2) and Rare Gas Atoms

5 Interaction Between Cs* (7S, 5D / ) and Rare 5 2

Gas Atoms B. S A Y E R , M.

FERRAY,

J. P. V I S T I C O T , and J. L O Z I N G O T

Downloaded by UNIV LAVAL on July 11, 2016 | http://pubs.acs.org Publication Date: March 8, 1982 | doi: 10.1021/bk-1982-0179.ch005

Centre d'Etudes Nucléaires de Saclay, Service de Physique Atomique, 91191 Gif-sur-Yvette, Cedex, France

Information concerning the interaction potentials of Cs*(7S, 5D)-rare gas pairs i s obtained by inter preting the temperature dependence of the 6S-7S,5D far wing and satellite profiles. A sensitive laser fluorescence technique i s used to obtain the ab sorption coefficient of the mixture. The collision induced o s c i l l a t o r strength, a rapidly varying function of the interatomic distance in the case of such forbidden transitions, i s also deduced. Ex perimental potentials and o s c i l l a t o r strengths are compared with available calculated values.

In t h e q u a s i s t a t i c t h e o r y , t h e p r o f i l e o f t h e f a r w i n g s o f an a t o m i c l i n e i s c l o s e l y r e l a t e d t o t h e i n t e r a t o m i c p o t e n t i a l s at r e l a t i v e l y short i n t e r a t o m i c d i s t a n c e s (6-12 a . u . ) . According to t h e Franck-Condon p r i n c i p l e , the r a d i a t i v e t r a n s i t i o n occurs a t a w a v e l e n g t h X , when t h e d i s t a n c e R between t h e two atoms i s s u c h t h a t t h e d i f f e r e n c e between upper and l o w e r p o t e n t i a l s V» V-| i s e q u a l t o h c / X . The a b s o r b e d ( o r e m i t t e d ) l i g h t i n t e n s i t y p e r u n i t w a v e l e n g t h i s t h u s p r o p o r t i o n a l t o 4TTR f ( R ) e x p ( - V / k T ) dR/dX w h e r e V i s t h e p o t e n t i a l o f t h e i n i t i a l l e v e l and f ( R ) t h e o s c i l l a t o r s t r e n g t h o f t h e t r a n s i t i o n . An A r r h e n i u s p l o t ( l o g a r i t h m o f t h e i n t e n s i t y as a f u n c t i o n o f 1/T) n o r m a l l y y i e l d s a s t r a i g h t l i n e , t h e s l o p e o f w h i c h g i v e s V ( X ) . The p o t e n t i a l o f t h e o t h e r l e v e l i s t h e n o b t a i n e d by a d d i n g ( o r s u b t r a c t i n g ) h c / X . I f t h e dependence o f one o f t h e p o t e n t i a l s v e r s u s R i s known, t h e dependence o f t h e o t h e r p o t e n t i a l c a n be d e r i v e d . Moreover t h e a b s o l u t e measurement o f t h e i n t e n s i t y o f t h e f a r w i n g a l l o w s t h e d e t e r m i n a t i o n o f t h e o s c i l l a t o r s t r e n g t h f f o r each v a l u e o f X and o f R i f X ( R ) i s m o n o t o n i c . T h i s i s t h e e x t e n s i o n from w e l l known m o l e c u l a r s p e c t r o s c o p i c methods o f d e t e r m i n i n g p o t e n t i a l s to t h e t r a n s i e n t s i t u a t i o n o f c o l l i d i n g atoms. 2

0097-6156/82/0179-0051 $05.00/0 © 1982 American Chemical Society

Gole and Stwalley,; Metal Bonding and Interactions in High Temperature Systems ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

METAL BONDING AND INTERACTIONS

52 Choice of

We c h o o s e t o s t u d y t h e f o r b i d d e n t r a n s i t i o n s o f t h e c e s i u m atom between t h e g r o u n d s t a t e 6S and t h e e x c i t e d s t a t e s 75 and 5 D / i n t h e p r e s e n c e o f r a r e g a s e s (RG) (1_, 2, 3). The r e a s o n s f o r t h i s c h o i c e are the f o l l o w i n g : 1. A l k a l i - r a r e gas i n t e r a c t i o n p o t e n t i a l s a r e e a s i e r to c a l c u l a t e . F o r t h e p a i r s C s ( 7 S ) - R G and C s ( 5 D ) - R G , t h e P a s c a l e and V a n d e p l a n q u e c u r v e s ( 4 j and t h o s e o f C z u c h a j and S i e n k i e w i c z ( 5 j a r e a v a i l a b l e . 2. The i n t e r a c t i o n w i t h t h e p e r t u r b e r l e a d s t o a m i x i n g o f t h e w a v e f u n c t i o n s w h i c h makes t h e t r a n s i t i o n s l i g h t l y allowed. Under t h e s e c o n d i t i o n s t h e i n t e r p r e t a t i o n of experimental r e s u l t s i s a l i t t l e more c o m p l i c a t e d , b u t i n f o r m a t i o n on t h e v a l u e o f the o s c i l l a t o r s t r e n g t h o f the c o l l i s i o n induced t r a n s i t i o n can be o b t a i n e d and compared w i t h t h e p r e d i c t i o n s o f P a s c a l e (6) and C z u c h a j ( 7 J . 3. The s h a p e s o f t h e c a l c u l a t e d C s - r a r e gas p o t e n t i a l c u r v e s show an a v o i d e d c r o s s i n g o f t h e c u r v e s a s s o c i a t e d w i t h t h e 7S and 5 D / , = ^ (5d Z) s t a t e s (Figure 1). Such a s i t u a t i o n c h a r a c t e r i z e s a s t r o n g c o u p l i n g between t h e two s t a t e s and t h e shape o f t h e c a l c u l a t e d p o t e n t i a l c u r v e s i s t h e n v e r y s e n s i t i v e t o t h e c a l c u l a t i o n met hod. The com p a r i s o n between t h e o r e t i c a l p r e d i c t i o n s and e x p e r i m e n t a l r e s u l t s i s e x p e c t e d t o be o f p a r t i c u l a r i n t e r e s t i n t h i s range o f i n t e r a t o m i c d i s t a n c e s . 4. In i t s i n t e r p r e t a t i o n a l i n e w i n g p r o f i l e i s o b v i o u s l y assumed n o t t o o v e r l a p w i t h o t h e r w i n g s . T h i s a p p l i e s t o t h o s e a s s o c i a t e d w i t h 6S-7S and 6S-5D / i 2 except i n a narrow s p e c t r a l r e g i o n f o r the c a s e ' o f h e l i u m p e r t u r b e r s ( 8 ) . 5. Another c o n d i t i o n , r e l a t e d to the p o s s i b i l i t y of s i m p l y i n t e r p r e t i n g t h e t e m p e r a t u r e dependence o f t h e w i n g p r o f i l e , i s t h a t one p o i n t i n t h e s p e c t r u m s h o u l d be r e l a t e d t o one s i n g l e p o i n t o f t h e p o t e n t i a l curve. In t h e p r e s e n t c a s e t h i s i s a l w a y s v e r i f i e d except i n the neighborhood of extrema of the d i f f e r e n c e AV between t h e p o t e n t i a l s o f t h e u p p e r and l o w e r s t a t e s o f t h e t r a n s i t i o n . However t h i s r e g i o n , which corresponds to the s o - c a l l e d s a t e l l i t e , i s n o t amenable t o i n t e r p r e t a t i o n by t h e q u a s i s t a t i c t h e o r y and w i l l be c o n s i d e r e d l a t e r o n . 5


Transitions

2

5

5

Experimental

2

m

2 j m =

Method

To d e t e r m i n e t h e t e m p e r a t u r e dependence o f t h e f a r w i n g p r o f i l e , we have e i t h e r t o work a t h i g h a t o m i c d e n s i t y o r t o use a s e n s i t i v e method o f measurement. In t h e p r e s e n t s i t u a t i o n t h e


5.

SAYER ET AL.

Cs*(7S,5D / ) 5

and

2

Rare Gas

53

Atoms

c o n c e n t r a t i o n o f b o t h c o n s t i t u e n t s must n o t be t o o h i g h b e c a u s e o f the r i s k o f s t r o n g a b s o r p t i o n o r i g i n a t i n g from e i t h e r a l k a l i d i m e r s o r a l k a l i atoms i n t e r a c t i n g s i m u l t a n e o u s l y w i t h two p e r turbers. To a v o i d t h e s e e f f e c t s we c h o o s e t h e f o l l o w i n g e x p e r i mental c o n d i t i o n s : Nc ^ 10 cm" , N < 10 cm . Thus i t i s n e c e s s a r y t o use a v e r y s e n s i t i v e measurement m e t h o d . For t h i s p u r p o s e t h e a b s o r p t i o n s p e c t r u m has been d e t e r m i n e d by a l a s e r fluorescence technique, described i n d e t a i l elsewhere (8). B r i e f l y i t i s as f o l l o w s : the a b s o r p t i o n of a photon photoexc i t e s a c e s i u m atom w h i c h i s p e r t u r b e d by a r a r e gas atom f r o m i t s g r o u n d s t a t e t o t h e 7S o r 5D / m=h state. The main d e - e x c i t a t i o n p a t h o f t h i s atom i s t h e r a d i a t i v e c a s c a d e t h r o u g h t h e only allowed t r a n s i t i o n s : 7S o r 5D -> 6P + 6S. To d e t e c t t h e a b s o r p t i o n we o b s e r v e t h e f l u o r e s c e n c e a t 852.1 nm ( 6 P / + 6S / ). The s e n s i t i v i t y o f t h i s method i s s u c h t h a t i t i s p o s s i b l e t o d e t e c t an a b s o r p t i o n o f a b o u t 1 0 ~ p e r cm. The e x p e r i mental d e v i c e i s s i m p l e : t h e beam o f a CW t u n a b l e dye l a s e r p a s ses t h r o u g h a P y r e x c e l l c o n t a i n i n g t h e c e s i u m - r a r e gas m i x t u r e and t h e f l u o r e s c e n c e l i g h t i s d e t e c t e d a t a r i g h t a n g l e . The f a r w i n g p r o f i l e k ( A ) i s o b t a i n e d when t h e w a v e l e n g t h o f t h e l a s e r i s swept. 1 £ t

3

1 9

s

- 3

R G

5 29


3

2

1 2

7

Results The r e s u l t s o b t a i n e d a r e shown i n F i g u r e 2 as w e l l as F i g u r e 1. The V 5 5 p o t e n t i a l i s d e d u c e d f r o m t h e s l o p e o f t h e s t r a i g h t l i n e r e p r e s e n t i n g l o g k ( A ) = (|>(1/T) f o r v a r i o u s v a l u e s o f A. The u p p e r s t a t e p o t e n t i a l V = Vss + hc/A i s p l o t t e d as a f u n c t i o n o f V 5 S . T h i s r a t h e r u n u s u a l r e p r e s e n t a t i o n i s used h e r e i n o r d e r t o take the b e s t advantage of e x p e r i m e n t a l r e s u l t s , the o n l y u n c e r t a i n t i e s w h i c h a p p e a r b e i n g due t o e x p e r i m e n t a l e r r o r and t o t h e v a l i d i t y o f q u a s i s t a t i c t h e o r y . Experimental points are p l o t t e d i n F i g u r e 2 w i t h i n c l i n e d e r r o r bars because the u n c e r t a i n t i e s i n V and V 5 S a r e o b v i o u s l y t h e same. The p o i n t s o f t h e u p p e r p a r t c o r r e s p o n d t o t h e 6S-7S t r a n s i t i o n . I t i s t o be n o t e d t h a t t h e d e p t h o f t h e p o t e n t i a l w e l l d e c r e a s e s f r o m Xe t o Ne (1000 c m " f o r X e , 700 c m " f o r K r , 400 c m " f o r A r ) . If a w e l l e x i s t s f o r Ne i t s d e p t h i s l e s s t h a n 50 c m " . Considering the p o i n t s corresponding t o 6 S - 5 D / (lower part of Figure 2 ) , we o b s e r v e t h a t t h i s t r a n s i t i o n o c c u r s i n a p o t e n t i a l r e g i o n o f t h e g r o u n d s t a t e and o f t h e e x c i t e d s t a t e w h i c h i s more r e p u l s i v e when t h e r a r e gas i s l i g h t e r . I t i s i n t e r e s t i n g to note t h a t , as we h o p e d , t h e p o t e n t i a l s a r e w e l l d e t e r m i n e d i n t h e r e g i o n o f t h e a v o i d e d c r o s s i n g , e x c e p t p e r h a p s i n t h e c a s e o f xenon f o r w h i c h t h e 6S-7S t r a n s i t i o n seems t o o c c u r a l i t t l e f a r t h e r than the c r o s s i n g . For the t h r e e o t h e r r a r e gases the s m a l l e s t d i f f e r e n c e between t h e p o t e n t i a l s i s a l m o s t i n d e p e n d e n t o f t h e n a t u r e o f t h e p e r t u r b e r , a b o u t 1700 c m " . T h i s d i f f e r e n c e seems s l i g h t l y l e s s f o r xenon. In F i g u r e s 1 and 2 t h e c a l c u l a t e d p o t e n t i a l s a r e a l s o u

u

1

1

1

1

5

2

1


METAL

BONDING AND

INTERACTIONS


54


Gole and Stwalley,; Metal Bonding and Interactions in High Temperature Systems ACS Symposium Series; American Chemical Society: Washington, DC, 1982. 5/2>m

'

R (a.u.)

1

1—;— r

Journal of Physics B

Figure 2. Potential curves of the 7S and 5D = u states of Cs-rare gas pairs (2); comparison between experimental results ( ) and curves calculated in Ref. 4 ( ; and in Ref. 5 (• •

1


56


plotted. For those corresponding t o 5 D / k , various s i t u a tions are observed: good agreement w i t h t f i e P a s c a l e - V a n d e p l a n q u e p o t e n t i a l s f o r A r and w i t h t h o s e o f C z u c h a j and S i e n k i e w i c z f o r K r , b u t a l l t h e c a l c u l a t e d p o t e n t i a l s a p p e a r t o o r e p u l s i v e f o r Xe and Ne. In t h e s e l a s t two c a s e s t h e minimum e n e r g y between t h e two t h e o r e t i c a l c u r v e s i s much s m a l l e r t h a n t h a t d e t e r m i n e d e x perimentally. No a v o i d e d c r o s s i n g i s o b s e r v e d on t h e e x p e r i m e n tal curves. As p r e v i o u s l y i n d i c a t e d t h e d e t e r m i n a t i o n o f t h e e x c i t e d s t a t e p o t e n t i a l c u r v e s r e q u i r e s a knowledge o f t h e p o t e n t i a l curve o f the ground s t a t e . For t h i s p o t e n t i a l curve, t h e o r e t i c a l ( 4 , 5_, 9) a s w e l l as e x p e r i m e n t a l ( 1 0 , 12) d e t e r m i n a t i o n s e x i s t , b u t do n o t a g r e e p e r f e c t l y among t h e m s e l v e s . Taking i n t o a c c o u n t b o t h t h e s e i m p r e c i s i o n s and t h e e x p e r i m e n t a l u n c e r t a i n t i e s , we p r o p o s e c r o s s - h a t c h e d a r e a s i n F i g u r e 1 where t h e p o t e n t i a l c u r v e s a r e most p r o b a b l y l o c a t e d . The p l o t o f p o t e n t i a l v e r s u s R i n F i g u r e 1 i s more f a m i l i a r t h a n t h a t as a f u n c t i o n o f V 5 5 , b u t makes t h e c o m p a r i s o n between e x p e r i m e n t a l and c a l c u l a t e d curves l e s s p r e c i s e than i s a c t u a l l y the case. F o r t h e p a r t i c u l a r c a s e o f t h e i n t e r a c t i o n w i t h H e , we have t o be c a r e f u l when a p p l y i n g t h e q u a s i s t a t i c t h e o r y t o s u c h a l i g h t p e r t u r b e r as h e l i u m . N e v e r t h e l e s s t h e t e n t a t i v e use o f t h i s t h e o r y l e a d s t o t h e r e s u l t s g i v e n i n F i g u r e s 1 and 2. The p o t e n t i a l s o f t h e 5D«j/ s t a t e d i f f e r w i d e l y from those c a l c u l a t e d and we t h i n k t h a t {he u n c e r t a i n t y due t o t h e l i m i t a t i o n s o f t h e q u a s i s t a t i c t h e o r y cannot e x p l a i n such a d i s c r e p a n c y . Very l i t t l e i n f o r m a t i o n has been o b t a i n e d f o r t h e 7S s t a t e b e c a u s e u n l i k e the s i t u a t i o n w i t h o t h e r r a r e g a s e s , t h e wing o f t h e 6S-7S t r a n s i t i o n p r o b a b l y a r i s e s from a very narrow i n t e r a t o m i c d i s t a n c e region. A l t h o u g h t h e k n o w l e d g e o f t h e 7S p o t e n t i a l i s l i m i t e d t o one p o i n t , t h e minimum e n e r g y d i f f e r e n c e between t h e two c u r v e s can be e s t i m a t e d a s l e s s t h a n 1000 c m " , i . e . s m a l l e r t h a n t h a t o b t a i n e d f o r o t h e r r a r e g a s e s (1700 c m " ) . In F i g u r e 1 t h e 5D p o t e n t i a l c u r v e e x h i b i t s an i n f l e c t i o n p o i n t i n the q u a s i s t a t i c p a r t o f the p r o f i l e . This i s evidence f o r a s t r o n g i n t e r a c t i o n w i t h t h e 7S p o t e n t i a l c u r v e w h i c h i s i t s c l o s e s t neighbor. In t h i s c a s e an a v o i d e d c r o s s i n g p r o b a b l y e x ists. This i n t e r a c t i o n could e x p l a i n the large e x c i t a t i o n t r a n s f e r between t h e s e two s t a t e s , s u s p e c t e d e a r l i e r ( 8 ) . Concerning the o s c i l l a t o r s t r e n g t h o f the c o l l i s i o n induced t r a n s i t i o n s b e tween t h e s t a t e s i n v o l v e d and t h e g r o u n d s t a t e , t h i s can be d e t e r m i n e d f r o m an a b s o l u t e measurement o f t h e a b s o r p t i o n c o e f f i cient. S i n c e o u r e x p e r i m e n t a l method does n o t y i e l d a b s o l u t e v a l u e s o f k ( X ) , we have s c a l e d o u r a b s o r p t i o n p r o f i l e s w i t h t h o s e o f Moe e t a l . ( 1 3 J . The o s c i l l a t o r s t r e n g t h f o f t h e 6S-7S t r a n s i t i o n i s g i v e n i n F i g u r e 3 as a f u n c t i o n o f t h e i n t e r a t o m i c d i s tance, f p a s s e s t h r o u g h a maximum v a l u e w h i c h i s i n g e n e r a l w e l l p r e d i c t e d by t h e c a l c u l a t i o n s o f P a s c a l e and o f C z u c h a j . This v a l u e , o f t h e o r d e r o f magnitude o f a few times 1 0 " , i n d i c a t e s t h a t t h e t r a n s i t i o n i s a l m o s t a l l o w e d i n a l i m i t e d r e g i o n o f R.


5

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2

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1

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Gole and Stwalley,; Metal Bonding and Interactions in High Temperature Systems ACS Symposium Series; American Chemical Society: Washington, DC, 1982. 5/2

I

10 Journal of Physics B

8

111I 6

Figure 3. Oscillator strength of the Cs(6S-7S) and Cs(6S-5D ) transitions (1-3) induced by collision with various rare gases; comparison with values calculated in Ref. 6 ( ) and in Ref. 1 (- - -). The horizontal error bars are very broad when the absorption occurs in a flat part of the 6S potential curve.

6S - 7 S


u\ ^


58

The a g r e e m e n t w i t h c a l c u l a t i o n s i s p a r t i c u l a r l y good f o r X e , f o r which the c a l c u l a t e d p o t e n t i a l s are r e l a t i v e l y f a r from our d e termined values. We may n o t e t h a t t h e o s c i l l a t o r s t r e n g t h i s v e r y s e n s i t i v e t o t h e m i x i n g o f t h e 7S and 6P w a v e f u n c t i o n s r e s p o n s i b l e f o r t h e t r a n s i t i o n moment, w h i l e t h e p o t e n t i a l c u r v e s a r e m a i n l y s e n s i t i v e t o t h e m i x i n g o f t h e w a v e f u n c t i o n s o f t h e 7S and 5D s t a t e s i n t h e r e g i o n i n v o l v e d . Information o b t a i n e d from t h e o s c i l l a t o r s t r e n g t h a p p e a r s c o m p l e m e n t a r y t o t h a t g i v e n by the comparison o f the p o t e n t i a l s .


Extension

to the S a t e l l i t e Region

The q u a s i s t a t i c t h e o r y does n o t a p p l y i n t h e s a t e l l i t e r e g i o n , b u t some i n f o r m a t i o n can be d e r i v e d f r o m t h i s r e g i o n by t h e use o f t h e semi c l a s s i c a l method o f S z u d y and B a y l i s ( 1 4 ) . In a r e c e n t a r t i c l e t h e s a t e l l i t e p r o f i l e and i t s t e m p e r a t u r e dependence a r e c a l c u l a t e d f o r v a r i o u s a n a l y t i c a l r e p r e s e n t a t i o n s o f t h e p o t e n t i a l d i f f e r e n c e between u p p e r and l o w e r s t a t e s and o f t h e o s c i l l a t o r s t r e n g t h ( 1 5 ) . By v a r y i n g t h e p a r a m e t e r s o f t h e s e a n a l y t i c a l forms we have t r i e d t o f i t t h e e x p e r i m e n t a l p r o f i l e and i t s t e m p e r a t u r e d e p e n d e n c e . For example, the l e f t hand c u r v e o f F i g u r e 4 g i v e s t h e b e s t f i t o f t h e e x p e r i m e n t a l p r o f i l e (dotted l i n e ) obtained f o r the Cs-Ar p a i r . The p o t e n t i a l o f t h e u p p e r s t a t e used f o r t h i s f i t ( d o t t e d l i n e ) i s p l o t t e d i n F i g u r e 4b and i s s e e n t o e x t r a p o l a t e t o t h e one d e d u c e d f r o m t h e quasistatic interpretation (full line). Such a g r e e m e n t i s u n o b t a i n a b l e ( 1 5 ) i f o t h e r q u i t e d i f f e r e n t p a r a m e t e r s a r e u s e d , and c o n s e q u e n t l y t h i s method can p r o v i d e u s e f u l i n f o r m a t i o n f r o m t h e s a t e l l i t e region.

Conclusion From t h e p r e s e n t s t u d y i n t e r e s t i n g i n f o r m a t i o n has been o b t a i n e d c o n c e r n i n g t h e C s ( 7 S ) - R G and C s ( 5 D ) - R G p o t e n t i a l c u r v e s . These c u r v e s a r e n o t e n t i r e l y d e t e r m i n e d , p a r t l y b e c a u s e o f t h e i m p r e c i s e knowledge o f t h e g r o u n d s t a t e p o t e n t i a l . I f i n f o r m a t i o n about t h i s p o t e n t i a l i s o b t a i n e d i n the f u t u r e , f o r example, from s c a t t e r i n g e x p e r i m e n t s , improvements i n t h e d e t e r m i n a t i o n o f V 7 s ( R ) and V ^ D ( R ) can be o b t a i n e d by u s i n g t h e p r e s e n t r e s u l t s . However t h e i n f o r m a t i o n g i v e n h e r e i s a l r e a d y p r e c i s e enough t o g u i d e new i n t e r a c t i o n p o t e n t i a l c a l c u l a t i o n s .



l/2

5/2

Journal of Physics B

Figure 4. a: Comparison between experimental (- • •) and calculated ( ) satellite profiles for the Cs (6S -5D )-Ar transition (IS), b: Potential of the excited state corresponding to the calculation.



60 Literature Cited

1. 2. 3.


4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

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RECEIVED August 26,

1981.


2) and Rare Gas Atoms

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