CALCULATIONS OF RADIATIVE AND NON-RADIATIVE DECAY RATES FOR DOUBLY-EXCITED STATES IN HIGHLY IONIZED Ar

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CALCULATIONS OF RADIATIVE AND NON-RADIATIVE DECAY RATES FOR

DOUBLY-EXCITED STATES IN HIGHLY IONIZED Ar

J. Hansen

To cite this version:

J. Hansen. CALCULATIONS OF RADIATIVE AND NON-RADIATIVE DECAY RATES FOR

DOUBLY-EXCITED STATES IN HIGHLY IONIZED Ar. Journal de Physique Colloques, 1989, 50

(C1), pp.C1-603-C1-607. �10.1051/jphyscol:1989166�. �jpa-00229366�

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CALCULATIONS

OF

RADIATIVE

AND

NON-RADIATIVE DECAY RATES FOR DOUBLY-EXCITED STATES IN HIGHLY IONIZED A r

J.E. HANSEN

Zeeman Laboratory, University of Amsterdam, Plantage Muidergracht

4,

NL-1018 TV Amsterdam. The Netherlands

ABSTRACT

C a l c u l a t i o n s a r e r e p o r t e d o f r a d i a t i v e and n o n - r a d i a t i v e d e c a y r a t e s f o r d o u b l y e x c i t e d s t a t e s o f t h e t y p e I s n a n ' f i ' i n 2 w i t h n and n ' i n t h e r a n g e

6

t o

9.

T h i s t y p e o f c o n f i g u r a t i o n i s e x p e c t e d t o be formed i n c h a r g e e x c h a n g e c o l l i s i o n s between ArI6+ a n d t h e n e u t r a l r a r e g a s e s and t h e r a t i o b e t w e e n t h e r a d i a t i v e a n d t h e t o t a l d e c a y r a t e is one o f t h e e x p e r i m e n t a l l y a c c e s s i b l e p a r a m e t e r s . We show t h a t t h e r a t i o i s d e p e n d e n t o n t h e p r o x i m i t y o f t h e c o n f i g u r a t i o n t o t h e I s nfi 2 l i m i t s i n and t h a t t h e r a t i o s d e c r e a s e s i g n i f i c a n t l y a s s u c h l i m i t s a r e p a s s e d .

INTRODUCTION

S i n g l e e l e c t r o n c a p t u r e i n c h a r g e e x c h a n g e c o l l i s i o n s i s by now a f a i r l y w e l l u n d e r s t o o d p r o c e s s w h i l e much l e s s i s known a b o u t p i c k u p o f two e l e c t r o n s . Most e v i d e n c e s o f a r i n d i c a t e t h a t t h e p i c k up i n many c a s e s c a n be u n d e r s t o o d as a s e q u e n c e o f two i n d e p e n d e n t e v e n t s b u t some e x p e r i m e n t a l e v i d e n c e h a s b e e n i n t e r p r e t e d a s i n d i c a t i n g a c o r r e l a t e d p r o c e s s /I/. F o r a r e c e n t r e v i e w s e e R e f e r e n c e /2/ a n d r e f e r e n c e s t h e r e i n . I n o r d e r t o

u n d e r s t a n d which i n t e r p r e t a t i o n i s c o r r e c t a n d u n d e r what c i r c u m s t a n c e s , knowledge a b o u t which s t a t e s a r e b e i n g p o p u l a t e d would be h e l p f u l . The

c l a s s i c a l m o d e l s p r o p o s e d , s e e /2/, seem t o g i v e a f a i r l y good a c c o u n t o f t h e n , n 1 p o p u l a t i o n d i s t r i b u t i o n , b u t much l e s s i s known a b o u t t h e f i , ~ '

d i s t r i b u t i o n .

Doubly e x c i t e d s t a t e s i n n e u t r a l atoms h a v e been s t u d i e d f a i r l y e x t e n s i v e l y i n r e c e n t y e a r s b u t l e s s i s known a b o u t t h e p r o p e r t i e s o f t h i s t y p e o f s t a t e i n h i g h l y i o n i z e d s y s t e m s .

U s i n g t r a n s l a t i o n a l e n e r g y g a i n s p e c t r o s c o p y i t i s p o s s i b l e t o d e t e r m i n e t h e r a t i o R between t h e r a d i a t i v e a n d t h e t o t a l d e c a y r a t e f o r t h e d o u b l y e x c i t e d s t a t e s

/3/.

We h a v e c o n s i d e r e d w h e t h e r t h i s i n f o r m a t i o n c a n be u s e d t o d e c i d e which s t a t e s a r e p o p u l a t e d i n p i c k - u p t o c o n f i g u r a t i o n s o f t h e t y p e I s n.!,nle' i n c h a r g e e x c h a n g e c o l l i s i o n s i n v o l v i n g ArI6+ and n e u t r a l r a r e 2 g a s e s . F o r t h i s p u r p o s e c a l c u l a t i o n s h a v e b e e n c a r r i e d o u t o f r a d i a t i v e and n o n - r a d i a t i v e d e c a y r a t e s a v e r a g e d o v e r t h e s t a t e s o f a nJnl.!,' c o n f i g u r a t i o n

(n s n ' Z 8 ) f o r a number o f J , f i ' v a l u e s i n ~ r ' ~ + . The r e s u l t s show t h a t t h e

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1989166

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C1-604 JOURNAL DE PHYSIQUE

d i s t a n c e from a p a r t i c u l a r c o n f i g u r a t i o n t o t h e n e x t l o w e r l i m i t i s a n i m p o r t a n t f a c t o r i n d e t e r m i n i n g t h e r a t i o ~ ( n t , n ' ~ ' ) . I n n e u t r a l a t o m s t h i s d i s t a n c e i s a l s o i m p o r t a n t b u t a l l t h e c o n f i g u r a t i o n s u n d e r c o n s i d e r a t i o n c a n i n t h i s c a s e u s u a l l y d e c a y t o o n e and t h e same l i m i t w h i l e t h i s i s n o t t h e c a s e f o r l a r g e n , n l v a l u e s i n h i g h l y i o n i z e d atoms. With i n c r e a s i n g e n e r g y o f t h e bound s t a t e a new continuum m i g h t become a v a i l a b l e and b o o s t t h e non- r a d i a t i v e d e c a y r a t e . T h a t t h e n o n - r a d i a t i v e d e c a y o f d o u b l y e x c i t e d s t a t e s i s p r e f e r e n t i a l l y t o t h e n e a r e s t continuum h a s been o b s e r v e d e x p e r i m e n t a l l y , s e e N i e h a u s /2/ and r e f e r e n c e s t h e r e i n , and i s due t o t h e b e t t e r o v e r l a p between low-energy continuum w a v e f u n c t i o n s a n d t h e bound o r b i t a l s .

METHOD

The c a l c u l a t i o n s were c a r r i e d o u t u s i n g t h e s u i t e o f p r o g r a m s d e s c r i b e d by Cowan /4/. The a p p r o x i m a t e - r e l a t i v i s t i c HFR method i n t r o d u c e d by Cowan and G r i f f i n

/5/

was u s e d i n a s i n g l e c o n f i g u r a t i o n a p p r o x i m a t i o n i n which t h e r a d i a t i v e d e c a y o f t h e n a n ' a ' c o n f i g u r a t i o n t o a l l l o w e r l y i n g n " ( Q + l ) n ' f i l and n.P,nU(Q'+l) c o n f i g u r a t i o n s were c o n s i d e r e d as w e l l a s t h e a u t o i o n i z a t i o n t o t h e 4 s , 5s and 6 s l i m i t s . No s c a l i n g o f t h e r a d i a l i n t e g r a l s was used. The t o t a l d e c a y r a t e s were c a l c u l a t e d a s s u m i n g t h e c o n f i g u r a t i o n t o be

s t a t i s t i c a l l y p o p u l a t e d and t h e r a t i o R ( n i , n t q , ' ) b e t w e e n t h e r a d i a t i v e d e c a y r a t e s a n d t h e t o t a l o n e s e v a l u a t e d . The c o n f i g u r a t i o n s c o n s i d e r e d were t h e n s n ' i , n d n ' i and n d n ' k c o n f i g u r a t i o n s f o r n , n t = 6 , 7 , 8 a n d 9. T h i s c h o i c e o f c o n f i g u r a t i o n s i s s u g g e s t e d by t h e two s t e p m o d e l s i n which t h e p i c k up is u n d e r s t o o d a s two i n d e p e n d e n t e v e n t s which l i m i t s t h e n , n l v a l u e s t o n N" n ' . One d i f f i c u l t y i n t h e c a l c u l a t i o n s i s t h a t i t i s known t h a t d o u b l y e x c i t e d s t a t e s o f t h e t y p e n f i n ' a ' i n t h e He s e q u e n c e a r e s t r o n g l y c o r r e l a t e d and t h a t t h e i n d i v i d u a l s t a t e s c a n n o t be d e s c r i b e d by s i n g l e - c o n f i g u r a t i o n c a l c u l a t i o n s . However, s i n c e we a r e a v e r a g i n g o v e r a l l s t a t e s o f a p a r t i c u l a r c o n f i g u r a t i o n , t h e e f f e c t o f c o n f i g u r a t i o n i n t e r a c t i o n i s p r o b a b l y n o t s e v e r e a l t h o u g h i t c a n be e x p e c t e d t o r e d u c e t h e s p r e a d i n R ( n ! , , n a r ) a s a f u n c t i o n o f

a,!,'.

RESULTS

The p o s i t i o n o f t h e n , n 1 = 6 , 7 ; 7 , 7 ; 7 , 8 ; 7 , 9 ;

8,8;

8 , 9 a n d 9 , 9 c o n f i g u r a t i o n s r e l a t i v e t o t h e I s 4 1 ; 5P,; 6 a a n d 7 & 2 l i m i t s a r e shown i n F i g u r e 1.

It c a n b e s e e n t h a t t h e n , n 1 = 7 , 6 c o n f i g u r a t i o n s c a n a u t o i o n i z e o n l y t o t h e 4 ~ e e ' c o n t i n u a w h i l e n , n l = 7 , 7 ; 7 , 8 ; 7 , 9 and

8,s

c a n d e c a y a l s o t o 5 a a a ' c o n t i n u a . I n f a c t n , n l = 7 , 7 i s v e r y c l o s e t o t h e 5 4 l i m i t s . The n , n ' = 8 , 9 and 9 , 9 c o n f i g u r a t i o n s c a n i n a d d i t i o n decay t o 6 a e a t c o n t i n u a . T h i s s i t u a t i o n i s i m p o r t a n t f o r a n u n d e r , s t a n d i n g o f t h e v a r i a t i o n i n R a s a f u n c t i o n o f n Q , n l a ' . The c a l c u l a t e d R v a l u e s a r e a l l c o n s i d e r a b l y s m a l l e r t h a n 1 and show a d e c r e a s e when a c o n f i g u r a t i o n i s l o c a t e d j u s t above a l i m i t a s f o r example 7 g 7 Q 1 a n d 8 a 9 a ' . The c a l c u l a t e d v a l u e s o f R a r e g i v e n i n T a b l e I.

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T a b l e I.

C a l c u l a t e d v a l u e s o f t h e r a t i o R ( n l , n q i ' ) between t h e r a d i a t i v e a n d t h e t o t a l d e c a y r a t e s f o r I s n a , n f i . f c o n f i g u r a t i o n s i n *rq4+ 2 a v e r a g e d o v e r a l l s t a t e s o f t h e n $ , n f i f c o n f i g u r a t i o n s i n a s i n g l e c o n f i g u r a t i o n a p p r o x i m a t i o n u s i n g HFR wavefunc t i o n s

...

C o n f i g u r a t i o n n s n f i r . d n f i ndn 'k

9 , 8 *

5

0.012

5

0.021

5

0.023

9 , 9 *

5

0.017

5

^0.033

<_

0.045

...

*

a u t o i o n i z a t i o n t o 6 h e i h a s been n e g l e c t e d .

The d e c r e a s e i n R a t 8 ~ 9 ~ ' i s much s m a l l e r t h a n a t 7 a 7 i f . T h i s i s b e c a u s e t h e d i s t a n c e b e t w e e n l i m i t s d e c r e a s e w i t h i n c r e a s i n g n. Thus t h e d i f f e r e n c e i n t h e , e n e r g y o f t h e f r e e e l e c t r o n between two c o n s e c u t i v e l i m i t s n a n d n + l d e c r e a s e s w i t h n and t h e " b o o s t " i n a u t o i o n i z a t i o n c o n s e q u e n t l y d e c r e a s e s . The d i f f e r e n c e i n a u t o i o n i z a t i o n t o n = 5 compared t o n=4 l i m i t s is t y p i c a l l y a f a c t o r 2 5 w h i l e t h e d i f f e r e n c e b e t w e e n n=6 and n = 5 i s a b o u t 10 t i m e s s m a l l e r . The e x p e r i m e n t a l o b s e r v a t i o n t h a t a u t o i o n i z a t i o n i s t o t h e n e a r e s t l i m i t o n l y /2/ i s t h e r e f o r e l i k e l y t o be l e s s s t r i c t l y t r u e a t h i g h v a l u e s o f n.

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C1-606 JOURNAL

DE

PHYSIQUE

T h e r e i s a d e p e n d e n c e on g and 1' a l s o a s i t c a n be s e e n t h a t R i n c r e a s e s w i t h i n c r e a s i n g .P,,fif. T h i s i s e x p e c t e d s i n c e a u t o i o n i z a t i o n h a s a dependence on l / i k where k h a s been f o u n d t o be l a r g e r t h a n

5

f o r some t y p e s of d e c a y s

/ 6 / .

Such a s t r o n g dependence i s n o t o b s e r v e d f o r t h e R v a l u e s b u t t h e v a r i a t i o n seems s i g n i f i c a n t . F o r a c o n f i g u r a t i o n l i k e 8d8k, R i s

c a l c u l a t e d t o b e 0.12. It i s i n t e r e s t i n g t h a t a v a l u e o f 0.16 h a s been

measured by H v e l p l u n d /3/ f o r d o u b l e c a p t u r e i n x e q 5 + on A r where s i m i l a r n , n f v a l u e s a r e e x p e c t e d t o be p o p u l a t e d . I f i t i s p o s s i b l e t o make a n y c o n c l u s i o n s from t h i s v a l u e o b t a i n e d f o r a d i f f e r e n t s y s t e m i t would be t h a t t h e e l e c t r o n s a p p e a r t o be p i c k e d u p p r e f e r e n t i a l l y w i t h a l a r g e .P, v a l u e . I n r e a l i t y i t ^{c a n} be e x p e c t e d t h a t a c o n s i d e r a b l e number o f l e v e l s from d i f f e r e n t c o n f i g u r a t i o n s a r e p o p u l a t e d and t h e e x p e r i m e n t a l v a l u e s c a n be e x p e c t e d t o be a c o m p l i c a t e d a v e r a g e o v e r d i f f e r e n t c o n f i g u r a t i o n s . From t h e numbers shown i n T a b l e I i t i s p r o b a b l y n o t r e a l i s t i c t o e x p e c t t h a t i t i s p o s s i b l e t o u s e e x p e r i m e n t a l v a l u e s o f R t o i d e n t i f y t h e s t a t e s which a r e p o p u l a t e d i n d ~ u b l e c a p t u r e . F o r t h a t t h e v a r i a t i o n between t h e c a l c u l a t e d R v a l u e s a p p e a r s t o b e t o o s m a l l . Even t h o u g h o n l y a few d i f f e r e n t t y p e s o f c o n f i g u r a t i o r s h a v e b e e n c o n s i d e r e d i t seems u n l i k e l y t h a t a much l a r g e r v a r i a t i o n e x i s t s . However, i t m i g h t be p o s s i b l e t o o b s e r v e t h e d i s c o n t i n u i t i e s i n R when t h e p o p u l a t e d l e v e l s c r o s s a i o n i z a t i o n l i m i t . S i m i l a r l y , i n s i n g l e - e l e c t r o n p i c k up t h e e l e c t r o n i s e x p e c t e d t o be p i c k e d up i n s t a t e s w i t h l a r g e r v a l u e s o f g when t h e r e l a t i v e v e l o c i t y o f t h e c o l l i s i o n p a r t n e r s i n c r e a s e s

/7,8/.

I f t w o - e l e c t r o n p i c k - u p i s a c o m b i n a t i o n o f two s i n g l e p i c k - u p ' s i t m i g h t be p o s s i b l e , j u d g i n g from t h e r e s u l t s i n T a b l e I t o o b s e r v e a v e l o c i t y d e p e n d e n c e o f R.

F i n a l l y , i t s h o u l d b e m e n t i o n e d t h a t t h e same p r o c e s s i s o f i n t e r e s t i n t h e c a s e o f n e u t r a l i z a t i o n o f h i g h l y i o n i z e d a t o m s a t s u r f a c e s , s e e f o r example t h e r e v i e w by F.W. Meyer i n t h e s e p r o c e e d i n g s /9/. The main

d i f f e r e n c e i s t h a t t h e i n i t i a l s t a t e s i n t h i s t y p e o f e x p e r i m e n t a r e e x p e c t e d t o h a v e v e r y low a n g u l a r momentum.

ACKNOWLEDGEMENT

I w i s h t o t h a n k P. H v e l p l u n d f o r d r a w i n g my a t t e n t i o n t o t h i s problem a n d f o r s t i m u l a t i n g d i s c u s s i o n s .

REFERENCES

/ I / S t o l t e r f o t h , N., H a v e n e r , C.C., P h a n e u f , R.A., Swenson, J.K., S h a f r o t h , S.M. and Meyer, F.W., Phys. Rev. L e t t .

57

(1986) 74.

/ 2 / N i e h a u s , A., Nucl. I n s t r . Meths. B U (1988) 359.

3

H v e l p l u n d , P., P r i v a t e Communication 1986.

/4/

Cowan, R.D., The Theory o f Atomic S t r u c t u r e and S p e c t r a , ( u n i v e r s i t y o f C a l i f . P r e s s , ~ e r k e l e ~ ) (1981) Ch. 8 a n d 16.

/5/

Cowan, R.D. a n d G r i f f i n , D.C., J. Opt, Soc. Am.

&

(1976) 1010.

/6/ s e e r e f . 4 page 557.

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/8/ C h a r l e s , P., B r i a n d , J.P., E s s a b a a , S., Bliman, S. and O l s o n , R., t h e s e p r o c e e d i n g s .

/q/

Meyer, F.W., H a v e n e r , C.C., Reed, K.J., Snowdon, K.J. a n d Z e h n e r , D.M., t h e s e p r o c e e d i n g s .