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MULTIPLET EFFECTS ON K FLUORESCENCE YIELDS OF MULTIPLY-CHARGED IONS
F. Combet Farnoux
To cite this version:
F. Combet Farnoux. MULTIPLET EFFECTS ON K FLUORESCENCE YIELDS OF MULTIPLY-CHARGED IONS. Journal de Physique Colloques, 1987, 48 (C9), pp.C9-199-C9-202.
�10.1051/jphyscol:1987929�. �jpa-00227347�
Colloque C9, supplément au n°12. Tome 48, décembre 1987 C9-199
MULTIPLET EFFECTS ON K FLUORESCENCE YIELDS OF MULTIPLY-CHARGED IONS
F. COMBET FARNOUX
Laboratoire de Photophysique Moléculaire du CNRS, Bât. 213, Université Paris-Sud, F-91405 Orsay Cedex, France
jlésumé - Ce t r a v a i l présente des r é s u l t a t s originaux obtenus à p a r t i r de deux modèles théoriques d i f f é r e n t s pour l e s p r o b a b i l i t é s de t r a n s i t i o n X e t Auger a i n s i que l e s rendements de fluorescence K de c e r t a i n s ions multichargés d'alumi- nium (Z = 13) . L'étude e t l a comparaison de ces d i f f é r e n t s r é s u l t a t s permet- t e n t de mettre en évidence que non seulement l e rendement de fluorescence mais aussi l ' i n f l u e n c e des é t a t s m u l t i p l e t s i n i t i a u x pour l e s configurations
(1s)(2s)^(2p)n croissent avec l e degré d ' i o n i s a t i o n .
Abstract-This work r e p o r t s o r i g i n a l r e s u l t s using two d i f f e r e n t t h e o r e t i c a l models t o c a l c u l a t e the X-ray and Auger t r a n s i t i o n p r o b a b i l i t i e s as well as the K f l u o - rescence y i e l d s for some multiply-charged ions of aluminium (Z = 13). The
study and comparison between these various r e s u l t s allow us to point out t h a t not only the fluorescence y i e l d but also the influence of t h e i n i t i a l m u l t i p l e t s t a t e s within the (1s) (2s)^(2p)n configurations i n c r e a s e s with t h e i o n i s a t i o n degree.
Experimental measurements of X-ray production cross sections i n ion-atom c o l l i s i o n s allow t o obtain the i o n i s a t i o n cross sections for a specific configuration, provided t h e fluorescence y i e l d i s Hcnown, In heavy ion-atom c o l l i s i o n s , single K and multiple L-shell vacancies a r e produced for bombarding energies > 1 MeV/amu. Vacan- c i e s i n a multiply-ionised atom couple to form a m u l t i p l e t s t r u c t u r e t h a t strongly influences t h e decay p r o p e r t i e s of the system. For an atom which contains an i n n e r - s h e l l hole and a p a r t i a l l y f i l l e d s h e l l , i t has already been shown (1) t h a t the Auger and X-ray t r a n s i t i o n p r o b a b i l i t i e s t o the inner l e v e l , and hence t h e fluorescence y i e l d of the excited s t a t e can d i f f e r by many orders of magnitude among various m u l t i - p l e t s t a t e s of a given i n i t i a l hole configuration. For multiply-ionised atoms, i n absence of simultaneous high r e s o l u t i o n measurements of X-ray and Auger spectra l i k e l y t o y i e l d d e t a i l e d evidence on the p r o p e r t i e s of individual m u l t i p l e t s t a t e s , t h e o r e t i - cal c a l c u l a t i o n s are strongly needed i n both c o l l i s i o n and plasma p h y s i c s , as well as i n a s t r o p h y s i c s . Up to now, only ions of neon ( 2 ) , argon (3) ,and some i s o e l e c t r o n i c s e r i e s (4-) have been studied extensively.
My previous work (5) concerning multiionised configurations of Ne, Al, Si and 01 had pointed out t h a t : 1°) The K fluorescence y i e l d s are found increasing with the i o n i s a t i o n degree, but s t r i p p i n g of outer s h e l l s has a smaller e f f e c t than creating an empty inner subshell of spectator e l e c t r o n s ,
2°) While multiple 2p vacancies a l t e r t h e K fluorescence y i e l d OJ only s l i g h t l y as long as two 2s e l e c t r o n s are p r e s e n t , W K may be up to four times g r e a t e r i f one or two vacancies are simultaneously created i n the 2s sub- s h e l l . Whereas t h i s f i r s t study used e s s e n t i a l l y a c e n t r a l p o t e n t i a l model (model I introducing t h e Herman and Skillman (6) p o t e n t i a l ) , these f i r s t r e s u l t s had to be checked using another model taking i n t o account t h e various m u l t i p l e t e f f e c t s r e a l i s - t i c a l l y (model I I ) i n order t o point out how the value averaged over a l l the i n i t i a l and f i n a l s t a t e s i s a l t e r e d when each m u l t i p l e t i s introduced with i t s s t a t i s t i c a l weight.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987929
C9-200 JOURNAL DE PHYSIQUE
In order t o point o u t quantitatively t h e importance of multiplet e f f e c t s in t h e
determination of U K for~mme_aluminium i o n s (within t h e configurations (1s) ( 2 ~ ) ~ ( 2 ~ ) ~ ) I have determined both Auger anaaX-ray t r a n s i t i o n p r o b a b i l i t i e s f o r each multiplet LS
of t h e configuration n, using t h e following d e f i n i t i o n s and approximations:
rR
(LS,n)W K ( ~ s , n ) = (1
rR(Ls,n)
+
rA(Ls,n)being t h e r a d i a t i v e width and
rA
t h e Auger width of t h e decaying multiplet state.The e f f e c t i v e fluorescence y i e l d of a given configuration n i s written :
when assuming t h a t t h e various LS initial multiplet s t a t e s a r e s t a t i s t i c a l l y populated.
I n t h e present work both ( 1 ) and (2) have been used within model 11, with the purpose of comparing
w
K(nf with the averaged W K determined within model I, according t o the following formula :(3) where TA i s t h e Auger decay r a t e and T the r a d i a t i v e decay r a t e ; T i s a summation over all p a r t i a l non r a d i a t i v e decay rages
rA,
eachr
c o r r e s p o n d g to a t r a n s i t i o n involving two electrons n l l l and n 1 The l s vacancy 4s f i l l e d and one electron i s ejected to the continuum E 1, viz %s transition:_,
with ~ = < ~ ( 1 s ~ ~ 1 ~ ) \ 1 / r ~ ~ \ ~ ( n ~ 1 ~ ~ n ~ ) > (5) The antisymetrised wave functions
@
a s well a s the c o e f f i c i e n t s N depend on t h e type of coupling introduced i n t h e model; in G S coupling, t h e m a t r i i element Mcan be written i n terms of angular c o e f f i c i e n t s xpressed with 3 j and 6 j symbols and r a d i a l i n t e g r a l s
%,
t h e generalised S l a t e r d g r a l s defined a s follows:The determination of TX
,
t h e total decay r a t e corresponding t o t h e f i l l i n g of an 1 s vacancy i s obtained in model I by summing a l l p a r t i a l X decay r a t e s over all indi- vidual t r a n s i t i o n s , each one being represented i n dipolar approximation by :4
E i s t h e X t r a n s i t i o n energy, t h e index f representing t h e n$f o r b i t a l of t h e electron which f i l l s t h e 1 s vacancy.
The l a t t e r formula means t h a t only the average value of t h e t r a n s i t i o n i s considered, without taking i n t o account t h e multiplet stru- cture and t h a t t h e c o e f f i c i e n t s of t h e r a d i a l i n t e g r a l s have to be modified within t h e f?XUIe~rk of model I1 when determining bothrA
andrX
f o r individual multiplet s t a t e s.
I have determined t h e corresponding coefficients v i a t h e general formulas previously published by Mc Guire (7) but a l l r a d i a l i n t e g r a l s (both dipolar and gene- r a l i s e d S l a t e r i n t e g r a l s ) introduced in both models I and I1 have been calculated with t h e Herman and Skillman (6) wave functions corresponding to t h e average configuration of t h e i n i t i a l ion ( L e e involving an I s vacancy).
This approximation i s consistent with my choice of average Auger and X-ray energies f o r all multiplet t r a n s i t i o n -rate calculations, this choice neglecting &e multiplet energy s p l i t t i n g whose influence i s weak when both Auger and X-ray energies are g r e a t e r than 1 keV.My r e s u l t s obtained with model I a r e presented in Table 1 f o r aluminium i o n s c01- responding to various configurations which d i f f e r , e i t h e r by t h e successive stripping of t h e outer subshell, o r by production of an e x t r a h e r vacancy in presence of one o r several o t h e r inner holes.
Aluminium C o n f i g u r a t i o n - 1s2s22pb3s23p 1s2s22p63s2
1s2s22p63s 1s2s22p6
1s2s22p5
1s2s22p4' 1s2s22p3
1s2s 2p 2 2 1s2s22p 1s2s22p53s23p 1 s2s22p43s23p 1s2s22p33s23p 1s2s22p23s23p 1s2s22p 3s23p 1a2s2p63s23p 1s2s2p53s23p 1s2s2p43s23p 1s2s2p33s23p 1s2s2p23s23p 1 s2s2p 3s23p 1s2p63s23p 1s2pSs23p 1s2p 3s23p
Ex(eV) 2p - > 1 s 1558.08 1558.6 1559.2 1560.4 1572.2 1585.8 1601.0 1618.0 1636.8 1569.0 1581.48 1595.6 1611.4.
1629.0 1565.9 1578.01 1591.8 1607.4 1624.6 1643.98 1574.6 1603.2 1661.0
Ex(eV) 3 p - ^ l s 1682.34
1693.8 1727.6 1763.6 1801.8 1841.96 1688.8 1721.9 1757.2 1794.8 1834.4 1876.1 1716.3 1787.8 1911.2
T o t a l Rate Auger 14.4262 14.3074 14.3058 13.9345 11.6625 9.2392 6.8012 4.5737 2.8523 12.3638 10.1269 7.8714 5.7594 4.0580 12.575 10.1045
7.5349 5.0532 2.9021 1.3452 11.100
6.6687 0.5526
( l O ^ A w u . ) X 0.6749 0.6702 0.6737 0.6755 0.6092 0.5264 0.4254 0.3048 0.1632 0.6113 0.5326 0.4373 0.3236 0.1900 0.7208 0.6534 O.5684 O.4668 0.3459 0.2042 0.654 0.6058 0.2194
Averaged
^ K 0.044 0.0447 0.045 0.046 * 0.0496 * 0.0539 * 0.0589 * 0 . 0 6 2 5 * 0.0541 * 0.0471 0.0499 0.0526 0.0532 0.0447 0.0542 0.0606 0.0701 0.0845 0.1065 0.1318 0.056 0.0833 0.2842 Table 1 - Energies (in eV) of X-ray t r a n s i t i o n s f i l l i n g the 1s vacancy for i n i t i a l 1s2s22pn3sm3pu ,1s2s22pn3s23p, 1s2s2pn3s 3p and 1s2p 3 s 3p configurations of ionised Al, Total Auger and X-ray r a t e s (in m u l t i p l e s of 10"** a«u.) and averaged fluorescence y i e l d W calculated within model I .
I t i s remarkable to n o t i c e i n Table 1 t h a t for a l l groups of configurations, CO increases with t h e i o n i s a t i o n degree up t o the configuration which keeps only one e l e c t r o n on t h e 2p s u b s h e l l . Both 2p—^1s and 3 p ^ 1 s t r a n s i t i o n energies increase as much r a p i d l y as the stripped subshell i s more i n n e r , whereas both Auger and X-ray t o t a l r a t e s are decreasing . I n Table 1 , 6 values of CJ„ are reported with an a s t e - r i s k which means t h a t these values can be compared with the effective configuration fluorescence y i e l d s t0 (n) reported next page i n Table 2 and determined i n t h e present work, within the framework of model I I which takes i n t o account t h e m u l t i p l e t e f f e c t s , as explained i n t h e previous page. I t i s important t o remark t h a t t h i s comparison allows us t o point out a discrepancy between the r e s u l t s of both t a b l e s which increases with t h e i o n i s a t i o n degree. In other words, taking i n t o account the m u l t i p l e t e f f e c t s i n a determination of t h e K fluorescence y i e l d of multiionised atoms i s e s s e n t i a l as soon a s the atom has l o s t more than 3 e l e c t r o n s . Moreover, i n case of i n i t i a l m u l t i - p l e t s for which Auger or X-ray decay channels are closed i n LS coupling, t h e i n i t i a l s t a t e s should be expressed i n intermediate coupling.
C9-202 30URNAL DE PHYSIQUE
Multiplet n
6 5
4
3
2
1
2S
1P 3p .
2S 2p , 4p . 2D .
3
s -
5
s •
1P
h
1D -
3D "
2S 2p .
^P
2D
1P 3p .
Auger transition probability K-L1L1 K - L ^ ^ K-L2 3L2 3
11.110 2.265 2.265 13.671 3.671 3.671 3.671 5.112 5.112 15.112 5.112 5.112 5.112 6.536 6.536 6.536 [6.536 7.980 7.980
36.750 28.24.2 37.6^6 32.114 21.4245 37.4645 32.114 12.096 36.162 18.114 30.1445 18.114.
30.1445 20.305
6.818 27.039 20.305 0.0699 14.878
91.484 73.278 73.278 52.5055 43.2795 43.2795 67.36
0.
0.
30.574 30.574 41.853 41.853 12.6275
0.
0.
31.5695
— — —
Total 139.344-7 113.785 123.1895
98.2905 78.3752 94.4152 113.14.5
27.208 51.274 63.8 75.8305 75.079 87.1095 49.4685 23.354 43.575 68.4105 18.0499 32.858
X-ray transition probability
6.755 10.08
5.04 5.641 11.282 2.8215 5.641 12.527
0.
9.394 3.133 9.394 3.133 3.465 10.395
0.
3.4-65 7.370 0.
<*>K(LS,n)
0.0462 0.0814 0.0393 0.0543 0.1258 0.0290 0.04.75 0.3152 0.
0.1283 0.0397 0.1112 0.0347 0.0654 0.308 0.
0.0482 0.2899 0.
c^W
0.0462 0.0498
0.0562
0.0691
0.0820
0.0724
Table 2 - Auger and X-ray t r a n s i t i o n p r o b a b i l i t i e s (in m u l t i p l e s of 10"^a.u.) to the K s h e l l for i n i t i a l (1s) ( 2 s )2( 2 p )n configurations of ionised Al, m u l t i p l e t fluorescen-
ce y i e l d s CJ (LS,n) and effective configuration fluorescence y i e l d s O (n) calculated for s t a t i s t i c a l population, using model I I .
(1) Mc.GUIRE,E.J., Phys.Rev.A 10 (1974) 32
(2) BHALLA,C.P.,F0LLAND, N.0. and HEIN, M.A. Phys.Rev.A 8 (1973) 64.9
CHEN, M.H., CRASEMANN, B. and MATTHEWS, D.L. Phys.Rev.Lett. 34 (1975) 1309 (3) BHALLA, C.P. Phys.Rev. A 8 (1973) 2877
(4) CHEN ,M.H. , CRASEMANN, B., KARIS ,Kh.R. and MARK , H. Phys.Rev.A24 (1981) 1852 (5) COMBET FARNOUX ,F. in " Electronic and Atomic Collisions " Abstracts of the 14th
I.C.P.E.A.C, 1985 , Palo Alto ,California (USA) p.546
(6) HERMAN ,F. and SKILLMAN ,S. "Atomic Structure Calculations" (Prentice Hall, Englevood Cliffs, N . J. , 1963)
(7) Mc.GUIRE ,E.J. , in Atomic Inner-Shell Processes, Bernd Crasemann Editor , (Academic Press, New York, 1975 ) Vol.1 , p.293
