SHARING OF THE ALIGNMENT IN DOUBLY IONIZED HEAVY ATOMS

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SHARING OF THE ALIGNMENT IN DOUBLY IONIZED HEAVY ATOMS

T. Papp, L. Kocbach

To cite this version:

T. Papp, L. Kocbach. SHARING OF THE ALIGNMENT IN DOUBLY IONIZED HEAVY ATOMS.

Journal de Physique Colloques, 1987, 48 (C9), pp.C9-243-C9-246. �10.1051/jphyscol:1987940�. �jpa-

00227358�

JOURNAL DE PHYSIQUE

Colloque C 9 , suppl6ment au n012, Tome 48, decembre 1987

SHARING OF THE ALIGNMENT IN DOUBLY IONIZED HEAVY ATOMS

T. PAPP and L. KOCBACH

I n s t i t u t e of Nuclear Research of the Hungarian Academy of Sciences (ATOMKI), Pf. 5 1 , H-4001 Debrecen, Hungary and Department of Physics, U n i v e r s i t y of Bergen, N-5000 Bergen-U, Norway

A b s t r a c t : Angular d i s t r i b u t i o n of L3 x-ray lines was calculated f o r doubly ionised atoms (L3, M ) i n t h e framework of semiclassical approximation. Hydrogen-like wavefunctions, s t r a i g h t l i n e projectile p a t h and independent electron p i c t u r e were assumed f o r t h e description of t h e i o n i s a t i o n process. From t h e calculation it was concluded, t h a t t h e alignment t r a n s f e r a n d t h e dealignment modifies significantly t h e L3 subshell alignment.

In t h e l a s t y e a r s t h e L3-subshell alignment s t u d i e s i n heavy element were extended f o r heavy projectiles (111, [2]). In t h e s e measurements t h e diagram and s a t e l l i t e lines were not resolved, and t h e obtained anisotropy parameters of t h e x-ray t r a n s i t i o n s

c h a r a c t e r i s e t h e alignment of t h e multiply ionised atoms. In t h e multiply ionised atoms before t h e x-ray t r a n s i t i o n s dif f Went

processes may take place, which s h a r e on t h e alignment. The Auger and Coster-Kronig processes can c a r r y o u t p a r t of t h e anisotropy of t h e ionised atomic ensemble, and t h e y can modify t h e vacancy

d i s t r i b u t i o n s . The holes i n t e r a c t t h r o u g h t h e Coulomb field, and (as i n t h e p e r t u r b e d angular correlation) t h e alignment can be t r a n s f e r r e d between t h e d i f f e r e n t subshells. T h i s i n t e r a c t i o n i s large between t h e L 3 and M subshells, while it i s small between t h e L3 and N subshells ( t h e only exception i s t h e N3 subshell). To get b e t t e r understanding of t h l s processes, a s a f i r s t step, we studied t h e alignment of t h e doubly ionised atoms.

T O see t h e importance of t h e double ionisation,at f i r s t t h e doulsle i o n i s a t i o n cross sections were calculated i n t h e following way:

t h e i o n i s a t i o n p r o b a b i l i t i e s a s functions of t h e impact parameter were calculated i n t h e semiclassical approximation (SCA) [3] f o r t h e L and M subshells, and t h e product of them f o r t h e L3 and t h e d i f f e r e n t M-s were i n t e g r a t e d over t h e impact parameter. Here and i n t h e

followings s t r a i g h t l i n e projectile p a t h was used i n t h e SCA

calculations, and t h e v a l i d i t y of t h e independent electron p i c t u r e was assumed. In t h i s calculation t h e (i-i/n)n-i t y p e f a c t o r s (where n i s t h e number of t h e electrons on t h e regarded subshell) were neglected

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987940

C9-244 JOURNAL DE PHYSIQUE

(Papp e t a l . 1987, t o be published i n J. Phys. B.: A t . Mol. Phys.). The r a t i o of t h e double i o n i s a t i o n cross sections to t h e L3 subshell

i o n i s a t i o n cross section a r e proportional t o Zi (ZI denotes t h e atomic number of t h e projectile). A s a t y p i c a l example, t h e r e s u l t s of our calculation a r e shown i n fig. 1 f o r uranium t a r g e t . The double i o n i s a t i o n cross section can r e a c h r e l a t i v e l y large value w i t h i n c r e a s i n g Z l .

I I 1 1 1 1 1 1 1 I 1 1 , 1 1 1 1

1 10

p r o j e c t i l e energy (MeVla. m. u.)

Figure I. Double L3Mi ( i = l , E , . . . , 5 ) t o s i n g l e L3-subshell i o n i s a t i o n c r o s s s e c t i o n r a t i o s f o r uranium bombarded by l i g h t i o n s a s a f u n c t i o n of

-

...

^{- .---}

, . - ^. - .

- -

Since t h e f i n e s t r u c t u r e i n t e r a c t i o n energies [6] between t h e L3 and M subshell holes a r e comparable w i t h t h e widths of t h e double ionised s t a t e s 15'61, t h i s i n t e r a c t i o n can modify t h e alignment of t h e L3 subshell and t h e angular d i s t r i b u t i o n of t h e L3 x-ray lines. The a n g u l a r d i s t r i b u t i o n of t h e L3 x-ray lines of doubly ionised atoms w i t h a n aligned M vacancy can be described by t h e well-known perturbed a n g u l a r c o r r e l a t i o n method [TI. In t h i s method t h e ionised atomic ensemble i s characterised by t h e density matrix. In t h e independent electron p i c t u r e t h e elements of t h e density matrices of doubly

ionlsed atoms a r e t h e products of t h e scattering amplitudes of t h e two holes. In t h e p r e s e n t work t h e s c a t t e r i n g amplitudes were calculated f o r t h e L3 and M subshell a s a function of t h e impact parameter i n SCA, and t h e density matrix elements created from t h e amplitudes were i n t e g r a t e d over t h e impact parameter. For calculation of t h e angular d i s t r i b u t i o n we used t h e f i n e s t r u c t u r e energy s p l i t t i n g value of P a r e n t e a t a1 141.

The L3 x-ray angular d i s t r i b u t i o n of singly and doubly ionised atomic ensemble can be w r i t t e n a s

wnere t h e !3 a n i s o t r o p y parameter i s

Here I denotes t h e r a t i o of t h e double ionisation cross section to t h e L3 subshell i o n i s a t i o n . A ( ~ ) and A(?) a r e t h e L3-subshell alignment parameter of t h e singly and doubly ionised atoms. The A2 alignment parameter c h a r a c t e r i s e t h e atomic ensemble before t h e x-ray

t r a n s i t i o n , and contains t h e e f f e c t of t h e i n t e r a c t i o n between t h e holes, and it i s not determined completely by t h e ionisation

processes. For t h e s u p e r Coster-Kronig t r a n s i t i o n p r o b a b i l i t i e s i n t h e M-shell we used t h e value of reference 163, and assumed t h a t these t r a n s i t i o n s do not depend on t h e magnetic quantum number of t h e holes.

/ ---single ionir. SCA

/

-

#/'

double ioniz. SCA

Flgure 2. L i g h t Ion induced a n i s o t r o p y parameter ( B ) of Au. Curves show SCA r e s u l t s f o r N impact, assuming:

-- -

-

.

There exist experimental d a t a only f o r C and 0 ion impact on gold [i] i n broad range of impact energy. For t h i s reason we present t h e r e s u l t of o u r calculation f o r N ion impact on gold, since the

calculated alignment parameter h a s only small differences when Zi i s changed by one. Our calculation slluws (fig. 2), t h a t t h e anisotropy parameter of t h e emitted x-rays of t h e singly and doubly ionised atoms d i f f e r s s i g n i f i c a n t l y from t h e singly ionised one, and t h e angular d i s t r i b u t i o n of t h e s a t e l l i t e lines a r e q u i t e d i f f e r e n t from t h e diagram line. I t can be seen from fig. 2, t h a t t h e second hole

produces not only dealignment, b u t it produces alignment t r a n s f e r too.

T h i s calculation shows t h e importance of t h e double ionisation i n t h e LJ Subshell alignment studies. We remarlt t h a t t h e validity of o u r r e s u l t s i s limited by t h e used simple wavefunctions. Using more r e f i n e d wavef unctions, and performing calculations w i t h inclusion of h i g h e r - o r d e r terms of t h e Born s e r i e s C83, theoretical d a t a i n b e t t e r agreement w i t h t h e experimental ones can be obtained.

Acltnowledgement.

One of t h e a u t h o r s (T.P.) wishes t o express h i s t h a n k s f o r t h e h o s p i t a l i t y a t t h e Dept. of Physics, University of Bergen, where t h e calculations were c a r r i e d out.

JOURNAL DE PHYSIQUE

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