a t e s . The method of e v a l u a t i n g the o v e r l a p i n t e g r a l s i s t h a t of P ryce ( 1976 ) , i n wh ich a g e n e r a t i n g f u n c t i o n was d e r i v e d whose c o e f f i c i e n t s are p r o p o r t i o n a l to the o v e r l a p i n t e g r a l s between the d i f f e r e n t v i b r a t i o n a l s t a t e s . The F ranck-Condon - 33 -f a c t o r s t ake the f o rm: PD 2/2 / \ 2 F t v ' . v " ) - < ^ 1 ^ ! > P e " r " " ( G ( V . V ) 2 » / v 1 v " where 6 ( v ' , v " ) i s the c o e f f i c i e n t of s t i n the expan s i on o f the g e n e r a t i n g f u n c t i o n H ( s , t ) : -Q 'Ds Q"Dt 2Pst R s 2 - R t 2 H ( s , t ) = e e e e e The q u a n t i t i e s P, R, Q' and Q" a re c o n s t a n t s f o r any two g i v e n e l e c t r o n i c s t a t e s , whi1e D v a r i e s w i t h the s e p a r a t i o n o f the e q u i l i b r i u m p o s i t i o n s i n the upper and l ower e l e c t r o n i c s t a t e s . The d e f i n i t i o n s a r e : n = h I n U ' / o o " ) P = sech n R = tanh n - n / 2 Q'= e sech ri n / 2 Q"=e sech n D = 9 / m/h (OJ'CO'T4 The f i r s t few c o e f f i c i e n t s G ( v ' , v " ) a r e : G(0,0) = 1 G(1,0) = -Q'D G(2 ,0) = % Q 1 2 D 2 + R G ( l , l ) = 2P - Q 1 Q"D 2 G ( 2 , l ) = -2PQ'D + JgQ ' 2 Q " D 3 + RQ"D G(2,2 ) = 2 P 2 - R 2 + JsRQ" 2 D 2 - J^RQ' 2 D 2 - 2PQ 'Q "D 2 + % Q , 2 Q " 2 D 4 - 34 -2.8 E l e c t r o n i c C o n f i g u r a t i o n and Band Contour In the t h r e e - s t e p i o n i z a t i o n of l^, a r i s i n g from a r e s onan t t w o - s t e p t r a n s i t i o n from the X 0 + s t a t e to some 9 i n t e r m e d i a t e e v e n - p a r i t y s t a t e , f o l l o w e d by non - r e s onan t i o n i z a t i o n , i t would be u s e f u l to have f i r m t h e o r e t i c a l p r e d i c t i o n c o n c e r n i n g the i n t e n s i t i e s 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 s t r u c t u r e . The i n t e n s i t i e s of the i n d i v i d u a l r o t a t i o n a l members w i t h i n a g i v e n v i b r a t i o n a l band a re p r o p o r t i o n a l to t h r e e f a c t o r s : (a) a Bo l tzmann f a c t o r - F v ( J " ) h c / k T e , (b) the f r e q u e n c y v o f the t r a n s i t i o n , and (c ) the t r a n s i t i o n p r o b a b i l i t y between the two r o t a t i o n a l s t a t e s . The dependence on the f r equency over the range used i n t h i s r e s e a r c h may be n e g l e c t e d , s i n c e the v a r i a t i o n i s o n l y 4%. The t r a n s i t i o n p r o b a b i l i t y i s t h a t p a r t of ^ g 'MI ^m]> which depends on J 1 and J " , and i s r e p r e s e n t e d by ana logues to the Hon l -London f a c t o r s a p p e a r i n g i n one-photon a b s o r p t i o n . S i n c e i s a heavy m o l e c u l e , h i gh r o t a t -i o n a l quantum numbers are e n c o u n t e r e d , even i n the v i c i n i t y o f the band peak, and the ana logues to the Hon l -London f a c t o r s may be used i n t h e i r a p p r o x i m a t i o n f o r l a r g e J . These f a c t o r s a re a s y m p t o t i c a l l y m u l t i p l e s o f ( 2J+1 ) , the s t a t i s t i c a l w e i g h t i n g f a c t o r o f the r o t a t i o n a l s t a t e s . Thus the t r a n s -i t i o n p r o b a b i l i t y i s e s s e n t i a l l y c o n s t a n t i n each b r a n c h . The i n t e n s i t y d i s t r i b u t i o n w i t h i n a r o t a t i o n a l branch t h e r e -f o r e re semb le s c l o s e l y the p o p u l a t i o n d i s t r i b u t i o n o f the - 35 -i n i t i a l r o t a t i o n a l s t a t e s : -F ( J " ) h c / k T i ( J ) = C(2J+1) e v The r o t a t i o n a l term F ( J " ) o f e q u a t i o n 2.7 s i m p l i f i e s s i n c e 2 the s y m m e t r i c - t o p term (A" - B^")Q" v an i s he s i n the ground e l e c t r o n i c s t a t e of I 2, and s i n c e the sma l l c o r r e c t i o n term D v " i s n e g l i g i b l e (=10~ 7 B " ) • The r e l a t i v e i n t e n s i t y of the t r a n s i t i o n s of any s i n g l e b ranch i s then d e s c r i b e d by ( J = J " ) : -B " J ( J + l ) h c / k T i ( J ) = C(2J+1) e v S i n c e the bands o f I o d i ne a re u n r e s o l v e d , the i n t e n s i t y d i s t r i b u t i o n may be t r e a t e d as an e s s e n t i a l l y c o n t i n u o u s f u n c t i o n o f J . The c o n t o u r o f a s i n g l e b ranch may be de te rm ined by c o n v o l u t i n g the i n t e n s i t y d i s t r i b u t i o n i ( J ) w i t h the l a s e r s p e c t r u m , app rox imated as a s qua r e - t opped wave 1.5 c m - * w ide . The c o n t o u r I ( v ^ ) o f a branch exp re s sed as a f u n c t i o n o f l a s e r f r e q u e n c y i s : J 2 I ( v 4 ) = J i ( 0 ) dJ J l k T - B v " J ( J + l ) h c / k T e h c B / -Jjd^ + D/a - J 2 ( 0 2 + D/a a(e - e ) where a = k T / h c B v " - 36 -The l i m i t s of i n t e g r a t i o n a re de te rm ined by the l a s e r band-w i d t h . Thus: J 2 = J ( v £ + 0.75 c m " 1 ) , and J1 = J ( ^ £ - 0.75 c m " 1 ) . The l i m i t s o f i n t e g r a t i o n f o r each branch may be deduced from e q u a t i o n s 2.14 to 2 .17. P l a c i n g the ze ro of at v / 2 , the r e s u l t s a re as f o l l o w s f o r the case |AB|<<Bv 1 : 0-BRANCH 2B ' / /2B ' \ 2 2v„ - 2B 1 J Q = - J L . ± j ( — v - ) + _ * (2 .14) AB V \ AB / AB P-BRANCH J p . V t / ^ ( , 1 5 ) AB V \AB / AB R-BRANCH B ' / /B ' \ 2 2v„ - 2B 1 J R = - ± / (—1 + — * (2 -16) AB V \AB / AB S-BRANCH 2 V , / / 2 Bv'\ + 2 v* " 6 Bv' Oc = - ± / — H (2 .17) 5 AB V V AB / AB The c o n t o u r o f the Q-BRANCH i s s i m p l y : j / \ 9 . . /1.5\ " 2 V a A B I Q ( v 4 ) = 2a s i n h ^ - j e The r e q u i r e m e n t t h a t J be r e a l and p o s i t i v e p l a c e s r e s t r i c t -i on s upon the f o r wh ich t h e r e a re c o n t r i b u t i o n s to the i n t e n s i t y . - 37 -P r e d i c t i o n o f the band c o n t o u r s f o r the v a r i o u s e l e c t r o n i c c o n f i g u r a t i o n s p o s s i b l e i n the r e s onan t s t a t e r e q u i r e s a knowledge o f the r e l a t i v e branch i n t e n s i t i e s . For a g i v en e l e c t r o n i c c o n f i g u r a t i o n i t i s n e c e s s a r y to sum over a l l p o s s i b l e i n t e r m e d i a t e e l e c t r o n i c s t a t e s to a r r i v e a t the two-photon a n a l o g u e s . t o the Hon l -London f a c t o r s . The c a l c u l a t i o n s were c a r r i e d out by P ryce (1976) w i t h the f o l -l o w i n g res u l t s : ^ T r a n s i t i o n Branch"" 0+ - 0 + g g g 9 J ( J - 2 ) . ( 2 J - 1 ) ( J - 2 ) ( J - 3 ) 4 ( 2 J -1) P Q R S (2J+1) 0 2J(J+1) ( a - g ) 2 3 ( 2 J - 1 ) ( 2 J + 3 ) + f ( a + 2 3 ) 2 1 ( J + l ) ( J +2 ) (2J+3) ( a - g ) %(J+1) 3 ( 2 J+ l ) 2 ( 2 J - 1 ) ( 2 J +3 ) ( J + l ) ( J +3 ) (2J+3) 3 ( J - 1 ) ( J + 2 ) ( 2 J + 1 ) 2 ( 2 J - 1 ) (2J + 3) %(J+3) ( J + 3) ( J + 4) 4(2J+3) In the 0 -> 0 t r a n s i t i o n , a and g a re c o n t r i b u t i o n s from - 38 -i n t e r m e d i a t e 0* and l u s t a t e s r e s p e c t i v e l y , n o r m a l i z e d so 2 2 t h a t 3a + 4ag + 8g = 1 . The r e l a t i v e branch s t r e n g t h s may, f o r l a r g e r o t a t i o n a l e n e r g i e s , be exp re s sed i n d e p e n d -e n t l y o f J as f o l l o w s : (1) For Og -> 0^ the R and P branches are t o t a l l y a b s e n t , and 0:Q:S = 3:2+x:3 where x i s a p o s i t i v e q u a n t i t y whose a c t u a l v a l u e depends on d e t a i l s o f the i n t e r m e d i a t e s t a t e s . The extreme band c on t ou r s a re 3:2:3 and a c o n t o u r wh ich i s e n t i r e l y Q-1 i k e . (2) For Og ->• l g the Q branch i s ab sent and the o t h e r branches a re a l l e q u a l l y s t r o n g . 0:P:Q:R:S = 1 : 1 : 0 : 1 : 1 . (3) For 0* -> 2 the r a t i o s a re 0:P:Q:R:S = 1 : 4 : 6 : 4 : 1 . y y Once the r o t a t i o n a l a n a l y s i s has been c a r r i e d o u t , the band c o n t o u r f o r each e l e c t r o n i c c o n f i g u r a t i o n may be p r e d i c t e d by summing the c o n t r i b u t i o n s of a l l b r anche s . A l l bands of a v i b r a t i o n a l p r o g r e s s i o n would be s i m i l a r i n c o n t o u r . I t i s no tewor thy t h a t f o r ve ry l a r g e J , a l l band c o n f i g u r a t i o n s become Q - l i k e (pure e x p o n e n t i a l ) : -2v /aAB I ( v £ ) <* e In a p l o t o f 1n ( I ) a g a i n s t v £ we may de te rm ine AB f rom the s l o p e a t h igh ene rgy . The method i n i n h e r e n t l y a p p r o x i m a t e , but w i l l s e r ve to check the F ranck-Condon r o t a t i o n a l a n a l y s i s . - 39 -3. INSTRUMENTATION AND EXPERIMENTAL DESIGN 3.1 I n t r o d u c t i o n The l i g h t s ou rce used to p h o t o i o n i z e the I od i ne was a M o l e c t r o n DL-300 t u n a b l e dye l a s e r pumped by a UV-1000 n i t r o g e n l a s e r , wh ich p r o v i d e d 5-nsec p u l s e s of bandwidth 0 0.2A. A d i g i t a l g r a t i n g d r i v e m e c h a n i c a l l y tuned the l a s e r . T r i p l e - p h o t o n i o n i z a t i o n o f the Ig m o l e c u l e r e q u i r e s an e x -c i t i n g energy _> 25 ,271 +.3 cm - ' ' ' ( s e c t i o n 2 . 5 ) , which c o r r e s -o ponds to photons of wave leng th <_ 3957 ± 1A. The l a s e r dye chosen was B u t y l PBD i n the s o l v e n t p -d i o xane which l a s e s over 0 3650-3800A; t h i s dye p r o v i d e s the h i g h e s t o u t p u t power a v a i l -a b l e a t p r e s e n t i n t h i s r e g i o n o f the s p e c t r u m . The l a s e r beam was f o cu sed w i t h a 9 3/4 cm q u a r t z l en s between the e l e c t r o d e s o f a g l a s s c e l l c o n t a i n i n g I od ine vapor a t i t s s a t u r a t e d vapor p r e s s u r e ( F i g u r e 1 ) . G rea t s e n s i t i v i t y was a c h i e v e d by f o c u s i n g the l a s e r very c l o s e to the n e g a t i v e e l e c t r o d e i n o r d e r to a c c e l e r a t e the p r oduc t e l e c t r o n s ove r the l o n g e s t p o s s i b l e d i s t a n c e . An oven was b u i l t to house the I od i ne c e l l f o r the p r o d u c t i o n o f h i g h -t empe ra tu re s p e c t r a . The s i m u l t a n e o u s m o n i t o r i n g o f a sma l l p o r t i o n o f the l a s e r o u t p u t a long w i t h the p h o t o i o n i z a t i o n s i g n a l was r e -q u i r e d both f o r c a l c u l a t i o n o f the wavenumbers of the band heads and f o r d e t e r m i n a t i o n o f the r e l a t i v e band i n t e n s i t i e s . Thus a beam s p l i t t e r o f low r e f l e c t i v i t y was r e q u i r e d immed-- 40 - \ o o r -VvVH l " cc o CC t— o < <C vO o cr: — x CJJ O LU CC m h < Z CL. o — Q: 1- I < < 3 0 0 : 0 X C 3 O L U CC CQ ( - < Z CL. < CC Q n: < cr: u 1 o 1 c_> o O LU " 5 CC <2> E O o 1 c n o c; z LU CO CO . < E O ANODE CATHODE j -1 CO C CC LU CC UJ 1— LU CC _ l r - CO 1— LU t o — LU z O \-a. v D L u z: LU CC LU — u-\ < _1 LU :C r— rsi O — Q_ O _ i v O z I CC ZD — CO >- LU 2: — 1- c o CC U_ O < LU < CO cr: 1— LU ZD < LU O z a: C3 U . 1-X LU < z a_ ATT A 1 1 LU CQ < <_> rsl 3 fD CL CL < Z1 LU CC \ - LU < H -- I f— CL. — _ l Q_ LU CO I— — 2 : O < ZD LU _ 1 CQ - 41 -l a t e l y i n f r o n t o f the l a s e r . A l u c i t e p l a t e o f t h i c k n e s s 4.3 mm se r ved w e l l . To f a c i l i t a t e d e t e r m i n a t i o n of the r e l -a t i v e band i n t e n s i t i e s , the d i r e c t r e f l e c t e d l a s e r l i g h t was measured w i t h p h o t o m u l t i p i i e r tube EMI 6256S. A t t e n u a t i n g m a t e r i a l s were used to s h i e l d the pho toca thode i n o r d e r to e l i m i n a t e o p t i c a l s a t u r a t i o n o f the p h o t o m u l t i p i i e r . These m a t e r i a l s , namely a h i g h - n e u t r a l - d e n s i t y f i l t e r and one, and i n some cases two, sheet s o f d i f f u s i n g g l a s s , p r o v i d e d an a t t e n u a t i o n on the o r d e r o f 10^ (Append ix A ) . A F a b r y - P e r o t i n t e r f e r o m e t e r was i n t r o d u c e d i n t o the path of the r e f l e c t e d beam ( F i g u r e 1) as a ve ry a c c u r a t e means of measu r i ng the wave-number s e p a r a t i o n of the p h o t o i o n i z a t i o n - b a n d heads. The p l a t e s e p a r a t i o n was a d j u s t e d to 0.05020 cm; the gap between the p l a t e s was at a t m o s p h e r i c p r e s s u r e . As the l a s e r was t u n e d , the i n t e r f e r o m e t e r p r o v i d e d c l o s e l y - s p a c e d f r i n g e s whose s e p a r a t i o n c o u l d be a c c u r a t e l y c a l i b r a t e d . A 4 cm 2 g l a s s l e n s was used to expand the beam to f i l l r o u g h l y 7 cm o f the i n t e r f e r o m e t e r p l a t e . A s econd , l a r g e - d i a m e t e r g l a s s l e n s c o l l e c t e d the l i g h t f rom the i n t e r f e r o m e t e r and f ocu sed the c e n t e r o f the f r i n g e s on a p i n h o l e i n aluminum f o i l p r e -ceed i n g the a t t e n u a t i n g f i l t e r s o f the p h o t o m u l t i p i i e r . The p u l s e d s i g n a l s from the p h o t o m u l t i p i i e r and the I od i ne c e l l were fed to two s e p a r a t e boxcar i n t e g r a t o r s , each t r i g g e r e d by the synchronous o u t p u t o f the n i t r o g e n l a s e r . The boxcar i n t e g r a t o r s c o n v e r t e d the r e p e t i t i v e - 42 -waveforms to dc s i g n a l s c o n s i s t i n g of the t i m e - a v e r a g e of a number o f p u l s e peak s , the number de te rm ined by the s i g n a l -t o - n o i s e improvement d e s i r e d . The boxcar o u t p u t s were d i s -p l a y e d i n ana logue form on a two -channe l c h a r t r e c o r d e r . Fused q u a r t z was employed i n c r i t i c a l p l a c e s , f o r example i n the window o f the p h o t o m u l t i p i i e r t u b e , i n the l e n s f o c u s i n g the l a s e r beam i n t o the I od i ne c e l l , and i n the window of the oven , s i n c e the t r a n s m i s s i o n i s e x c e l l e n t [98.9% a t 1 cm ( K o l l e r , 1965)] f a r i n t o the u l t r a v i o l e t . The o p e r a t i n g c h a r a c t e r i s t i c s and c a l i b r a t i o n of the major p i e c e s o f appa ra tu s i s d e s c r i b e d i n the f o l l o w i n g s e c t i o n . 3.2 C a l i b r a t i o n and O p e r a t i n g C h a r a c t e r i s t i c s 3.2.1 La se r The l i g h t s ou r ce was a s t a t e - o f - t h e - a r t M o l e c t r o n DL-300 p u l s e d t u n a b l e o r g a n i c dye l a s e r , whose e n g i n e e r i n g de s i gn f o l l o w s Hansch (1972) pumped by a UV-1000 n i t r o g e n 0 l a s e r a t 3371 A. The l a s e r p r o v i d e s 5 - n s e c p u l s e s a t r e p e t i t i o n r a t e s anywhere between 5 and 50 pp s , the h i g h e s t t i m e - a v e r a g e d power ou tpu t o c c u r r i n g a t the r a t e 10 pps. The d i s c h a r g e channe l de s i gn of the n i t r o g e n l a s e r d e l i v e r s a peak power o f 1 MW per p u l s e a t 10 pps. The dye l a s e r i s de s i gned to a l l o w dye i n t e r c h a n g e , thus a c h i e v i n g the wide 0 t u n i n g range o f 3600-7400A, f o r wh ich the o u t p u t power de -pends upon the p a r t i c u l a r dye and s o l v e n t cho sen . A h igh d i s -- 43 -p e r s i o n e c h e l l e g r a t i n g i n L i t t r o w mount f u n c t i o n s as a wave-l e n g t h - s e l e c t i v e end r e f l e c t o r i n the dye l a s e r c a v i t y . Tuning of the dye l a s e r i s a c c o m p l i s h e d by a s i m p l e r o t a t i o n o f the g r a t i n g . In the absence of a F a b r y - P e r o t i n t e r c a v i t y e t a l o n , o the bandwidth o f the d y e - l a s e r ou tpu t i s a p p r o x i m a t e l y 0.2A, -1 0 or 1.5 cm a t 3750A. Th i s bandwidth may i n p r a c t i c e be s l i g h t l y na r rower due to the t h i r d - p o w e r dependence of the p h o t o e l e c t r o n s i g n a l . The beam d i v e r g e n c e i s 2 mrad. An i n -t e r c a v i t y beam expand ing t e l e s c o p e t o g e t h e r w i t h the h i gh q u a l i t y d i f f r a c t i o n g r a t i n g p r o v i d e s e x c e l l e n t wave leng th r e p -0 r o d u c i b i l i t y (0.01A) f rom shot to s h o t . A m p l i t u d e s t a b i l i t y i s a l s o ensured from shot to shot by u s i n g an a u t o m a t i c s t i r r e r , m a g n e t i c a l l y d r i v e n , to c i r c u l a t e the l i q u i d dye i n a 2 cm c e l l , i n o r d e r to r e t u r n the dye to o p t i c a l homogeneity b e f o r e the a r -r i v a l o f the next pump p u l s e . The a m p l i t u d e i s not s t a b l e over the l ong t e r m , however, as p h o t o d i s s o c i a t i o n w i t h i n the dye s o l -u t i o n both dec rea se s the dye c o n c e n t r a t i o n and i n t r o d u c e s impur -i t i e s i n the form o f d i s s o c i a t i o n p r o d u c t s . M o l e c t r o n recommends, a f t e r Hansen ( 1972 ) , the r e l -a t i v e l y h i gh c o n c e n t r a t i o n o f dye i n s o l v e n t o f 5 x 10 m o l e / l i t e r as be ing i n s e n s i t i v e to sma l l amounts o f i m p u r i t -i e s or to dye d e c o m p o s i t i o n . With a m o l e c u l a r we i gh t 354.45 gm/mole, 3.54 mg o f the o r g a n i c dye B u t y l PBD are 3 r e q u i r e d i n 2 cm of s o l v e n t . At t h i s c o n c e n t r a t i o n , the l i f e t i m e o f a sample of B u t y l PBD i n p -d i oxane i s a p p r o x i m a t e l y s i x hours o f c o n t i n u o u s use a t 10 pps. The peak power o b t a i n e d - 44 -f rom a f r e s h sample of dye i s 20 x 10 j o u l e s per p u l s e , 0 or 40 KW per p u l s e , a t 3760A. The e m i s s i o n cu rve over the 0 u s e f u l range 3650-3800A i s g i v e n i n F i g u r e s 10 and 11. Note t h a t the e m i s s i o n v a r i e s w i t h the age of the dye. I t i s c o n c e i v a b l e t h a t the ou tpu t ang le of the l a s e r beam changes s 1 i g h t l y as the l a s e r g r a t i n g i s r o t a t e d . Th i s was of no p r a c t i c a l c o n c e r n , however, as i t was e x p e r i m e n t a l l y de te rm ined t h a t the i n t e n s i t y of the p h o t o e l e c t r o n s i g n a l i s i n s e n s i t i v e to sma l l r o t a t i o n s of the I o d i n e chamber. 3.2.2 Scann ing System A mechan i ca l s c a n n i n g system f o r the g r a t i n g of the dye l a s e r was a s s emb led , as a means o f chang ing the l a s e r ' s wave leng th i n a c o n t i n u o u s and smooth manner. Synchronous s t e p p i n g motor HS50 and the accompanying t r a n s l a t o r module STM1800C (manu fac tu red by SLO-SYN) were used f o r t h i s a s semb ly . The t r a n s l a t o r module i s a p l u g - i n p r i n t e d c i r c u i t board w i t h l o g i c c a p a b i l i t i e s f o r d r i v i n g a SLO-SYN motor i n s t e p p i n g a p p l i c a t i o n s . B i d i r e c t i o n a l o p e r a t i o n o f the motor i s p o s s i b l e a t r a t e s up to 2000 s teps per second. The e x t e r n a l t r i g g e r i n g p u l s e r e q u i r e m e n t i s an 8 to 10 v o l t n e g a t i v e change o f v o l t a g e , and a minimum p u l s e w i d t h of 30 y s e c . The t r a n s l a t o r module r e q u i r e s a power s upp l y wh ich can p r o v i d e -25 v o l t s dc and + 12 v o l t s dc w i t h a maximum r i p p l e o f 5%. The c i r c u i t d iagram of the power s upp l y which was b u i l t i s g i v en i n F i g u r e 2 (Mi 11 man and H a l k i a s , 1972) . - 45 -The w i r i n g c o n n e c t i n g the SLO-SYN motor to the t r a n s -l a t o r module i s shown i n F i g u r e 3. Two heavy -du ty 5.5ft c u r r e n t - l i m i t i n g r e s i s t o r s (shown as R i n the F i g u r e ) a re r e q u i r e d to i n t e r f a c e the motor and t r a n s l a t o r . The r e s i s -t o r s used a re ten-ohm v a r i a b l e r e s i s t o r s reduced to the r e -q u i r e d 5.5ft w i t h i n about ±5%, and a re r a t e d at 225 w a t t s . The wave leng th i n c rement produced by the d i g i t a l s c a n -0 n ing system i n t h i s p a r t i c u l a r a p p l i c a t i o n was 0.00383A per o s tep ove r the range 3650-3800A. S i n c e the l a s e r ' s bandwidth 0 was r ough l y 0.2A, an e s s e n t i a l l y c o n t i n u o u s ou tpu t was a c h i e v e d . The wave leng th i n c rement i s c a l c u l a t e d as f o l l o w s . The s t ep ang l e of the SLO-SYN motor i s 1.8° so the motor s h a f t makes 200 s t ep s per r e v o l u t i o n . One r e v o l u t i o n o f the o g r a t i n g c rank advances the l a s e r ' s wave leng th by 100A i n f i r s t o r d e r . S i n c e the d i f f r a c t i o n o r d e r a p p r o p r i a t e to the dye used i n t h i s r e s e a r c h i s s e ven , one r e v o l u t i o n of the o crank i s equal to 14.3A. Thus , when the motor d r i v e s the g r a t -o i n g d i r e c t l y , each s t ep advances the wave leng th by 0.0715A, not ve ry much s m a l l e r than the l a s e r b andw id th . By u s i n g a system o f f o u r g e a r s , however, the s tep s i z e was reduced by 0 a f a c t o r (64/32) x (112/12) = 18.7 to the v a l u e 0.00383A per s tep (3740 s t ep s per r e v o l u t i o n ) . M o l e c t r o n s p e c i f i e s t h a t the s m a l l e s t s tep p o s s i b l e f o r the g r a t i n g c rank o f the dye l a s e r b e f o r e l o s i n g a c c u r a c y due to s l i p p a g e co r r e spond s to a s t e p p i n g speed o f 400 s t ep s per r e v o l u t i o n ( R e y n o l d s , 1974) . g u r e 2 . C i r c u i t D i ag ram o f SLO-SYN T r a n s l a t o r DC Power S u p p l y Figure 3- SLO-SYN Synchronous Moto r W i r i n g D iag ram - 48 -A f t e r c a r e f u l a d j u s t m e n t s , however, t h i s quoted per fo rmance l i m i t was exceeded by a f a c t o r o f t e n . The q u a l i t y of the s c ann i ng system i s i n d i c a t e d i n the F a b r y - P e r o t i n t e r f e r e n c e f r i n g e s of F i g u r e 12, where o n l y o c c a s i o n a l s l i p p a g e i s a p p a r e n t . 3.2.3 I od i ne Chamber The g l a s s c e l l c o n t a i n i n g I od i ne vapor i n wh ich the p h o t o i o n i z a t i o n o c c u r r e d i s shown i n F i g u r e 1. The 2 mm py rex window th rough wh ich the l a s e r beam e n t e r e d the c e l l has a v i r t u a l l y c o n s t a n t t r a n s m i s s i o n of 92% ± 1% over 3650-0 3800A, the s p e c t r a l range o f i n t e r e s t ( K o l l e r , 1965) . The l a s e r beam was f o cu sed between pa r a l 1 e l - p l a t e e l e c t r o d e s s e p -a r a t e d by 1.1 cm. A F l u k e 415B H.V. dc power s upp l y was used to m a i n t a i n the e l e c t r o d e s a t a c o n s t a n t p o t e n t i a l d i f f e r e n c e . A c c o r d i n g to the s e n s i t i v i t y d e s i r e d , the e l e c t r o d e v o l t a g e c o u l d be a d j u s t e d to any p o i n t i n the range -200 to -400 V ( 2 0 ° C ) . Lower v o l t a g e s d i d not p r o v i d e an adequate s i g n a l , and h i g he r v o l t a g e s caused an a r c i n s t a b i l i t y . In o r d e r to o b t a i n adequate s e n s i t i v i t y a t h i gh t e m p e r a t u r e s , t h i s range had to be exceeded up to -430 V. The c e l l was c o n s t r u c t e d w i t h s t a i n l e s s - s t e e l e l e c t r o d e s a f t e r Brackmann ( 1958 ) , who obse rved t h a t h i s I od i ne u l t r a -v i o l e t - p h o t o n - c o u n t e r s wh ich employed t h i s meta l f o r t h e i r e l e c t r o d e s had the l o n g e s t l i f e t i m e s . The t ung s t en l ead s p r o j e c t th rough the g l a s s o f our c e l l th rough a s t a n d a r d - 49 -S t u p a k o f f s e a l . The c e l l was e vacua ted to 1 0 ~ 6 t o r r b e f o r e the I od i ne was d i s t i l l e d i n t o i t . The c e l l was f i t t e d w i t h a l ong stem c o n t a i n i n g a r e s e r v e s upp l y o f s o l i d I o d i ne so t h a t the vapor p r e s s u r e i n s i d e was a lways the s a t u r a t e d vapor p r e s s u r e o f I o d i n e . The l e n g t h o f the stem se rved to i s o l a t e the s o l i d I o d i ne a t a l ower t empera tu re than the rema inde r o f the c e l l when p l a c e d i n s i d e the o ven , to ensure t h a t contam-i n a t i o n o f the c e l l window and e l e c t r o d e s d i d not o c cu r when h i gh t empe ra t u r e s p e c t r a were t a k e n . 3.2.4 Oven The oven used to heat the I od i ne c e l l was c o n s t r u c t e d of one and o n e - h a l f i n c h t h i c k a sbe s t o s s h e e t i n g , cemented w i t h epoxy (maximum t empe ra t u r e 120°C) . The d i r e c t c u r r e n t power s upp l y t o the h e a t i n g e lement was a Sorenson NOBATRON DCR150-15A which s u p p l i e s h igh c u r r e n t at low v o l t a g e . In t h i s oven the t empe ra t u r e s t a b i l i t y was w i t h i n 0.2°C over one h o u r ' s o p e r a t i o n . I t was i m p o r t a n t to p r e v e n t s o l i d I od i ne from d e p o s i -t i n g on the c e l l window and e l e c t r o d e s . Thus the oven was de s i gned w i t h two compartments i n o r d e r to i s o l a t e the s upp l y of s o l i d I od i ne i n the stem o f the c e l l a t a l ower t empe ra tu re than the rema inder o f the c e l l . The upper compartment has i n n e r d imens ion s 5 3/4" x 5 3/4" x 6 " . The l a s e r beam e n -t e r e d th rough a 1.5 i n c h d i a m e t e r a p e r t u r e c o ve red w i t h a q u a r t z p l a t e to m i n i m i z e heat l o s s . The l ower compartment - 50 -wh i ch houses the stem o f the c e l l has i n n e r d imens i on s I V x 4" x 4 " . The h e a t i n g e lement f o r the oven i s Nichrome w i r e a t seven ohms per f o o t wound many t imes around the i n -t e r i o r . The l e n g t h o f Nichrome w i r e i n the upper compa r t -ment i s 270" and i n the l o w e r , 2 6 " , f o r a t o t a l o f 173ft. S i n c e the power d i s s i p a t e d per u n i t volume i n the upper com-par tment i s about 1.3 t imes t h a t i n the l o w e r , the two com-pa r tment s m a i n t a i n a s u f f i c i e n t t empe ra tu re d i f f e r e n c e even though the upper one must n e c e s s a r i l y s u s t a i n a g r e a t e r heat l o s s . From t e s t s done on the empty oven , the t empe ra tu re i n the upper compartment i s about 1.13 t imes t h a t i n the l ower over the range 22° - 100°c. 3.2.5 P h o t o m u l t i p l i e r EMI tube 6256S used to m o n i t o r the l a s e r i n t e n s i t y i s a 1 cm c a t h o d e , 13 - s tage p h o t o m u l t i p l i e r w i t h f u s e d - q u a r t z window. With a r i s e t ime o f 7 nsec and a c a p a c i t y f o r peak c u r r e n t s up to 300 mamp, t h i s tube i s adequate f o r pu l s ed o p e r a t i o n . The end-window, s e m i - t r a n s p a r e n t pho toca thode and the v e n e t i a n - b l i n d type dynodes a re coa ted w i t h CsSb which o has a f l a t re sponse cu rve over the s p e c t r a l range 3650-3800A of l a s e r dye PBD. The quantum e f f i c i e n c y i n t h i s range i s 0.13 ± 3%. The n o i s e c h a r a c t e r i s t i c s a re good. Tube 6256S i s de s i gned to have very low anode dark c u r r e n t , l e s s than 0.5 myamp a t -1000 v o l t s . A mu-metal s h i e l d was used to p r o -t e c t the d e t e c t o r from s t r a y magnet i c f i e l d s . The dc v o l t a g e - 51 -a p p l i e d to the p h o t o c a t h o d e , t y p i c a l l y on the o r d e r of -600 V, was s u p p l i e d by Regu l a t ed H.V. Supp ly RE-1602 ( N o r t h e a s t Sc. Corp. ). For good l i n e a r i t y and g a i n s t a b i l i t y , the c u r r e n t drawn from the power s upp l y by the dynodes must not m a t e r i a l l y change the v o l t a g e between the dynodes. Th i s r e q u i r e m e n t means t h a t t h i s anode c u r r e n t I, must be a c o n s i d e r a b l y s m a l l e r than the b l e e d e r c u r r e n t I^  th rough the p o t e n t i a l d i v i d e r . A good r u l e o f thumb i s t h a t I <_ 1^/10. Pu l s e s of l a r g e a m p l i t u d e may be accommodated p r o v i d i n g t h a t by -pass c a p a c i t o r s are used between the l a s t few s t a g e s , where the c u r r e n t s a re g r e a t e s t , and p r o v i d i n g t h a t the mean anode c u r r e n t <I > s a t i s f i e s the above r e -a q u i r e m e n t . Measurement o f the l a s e r ' s i n t e n s i t y i n v o l v e d pu l s e s of l a r g e a m p l i t u d e and ve ry s h o r t d u r a t i o n , and to t h i s end c h a i n r e s i s t o r s were chosen such t h a t < I a > m a x = 1^/50, and by -pas s c a p a c i t o r s were connec ted between the l a s t f o u r s tages of the p h o t o m u l t i p ! i e r c i r c u i t ( F i g u r e 4 ) . The l i n e a r i t y of the p h o t o m u l t i p l i e r was t e s t e d u s i n g f o u r 0 i d e n t i c a l n e u t r a l d e n s i t y f i l t e r s at wave leng th 3760A, ve r y near the l a s e r ' s peak i n t e n s i t y . The re sponse i s l i n e a r , as shown i n F i g u r e 5. In o r d e r to a v o i d o p t i c a l s a t u r a t i o n o f the p h o t o m u l t i p l i e r , d i f f u s i n g g l a s s a t a d i s t a n c e of 2 cm from the c a t h o d e , f o l l o w e d by a h i g h - n e u t r a l -d e n s i t y f i l t e r , were used to s h i e l d the c a t h o d e . The t o t a l 52 -1 OOK f — - A A A r MEG 560K Photocathode Dynode 1 D 2 D 9 0.01 yF 0.01 yF 0.01 yF 0.08 yF 560K 560K 560K 560K 560K Load D 10 D 11 D 12 D 13 Anode Figure k. EMI 6256S Photomult ip l ier Tube C i r c u i t - 54 -o p t i c a l a t t e n u a t i o n o f t he se m a t e r i a l s as a f u n c t i o n o f wave leng th i s p r e s e n t e d i n Append ix A. 3.2.6 Boxcar I n t e g r a t o r Two boxcar i n t e g r a t o r s were employed: (a) P r i n c e t o n A p p l i e d Research Model 160, w i t h i n p u t impedance lOOKft i n "normal r e s o l u t i o n " mode, and w i t h maximum a c c e p t a b l e i n p u t v o l t a g e o f 200V peak, was used to p roce s s the p h o t o i o n i z a t i o n s i g n a l , and (b) PAR Model CW-1, w i t h i n p u t impedance lOKft and maximum v o l t a g e 200V peak, was used to p roce s s the s i g n a l f rom p h o t o m u l t i p l i e r EMI 6256S when t h i s d e t e c t o r was needed. The purpose o f a boxca r i n t e g r a t o r i s to e x t r a c t a r e p e t i t i v e waveform from n o i s e . S i n c e the two s i g n a l s ment ioned above c o n s i s t e d o f r e p e t i t i v e p u l s e s f o r which the r a t i o of u s e f u l s i g n a l t ime to dead t ime was on the o r d e r of 10 to 1 and -4 10 to 1 r e s p e c t i v e l y , the boxcar i n t e g r a t o r was p a r t i c u l a r l y u s e f u l i n our r e s e a r c h . In e s s e n c e , the boxca r s y n c h r o n o u s l y samples an i n p u t s i g n a l u s i n g a v a r i a b l e - w i d t h , v a r i a b l e - d e l a y g a t e , which can be f i x e d a t any p o i n t on , or s l o w l y scanned a c r o s s the i n p u t s i g n a l . The boxca r uses n e g a t i v e feedback i n an i n t e g r a t o r c i r c u i t so t h a t the o u t p u t a s y m p t o t i c a l l y a p -proaches the average v a l u e o f the i n p u t s i g n a l -over the a p e r -t u r e t ime i n t e r v a l . A t r i g g e r p u l s e wh ich i s s y n c h r o n i z e d w i t h the e x t e r n a l event under s tudy can be a p p l i e d to the boxcar to c o n t r o l the t i m i n g o f the g a t e . I f the gate i s f i x e d on - 55 -a s i n g l e p o i n t o f the i n p u t s i g n a l , the boxcar ou tpu t w i l l r i s e a s y m p t o t i c a l l y toward the average va l ue o f the i n p u t s i g n a l a t the sampled p o i n t . I f the gate i s be ing scanned a c r o s s the i n p u t s i g n a l , , the synchronous waveform w i l l be rep roduced a t the o u t p u t . The boxcar i s l i n e a r to w i t h i n ±0 .25% o f f u l l - s c a l e , and has ga i n s t a b i l i t y ± 0 . 5 % . There a re two i m p o r t a n t r e l a t i o n s h i p s between the b o x c a r ' s c o n t r o l s e t t i n g s . The obse rved t ime c o n s t a n t (OTC), which i s the r e a l t ime r e q u i r e d f o r the p r o ce s s ed ou tpu t s i g -na l to reach 63% of i t s f i n a l v a l u e , and the s i g n a l - t o - n o i s e improvement r a t i o (SNIR) a re exp re s sed as f o l l o w s : 0 T C = ( f ) ("AT) { 3 - 1 ) SNIR = / 2 x OTC x f (3 .2 ) The c o n t r o l s e t t i n g s a re d e f i n e d as f o l l o w s : TC = s e t t i n g of the t ime c o n s t a n t d i a l . f = p u l s e r e p e t i t i o n f r e q u e n c y . AT = a p e r t u r e t i m e , or gate w i d t h . A l l pa rameter s a re va l ued i n sec or sec 3.2.7 Cha r t Reco rde r The model used (Ken t ) was a two-channe l r e c o r d e r w i t h a wide v a r i e t y of s e n s i t i v i t y s e t t i n g s . The c h a r t span o f ten i n che s a l l o w e d r e a s o n a b l e a c c u r a c y i n the measurements. A l i n e a r i t y check was pe r fo rmed on two of the s e n s i t i v i t y 10 10 INPUT SIGNAL (ARBITRARY UNITS) INPUT SIGNAL (ARBITRARY UNITS) F i g u re 6. Te s t L i n e a r i t y o f C h a r t R e c o r d e r a t Two S e n s i t i v i t y S c a l e s : (a) 10 V o l t s Maximum, and (b) 5 V o l t s Maximum - 57 -s c a l e s (5 and 10 v o l t s maximum) used most o f t e n . V o l t a g e p u l s e s were fed th rough boxca r i n t e g r a t o r CW-1 and the dc ou tpu t was s u b s e q u e n t l y a p p l i e d to the c h a r t r e c o r d e r ; the p u l s e a m p l i t u d e was a l s o measured i n d e p e n d e n t l y on an o s c i l l o s c o p e . The c h a r t r e c o r d e r ' s re sponse to a p p l i e d v o l t a g e i s i n d i c a t e d i n F i g u r e 6. Except f o r the f i r s t , and p o s s i b l y the l a s t , i n c h of c h a r t , the re sponse i s l i n e a r . 3.3 S i g n a l P r o c e s s i n g The p r o c e s s i n g o f the e l e c t r i c s i g n a l f rom the I o d i ne chamber was done w i t h boxca r i n t e g r a t o r PAR 160. The o f f -r e s onan t s i g n a l was n e g l i g i b l e so t h a t no dc o f f s e t was r e q u i r e d i n the boxcar i n t e g r a t o r or the c h a r t r e c o r d e r . The main s ou r ce of n o i s e i n the i n s t r u m e n t s was e l e c t r i c a l p i c k u p wh ich was reduced by a l a r g e e x t e n t th rough c a r e f u l s h i e l d i n g . As w i t h any s i g n a l a v e r a g e r , the o p e r a t i o n o f the boxca r i n t e g r a t o r must ba l ance a g a i n s t s i g n a l r e s o l u t i o n the s i g n a l - t o - n o i s e improvement d e s i r e d . S i n c e a l a r g e s i g n a l - t o - n o i s e improvement r a t i o was not r e q u i r e d , t h i s c o u l d be s a c r i f i c e d i n o r d e r to o b t a i n a r e s o l u t i o n o f the p h o t o -i o n i z a t i o n bands l i m i t e d o n l y by the bandwidth of the l a s e r . With a t e r m i n a t i n g impedance of lOOKfi on the c e l l , the s i g n a l p u l s e had h a l f - w i d t h 70 p sec . The p u l s e shape, r ep roduced by the boxcar i n t e g r a t o r i n the s cann i ng mode, i s i l l u s t r a t e d i n F i g u r e 7. The a p e r t u r e w i d t h o f the boxcar i n t e g r a t o r was 10 ysec and the TC pa rameter was s e t a t 0.1 msec. At the \ - 5-8 -' (MILLISECONDS) F i g u r e 7 • P h o t o e l e c t r o n S i g n a l P u l s e S h a p e a t T e r m i n a t i n g I m p e d a n c e 100 KQ - 59 -r e p e t i t i o n f r e q u e n c y 10 pps of the l a s e r t h i s gave, a c c o r d i n g to e q u a t i o n s 3.1 and 3 .2 , a s i g n a l - t o - n o i s e improvement r a t i o o f 4.5 and an e x p e r i m e n t a l t ime c o n s t a n t o f 1 s e c o n d , e f f e c t -i v e l y a v e r a g i n g over ten l a s e r p u l s e s . The magn i tude of the p r o ce s s ed s i g n a l was max imized by i n t r o d u c i n g a de l a y o f a p p r o x i m a t e l y 3 ysec between the b e g i n n i n g o f the i n p u t p u l s e and the open ing o f the boxca r a p e r t u r e . V i b r a t i o n a l a n a l y s i s o f the spect rum r e q u i r e d the e x -p e r i m e n t a l measurement of the energy s e p a r a t i o n o f the p h o t o -i o n i z a t i o n bands. To f a c i l i t a t e t h i s measurement, a p o r t i o n o f the l a s e r l i g h t was passed th rough a F a b r y - P e r o t i n t e r -f e r o m e t e r , y i e l d i n g , as the l a s e r s canned , o p t i c a l f r i n g e s o f e s s e n t i a l l y c o n s t a n t energy s e p a r a t i o n which were r e c o r d e d s i m u l t a n e o u s l y w i t h the p h o t o e l e c t r o n s i g n a l on a two - channe l c h a r t r e c o r d e r . A sample of the data i s p r e s e n t e d i n F i g u r e 12. The i n s t r u m e n t s used to r e c o r d the F a b r y - P e r o t f r i n g e s were p h o t o m u l t i p i i e r EMI 6256S and boxcar i n t e g r a t o r CW-1. S i n c e the ou tpu t of the F a b r y - P e r o t i n t e r f e r o m e t e r was weak, a r e l a t i v e l y h i gh ca thode v o l t a g e , -800V, was r e q u i r e d on the p h o t o m u l t i p i i e r . The aim i n the p r o c e s s i n g o f the F a b r y -P e r o t s i g n a l w i t h the boxca r i n t e g r a t o r was good r e s o l u t i o n o f the f r i n g e s r a t h e r than a l a r g e s i g n a l - t o - n o i s e improvement r a t i o . Thus the TC pa rameter was s e t a t i t s l o w e s t p o s s i b l e v a l u e , 0.1 msec, on boxca r i n t e g r a t o r CW-1. The h a l f - w i d t h o f the s i g n a l p u l s e from the p h o t o m u l t i p i i e r was 6.8 ysec a t - 60 -a t e r m i n a t i n g impedance o f 10 Kft , and the a p e r t u r e w i d t h of the boxca r i n t e g r a t o r was s e t at 10 y s e c . The magn i tude of the o u t p u t s i g n a l was max imized by d e l a y i n g the boxcar a p e r -t u r e a p p r o x i m a t e l y 0.8 ysec from the b e g i n n i n g o f the i n p u t p u l s e . The quoted s e t t i n g s of boxca r i n t e g r a t o r CW-1 p r o -duced an e x p e r i m e n t a l t ime c o n s t a n t o f 1 second and a s i g n a l - t o - n o i s e improvement r a t i o of 4 . 5 . The s c ann i ng r a t e of the l a s e r was such t h a t the p e r i o d o f the f r i n g e s was about 24 seconds . In the r e c o r d i n g o f the F a b r y - P e r o t f r i n g e s , the boxca r s e n s i t i v i t y and c h a r t r e c o r d e r s e n s i t i v i t y were each 5 v o l t s FSD, g i v i n g a f r i n g e a m p l i t u d e between 10% and 20% of the f u l l c h a r t s c a l e ( F i g u r e 12 ) . In t h i s a p p l i c a t i o n , the p o t e n t i a l d i f f e r e n c e a c r o s s the e l e c t r o d e s of the I od i ne c e l l was s e t ve ry h igh (-400 V ) , j u s t below the a r c t h r e s h o l d a t 20°C. Th i s a c t i o n was taken to i n c r e a s e the v i s i b i l i t y o f the weaker bands. The i n e v i t a b l e s a t u r a t i o n o f the s t r o n g e s t bands under these c o n d i t i o n s was un impo r t an t i n t h i s a p p l i c -a t i o n , as the p o s i t i o n s o f the bands, r a t h e r than t h e i r amp-l i t u d e , was the i tem o f be measured. The c h a r t r e c o r d e r s e n s i t i v i t y on the channe l on wh ich the p h o t o i o n i z a t i o n s i g n a l was r e c o r d e d was m a i n t a i n e d a t 5 v o l t s FSD, w h i l e the s e n s i t -i v i t y of boxcar i n t e g r a t o r PAR 160 was v a r i e d between 1 v o l t and 100 mvo l t FSD d u r i n g a comp le te scan i n o r d e r to magn i fy the weaker p h o t o i o n i z a t i o n bands. The data nece s s a r y f o r a d e t e r m i n a t i o n o f the band - 61 -i n t e n s i t i e s r e q u i r e d , a l ong w i t h the p h o t o i o n i z a t i o n s i g n a l , the s i m u l t a n e o u s m o n i t o r i n g o f the l a s e r i n t e n s i t y . The F a b r y - P e r o t i n t e r f e r o m e t e r was removed so t h a t the d i r e c t r e f l e c t e d l a s e r l i g h t c o u l d be r e c o r d e d . The r e c o r d i n g i n s t r u m e n t s used were p h o t o m u l t i p l i e r EMI 6256S a t a ca thode v o l t a g e -600 V f o l l o w e d by boxca r i n t e g r a t o r PAR CW-1. In t h i s a p p l i c a t i o n the s i g n a l - t o - n o i s e c h a r a c t e r i s t i c s were of pr ime i m p o r t a n c e . S i n c e the l a s e r i n t e n s i t y i s a s l o w l y v a r y i n g f u n c t i o n of wave leng th ( F i g u r e s 10 and 1 1 ) , r e s o l u t i o n c o u l d be s a c r i f i c e d to a c h i e v e e x c e l 1ent s i g n a 1 - t o - n o i s e c h a r a c t e r i s t i c s . The boxca r s e t t i n g s were TC = 1 msec and gate w i d t h 10 usee so t h a t at the p u l s e r e p e t i t i o n f r e q u e n c y o f 10 pp s , the s i g n a l - t o - n o i s e improvement r a t i o was 14 and the e x p e r i m e n t a l t ime c o n s t a n t was 10 seconds ( e q u a t i o n s 3.1 and 3 . 2 ) , e f f e c t i v e l y a v e r a g i n g over 100 l a s e r p u l s e s . The p r o ce s s ed s i g n a l was max imized by d e l a y i n g the samp l i ng gate 0.8 usee from the b e g i n n i n g o f the i n p u t p u l s e . On a l l scans taken the s e n s i t i v i t y of the boxca r was 0.5 v o l t FSD and of the c h a r t r e c o r d e r , 1 v o l t FSD. In the r e c o r d i n g o f the p h o t o i o n i z a t i o n s i g n a l , the e l e c t r o d e v o l t a g e was v a r i e d between -200 and -400 V, and the s e n s i t i v i t i e s o f the r e c o r d -i n g i n s t r u m e n t s were c o n s t a n t t h r oughou t at 100 mV FSD ( b o x c a r ) and 5 v o l t s FSD ( c h a r t r e c o r d e r ) , i n t h i s a p p l i c a t i o n . P h o t o i o n i z a t i o n data were a l s o produced f o r heated I o d i ne vapor . The l a s e r i n t e n s i t y was r e c o r d e d s i m u l t a n e o u s l y - 62 -as d e s c r i b e d above. T h e o r e t i c a l l y , a ve ry h i gh vapor temp-e r a t u r e i s d e s i r a b l e i n o r d e r to c r e a t e s i g n i f i c a n t change i n the p o p u l a t i o n of the upper v i b r a t i o n a l s t a t e s o f the ground e l e c t r o n i c s t a t e of the m o l e c u l e . As the vapor i n -c r e a s e s i n d e n s i t y , however, r e c o m b i n a t i o n p r o ce s s e s dec rea se the s i g n a l i n t e n s i t y , so t h a t ve ry h i gh t empe ra t u r e s are not p r a c t i c a l . The l ower compartment o f the oven which housed the I-£ chamber was h e l d a t a t empe ra t u r e i n the v i c i n i t y of 90°C, wh ich produced a t empe ra tu re o f about 100°C i n the upper compartment. Th i s r e q u i r e d an a p p l i e d v o l t a g e of 120 v o l t s d c ; the oven drew 0.69 amp of c u r r e n t th rough the h e a t -i ng u n i t o f impedance 173ft. The s a t u r a t e d vapor p r e s s u r e w i t h i n the c e l l was r a i s e d to a lmos t 27 mm Hg, governed by the l o w e s t t empe ra tu re i n the oven , compared w i t h 0.2 mm a t room t empe ra tu re (Ge r r y and G i l l e s p i e , 1932) , and the p h o t o -i o n i z a t i o n s i g n a l was c o n s i d e r a b l y weakened. The o v e r a l l s e n s i t i v i t y o f the r e c o r d i n g i n s t r u m e n t s was i n c r e a s e d over t h a t used i n e xpe r imen t s pe r fo rmed a t 20°C. E l e c t r o d e v o l t -ages up to -430 V were p o s s i b l e -without, e l e c t r i c a l s a t u r a t i o n . F i g u r e 8 i l l u s t r a t e s t h a t the band c o n t o u r d i d not change w i t h e l e c t r o d e v o l t a g e , as i n d i c a t e d f o r the (2 -0 ) band a t t h r e e v o l t a g e s between -150 and -430 V. The v o l t a g e de -pendence of the peak s i g n a l i n t e n s i t y i s e x p o n e n t i a l as i l l u s t r a t e d i n F i g u r e 9. The s e n s i t i v i t i e s t h r oughou t of the boxca r i n t e g r a t o r PAR 160 and c h a r t r e c o r d e r were 100 mvo l t and 1 v o l t FSD r e s p e c t i v e l y ( a l l bands on s c a l e a t -340 V ) . - 63 -~v *-Figure 8 . Voltage Dependence Il l u s t r a t e d for of the Iodine Band Contour a Typical Band at 100°C - Gk -1000 (A o > < cn CL O too 9 10 9 9 9 1 0 0 2 0 0 A P P L I E D V O L T A G E 3 0 0 Figure 9 • Volt a g e -Dependence of the Intensity Peak Signal - 65 -4. DATA ANALYSIS 4.1 I n t r o d u c t i on S t r ong r e s onan t s i g n a l s were found as the l a s e r f r e q u e n c y was s canned . The o f f - r e s o n a n t v o l t a g e was n e g l i g i b l e . The spect rum c o n s i s t s of a s e r i e s of a p p r o x i m a t e l y e q u a l l y spaced v i o l e t - d e g r a d e d bands. A t y p i c a l spect rum at 20°C i s p r e s e n t e d i n F i g u r e 10, and a t y p i c a l hot scan {- 100°C) i n F i g u r e 11, accompanied by the l a s e r o u t p u t . No bands were o found to the red of 3800A i n s p i t e of the c o n s i d e r a b l y g r e a t e r l a s e r power i n t h i s r e g i o n . A p a r t o f the spect rum i s shown at h i g h e r r e s o l u t i o n i n F i g u r e 12. The number of i on s p r o -duced a t the peak of the s t r o n g e r bands i s on the o r d e r of 1 0 1 2 per pu l s e a t -350 V. The a p p r o x i m a t e l y c u b i c l a s e r p o w e r - s i g n a l r e l a t i o n ( s e c t i o n 4.2) t o g e t h e r w i t h the f a c t t h a t s i n g l e and doub le photons were e n e r g e t i c a l l y unab le to i o n i z e the m o l e c u l e s , p l u s the a s s u r ance t h a t no re sonances can o c cu r f o r one -photon a b s o r p t i o n from the ground s t a t e ( s e c t i o n 2 . 5 ) , make i t r e a s o n a b l e to a s s i g n the ob se r ved resonance s i g n a l as two " + photon resonance from the v i b r a t i o n a l l e v e l v of the X 0^ i ground s t a t e to a v i b r a t i o n a l l e v e l v o f an i n t e r m e d i a t e s t a t e o f symmetry g f o l l o w e d by a nonresonant t r a n s i t i o n to an i o n i z e d s t a t e . A f t e r some t r i a l and e r r o r to a s c r i b e the peak s , one q u i c k l y a r r i v e s a t the a s s i gnment of the t r a n s i t i o n s as p r e s en ted i n F i g u r e s 10, 11, and 12. D e t a i l e d v i b r a t i o n a l F i g u r e 10. T y p i c a l P h o t o e 1 e c t r o n S p e c t r u m o f I o d i n e Vapor a t 20°C A c c o m p a n i e d by L a s e r O u t p u t Fi gure 11. Typical Photoelectron Spectrum of Iodine Vapor at 100°C Accompanied by-Laser Output F i g u r e 12. P o r t i o n o f t he P h o t o e l e c t r o n Spec t rum a t H i g h e r R e s o l u t i o n Accompan ied by F a b r y - P e r o t F r i n g e s - 69 -and r o t a t i o n a l a n a l y s i s o f the band system i s c a r r i e d o u t , and the p o s s i b l e e l e c t r o n i c c o n f i g u r a t i o n s o f the new s t a t e a re e x p l o r e d . The e f f e c t o f i m p u r i t i e s i n the sample i s d i s -cussed b r i e f l y . 4.2 Power-Dependence o f the P h o t o i o n i z a t i o n S i g n a l As s i n g l e - and d o u b l e - p h o t o n e x c i t a t i o n a re e n e r g e t i c -a l l y unab le to i o n i z e the I 2 m o l e c u l e s ( s e c t i o n 2 . 6 ) , any ob se r ved re sonance s i g n a l must be the ' r e s u l t of e x c i t a t i o n by t h r e e or more pho ton s . The power-dependence I ^ of the p h o t o -i o n i z a t i o n s i g n a l , upon the i n t e n s i t y I o f the i n c i d e n t l i g h t , was measured e x p e r i m e n t a l l y a t the peaks of s e v e r a l bands. The bands chosen were tho se o f the (v - 0) p r o g r e s s i o n s from (0 -0 ) to (4 -0 ) i n c l us i ve, p 1 us the (1-1) band. Th i s c h o i c e a l l o w e d i n v e s t i g a t i o n of the power dependence over a range of ( u n a t t e n u a t e d ) s i g n a l s t r e n g t h s . The magnitude of the ou tpu t s i g n a l was de te rm ined as the l a s e r i n t e n s i t y was v a r i e d w i t h up to f o u r c a l i b r a t e d n e u t r a l d e n s i t y f i l t e r s . The f i l t e r s , wh ich were i d e n t i c a l , each have a d e n s i t y K(x) as noted i n Tab le I I . The power dependence N may be de te rm ined from the s l o p e o f a p l o t o f the l o g of the p h o t o i o n i z a t i o n s i g n a l i n -t e n s i t y ve r su s the number o f f i l t e r s a t t e n u a t i n g the l a s e r beam ( s e c t i o n 2 . 1 ) . The r e l a t i o n s h i p i s ( e q u a t i o n 2 . 2 ) : A sample p l o t i s g i v e n ( F i g u r e 13) f o r the (1 -0 ) band. - 7 0 -10 i — 0 1 2 3 Number o f F i 1 t e r s -»-F i g u r e 13. Dependence o f S i g n a l I n t e n s i t y on L a s e r Power I l l u s t r a t e d f o r t he (1-0) Band . - 71 -Band A LASER o (A) F i 1 t e r Dens i t y K ( A ) Power Dependence N= - s l o p e / K ( X ) (0 -0) 3733.10 0.164 2. 34 (1 -1 ) 3731.18 0.164 2. 50 (1 -0) 3716.44 0.166 2.23 (2-0) 3699.98 0. 167 2. 31 (3 -0) 3683.76 0.168 2.69 ( 4 - 0 ) 3667.78 0. 169 2. 75 Tab le I I . Power-Dependence of the P h o t o i o n i z a t i o n S i g n a l - 72 -The power-dependence o f the chosen bands v a r i e s from 2 2 3 2 75 I ' to I * (Tab le I I ) . In g e n e r a l , the s t r o n g e r the band, the l e s s e r i s the power-dependence measured. As the e l e c t r i c s i g n a l may not be p e r f e c t l y l i n e a r l y r e l a t e d to the t r i p l i n g p roce s s because of p o s s i b l e s a t u r a t i o n and a va l anche 3 breakdown, the r e s u l t s are c o n s i s t e n t w i t h the e xpec ted I r e l a t i o n . 4.3 V i b r a t i o n a l A n a l y s i s i i The v i b r a t i o n a l c o n s t a n t s oo and w x„ , p l u s the e e e ^ minimum energy T g o f the e l e c t r o n i c p o t e n t i a l w e l l may be de te rm ined f o r the upper ( r e s o n a n t ) e l e c t r o n i c s t a t e of by measur ing the s e p a r a t i o n of the heads o f the p h o t o i o n i z a -t i o n bands, as d e s c r i b e d i n s e c t i o n 2.6. Measurements o f the s p a c i n g of the p h o t o i o n i z a t i o n band heads , i n u n i t s c o r r e s -pond ing to the number of F a b r y - P e r o t f r i n g e s , were taken from t h r e e d i f f e r e n t c h a r t s each of which r e co rded the l a s e r l i g h t , passed th rough a F a b r y - P e r o t i n t e r f e r o m e t e r , s i m u l t a n -e o u s l y w i t h the I 2 p h o t o i o n i z a t i o n s i g n a l . The measurements from the t h r e e c h a r t s a re t a b u l a t e d i n Tab le I I I f o r the II i (0-v ) and (v -0) bands, and a re t a b u l a t e d i n Tab le VII f o r n i i the (1 - v ) and (v -1) bands of l^- Each of the (v -1) bands i i s r e s o l v e d from the accompanying (v -0) band, w h i l e the II bands o f the (1 - v ) p r o g r e s s i o n a re o n l y o c c a s i o n a l l y d i s t i n c t . Hence Tab le VII c o n t a i n s o n l y s e l e c t e d e n t r i e s . S i n ce the wave leng th t u n i n g system o f the dye l a s e r was pushed beyond - 73 -i t s quoted pe r fo rmance l i m i t ( s e c t i o n 3 . 2 ) , the o p e r a t i o n o f t h i s system was at some p o i n t s s l i g h t l y e r r a t i c . Th i s e f f e c t was the main source of u n c e r t a i n t y i n the measurement o f the s e p a r a t i o n of the bands. The magni tude of the u n c e r t a i n t y i n the measurements p r e s e n t e d i n Tab l e s I I I and VI I i s b e t t e r than 1% of the d i s t a n c e between two a d j a c e n t bands. The F a b r y - P e r o t i n t e r f e r o m e t e r may be c a l i b r a t e d by II compar ing the s p a c i n g o f the (0 -v ) bands w i t h the we l l - k nown v i b r a t i o n a l l e v e l s o f the ground e l e c t r o n i c s t a t e of \ ^ wh ich a re d e s c r i b e d i n s e c t i o n 2.6 and l i s t e d i n Tab le I. Once the c a l i b r a t i o n of the f r i n g e s i s c o m p l e t e , the s e p a r a t i o n o f the i i (v -0) and (v -1) bands may be c o n v e r t e d to wavenumber u n i t s , and the v i b r a t i o n a l c o n s t a n t s c a l c u l a t e d f o r the upper e l e c -t r o n i c s t a t e . The F a b r y - P e r o t i n t e r f e r o m e t e r was c a l i b r a t e d u s i n g f o u r p a i r s of bands , f rom (0 -0 ) to (0 -4 ) i n c l u s i v e . The c a l c u l a t i o n s are p r e s e n t e d i n Tab le IV and y i e l d an a v e r -age c a l i b r a t i o n of 9.961 ± 0.034 c m - * per f r i n g e . A p p l y i n g t h i s c a l i b r a t i o n f a c t o r , the s e p a r a t i o n i n wavenumber u n i t s II i of the (0-v ) and (v -0) p h o t o i o n i z a t i o n bands o f l^, averaged ove r t h r e e c h a r t s , i s g i v e n i n Tab l e V. S i m i l a r i l y , Tab le n i V I I I c o n t a i n s the s e p a r a t i o n o f the (1-v ) and (v -1) bands i n wavenumber u n i t s . i i C a l c u l a t i o n of the v i b r a t i o n a l c o n s t a n t s u& and w g x e was c a r r i e d out s e p a r a t e l y w i t h the (v -0 ) p r o g r e s s i o n and i i the (v -1) p r o g r e s s i o n of I ? . C o n s i d e r f i r s t the (v -0) bands. - 74 -Tab le V c o n t a i n s the s e c o n d - d i f f e r e n c e s i n the v i b r a t i o n a l energy w h i c h , a c c o r d i n g to e q u a t i o n 2 .5 , a re i n a f i r s t i a p p r o x i m a t i o n equal to 2 u e x e . The average of these measured second d i f f e r e n c e s i s 1.195 cm - ' ' ' , and thus the e x p e r i m e n t a l l y de te rm ined v a l ue of the anharmonic v i b r a t i o n a l c o n s t a n t " e x e i s 0.06 cm-"*" f o r the upper e l e c t r o n i c s t a t e of I 2- Th i s v i b r a t i o n a l c o n s t a n t was then used i n the c a l c u l a t i o n of the i harmonic v i b r a t i o n a l c o n s t a n t u e as f o l l o w s . Keeping o n l y the f i r s t two terms o f e q u a t i o n 2 .4 , the f i r s t - d i f f e r e n c e s i n the e x p e r i m e n t a l v i b r a t i o n a l energy may be e x p r e s s e d : AG C = o> ' - w„x Q (2v + 2 ) E e e e v ' where v i s the quantum number of the l ower v i b r a t i o n a l s t a t e i n v o l v e d i n the c o m p a r i s o n . Thus , u> ' = AG C + co x ( 2 v ' + 2) . e E e e 1 _ i Us ing the e x p e r i m e n t a l v a l u e <±>exe = 0.060 cm , s e v e r a l • c a l c u l a t i o n s o f oo g a re p r e s e n t e d i n Tab le VI f o r bands of the (v -0 ) p r o g r e s s i o n . The average o f the v a l u e s de te rm ined f o r a>e of the upper e l e c t r o n i c s t a t e i s 241.45 cm V i b r a t i o n a l a n a l y s i s c a r r i e d out on bands of the (v -1) p r o g r e s s i o n was more comp lex , s i n c e the (2 -1 ) band i s not r e s o l v e d from (1 -0 ) and i t s p o s i t i o n cannot be measured. C a l c u l a t i o n o f the anharmonic v i b r a t i o n a l c o n s t a n t " J g x e proceeded as f o l l o w s . From da ta i n Tab le V I I , the f r i n g e s e p a r a t i o n o f the (1 -1 ) and (3 -1 ) bands i s 47.894 f r i n g e s f o r a doub le -quantum t r a n s i t i o n . Thus, u s i n g the n o t a t i o n o f - 75 -T a b l e V I I I , we ha ve : 2x:•+ 2y = 47.894 . (4 .1 ) We a l s o know the f o l l o w i n g second d i f f e r e n c e s from Tab le V I I I : 9 .961(2x - 2y) = 2u>exe' , (4 .2 ) 9.961 (2y) - 237.19 = 2u , e x e ' , ( 4 .3 ) where UJ X must be i n wavenumber u n i t s . The s e t o f t h r e e e e e q u a t i o n s i n t h r e e unknowns, 4 . 1 , 4.2 and 4 . 3 , may e a s i l y be s o l v e d by s u b s t i t u t i o n . The o n l y unknown of v a l u e i s 2 w e x e , f o r wh ich the s o l u t i o n i s 0.897 c m - 1 . One o t h e r e v a l u a t i o n o f the second d i f f e r e n c e 2w x i s a v a i l a b l e d i r e c t l y f rom the e e data of Tab le V I I I , u s i n g the ( 3 - 1 ) , (4 -1 ) and (5 -1 ) bands. T h i s v a l u e i s 2.13 c m - * . Thus the average v a l u e of w e x e o b t a i n e d from the bands of the (v -1) p r o g r e s s i o n i s 0.76 cm Tab le IX c o n t a i n s the c a l c u l a t i o n s l e a d i n g to a d e t e r m i n a t i o n o f the harmonic v i b r a t i o n a l c o n s t a n t w , s i m i l a r to the a n -a l y s i s o f the (v -0) bands. Two e v a l u a t i o n s o f u e a re a v a i l -a b l e d i r e c t l y f rom the t a b l e , w h i l e a t h i r d may be o b t a i n e d as f o l l o w s . The e x p r e s s i o n s : 9 .961(2x ) + 3.04 = w ' , (4 .4 ) 9 .961(2y ) + 4.56 = o> ' (4 .5 ) from Tab l e V I I I p l u s e q u a t i o n 4 . 1 : 2x + 2y = 47.894 g i v e t h r e e e q u a t i o n s i n t h r e e unknowns w h i c h , when s o l v e d by s u b s t i t u t i o n f o r oo , y i e l d the v a l u e 242.33 cm . The average o f the e x p e r i m e n t a l l y de te rm ined v a l u e s o f u e i s - 76 -then 242.76 c m " 1 . The v i b r a t i o n a l a n a l y s i s c a r r i e d out s e p a r a t e l y w i t h i i the (v -0) and (v -1) p r o g r e s s i o n s ag rees very w e l l : iu ' = 241.45 c m " 1 ± 1% ve r su s 242.76 c m " 1 ± 1% and e 1 -1 -1 oj x = 0.60 cm ve r su s 0.76 cm r e s p e c t i v e l y . These e e e v a l u a t i o n s of the v i b r a t i o n a l c o n s t a n t s w and oo x„ e e e, r e l i e d upon a s i m p l e a v e r a g i n g p r o c e d u r e . The compar i son of measured t r a n s i t i o n e n e r g i e s w i t h c a l c u l a t e d e n e r g i e s i s g i v en g r e a t e r i n t e r n a l c o n s i s t e n c y , however, by a p p l y i n g a l e a s t - s q u a r e s f i t o f the o b s e r v a t i o n s to a q u a d r a t i c f u n c t i o n : E ( v ' ) = T e + w e ' ( v ' + h) - « e x e ' ( v ' + h)2 w i t h each o b s e r v a t i o n g i v en equal s t a t i s t i c a l we i gh t ( P r y c e , 1976) . In o r d e r to de te rm ine the a b s o l u t e p o s i t i o n s of the re sonances ob se r ved i n I 2> the wave leng th ou tpu t of the dye l a s e r must be e s t a b l i s h e d . The energy o f the (0-0) t r a n s i t i o n was p l a c e d a t 53,576.00 ± 1 c m " 1 by Dalby and Tai (1976) u s i n g a 3-meter Ebe r t s p e c t r o m e t e r p l u s a n i c k e l a r c r e f e r e n c e s pec t r um. The l a r g e e r r o r a r i s e s from the f a c t t h a t the p o s i t i o n a t wh ich the l a s e r c a l i b r a t i o n was done r e l a t i v e to the peaks i n the I 2 r e sonance spect rum was not w e l l - d e f i n e d . The l e a s t - s q u a r e s a n a l y s i s o f P r yce (1976) g i v e s the r e s u l t s : E ( v ' ) = 53,562.75 ± 0.35 + (241.4 ± 0 . 4 ) ( v " + h) - (0 .58 ± 0 . 0 6 ) ( v ' + h)2 c m " 1 . The e r r o r s quoted are r e l a t i v e e r r o r s . S i n c e the a b s o l u t e - 77 -Band S e p a r a t i o n o f S u c c e s s i v e Band Heads Cha r t A Reverse Char t B Cha r t C Average Scan on A (Number of F a b r y - P e r o t F r i n g e s ) (0 -4 ) 10.553 * 10 .553 (0 -3 ) 10.577 * 10 .577 (0-2) 10.705 10.614 10 . 660 (0 -1 ) 10.600 10.743 10 .672 (0-0) 12.212 11.931 11.986 12 . 043 (1 -0 ) 11.847 12.175 12.071 12 .031 (2 -0 ) 12.047 11.841 11.914 11 . 934 (3 -0 ) 11.824 11 .918 11.883 11.915 11 .885 (4 -0 ) 11.759 11 . 588 12.063 11 .803 (5 -0 ) * Bands not d i s t i n c t . Bands not marked were not i n c l u d e d i n the s c an . n i Tab le I I I . F r i n g e S e p a r a t i o n of the (0-v ) and (v -0) Bands of I Band Separation in Number (n) of Fabry-Perot Fringes (Table II I) True Fringe Spacing (2n) of Vibrational Levels AG 1 (cm ) (Table I) Ca l ibrat ion of Fringes = AG/2n _ i (cm per fr inge) (0 -0 ) (0 -1 ) (0 -2) (0 -3 ) (0 -4 ) 10.672 10.660 10.577 10.553 21. 344 21.320 21.154 21.106 213.34 9.995 212.11 9.949 210.87 9.968 209.63 9.932 Mean = 9.961 ± 0.034 _ l cm per f r i n g e Tab le IV. C a l i b r a t i o n of the F a b r y - P e r o t I n t e r f e r o m e t e r . Separation in Number Fringe Separation Experimental Second Difference Band (n) of Fabry-Perot Fringes of Bands for Double-Quantum Energy Separation 2 A G c ^ 2CJ x ' E e e (Table IV) Transit ion (2n) l AG £ (cm ) _ i (cm ) (0 -4 ) 10.553 21.106 210.24 (0 -3 ) 10.577 21.154 210.71 (0 -2 ) 10.660 21.320 212.37 (0 -1 ) 10.672 21.344 212.61 (0 -0 ) 12.043 24.086 239.92 (1 -0 ) 0. 24 12.031 24.062 239.68 (2 -0 ) 1. 94 11.934 23.868 237.74 (3 -0 ) 0.96 11.885 23.770 236. 78 (4 -0 ) 1.64 11.803 23.606 235.14 (5 -0 ) II I Tab le V. Energy S e p a r a t i o n o f the (0-v ) and (v -0) Bands of I - 80 -Band AG E (Tab le V) X = 0 .60 (2v ' +2 ) E x p e r i menta 1 E v a l u a t i o n o f co 1 e (AGE+,X) ( c m " 1 ) ( c m - 1 ) ( c m - 1 ) (0 -0) 239.92 1 .20 241.12 (1 -0 ) 239.68 2.40 242.08 (2-0) 237.74 3.60 241.34 (3-0) 236.78 4.80 241.58 (4 -0 ) 235.14 6.00 241 . 14 (5-0) Tab le V I . E x p e r i m e n t a l E v a l u a t i o n ( v ' - 0 ) P r o g r e s s i o n of cog 1 Us i ng the - 8 1 -Band S e p a r a t i o n o f Band Heads f r o m ( 0 - 0 ) C h a r t A R e v e r s e C h a r t B C h a r t C A v e r a g e S c a n on A (Number o f F a b r y - P e r o t F r i n g e s ) ( 1 - 5 ) * ( 1 - 4 ) -30.435 -30.435 ( 1 - 3 ) * ( 1 - 2 ) * (1 - D 1.412 1 .436 1 . 300 1 . 383 ( 2 - 1 ) ** * * ( 3 - 1 ) 25.389 * 25. 271 25.330 ( 4 - 1 ) 37.224 37.365 37 .213 37. 143 37.236 ( 5 - 1 ) 49.024 49.118 49 .042 48. 957 49.035 * Band n o t d i s t i n c t . B ands n o t m a r k e d were n o t i n c l u d e d i n t h e s c a n . F a b r y - P e r o t f r i n g e s e r r a t i c . T a b l e V I I . F r i n g e S e p a r a t i o n o f t h e ( 1 - v " ) and ( v ' - l ) B ands o f I „ . Band Separation in Number (n) of Fabry-Perot Fringes (Table VII) Fringe Separation of Bands for Double-Quantum Transit ion (2n) Experimental Energy Separation 1 AG E (cm ) Second Difference 2 E e e l (cm ) (1-4) (1-D (2-1) (3-1) (4-1) 31.818 11.906 11.799 63.636 2x 2y 23.812 23.598 638.88 9 .961(2x ) 9 .961(2y ) 237.19 235.06 2^ x Q e e 2w x Q e e 2 .13 (5-1) II I Tab l e V I I I . Energy S e p a r a t i o n of the (1-v ) and (v -1 ) Bands o f I - 83 -Band ( Tab l e V I I I ) ( c m " 1 ) X = 0 .76 (2v ' +2 ) ( c m " 1 ) E xpe r i mental E v a l u a t i o n o f co 1 (AG E + X ) e ( c m " 1 ) (1-D 9.961(2x) 3.04 9.961(2x)+3.04 (2 -1 ) 9 .961(2y) 4.56 9.961(2y)+4.56 (3 -1 ) 237.19 6.08 243.28 (4 -1 ) 235.06 7.60 242.66 (5 -1 ) Tab le IX. E x p e r i m e n t a l E v a l u a t i o n o f cog 1 Us ing the ( v ' - l ) P r o g r e s s i o n . - 84 -T r a n s i t i o n Energy Band 1/A i n vacuum ( c m - 1 ) Observed C a l c u l a t e d A (0 -4 ) 52 ,730.08 52 ,730. 22 -0 .14 (1 -5 ) - 52,762.07 -(0 -3 ) 52,940.32 52,939.85 0.47 (1 -4 ) 52,969.68 52,970.46 - 0 . 78 (0 -2 ) 53,151.04 53,150.72 0. 32 (1 -3 ) - 53,179.09 -(0 -1 ) 53,363.40 53,362.83 0. 57 (1 -2 ) - 53,390.96 -(0 -0 ) 53,576.00 53,576.17 -0.1 7 (1 -1 ) 53,603.56 53,603.07 0.49 (i-o) 53,815.92 53,816.41 -0 .49 (2 -1 ) - 53,842.15 -(2 -0 ) 54,055.60 54,055.49 0.11 (3 -1 ) 54,080.62 54,080.07 0.55 (3 -0 ) 54,293.34 54,293.41 - 0 . 07 (4 -1 ) 54,317.82 54,316.83 0.99 (4 -0 ) 54,530.12 54,530.17 -0 .05 (5 -1 ) 54,552.88 54,552.43 0.45 (5 -0 ) 54,765.26 54 ,765.77 - 0 . 51 (6 -1 ) - 54,786.87 -Tab l e X. E n e r g i e s of the Observed Resonances i n I - 85 -p o s i t i o n was e s t a b l i s h e d much l e s s a c c u r a t e l y than the band s e p a r a t i o n s , the a b s o l u t e e r r o r i n t f e . - i s a t l e a s t 1 c m - 1 . Tab l e X l i s t s the p o s i t i o n s o f the ob se r ved re sonances i n i n wh ich the band s e p a r a t i o n s o f Tab le V and V I I I have been added or s u b t r a c t e d , as a p p l i c a b l e , to the one a b s o l u t e r e f e r e n c e energy a v a i l a b l e , t h a t of the (0 -0 ) t r a n s i t i o n . The agreement o f ob se rved and c a l c u l a t e d t r a n s i t i o n e n e r g i e s i s e x c e l 1ent ( Tab l e X ) . 4.4 R o t a t i o n a l A n a l y s i s Some q u a l i t a t i v e c o n c l u s i o n s r e g a r d i n g the r o t a t i o n a l c o n s t a n t s o f the m o l e c u l e may be drawn from the appearance of the p h o t o i o n i z a t i o n bands. The deg r ad i ng o f the bands to the v i o l e t i n d i c a t e s t h a t B ' 1 > B v " ( s e c t i o n 2 . 5 ) . The dec rea se i n the s l o p e of the bands as the t empe ra t u r e of the vapor i n c r e a s e s c o n f i r m s t h a t B 1 > B v " . F u r t h e r m o r e , the narrowness of the bands i n d i c a t e s t h a t the r o t a t i o n a l energy l e v e l s a re ve ry c l o s e l y spaced ( e q u a t i o n s 2.8 to 2.12) and i t i s e xpec ted t h a t B ' i s o n l y s l i g h t l y l a r g e r than B v " . The s e p a r a t i o n of the I od i ne n u c l e i i i n the upper ( r e s o n a n t ) 0 e l e c t r o n i c s t a t e s i s thus s l i g h t l y s m a l l e r than 2.666A, the s e p a r a t i o n i n the ground e l e c t r o n i c s t a t e . D e t a i l e d r o t a -t i o n a l a n a l y s i s i s done by the Frank-Condon method. The i n t e n s i t y S v , v „ o f a v i b r a t i o n a l t r a n s i t i o n i n the t r i p l e - p h o t o n i o n i z a t i o n spect rum of ^ depends upon the p o p u l a t i o n o f the i n i t i a l l e v e l , the Frank-Condon f a c t o r - 86 -between the v i b r a t i o n a l s t a t e s , the l a s e r i n t e n s i t y to a power N, and the p h o t o i o n i z a t i o n e f f i c i e n c y P ( v ' , v ) which i s an unknown f u n c t i o n o f the u p p e r - v i b r a t i o n a l - s t a t e quantum number and of the m o l e c u l e ' s t o t a l energy p r i o r to i o n i z a t i o n . We may w r i t e : 2 2 7 - G ( v " ) h c / k T V , v " = K<VlV> V P ( V . V ) E S i n c e the l a s e r i n t e n s i t y i s a s l o w l y v a r y i n g f u n c t i o n o f wave leng th ( F i g u r e s 10 and 11 ) , the a s s i gnment of the power-dependence N i s not c r i t i c a l . The power-dependence adopted i s an average v a l u e 2.7 f o r a l l the bands, r e p r e s e n t -ing c o n d i t i o n s i n wh ich t h e r e i s a minimum of o p t i c a l or e l e c t r i c a l s a t u r a t i o n i n the p h o t o i o n i z a t i o n p r o c e s s . The c o n v e r s i o n of S y , v „ to a b s o l u t e i n t e n s i t y i s c o n t a i n e d i n the c o n s t a n t K which i n c l u d e s the e f f e c t o f the e x p e r i m e n t a l pa rameter s which i n f l u e n c e i n t e n s i t y , such as e l e c t r o d e v o l t a g e and the c u r r e n t a m p l i f i c a t i o n w i t h i n the I od i ne c e l l . The r e l a t i v e band i n t e n s i t i e s were measured e x p e r i m e n t -a l l y a t I od i ne vapor t e m p e r a t u r e s 20°C and 100°C. Note t h a t the p o p u l a t i o n o f the h i g h e r v i b r a t i o n a l l e v e l s i n the ground e l e c t r o n i c s t a t e of I 2 i n c r e a s e s measurab ly (Tab le XI) over t h i s t empe ra tu re range. Two s e t s o f i n t e n s i t y measurements were o b t a i n e d a t 100°C, a t e l e c t r o d e v o l t a g e s -300 V and -430 V; t he se were a n a l y z e d i n d i v i d u a l l y s i n c e most o f the bands were v i s i b l e a t low e l e c t r o d e v o l t a g e s . At room temp-e r a t u r e , the bands d i f f e r e d much more i n magni tude than a t - 87 -Vibrat ional Relative Fraction of v" Energy Population Total Sample G(v")-G(0) e-[G(v")-G(0)]/kT (cm" 1) (%) I. VAPOR TEMPERATURE 20°C 0 0 1 64.9 1 213.34 0.351 22.8 2 425.45 0.124 8.05 3 636.32 0.0441 2.86 4 845.95 0.0158 1.03 5 1054.34 0.00567 0.37 6 1261.47 0.00205 0.13 Pa r t i t i on Function = 1.54 II. VAPOR TEMPERATURE 100°C 0 0 1 56.2 1 213.34 0.439 24.7 2 425.45 0.194 10.9 3 636.32 0.0860 4.83 4 845.95 0.0384 2.16 5 1054.34 0.0172 0.97 6 1261.47 0.00773 0.43 Pa r t i t i on Function = 1.78 Table XI. Relative Equil ibrium Population of Vibrat ional States in the Ground Electronic State of I0. - 88 -h i g h e r t e m p e r a t u r e s , and i t was n e c e s s a r y to combine the i n t e n s i t y measurements from s e v e r a l scans o b t a i n e d a t d i f -f e r e n t e l e c t r o d e v o l t a g e s . The r e l a t i v e i n t e n s i t i e s of the s t r o n g e s t p h o t o i o n i z a t i o n bands were de te rm ined from data o b t a i n e d w i t h minimum e l e c t r i c a l s a t u r a t i o n a t the low e l e c -t r o d e v o l t a g e -200 V. In a d d i t i o n , scans taken a t the i n t e r -med ia te e l e c t r o d e v o l t a g e -240 V and the maximum v o l t a g e -400 V, p u t t i n g the s t r o n g bands o f f - s c a l e i n both c a s e s , p r o v i d e d data f o r c a l c u l a t i o n o f the r e l a t i v e i n t e n s i t i e s of the r e m a i n i n g bands. The s t r e n g t h o f a v i b r a t i o n a l t r a n s i t i o n i s d i v i d e d among the v a r i o u s accompanying r o t a t i o n a l t r a n s i t i o n s . When a band i s u n r e s o l v e d , the s t r e n g t h o f the v i b r a t i o n a l t r a n s i t i o n i s t h e r e f o r e de te rm ined from the a rea under the band. In the p h o t o i o n i z a t i o n s pec t r um, however, i t s u f f i c e d to measure the a m p l i t u d e o f the band heads , as the bands a l l had a s i m i l a r shape a t a g i v en vapor t empe ra tu re and i n the absence o f s a t u r a t i o n . The dependence of the band a m p l i t u d e s upon the l a s e r power and upon the p o p u l a t i o n of the i n i t i a l v i b r a t i o n a l l e v e l was removed to a r r i v e a t e x p e r i m e n t a l " 2 v a l u e s S v , v „ c c < l i J v ' l ' J J v j ^ > P ( v ' , v ) . The p h o t o i o n i z a t i o n e f f i c i e n c y P ( v ' , v ) i s not w e l l e s t a b l i s h e d f o r m o l e c u l e s . However, the e f f e c t s of t h i s pa rameter were not e xpec ted to be l a r g e f o r the m a j o r i t y of t he bands , and P ( v ' , v ) was i n i t i a l l y assumed c o n s t a n t . The a b s o l u t e i n t e n s i t i e s were - 89 -not r e q u i r e d i n the r o t a t i o n a l a n a l y s i s . R a t h e r , n o r m a l i z a t i o n was c a r r i e d o u t , f o r each se t of d a t a , by summing the c o n t r i b -u t i o n s from a s i n g l e p r o g r e s s i o n and d i v i d i n g a l l band amp-l i t u d e s i n the chosen se t by t h i s v a l u e , so t h a t z S , „ = 1 j , v ' , v" and I S i „ = 1. Th i s r e s u l t e d i n e x p e r i m e n t a l band i n t e n -y i i v ,v s i t i e s which a re d i r e c t l y comparab le w i t h the t h e o r e t i c a l . 2 Franck -Condon f a c t o r s , f o r wh ich I * < ^ , 14> = 1 and • . <s2 V ' V V 2 K$> i I nP" = 1. The r e s u l t s a re p r e s e n t e d i n Tab le X I I . v" v v Tab le X I I I c o n t a i n s t h e o r e t i c a l F ranck-Condon f a c t o r s c a l c u l a t e d i n the harmonic a p p r o x i m a t i o n a c c o r d i n g to the method of s e c t i o n 2 .7 , f o r t r a n s i t i o n s between the ground " -1 1 -1 (o>e = 214.57 cm ) and two-photon r e sonan t (to = 241.4 cm ) e l e c t r o n i c s t a t e s o f Ir,. I t i s c l e a r from d i r e c t compar i son o f the F ranck-Condon f a c t o r s w i t h the e x p e r i m e n t a l band i n -0 t e n s i t i e s t h a t ] A r[ ( o r s ) l i e s between 0.075 and 0.125A. No te , however, t h a t the t r a n s i t i o n s t r e n g t h s of c e r t a i n o f the v i b -r a t i o n a l t r a n s i t i o n s va ry r a p i d l y , as a f u n c t i o n of 3, w i t h r e s p e c t to one a n o t h e r . Thus , the r a t i o s of c e r t a i n F r a n c k -Condon f a c t o r s p r o v i d e a much more s e n s i t i v e compar i son w i t h the e x p e r i m e n t a l d a t a . The f o u r most s e n s i t i v e r a t i o s a re 0 p r e s e n t e d i n Tab l e XIV f o r a narrow range of 3 (0.096 - 0 .104A) . Compar i son o f these t h e o r e t i c a l r a t i o s w i t h the mean e x p e r -imen ta l i n t e n s i t y r a t i o s y i e l d s f o u r v a l ue s o f .3 which are i n 0 c l o s e agreement. We may conc l ude t h a t | A r | = 0.0988A ± 2%. Thus, the i n t e r n u c l e a r s e p a r a t i o n i n the r e s onan t e l e c t r o n i c - 90 -Band R e l a t i v e I n t e n s i t y  Bands a t Bands a t Bands a t Mean 20°C 100°C 100°C (-300 V) (-430 V) (0 -0 ) (1 -0 ) (2 -0 ) (3 -0 ) (4 -0 ) (5 -0 ) 0.17 0. 39 0.31 0.11 0.022 0.004 0.1 1 0.20 0.27 0. 23 0.15 0.048 0.13 0.25 0.28 0.21 0.10 0.027 0.14 0. 28 0.28 0.18 0.090 0.026 (0-1 ) (1-1 ) (2-1 ) 0.32 (0 .22) 0.19 (0 .12) 0. 24 (0 .13) 0.25 (0 .16) (3-1 ) (4-1 ) (5-1 ) (6-1 ) (0 .071) (0 .024) (0 .006) (0 .11) (0 .12) (0 .080) (0.051 ) (0.093) (0.070) (0.029) (0 -2 ) (2 -2) (3 -2 ) 0.36 0.40 0.15 0. 30 (0 .17) 0. 35 0.15 (0 .17) (0 -3 ) (2 -3 ) 0.42 1.23 (0 .15) 0.42 (0 .24) 0.69 (0 .19) (0 -4 ) (1 -4) 0. 26 (0 .22) 1 .36 0.40 (0.098) 0.68 (0 .16) (1 -5 ) (0 .27) (0 .27) B r a c k e t e d v a l u e s have u n c e r t a i n t y up to a f a c t o r of 2. A l l o t h e r s a re a s s i g n e d an u n c e r t a i n t y o f 30%. Tab le X I I . R e l a t i v e I n t e n s i t i e s o f the P h o t o i o n i z a t i o n Bands of I „ . - 9 1 -Band ' F r a n c k - C o n d o n F a c t o r s  6 = 0.075 I 6 = 0 . 1 0 0 A 6 = 0.125 K ( 0 - 0 ) 0.299 0.117 0.035 ( 1 - 0 ) 0.338 0.236 0.111 ( 2 - 0 ) 0.213 0. 252 0. 180 ( 3 - 0 ) 0.097 0.189 0. 204 ( 4 - 0 ) 0.036 0.112 0. 178 ( 5 - 0 ) 0.012 0.056 0. 129 ( 0 - 1 ) 0. 383 0. 267 0.125 (1 - D 0.012 0.152 0.193 ( 2 - 1 ) 0.090 0.005 0. 109 ( 3 - 1 ) 0.197 0.045 0.01 3 ( 4 - 1 ) 0.166 0.1 32 0.011 ( 5 - 1 ) 0.092 0.153 0.070 ( 0 - 2 ) 0.222 0.287 0. 214 ( 2 - 2 ) 0.138 0.114 0.000 ( 3 - 2 ) 0.000 0.110 0.073 ( 0 - 3 ) 0.076 0.194 0.236 ( 2 - 3 ) 0.006 0.103 0.087 ( 0 - 4 ) 0.017 0.092 0. 188 ( 1 - 4 ) 0. 170 0.201 0.041 ( 1 - 5 ) 0.057 0.177 0.135 T a b l e X I I I . T h e o r e t i c a l F r a n c k - C o n d o n F a c t o r s f o r S e l e c t e d V i b r a t i o n a l T r a n s i t i o n s B e t w e e n t h e G r o u n d and R e s o n a n t E l e c t r o n i c S t a t e s o f L . T h e o r e t i c a l F r a n c k - C o n d o n - F a c t o r R a t i o s Mean Experimental Intensity Ratios O 0 0 0 0 3=0.096 A 3=0.098 A 3=0.100 A 3=0.102 A 3=0.104 A F ( l - l ) F ( 0 - 0) F ( 3 - 0) F ( 0 - 0) F ( l - 1) F ( l - 0) F ( l - 1) F ( 0 - 1) 0.943 1.111 1.296 1.500 1. 724 1.279 1.437 1.611 1.803 2.013 0.509 0.576 0.645 0.718 0.793 0.450 0.509 0.571 0.635 0.702 1.154 1 .353 0. 561 0.636 Tab le XIV. Comparison of the I 2 E x p e r i m e n t a l I n t e n s i t y R a t i o s w i t h the R a t i o s o f the T h e o r e t i c a l F ranck-Condon F a c t o r s from 3 = 0.096 to 0.104 A . - 93 " I o s t a t e i s r g = 2.567 ± 0.002A. The u p p e r - s t a t e r o t a t i o n a l c o n -s t a n t i s B ' = 0.04029 ± 0.00007 c m " 1 , and A B / B g " = 0.079 ± 3%. A p l o t , as a f u n c t i o n of t o t a l m o l e c u l a r ene r g y , of the r a t i o s of the mean e x p e r i m e n t a l band i n t e n s i t i e s to the c o r r e s p o n d i n g 0 t h e o r e t i c a l F ranck-Condon f a c t o r s a t 3 = 0.099A ( F i g u r e 1 4 ) , i n d i c a t e s t h a t the p h o t o i o n i z a t i o n y i e l d P ( v ' , v ) of i s not c o n s t a n t between 80,050 and 82,250 c m " 1 . T y p i c a l u n c e r t a i n t i e s i n the e x p e r i m e n t a l v a l u e s a re i n d i c a t e d i n the F i g u r e . The p h o t o i o n i z a t i o n y i e l d has an appa ren t re sonance i n the v i c i n i t y of 80,000 c m " 1 . T h e r e a f t e r , t h e r e i s a s l i g h t downward t r e n d w i t h i n c r e a s i n g m o l e c u l a r e n e r g y , as obse rved by Myer and Samson ( 1970 ) . Each o f s i x a b s o r p t i o n p r o g r e s s i o n s e x h i b i t i n d e p e n d e n t l y t he se two f e a t u r e s . The t r a n s i t i o n s ( 0 - 0 ) , ( 1 - 1 ) , ( 3 - 0 ) , (1 -0 ) and ( 0 - 1 ) , whose i n t e n s i t y r a t i o s were the b a s i s f o r d e t e r m i n i n g |Ar|, have t o t a l energy between 80,360 and 81,550 c m " 1 and thus l i e i n the p l a t e a u r e g i o n where the p h o t o i o n i z a t i o n y i e l d o f I 2 i s r o u g h l y c o n s t a n t . 4.5 Band Contour A n a l y s i s A p p l y i n g the r o t a t i o n a l a n a l y s i s o f the upper e l e c t r o n i c s t a t e ( s e c t i o n 4.4) to the branch c o n t o u r f o rmu l ae of s e c t i o n 2 .8 , wh ich c o n v o l u t e s the i n t e n s i t y d i s t r i b u t i o n of each r o t a -t i o n a l b ranch w i t h the l a s e r s p e c t r u m , one may c a l c u l a t e the c o n t o u r s of the f i v e s e p a r a t e r o t a t i o n a l b ranches 0, P, Q, R and S. Append ix B c o n t a i n s these i n t e r m e d i a t e c a l c u l a t i o n s . Knowing the i n t e n s i t y d i s t r i b u t i o n between the b r a n c h e s , \ - 3k- -8 RATIO OF NORMALIZED INTENSITIES TO THEORETICAL FRANCK CONDON FACTORS AGAINST FINAL ENERGY © y x v' • v A V o V v v = o = I = 2 = 3 = 4 = 5 v • © x • 80 000 81000 3T/ 82000 LASER + G cm -I 83000 Figure ]k. - 95 -d i s c u s s e d i n d e t a i l i n s e c t i o n 2 .8 , one may then sum the c o n -t r i b u t i o n s of a l l b ranches t o . a r r i v e a t the band c o n t o u r ap-p l i c a b l e to a p a r t i c u l a r e l e c t r o n i c t r a n s i t i o n . In two-photon a b s o r p t i o n to a r e sonan t s t a t e , t h r e e + + + e l e c t r o n i c t r a n s i t i o n s are p o s s i b l e : -0„ -> 0„ , 0„ -»- 1 , and K g g g g 0 -> 2 ( s e c t i o n 2 . 4 ) . The c o n t o u r s of the p h o t o i o n i z a t i o n y y bands of p r e d i c t e d f o r each of the t h r e e p o s s i b l e e l e c t r o n i c t r a n s i t i o n s at 20°C a re p r e s e n t e d i n F i g u r e s 15, 16 and 17. The 0 + -> 0 + c o n t o u r v a r i e s a c c o r d i n g to the r e l -g g a t i v e c o n t r i b u t i o n s of the 0* and l u i n t e r m e d i a t e s t a t e s . The two extreme cases p l u s an i n t e r m e d i a t e case a re d e p i c t e d i n F i g u r e 15 f o r t h i s e l e c t r o n i c t r a n s i t i o n . The peak of the band c o n t o u r f o r each e l e c t r o n i c t r a n s i t i o n l i e s ve ry c l o s e to the band o r i g i n v . 3 0 At a r e s o l u t i o n of 1.5 c m - 1 , the t h e o r e t i c a l band c o n -t o u r s a re too s i m i l a r to i n d i c a t e d e c i s i v e l y the e l e c t r o n i c c o n f i g u r a t i o n of the r e s onan t s t a t e o f l^. However, c e r t a i n of the t r a n s i t i o n s a re found to be h i g h l y i m p r o b a b l e . The band c on t ou r s ob se rved i n our numerous e x p e r i m e n t a l s p e c t r a have i n g ene ra l a smooth r i s e to the peak on the s teep s i d e , f o l l o w e d by e x p o n e n t i a l d r o p - o f f w i t h a s l i g h t h e s i t a t i o n o c c u r r i n g near the peak on t h i s s i d e . I t i s p r o b a b l e t h a t the Og 2g t r a n s i t i o n may be r u l e d out s i n c e the t h e o r e t i c a l band c o n t o u r shows f e a t u r e s of equal prominence on both s i d e s of the peak, c o n t r a r y to o b s e r v a t i o n . I t i s a l s o e v i d e n t - 96 -- 98 -- 99 -t h a t c o n t r i b u t i o n s to the 0 + -> 0 + t r a n s i t i o n may not be g g e q u a l l y sha red between 0 u and l ' u i n t e r m e d i a t e s t a t e s , as t h i s would r e s u l t i n a p u r e l y Q-1 i k e band, wh ich i s not o b s e r v e d . 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 of the e f f e c t on the p h o t o i o n i z a t i o n p r oce s s i n I ^  o f p o l a r i z i n g the l a s e r l i g h t (Dal by et a l . , 1976) f i r m l y r u l e s out the 0* 0* e l e c t r o n i c t r a n s i t i o n . Thus, the new e l e c t r o n i c s t a t e ob se rved i n Ir, has , w i t h h i gh p r o b -a b i l i t y , the d e s i g n a t i o n 1^. A l t h o u g h the band p o s i t i o n s were measured i n the v i b r a t i o n a l a n a l y s i s from the band peak r a t h e r from the band o r i g i n v , no c o r r e c t i o n was a p p l i e d to T g as t h i s r e q u i r e s an e xac t knowledge of the bandwidth of the e x c i t i n g ene rgy . I t was noted i n s e c t i o n 2.8 t h a t a t c o n s i d e r a b l e d i s t -ance from the band o r i g i n , a l l band c o n f i g u r a t i o n s become - ( v /102)(B ,,/AB) Q - l i k e w i t h c o n t o u r I ( v^ ) ^ e a t 20 C, where i s e xp re s sed i n wavenumbers. Thus the r a t i o AB/B v „ may be e s t i m a t e d from the band s l o p e a t l a r g e J . For bands ( 4 - 0 ) , ( 3 - 0 ) , (2 -0 ) and ( 0 - 3 ) , l n [ I ( v )] was p l o t t e d a g a i n s t l a s e r f r e q u e n c y v , each p l o t y i e l d i n g AB/B „ = 0 .07. A l t hough JO V t h i s method i s i n h e r e n t l y a p p r o x i m a t e , the r e s u l t s compare w e l l w i t h the more p r e c i s e F ranck-Condon r o t a t i o n a l a n a l y s i s which g i v e s AB/B v „ = 0.079 ± 3% ( s e c t i o n 4.4) 4.6 I m p u r i t y L i n e s S e v e r a l peaks o c cu r i n the p h o t o i o n i z a t i o n data wh ich a p p a r e n t l y a re not members o f the re sonance spect rum of I o s - 100 -be ing n e i t h e r b a n d - l i k e i n shape nor o f the c o r r e c t energy to f i t the v i b r a t i o n a l p r o g r e s s i o n s . Three such peaks are c l e a r l y v i s i b l e , and p o s s i b l y a d d i t i o n a l peaks e x i s t masked by the s t r o n g I od i ne s i g n a l . The p o s i t i o n s o f the peaks i n terms o f e x c i t i n g energy ( i n vacuum) a r e : V ! = 26,297.14 ± 1 c m - 1 , H a l f w i d t h 8 .09 c m " 1 v 2 = 26,915.22 ± 1 c m " 1 v 3 = 27,343.96 ± 1 c m " 1 The sou rce o f the f e a t u r e s has not been i d e n t i f i e d . The f e a t u r e s were deve l oped w i t h t e m p e r a t u r e , and remained a f t e r the I od i ne vapor was c o o l e d . Peak v 2 i s - s u p e r i m p o s e d on the (1 -0 ) band of l^* and i s ve ry weak. A l t hough peak v 3 i s p rominent i n ve ry h igh v o l t a g e s c a n s , i t s i n t e n s i t y i s too low to a l l o w a c c u r a t e measurement of i t s power dependence. The r e l a t i v e i n t e n s i t y of the two p rominent peaks i s I : I v - 16:1 a t 20°C. The s i g n a l a t v j depends upon the 2 02 l a s e r i n t e n s i t y to the power ln ' - 101 -5. DISCUSSION 5.1 R e s u l t s and C o n c l u s i o n s Quantum t h e o r y shows t h a t the I od i ne m o l e c u l e must pos ses s a r a t h e r l a r g e number o f v a l e n c e - s h e l l e l e c t r o n i c s t a t e s f o l l o w e d , m o s t l y a t h i g h e r e n e r g i e s , by Rydberg s t a t e s ( M u l . l i k e n , 1971) . For the f i r s t t i m e , a s i n g l e h i g h - e n e r g y e l e c t r o n i c s t a t e has been s e l e c t i v e l y p o p u l a t e d i n u s i ng the t e c h n i q u e s of m u l t i - p h o t o n s p e c t r o s c o p y . From both the r e q u i r e m e n t s of energy c o n s e r v a t i o n , and from e x p e r i m e n t a l c o n f i r m a t i o n , the n o n l i n e a r p h o t o e l e c t r i c s i g n a l was t h i r d -o r d e r i n the a p p l i e d f i e l d i n t e n s i t y . In p r i n c i p l e , t r i p l e -photon i o n i z a t i o n and t r i p l e - p h o t o n . d i s s o c i a t i o n were both p r e s e n t i n the p h o t o e l e c t r i c s i g n a l . S i n c e the d i s s o c i a t i o n y i e l d o f m o l e c u l a r I od i ne i s i n s i g n i f i c a n t i n compar i son w i t h the p h o t o i o n i z a t i o n - y i e l d t h roughou t the s p e c t r a l range i n v e s t i g a t e d (Myer and Samson, 1970) , the p redominant r e a c t i o n was t h a t o f t r i p l e - p h o t o n i o n i z a t i o n : I 2 + 3v •+ I 2 + + e - . I t i s r e a s o n a b l e to a s s i g n the obse rved resonances to v i b r a t i o n a l bands of two-photon t r a n s i t i o n s from the ground X 0* s t a t e to an I ? m o l e c u l a r s t a t e o f g symmetry. S i n c e s i n g l e -photon t r a n s i t i o n s f rom the ground s t a t e to such a s t a t e a re p a r i t y - f o r b i d d e n , t h i s i n t e r m e d i a t e s t a t e has not p r e v i o u s l y been ob se rved i n a b s o r p t i o n . F u r t h e r m o r e , the i n t e r m e d i a t e - 102 -s t a t e has no c o u n t e r p a r t i n e m i s s i o n s p e c t r a i n the l i t e r a t u r e . The v i b r a t i o n a l a n a l y s i s was s t r a i g h t - f o r w a r d and gave f o r the upper v i b r a t i o n a l - s t a t e e n e r g i e s {T g + G(v ) } : E ( v ' ) = 53,562.75 ± 1 + (241.4 ± 0 . 4 ) ( v " + h) - (0.58 ± 0 . 0 6 ) ( v ' + h)2 c m " 1 . The r o t a t i o n a l a n a l y s i s was c omp lex , . a s the bands were un r e -s o l v e d . F ranck-Condon f a c t o r s were c a l c u l a t e d from the o b s e r -ved r e l a t i v e band i n t e n s i t i e s , and used to de te rm ine the s i z e o f the I 2 m o l e c u l e i n the e x c i t e d s t a t e . The i n t e r n u c l e a r s e p a r a t i o n i n the r e s onan t e l e c t r o n i c s t a t e was e s t a b l i s h e d I 0 a t r g = 2.567 ± 0.002A, whereupon the r o t a t i o n a l c o n s t a n t i s B = 0.04029 ± 0.00007 c m " 1 . These r e s u l t s are c o n s i s t e n t e w i t h the ob se rved s l o p e o f the Q - l i k e c o n t o u r of the I od i ne bands a t l a r g e J . The s i z e d i f f e r e n c e of the m o l e c u l e i n the 0 upper s t a t e compared to i t s ground s t a t e ( n e a r l y 0.1A s m a l l e r ) i n d i c a t e s t h a t the r e s onan t e l e c t r o n i c s t a t e i s most p r o b a b l y a Rydberg s t a t e . F u r t h e r m o r e , the new s t a t e has e l e c t r o n i c energy s u f f i c i e n t l y h i gh to make the c a t e g o r y of a Rydberg s t a t e e x t r e m e l y p r o b a b l e , as a l a r g e number o f Rydberg s t a t e s a re obse rved i n I g , a l l a t e n e r g i e s above 51,500 c m " 1 ( V e n k a t e s w a r l u , 1970) . Three e l e c t r o n i c t r a n s i t i o n s a re p o s s i b l e i n two -photon a b s o r p t i o n to a r e s onan t s t a t e : 0* 0 * , 0g -> l g , and 0 + 2 . Each t r a n s i t i o n has a c h a r a c t e r i s t i c band c o n t o u r . g g - 103 -The t h e o r e t i c a l l y p r e d i c t e d band c o n t o u r s a re ve ry s i m i l a r a t a r e s o l u t i o n of 1.5 c m - 1 and do not i n d i c a t e d e c i s i v e l y the e l e c -t r o n i c c o n f i g u r a t i o n of the ob se rved r e s onan t s t a t e i n l^. The compar i son o f band c o n t o u r s r u l e s out o n l y the 0* -»- 2g t r a n s -i t i o n . A d d i t i o n a l i n f o r m a t i o n was ga ined from p o l a r i z a t i o n s t u d i e s , which show t h a t the r e s onan t e l e c t r o n i c s t a t e cannot have ze ro a n g u l a r momentum. Thus i t i s c onc l uded t h a t the new e l e c t r o n i c s t a t e has , w i t h h igh p r o b a b i l i t y , the d e s i g n a t i o n l g . The e l e c t r o n i c p o t e n t i a l of the new Rydberg s t a t e , app rox ima ted by a harmonic p o t e n t i a l f u n c t i o n , i s shown i n F i g u r e 18 as a f u n c t i o n of i n t e r n u c l e a r s e p a r a t i o n i n r e l a t i o n to the known v a l e n c e - s h e l l s t a t e s of m o l e c u l a r I o d i n e . The v a l e n c e - s h e l l p o t e n t i a l energy d iagram i s r ep roduced from M u l l i k e n (1971) i n which the cu r ve s f o r s t a t e s o f even (g) p a r i t y a re shown by f u l l l i n e s , and those f o r s t a t e s of odd (u) p a r i t y by dashed l i n e s . The p o t e n t i a l cu r ve s of M u l l i k e n a re z e r o t h o r d e r a p p r o x i m a t i o n s e xcep t f o r those o f the ground X 0* and the B s t a t e s wh ich a re r a t h e r a c c u r a t e l y known from y e x p e r i m e n t a l d a t a . The p o t e n t i a l cu r ve o f the new Rydberg s t a t e has a minimum energy o f 53 ,562.75 ± 1 cm -" ' ' a t i n t e r -0 n u c l e a r s e p a r a t i o n 2.567 ± 0.002A. The p h o t o i o n i z a t i o n e f f i c i e n c y P(v , v ) ob se rved i n I o d i ne has a broad f u n c t i o n a l dependence on t o t a l m o l e c u l a r energy ( F i g u r e 1 4 ) , e x h i b i t e d i n d e p e n d e n t l y be each of our s i x a b s o r p t i o n p r o g r e s s i o n s . The photo i o n i z a t i o n e f f i c i e n c y e x -- 104 -F i gu re 18. E l e c t r o n i c P o t e n t i a l D i ag ram I n c l u d i n g t he A p p r o x -imate P o t e n t i a l o f t h e New S t a t e S upe r impo sed on t h e Known V a l e n c e - S h e l l S t a t e s o f I 0. - 105 -h i b i t s the s l i g h t downward t r e n d w i t h i n c r e a s i n g m o l e c u l a r energy ob se rved by Myer and Samson (1970 ) . In a d d i t i o n , an appa ren t r e s o n a n c e , wh ich i s h e r e t o f o r e unob se r ved , o c c u r s i n the v i c i n i t y of 80,000 c m " 1 i n terms of t o t a l m o l e c u l a r ene rgy . Th i s r e s onan t s t a t e may o c cu r e i t h e r a t the l e v e l o f one photon or a t the l e v e l o f t h r e e pho ton s , c o r r e s p o n d i n g to e l e c t r o n i c energy i n the v i c i n i t y of 26,700 c m - 1 o r 80,000 c m - 1 r e s p e c -t i v e l y . S i n c e o n l y the h i g h - e n e r g y t a i l o f the re sonance was o b s e r v e d , t he se v a l u e s may be c o n s i d e r a b l y lower than q u o t e d . The resonance i n the p h o t o i o n i z a t i o n y i e l d P(v , v ) i s u n i d e n t i f i a b l e i n the c o n t e x t of known e l e c t r o n i c s t a t e s of m o l e c u l a r I o d i n e . F u r t h e r i n v e s t i g a t i o n i s r e q u i r e d to unde r s t and the na t u r e of t h i s f e a t u r e a p p e a r i n g i n the p h o t o -i o n i z a t i o n y i e l d of I 2 i n n o n l i n e a r a b s o r p t i o n . S e v e r a l s p e c t r a l f e a t u r e s were deve loped w i t h t emper -a t u r e which do not appear to be members of the re sonance s pec -trum o f 1 2 , be ing n e i t h e r b a n d - l i k e i n shape nor o f the c o r r e c t energy to f i t the v i b r a t i o n a l p r o g r e s s i o n s . One prominent i m -p u r i t y f e a t u r e was ob se r ved which was s e c o n d - o r d e r i n the a p p l i e d f i e l d i n t e n s i t y , the r e m a i n i n g i m p u r i t y f e a t u r e s be ing too weak f o r a c c u r a t e measurement. The p o s i t i o n o f the p r o -minent peak i n terms of e x c i t i n g energy i s 26,297.14 ± 1 c m - 1 w i t h h a l f - w i d t h 8.09 c m - 1 . The two weaker f e a t u r e s ob se r ved o c cu r a t 26.915.22 ± 1 c m - 1 and 27,343.96 ± 1 c m " 1 . I t i s pos -s i b l e t h a t a d d i t i o n a l peaks e x i s t masked by the s t r o n g I ? s i g n a l . - 106 -I d e n t i f i c a t i o n of the s ou r ce of the i m p u r i t y l i n e s i s a sub-j e c t f o r f u t u r e r e s e a r c h . I f the i m p u r i t y re sonances a l s o o c c u r a t the l e v e l o f two p h o t o n s , i t i s u n l i k e l y t h a t they, may be i d e n t i f i e d v i a a tomic or m o l e c u l a r wave leng th t a b l e s , s i n c e the t r a n s i t i o n would not e x i s t i n t r a d i t i o n a l a b s o r p t i o n a p e c t r o s c o p y ( the d i p o l e - d i p o l e • t r a n s i t i o n i s p a r i t y - f o r b i d d e n ) , and s i n c e t a b l e s of e m i s s i o n s p e c t r a are f a r from c o m p l e t e . 5.2 Fu tu re Research A number of s u b j e c t s f o r f u t u r e r e s e a r c h i n m o l e c u l a r I od i ne a r i s e d i r e c t l y from the p r e s e n t e x p e r i m e n t a l work. One i s the i d e n t i f i c a t i o n o f the i m p u r i t y l i n e s , wh ich most p r o b a b l y a r i s e from complex m o l e c u l a r s p e c i e s formed i n r e a c -t i o n s at h i gh t empe ra tu re s w i t h l^- Another i s the i n v e s t i g -a t i o n of the broad f u n c t i o n a l dependence on t o t a l m o l e c u l a r energy of the p h o t o i o n i z a t i o n e f f i c i e n c y of m o l e c u l a r I o d i n e ; the re sonance wh ich appears i n our data has no c o u n t e r p a r t among the e s t a b l i s h e d Rydberg or v a l e n c e - s h e l l s t a t e s of I 2-o The n o n l i n e a r a b s o r p t i o n o f I o d i ne to the red o f 3800A a l s o o f f e r s wide scope f o r i n v e s t i g a t i o n . In a more gene ra l v i e w , i t i s c l e a r t h a t the h i g h -r e s o l u t i o n t e c h n i q u e s o f l a s e r - i n d u c e d n o n l i n e a r a b s o r p t i o n s p e c t r o s c o p y w i l l y i e l d new and s i g n i f i c a n t s p e c t r o s c o p i c i n f o r m a t i o n from a g r e a t number of atoms and m o l e c u l e s ( V e n k a t e s w a r l u , 1976 ) , e s p e c i a l l y when a p p l i e d to p a r i t y -f o r b i d d e n and h i g h - e n e r g y s t a t e s . The e f f e c t s of p e r t u r -- 107 -b a t i o n s , S t a r k s h i f t s , l e v e l c r o s s i n g s , e t c . may be v e s t i g a t e d i n a tomic and m o l e c u l a r s t a t e s h e r e t o f o r e a c c e s s i b l e . - 108 -APPENDIX A CALIBRATION OF PHOTOMULTIPLIER FILTERS In o r d e r to a v o i d o p t i c a l s a t u r a t i o n of the p h o t o -m u l t i p l i e r , one o r two sheet s o f d i f f u s i n g g l a s s p l u s n e u t r a l d e n s i t y f i l t e r N.D.#3.0 were used to a t t e n u a t e the r e f l e c t e d p o r t i o n of the l a s e r beam. The m a t e r i a l s were c a l i b r a t e d w i t h a d e n s i t o m e t e r s e t to g i v e a c o n t i n u o u s scan between 0 3500-4000A. The q u a n t i t y measured i s c a l l e d the d e n s i t y K, K whereby the f i l t e r ' s a t t e n u a t i o n i s 10 . S i n ce the maximum d e n s i t y which may be measured i s 2 . 0 , N.D. f i l t e r #3.0, whi,ch has a d e n s i t y g r e a t e r than f o u r i n the u l t r a v i o l e t , c o u l d be c a l i b r a t e d o n l y by p l a c i n g two e x t r a f i l t e r s i n the r e f e r e n c e beam of the d e n s i t o m e t e r . The two e x t r a f i l t e r s (N.D.#0.9 and N.D.#1.0) had to be c a l i b r a t e d a l s o (see Tab le XV). The t o t a l d e n s i t y o f the m a t e r i a l s f o r the cases i n wh ich one or two p i e c e s of d i f f u s i n g g l a s s were used i s g i ven a t 0 20A i n t e r v a l s i n Tab l e XVI . - 109 -D e n s i t y of ND # A 0 (A) D e n s i t y of Re f e r ence F i l t e r s ND #0.9 ND #1.0 (a) (b) 3.0 With #0.9 and #1.0 i n Re fe rence Beam of Den s i t omete r ( c ) D e n s i t y of ND #3.0 (sum a , b , c ) 3600 1 .307 + 1.670 + 1.566 f 4 . 5 4 3 + + 3620 1.287 1, 648 1.537 4.472 3640 1.270 1.625 1.512 4.407 3660 1.258 1.604 1.497 4. 359 3680 1.245 1. 589 1.480 4.314 3700 1. 232 1. 573 1.468 4.273 3720 1.223 1.560 1.459 4.242 3740 1.213 1.546 1.450 4.209 3760 1.204 1.532 1.446 4. 182 3780 1.194 1. 520 1.411 4. 155 3800 1.185 1.511 1.436 4.132 3820 1.174 1.499 1.429 4.102 t t t Unce r t a i n t y U n c e r t a i n t y i n each measurement i s ± i n t o t a l d e n s i t y i s ± 0. 0. 002 006. • Tab l e XV. D e n s i t y of ND Wave leng th . F i l t e r #3.0 as a F u n c t i o n o f - 110 -A D e n s i t y of D i f f u s i n g G l a s s D e n s i t y of ND F i l t e r #3.0 T o t a l D e n s i t y I n c l u d i n g 0 (A) One Sheet Di f f u s e r Two Sheets Di f f u s e r 3600 1 .474 + 4 . 5 4 3 + t 6.017* ** 7.491 3620 1 .474 4.472 5.946 7 .420 3640 1 .474 4.407 5.881 7.355 3660 1 .474 4. 359 5.833 7 .307 3680 1 .471 4.314 5.785 7.256 3700 1 .469 4.273 5.742 7.211 3720 1 .469 4.242 5.711 7.180 3740 1 .469 4.209 5.678 7.147 3760 1 .470 4. 182 5. 652 7 .122 3780 1 .471 4.155 5. 626 7.097 3800 1 .471 4. 132 5.603 7.074 3820 1 .471 4.102 5. 573 7.044 U n c e r t a i n t y i n each measurement i s ± 0 .001. f U n c e r t a i n t y i s ± 0.006. * U n c e r t a i n ty i s ± 0.007. * U n c e r t a i n t y i s ± 0.008 Tab l e XVI . T o t a l D e n s i t y , as a F u n c t i o n of Wave l eng th , of M a t e r i a l s S h i e l d i n g P h o t o m u l t i p l i e r EMI 6256S. - I l l -APPENDIX B DETAILS OF BRANCH CONTOUR CALCULATIONS The r o t a t i o n a l a n a l y s i s o f s e c t i o n 4.4 a l l o w s c a l c u l a t i o n o f the con t ou r s o f the 0 , P, Q, R and S r o t a -t i o n a l branches e xpec ted i n two-photon a b s o r p t i o n . The c o n t o u r I ( v ) o f a s i n g l e branch was de te rm ined by c o n v o l u t i n g the i n t e n s i t y d i s t r i b u t i o n w i t h the l a s e r s p e c t r u m , as d e s c r i b e d i n s e c t i o n 2 .8. The parameter s i n v o l v e d a r e : AB = 0.002951 c m " 1 B ''= 0.03735 c m " 1 e B e ' = 0.04029 c m " 1 kT/hc = 204 c m " 1 a t 20°C La se r Bandwidth = 1.5 c m " 1 The c o n t o u r o f the Q-BRANCH i s d e s c r i b e d c o m p l e t e l y by: - ( 0 . 1 2 4 ) v I Q ( v £ ) = (5462) (1 - 0.911 e 1 ) , e ( - 0 .75 ,0 .75 ] - ( 0 . 1 2 4 ) v . = (1018) e '* , e [ 0 . 7 5 , - ) where the l a s e r f r e q u e n c y i s e xp re s s ed i n wavenumbers. The c o n t o u r s o f the 0, P, R and S branches were de te rm ined f r om: - J ± ( J i + D/5462 • . - J 2 ( J 2 + 1 )/5462 I ( v £ ) = 5462 (e " J -'•>•' - e ) w i t h the l i m i t s o f i n t e g r a t i o n , and J 2 , c a l c u l a t e d at ± 0 . 7 5 c m " 1 f rom e q u a t i o n s 2.14 to 2 .17. S i n ce the i n t e n s i t y d i s t r i b u t i o n i s an e s s e n t i a l l y c on t i nuou s f u n c t i o n - 1 1 2 -of r o t a t i o n a l quantum number J i n the spect rum of l^, non-i n t e g r a l v a l ue s o f J are c a r r i e d th rough the c a l c u l a t i o n . The r e s u l t s f o r each branch a r e : 0-BRANCH The The O-Branch forms a head a t v, 1 . 0 6 0 cm two components o f the branch are d e s c r i b e d by: (a) J 2 J i 2 7 . 3 1 + / 1 2 2 6 . 8 + 6 7 7 . 7 2 7 . 3 1 2 7 . 3 1 + / 2 1 0 . 2 + 6 7 7 . 7 v, (b) J 2 = 27.31 - /1226.8 + 677.7 = 0 . 5 0 Jx = 27.31 = 27.31 - /210.2 + 677.7 v, e ( - 1 . 8 1 , - ) v 0 e ( - 1 . 8 1 , - 0 . 3 1 ] Z £ V £ £ ( - 0 . 3 1 , o o ) v„ £ ( - 1 . 8 1 , - 0 . 7 5 ] v £ £ [ - 0 . 7 5 , 0 . 7 5 ) E ( - 1 . 8 1 , - 0 . 3 1 ] E [ - 0 . 3 1 , 0 . 7 5 ) P-BRANCH The P-Branch a l s o forms a head, a t v • 0 . 2 7 5 cm The two components o f the branch are d e s c r i b e d by: (a) J 2 1 3 . 6 5 + / 6 9 4 . 6 + 6 7 7 . 7 1 3 . 6 5 = 1 3 . 6 5 + / - 3 2 2 . 0 + 6 7 7 . 7 (b) J 2 = 1 3 . 6 5 - / 6 9 4 . 6 + 6 7 7 . 7 0 1 3 . 6 5 = 1 3 . 6 5 - / - 3 2 2 . 0 + 6 7 7 . 7 v. v £ E ( - 1 . 0 2 5 , ° ° ) £ ( - 1 . 0 2 5 , 0 . 4 7 5 ] v £ E [ 0 . 4 7 5 , - ) v £ £ ( - 1 . 0 2 5 , 0 . 7 5 ] e [ - 0 . 7 5 , 0 . 7 5 ) v £ ( -1 .025 ,0 .475 ] e [ 0 . 4 7 5 , 0 . 7 5 ) - 113 -R-BRANCH No head i s f o rmed. G 2 = -13.65 + Z667 . 3 + 6 7 7 . 7 v £ , v £ e ( - 0 . 7 1 , o o ) J i = 0 , vz e ( - 0 . 7 1 , 0 . 7 9 ] 1 3 . 6 5 + Z - 3 4 9 . 3 + 6 7 7 . 7 v £ , v £ e [ 0 . 7 9 , - ) S-BRANCH No head i s fo rmed. 0 2 = - 2 7 . 3 1 + / 1 1 7 2 . 2 + 6 7 7 . 7 v , v . e ( - 0 . 6 3 , - ) J i = . 0 , v £ e ( - 0 . 6 3 , 0 . 8 7 ] = - 2 7 . 3 1 + / 1 5 5 . 6 + 6 7 7 . 7 v £ , v £ e [ 0 . 8 7 , - ) Bakos , J . K i s s , A. Szabo, L. and T e n d 1 e r , M. B a l d w i n , G.C. B loembergen , N. Brackmann, R.T. F i t e , W.L. and Hagen , K.E. Cagnac , B . G r y n b e r g , G. and B i r a b e n , F. C o l l i n s , C.B. J ohn son , B.W. Popescu , D. Musa, G. P a s c u , M.L. and Pope scu , I. Col 1 i ns , C.B . J ohn son , B.W. Mi r z a , M.Y . Pope scu , D. and Pope scu , I. D a l b y , F.W. P e t t y - S i l , G. P r y c e , M.H.L. and Ta i , C.Y. 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Mi 11 man , J . and H a l k i a s , C C . M u l l i k e n , R.S. M u l l i k e n , R.S. Myer , J . A . and Samson , J . A . R . Nobs, A. and Wi e l and , K. Penne r , S.S. P e t t y , G. Ta i , C.Y. and D a l b y , F.W. P i n d z o l a , M.S. and K e l l y , H.P. P r y c e , M.H.L. 116 -1970b J . Chem..Phys. 5_2, 2683. 1974 P h y s i c a l Review 9, 2440. 1972a P h y s i c s L e t t e r s 39A, 21. 1972b Phys. Rev. L e t t e r s 29^ 1134. 1956 J . Chem. Phys . 2_5 , 753. 1973 IEEE J . Quantum E l e c t r o n . QE-9, 470. 1972 I n t n g t i a t z d EluctJion*.c6 : Analog and V^ig-ltaZ Ci.ficuZt& and SyAttmA, M c G r a w - H i l l , N.Y. 1934 P h y s i c a l Review 4_6 , 549. 1971 J . Chem. Phys. 55, 288. 1970 J . Chem. Phys. 5_2, 716. 1966 H e l v . Phys. A c t a 3±, 564. 1959 (luant-Ltat-ive Ihotzcuxtan Sp&ctx.o&copy and Gai> Emtiiiltv<Lt-i<i£>, Addi s on -Wesley I n c . , Read i n g , Mass. 1975 Phys. Rev. L e t t e r s _34 , 1207. 1975 P h y s i c a l Review U, 1543. 1976 P r i v a t e communci a t i o n . Reyno1ds , J . M o l e c t r o n Corp. R o b i n s o n , J.W. e d i t o r Rousseau, D.L. and W i l l i a m s , P.F. V e n k a t e s w a r l u , P. V e n k a t e s w a r l u , P. Young , J . F . Kung, A .H. B j o r k l u n d , G.C. and H a r r i s , S .E. Z e r n i k e , F. and M i d w i n t e r , J . E . 117 -1974 P r i v a t e commun i ca t i on . 1974 Handbook o^ SpuctioAcopy, Vol. I l l , CRC P r e s s , C l e v e l a n d , Oh io . 1974 Phys. Rev. L e t t e r s ^ 3 , 1368. 1970 Can. J . Phys. 48, 1055. 1976 P r i v a t e commun i ca t i on . 1973 IEEE Symposium: La6o.fi Qpti.dk 1973 Applied NonlsLntan. Opt-ia,, John Wi1ey & Sons, N.Y. 

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