Theoretical Simulation of Beam Foil Decay Curves for Resonance Transitions of Heavy Ions

--We have made a t h e o r e t i c a l study o f the in f luence o f cascades on heavy i o n beamf o i l l i f e t i m e s , concentrat ing on the resonance l i n e o f Kr V I I I . Using t h e o r e t i c a l data f o r the l i f e t i m e s and i n i t i a l populat ions o f exc i ted s tates, we have constructed decay curves s imu la t ing beam f o i l e x c i t a t i o n condi t ions . The t h e o r e t i c a l decay curve producing the best f i t w i t h experimental decays y i e l d e d the same l i f e t i m e as the experfments when subjected t o the same cascade analys is , bu t customary exponential f i t t i n g techniques were n o t ab le t o e x t r a c t the t h e o r e t i c a l pr imary l i f e t i m e a c t u a l l y used i n i t s const ruct ion. 1. In t roduct ion. -At the l a s t i n t e r n a t i o n a l Table I. Experimental, s imulated and t h e o r e t i c a l beam-foil conference, we discussed the o s c i l l a t o r l i f e t i m e s ( i n ns) f o r the 4p l e v e l o f Kr V I I I s t rengths o f resonance t r a n s i t i o n s i n some heavy Beam f o i 1 experiments Theory Simulat ion ions t h a t are o f specia l importance t o magnetic 0 .36~ , 0.39 5 0.26' 0.35' fus ion research [I]. A l a r g e discrepancy between 0 . 3 5 ~ . 0.35'~ 0.36 8 t h e o r e t i c a l and beam-foil data was found f o r the 0 . 2 5 ~ 4s-4p t r a n s i t i o n i n the Cul ike ions which re mained approximately constant along the sequence. On the basis o f the in fo rmat ion a v a i l a b l e a t t h a t time, we concluded t h a t i t was probably due main ly t o the neglect o f core p o l a r i z a t i o n e f f e c t s i n the ca lcu la t ions . I n the meantime, advanced ca lcu la t ions f o r the Cu sequence us ing the m u l t i c o n f i g u r a t i o n Hartree-Fock method 121 and many-body per tu rba t ion theory [3] have y ie lded i d e n t i c a l f-values which a re s t i l l 20-30% above those der ived from beamf o i l data. There can be l i t t l e doubt now t h a t these advanced t h e o r e t i c a l r e s u l t s f o r comparat i v e l y simple atomic systems are c lose t o the t r u e numbers. The puzzle remains, however, as t o why t h e beam-foil data should be so d i f f e r e n t . 1 Measurement e r ro rs appear t o be excluded since, as Table I shows, the f i v e experimental r e s u l t s 14-83 agree very c lose ly . Cascade ana lys is o f t h e experimental decay curves seemed t o i n d i c a t e on ly t h s presence o f a second l o n g l i v e d exponential . Nevertheless, i n order t o ga in a b e t t e r understandi n g o f cascade e f f e c t s we decided t o undertake a comprehensl/ve analys is o f them by way o f a theor e t i c a l s imu la t ion o f beam-foil decay curves [9]. 2. S imulat ion of Beam-Foil Decay Curves.-To perform a beam-foi l s imu la t ion one must have a v a i l a b l e the re levan t t h e o r e t i c a l t r a n s i t i o n p r o b a b i l i t i e s o r l i f e t i m e s , as we l l as t h e r e l a t i v e i n i t i a l populat ions o f the cascade s ta tes w i t h respect t o the pr imary l e v e l [ lo] . A. T r a n s i t i o n p r o b a b i l i t i e s . Our s imu la t ion s tud ies have shown t h a t the most c r i t i c a l p iece of data i s an accurate l i f e t i m e f o r the pr imary l e v e l . For the cascading t r a n s i t i o n s , l i f e t i m e s obtained from approximate t h e o r e t i c a l methods, such as the Coulomb approximation, appear t o be s a t i s f a c t o r y . B. I n i t i a l populat ions. De ta i led in fo rmat ion concerning the i n i t i a l d i s t r i b u t i o n o f exc i ted s ta tes a f t e r f o i l e x c i t a t i o n i s very sketchy. This i s espec ia l l y so f o r heavy ions which may show l e v e l d i s t r i b u t i o n s q u i t e d i f f e r e n t from l i g h t ions [9]. Considering t h i s r a t h e r unsa t i s fac to ry s t a t e o f a f f a i r s , we have based our s imu la t ion study n o t on uncer ta in assumptions about the populat ions, bu t instead on comparisons w i t h actual decay curves. A number o f r e l a t i v e l y simp1 e populat ion models were se lected and tes ted by f i t t i n g the r e s u l t a n t decay curves t o an actual beam-foil decay curve f o r the 4s-4p m u l t i p l e t o f Kr V I I I . One o f these populat ion Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979125 models achieved a very c lose fit, f a r super ior t o the others. I n t h i s model, the r e l a t i v e populat ion o f a l e v e l w i t h e f f e c t i v e p r i n c i p a l quantum number n* and o r b i t a l angular momentum quantum number L, compared t o the pr imary leve l , i s As another comparison, we show i n Fig. 2 a 2 s imu la t ion o f t h e decay o f the 4p PI/* l e v e l ( the 0 596 A l i n e ) o f Kr V I I I , a long w i t h the experimental