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Submitted on 1 Jan 1987
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DOUBLE X-RAY DECAY
K. Ilakovac, B. Bušić, J. Tudorić-Ghemo, V. Horvat
To cite this version:
K. Ilakovac, B. Bušić, J. Tudorić-Ghemo, V. Horvat. DOUBLE X-RAY DECAY. Journal de Physique
Colloques, 1987, 48 (C9), pp.C9-613-C9-616. �10.1051/jphyscol:19879102�. �jpa-00227209�
DOUBLE X-RAY DECAY( )
K . ILAKOVAC" , * * , B . B U ~ I ? * * , J . T U D O R I ~ - G H E M O * and V . HORVAT*
* F a c u l t y o f Science and Mathematics, U n i v e r s i t y o f Zagreb, PO Box 162, YU-41001 Zagreb, Yugoslavia
* * Rudjer ~ o s k o v i 6 I n s t i t u t e , PO Box 101 6 , YU-41001 Zagreb, Yugoslavia
t * *
Faculty o f E l e c t r i c a l Engineering, Zagreb, Yugoslavia ' F a c u l t y o f E l e c t r i c a l and Mathematical Engineering and Shipbuilding, S p l i t , Yugoslavia
A b s t r a c t - Weasurements of double x-ray decay on s i n g l e - K - s h e l l - vacancy atoms of s i l v e r and xenon were made w i t h a p a i r of high- - p u r i t y germanium d e t e c t o r s and a t h r e e - p a r a m e t e r a n a l y z i n g system.
The r e s u l t s f o r t r a n s i t i o n s of e l e c t r o n s from t h e 2 s , 3 s , 3 d , and S s , d s h e l l s t o t h e 1s s t a t e a r e p r e s e n t e d .
1. I n t r o d u c t i o n
The o r i g i n a l t h e o r y ( 1 ) o f double-photon decay w a s i n t r o d u c e d t o e x p l a i n t h e decay of m e t a s t a b l e 2 s s t a t e i n hydrogen and hydrogen- l i k e s y s t e m s . E l a b o r a t e e x p e r i m e n t a l ( 2 ) and t h e o r e t i c a l ( 3 ) i n v e s t i - g a t i o n s have g r e a t l y advanced o u r u n d e r s t a n d i n g o f t h e double-photon decay o f t h e m e t a s t a b l e s t a t e s i n b o t h t h e hydrogen- and h e l i u m - l i k e s y s t e m s .
A c l o s e l y r e l a t e d p r o c e s s t o t h e double-photon decay i n hydrogen-like systems i s t h e double-photon decay of atoms having a s i n g l e vacancy i n t h e K s h e l l ( 4 ) . I n s t e a d o f a 2s e l e c t r o n i n t h e h y d r o g e n - l i k e systems (which makes t r a n s i t i o n t o t h e 1s s t a t e ) one h a s a vacancy i n t h e 1s s h e l l which makes t r a n s i t i o n t o t h e 2 s s t a t e (and h i g h e r f i l l e d e l e c t r o n s t a t e s i n t h e a t o m ) . I n b o t h c a s e s t h e e l e c t r i c d i p o l e - e l e c t r i c d i p o l e ( E l 51) t r a n s i t i o n s dominate, and t h e v i r t u a l i n t e r m e d i a t e s t a t e s a r e t h e complete s e t of bound and unbound up s t a t e s . The d i f f e r e n c e s a r e q u i t e pronounced: t h e i n n e r - s h e l l s i n g l e - vacancy s t a t e s a r e r a t h e r c o m p l i c a t e d many body s y s t e m s ; t h e y a r e n e v e r m e t a s t a b l e , b u t have v e r y s h o r t l i f e t i m e s ( b e c a u s e of t h e v e r y f a s t Ka and Kfi x-ray e m i s s i o n and Auger p r o c e s s e s ) ; double decay of t h e single-K-shell-vacancy s t a t e o c c u r s v i a t r a n s i t i o n s of e l e c t r o n s
("1n part supported by US NSF (project PN-734)
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19879102
JOURNAL DE PHYSIQUE
from many h i g h e r s h e l l s .
A r e l a t i v i s t i c t h e o r y of double-photon decay u s i n g t h e time-dependent second-order p e r t u r b a t i o n t h e o r y and D i r a c - H a r t r e e - S l a t e r wave
f u n c t i o n s h a s r e c e n t l y been developed by Xu &id C~asemann 5 They a p p l i e d i t t o c a l c u l a t e t h e n s + 1s and nd + I s , n = 2 , 3 and 4 , double-decay r a t e s i n xenon atoms. I n t h e c a l c u l a t i o n t h e y i n c l u d e d a l l i n t e r m e d i a t e e l e c t r o n s t a t e s , b o t h occupied and unoccupied. A g e n e r a l p r o o f o f t h e v a l i d i t y o f t h e assumption t h a t occupied e l e c t r o n s t a t e s have t o be i n c l u d e d h a s r e c e n t l y been made by D . Guo ( p r i v a t e communication).
Bannett and Freund ( 6 ) r e p o r t e d t h e r e s u l t s of t h e i r measurements o f double-photon decay i n molybdenum atoms. Here we p r e s e n t t h e r e s u l t s o f o u r measurements f o r double decay i n xenon atoms ( 7 ) and t h e new r e s u l t s from s i l v e r .
2 . Apparatus and measurements
Two s e r i e s o f measurements were made, one w i t h r a d i o a c t i v e 109-Cd s o u r c e s and t h e o t h e r w i t h r a d i o a c t i v e 131-Cs s o u r c e s . The s o u r c e s were used as g e n e r a t o r s of single-K-shell-vacancy atoms o f s i l v e r and xenon, r e s p e c t i v e l y . I n e a c h measurement a s o u r c e was c e n t e r e d i n a narrow d o u b l e - c o n i c a l h o l e i n t h e c e n t e r of a 50 mm diam. x 3 mm t h i c k
s h i e l d . The s h i e l d w i t h t h e s o u r c e was p l a c e d between two h i g h - p u r i t y germanium d e t e c t o r s i n a c l o s e 180' geometry. S o l i d a n g l e o f e a c h d e t e c t o r was about 1 . 5 s t e r a d i a n . The p u l s e s from t h e d e t e c t o r s were f e d i n t o a f a s t - s l o w c o i n c i d e n c e system, a m p l i f i e r s , and a 1 2 8 x 5 1 2 ~ 5 1 2 t h r e e - p a r a m e t e r p u l s e h e i g h t a n a l y z e r . The d a t a were r e c o r d e d , e v e n t by e v e n t , on punched paper t a p e . For each c o i n c i d e n c e e v e n t t h r e e channel numbers were r e c o r d e d : time d i f f e r e n c e between t h e p u l s e s i n t h e two d e t e c t o r s ( k o ) , a m p l i t u d e ( e n e r g y ) i n d e t e c t o r 1 ( k l ) , and amplitude ( e n e r g y ) i n d e t e c t o r 2 ( k 2 ) . The a n a l y s i s o f d a t a was made i n a U N I V A C 1110 computer and i n a p e r s o n a l computer. S i n c e t h e ana- l y s i s of a l l r e c o r d s o f d a t a h a s n o t been completed, t h e r e s u l t s p r e - s e n t e d h e r e a r e p r e l i m i n a r y .
3 . A n a l y s i s o f d a t a a n d r e s u l t s
The peaks due t o t h e c r o s s - t a l k between t h e two d e t e c t o r s v i a t h e germanium K a and K g x r a y s , and t h e p e a k s due t o a c c i d e n t a l c o i n c i - d e n c e s o f K a and K g x r a y s o f s i l v e r and xenon, r e s p e c t i v e l y , were t h e b a s i s of t h e energy c a l i b r a t i o n . Three energy c a l i b r a t i o n s were made:
energy i n d e t e c t o r 1 ( E l ) v s . k l , energy i n d e t e c t o r 2 ( E 2 ) v s . k 2 , and E1+E2 v s . kl+k2. The l a s t c a l i b r a t i o n was i m p o r t a n t because i t determined t h e sum-energy s c a l e and t h e sum-energy r e s o l u t i o n o f t h e system. Accurate sum-energy c a l i b r a t i o n i s r e q u i r e d because c o n t r i b u - t i o n s of c l o s e l y spaced peaks i n sum-energy s p e c t r a had t o be d e t e r - mined.
Time s p e c t r a f o r s e v e r a l r e g i o n s of t h e k -k2 p l a n e were c a r e f u l l y a n a l y z e d t o make a p r o p e r c h o i c e of t h e time i n t e r v a l s and t o d e t e r - 1 mine t h e e f f i c i e n c y o f t h e c o i n c i d e n c e . FWHM o f t h e time s p e c t r a w a s between 20 and 30 n s . From t h e c o i n c i d e n t d a t a i n -40 n s time s l i c e s
T a b l e 1 . R e l a t i v e d i f f e r e n t i a l p r o b a b i l i t i e s f o r d o u b l e x - r a y d e c a y i n s i l v e r a t o m s
1 d Wx x - 9 - 1 - 2
B = -— . „ ,n _,„ i n u n i t s o f 1 0 k e V s r x x WK d E . d f l ^ d f i p
2 s + I s
El 5 . 5 8 6 . 7 7 8 . 1 3 1 3 . 4 1 1 4 . 7 4 1 5 . 8 6
B
X X
3 . 1 4 ± 1 , 3 . 0 3 ± . 4 . 8 3 ± , 4 . 2 3 ± . 3 . 4 7 ± .
2 . 9 8 ± 1 . 2 1 . 7 8 . 7 1 . 7 0 . 7 6 . 2 7
3 s + I s
El 6 . 4 2 7 . 6 1 8 . 7 6 1 6 . 1 8 1 7 . 3 4 1 8 . 4 9
B
X X
. 0 9 ± 1 . - . 5 8 ± . 2 . 1 6 ± 2 . 0 0 + . - . 6 6 ± , - . 7 4 ± 1
. 0 8 . 8 8 . 8 2 . 8 1 . 8 6 . 1 9
3 d + I s
El 6 . 5 9 7 . 7 5 8 . 9 0 1 6 . 3 5 1 7 . 4 7 1 8 . 7 0
B
X X
6 . 2 6 + . 7 9 4 . 3 7 + . 6 6 3 . 7 7 ± . 6 4 5 . 9 7 ± . 6 4 5 . 7 8 ± . 6 6
• 7 . 8 3 ± . 8 1
4 s , d -»• I s
El 6 . 7 7 7 . 8 9 9 . 0 9 1 6 . 5 1 1 7 . 6 7 1 8 . 8 3
B
X X
. 0 9 ± . 7 3 . 6 7 + . 6 8 . 2 5 ± . 6 6 . 0 4 ± . 6 6 . 0 1 ± . 6 6 . 0 2 ± . 7 1
T a b l e 2 . R e l a t i v e d i f f e r e n t i a l p r o b a b i l i t i e s f o r d o u b l e x - r a y d e c a y i n x e n o n a t o m s
1 x x —9 —1 - 2 dW
B = — —————— i n u n i t s o f 1 0 k e V s r x x W„ d E , d ( l , d S „
K 1 1 2
2 s +' I s
El
1 2 . 0 6 1 3 . 1 1 1 4 . 1 6 1 4 . 5 6 1 4 . 8 7 1 5 . 9 2 1 6 . 9 7
B xx
1 . 9 4 ± . 6 4 2 . 6 6 ± . 6 3 2 . 5 7 ± . 6 6 3 . 0 3 ± . 6 6 3 . 3 6 ± . 6 6 3 . 1 3 ± . 6 1 2 . 4 9 + . 6 7
3 s + I s
El 8 . 8 0 1 1 . 8 5 1 2 . 7 6 1 3 . 6 7 1 4 . 5 9 1 5 . 5 0 1 6 . 4 1 1 6 . 7 1 1 6 . 8 6 1 7 . 7 7 1 8 . 6 8 1 9 . 5 9 2 0 . 5 0 2 1 . 4 1 2 4 . 6 3
B xx
. 7 5 ± . 4 0 . 4 4 ± . 3 8 1 . 3 6 + . 5 5 2 . 2 5 ± . 6 1 . 4 1 ± . 5 3 . 2 5 ± . 3 9 . 7 2 ± . 4 9 . 5 5 ± . 4 3 . 6 6 + . 4 3 . 9 2 ± . 4 8 . 6 7 ± . 5 2 1 . 4 2 ± . 6 2 - . 2 7 ± . 3 5 . 7 7 ± . 4 1 . 1 6 ± . 3 2
3 d - I s
El 1 1 . 8 5 1 1 . 8 5 1 2 . 7 6 1 3 . 6 7 1 4 . 5 9 1 5 . 5 0 1 6 . 4 1 1 6 . 9 4 1 7 . 3 2 1 8 . 2 3 1 9 . 1 4 2 0 . 0 5 2 0 . 9 6 2 1 . 8 7 2 5 . 0 8
B
X X
5 . 0 8 ± . 6 9 5 . 1 5 ± . 8 0 3 . 8 5 ± . 8 4 6 . 1 8 ± . 9 0 6 . 2 8 ± . 8 5 6 . 5 0 ± . 8 5 3 . 9 3 ± . 7 2 4 . 3 1 ± . 7 5 3 . 7 4 + . 7 3 4 . 4 2 ± . 8 1 5 . 0 2 ± . 8 2 7 . 7 4 ± 1 . 0 0 5 . 2 3 ± . 8 0 4 . 9 1 ± . 7 8 3 . 0 1 ± . 5 7
4 s , d ->• I s
El 8 . 8 0 1 1 . 8 5 1 2 . 7 6 1 3 . 6 7 1 4 . 5 9 1 5 . 5 0 1 6 . 4 1 1 7 . 2 5 1 7 . 9 4 1 8 . 8 5 1 9 . 7 6 2 0 . 6 7 2 1 . 5 8 2 2 . 4 9 2 5 . 0 7
B
X X
. 8 6 ± . 3 3 1 . 5 6 ± . 5 7 1 . 6 5 ± . 5 6 1 . 1 3 ± . 4 7 2 . 2 3 ± . 5 9 1 . 0 9 ± . 4 9 1 . 1 3 + - . 4 3 . 6 9 ± . 4 4 . 9 2 ± . 4 5 1 . 4 7 ± . 5 3 2 . 4 5 ± . 6 0 . 5 4 ± . 4 3 . 7 1 ± . 4 2 . 9 1 ± . 4 2 . 8 3 ± . 3 6
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two-dimensional t a b l e s of numbers o f e v e n t s v s . k l and k 2 were made.
I n t h e t a b l e s o b t a i n e d i n t h e measurement w i t h 131-Cs two d i s t i n c t l i n e s a t c o n s t a n t sum e n e r g i e s were found. The measurement w i t h 109-Cd y i e l d e d one d i s t i n c t l i n e , w h i l e t h e o t h e r i s p a r t i a l l y masked by t h e peaks due t o t h e c r o s s - t a l k v i a germanium K a and KB x r a y s . Of c o u r s e , c o n t i n u o u s l i n e s i n o u r t a b l e s c o u l d have been due t o t h e c r o s s - t a l k between t h e d e t e c t o r s . A K a o r KB x r a y o f s i l v e r ( o r xenon) c o u l d e j e c t a K e l e c t r o n i n one germanium d e t e c t o r , and b r e m s s t r a h l u n g o f t h e e l e c t r o n c o u l d e s c a p e and be absorbed i n t h e o t h e r d e t e c t o r . Other p r o c e s s e s were a l s o c o n s i d e r e d : atomic c a s c a d e t r a n s i t i o n s , and Compton s c a t t e r i n g . A l l t h e s e p r o c e s s e s would y i e l d e i t h e r peaks a t t h e sum energy e q u a l t o t h e energy of K a o r KB x r a y s , o r continuum d i s t r i - b u t i o n s i n t h e sum-energy spectrum. The b a s i s f o r t h e i d e n t i f i c a t i o n o f t h e d a t a i n t h e observed l i n e s a t c o n s t a n t sum e n e r g y a s due t o t h e double x-ray decay a r e t h e e n e r g y s h i f t s . E.g. t h e l i n e a t lower sum energy i s c o n s i d e r e d t o be due t o t h e 2 s + Is double-photon decay because i t i s s h i f t e d w i t h r e g a r d t o t h e c r o s s - t a l k peaks a t sum-energy e q u a l t o t h e energy o f K a x r a y s e q u a l t o t h e d i f f e r e n c e o f t h e b i n d i n g energy o f t h e 2 s and 2p s t a t e s .
S e c t i o n s o f t h e c o n t i n u o u s d i s t r i b u t i o n s were summed a l o n g t h e c o n s t a n t sum-energy y i e l d i n g sum-energy s p e c t r a f o r t h e s e c t i o n s . The sum-energy s p e c t r a were a n a l y z e d by v a r i o u s curve f i t t i n g r o u t i n e s t o determine t h e c o n t r i b u t i o n s o f t h e 2 s + I s , 2p112 + l s , 2 ~ 3 . 2 + I s , 3s' I s , 3p112 + I s , 3p1,2 + I s , 3d + I s , and 4 s , d + 1s components. For 2p + I s and 3p -* 1s double x r a y t r a n s i t i o n s ' ( a n d c r o s s - t a l k ) o n l y upper l i m i t s were determined.
The r e s u l t s f o r s i l v e r atoms a r e shown i n Table 1 , and t h e r e s u l t s f o r xenon atoms i n Table 2. A comparison of t h e d a t a f o r xenon t o t h e c a l c u l a t e d r e s u l t s o f Mu and Crasemann ( 5 ) h a s shown an agreement i n t h e c e n t r a l energy r e g i o n f o r 3 s + I s , 3d + I s , and 4 s , d + 1s t r a n - s i t i o n s , b u t t h e t h e o r e t i c a l r e s u l t s f o r t h e 2 s + 1s a r e by a f a c t o r about 3 l a r g e r .
Acknowledgement - I t i s a p l e a s u r e t o thank P r o f . B . Crasemann f o r t h e encouragement and h e l p i n o u r i n v e s t i g a t i o n s , and t o M r . X. Mu f o r s e n d i n g u s new r e s u l t s of t h e c a l c u l a t i o n s p r i o r t o p u b l i c a t i o n .
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