BEAM-FOIL EXCITATION PHENOMENA

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BEAM-FOIL EXCITATION PHENOMENA

E. Veje

To cite this version:

E. Veje. BEAM-FOIL EXCITATION PHENOMENA. Journal de Physique Colloques, 1979, 40 (C1),

pp.C1-253-C1-258. �10.1051/jphyscol:1979153�. �jpa-00218433�

JOURNAL DE PHYSIQUE Colloque C1, supplkment au n

"

2 , Tome 40, fkvrier 1979, puge C1-253

BEAM-FOIL EXCITATION PHENOMENA E. Veje

P h y s i c s L a b o r a t o r y 11, H.C. 0 r s t e d I n s t i t u t e , U n i v e r s i t e t s p a r k e n 5, DK-2100 Copenhagen 8 Denmark

Rbsurnb. On d i s c u t e l e s processusd ' e x c i t a t i o n beam-foil

.

A b s t r a c t . W e d i s c u s s beam-foil e x c i t a t i o n p r o c e s s e s . INTRODUCTION

T h e r e a r e s e v e r a l s i t u a t i o n s where some b a s i c knowledge a b o u t t h e beam- f o i l e x c i t a t i o n mechanism can f a c i l i t a t e a n e x p e r i m e n t a l work and a l s o improve t h e q u a l i t y o f t h e r e s u l t s , though it h a s o f t e n been b e l i e v e d t o be p o s s i b l e t o deduce a t o m i c s t r u c t u r e d a t a from t h e beam-foil l i g h t s o u r c e w i t h o u t h a v i n g any i n f o r m a t i o n a v a i l a b l e a b o u t t h e e x c i t a t i o n p r o c e s s i t s e l f . Thus, Younger and Wiese have r e c e n t l y p o i n t e d o u t t h e need f o r r e l a t i v e l e v e l p o p u l a t i o n d a t a when t r e a t i n g c a s c a d e e f f e c t s 111. I n s e v e r a l e a r l i e r c a s e s o n l y o n e c a s c a d e component h a s been i n c l u d e d i n t h e d a t a r e d u c t i o n , and t h i s may r e s u l t i n a n i n c o m p l e t e

c a s c a d e c o r r e c t i o n [ l ] . A l s o , t h e beam-foil l i g h t s o u r c e i s known t o produce new

s p e c t r a l l i n e s , s e v e r a l o f which are i d e n t i f i e d a s t r a l i s i t i o n s b e t w e e n . m u l t i p l y e x c i t e d l e v e l s 121, and f o r t h e i d e n t i f i - c a t i o n o f such new l i n e s , some e x c i t a t i o n - mechanism knowledge c a n be v e r y u s e f u l .

The c o n c e p t o f c r o s s s e c t i o n s c a n n o t b e used when s e v e r a l atoms i n t e r a c t c o h e r e n t l y a s i n t h e beam-foil p r o c e s s . I n s t e a d , t h e l e v e l p o p u l a t i o n , d e f i n e d a s t h e p r o b a b i l i t y p e r p r o j e c t i l e f o r t h e p o p u l a t i o q o f a s p e c i f i e d l e v e l o r s t a t e , immediately a f t e r t h e p r o j e c t i l e h a s l e f t t h e f o i l , c a n be i n t r o d u c e d . The l e v e l p o p u l a t i o n i s t h e q u a n t i t y o f b a s i c

i n t e r e s t , and w e s h a l l i n t h i s a r t i c l e g i v e some examples o f how t h e l e v e l p o p u l a t i o n changes w i t h t h e p a r a m e t e r s which a r e e a s y

t o change i n a n e x p e r i m e n t , namely t h e p r o j e c t i l e e n e r g y and t h e f o i l tilt a n g l e . I n a d d i t i o n , examples w i l l be g i v e n of t h e l e v e l p o p u l a t i o n a s f u n c t i o n s o f t h e quantum numbers o f t h e e x c i t e d s t a t e s

( t h e " i n t r i n s i c a t o m i c ' p a r a m e t e r s )

.

However, we s h a l l n o t d i s c u s s t h e r e l a t i v e p o p u l a t i o n of t h e d i f f e r e n t magnetic s u b s t a t e s of t h e same l e v e l , o n l y t o t a l l e v e l ( o r term ) p o p u l a t i o n s w i l l b e t r e a t e d h e r e .

The p r o c e d u r e f o r measuring l e v e l p o p u l a t i o n s by u s e o f a quantum e f f i c i e n c y c a l i b r a t e d monochromator [33 i s w e l l e s t a b l i s h e d [ 4 ] .

GENERAL CONSIDERATIONS

The mean d i a m e t e r of t h e v a l e n c e s h e l l o f a n e u t r a l o r weakly i o n i z e d atom i s comparable t o t h e a v e r a g e d i s t a n c e between two neighbour atoms i n t h e f o i l . T h e r e f o r e , v a l e n c e s h e l l e l e c t r o n s and o u t e r e l e c t r o n s w i l l b e s t r o n g l y d i s t u r b e d a s l o n g a s t h e p r o j e c t i l e i s i n s i d e t h e f o i l . T h i s h a s r e c e n t l y been o b s e r v e d by G a i l l a r d e t a l . 151, who by u s i n g H 0

,

^H',

H; and 8; p r o j e c t i l e s found t h a t t h e i n i t i a l c h a r g e s t a t e of t h e p r o j e c t i l e i s d e s t r o y e d c o m p l e t e l y a s soon a s t h e

p r o j e c t i l e h a s s p e n t a t i m e o f 1.5.10-l5 s i n s i d e t h e f o i l . Only w i t h p r o t o n e n e r g i e s above 1 MeV and w i t h f o i l s a s t h i n a s 2 pg/cm2

,

t h e i n i t i a l c h a r g e s t a t e a f f e c t e d t h e r e s u l t a n t c h a r g e - s t a t e d i s t r i b u t i o n [ 5 ] .

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979153

C1-254 JOURNAL DE PHYSIQUE

T h e r e f o r e , i n most beam-foil e x p e r i m e n t s , t h e o u t e r - s h e l l e x c i t a t i o n s t a k e p l a c e when t h e p r o j e c t i l e l e a v e s t h e back of t h e f o i l . We have q u i t e r e c e n t l y o b s e r v e d s u r f a c e e f f e c t s i n beam-foil e x c i t a t i o n s w i t h magnesium p r o j e c t i l e s , 100-900 keV, and a l s o w i t h c a r b o n p r o j e c t i l e s , 4-20 MeV.

B e s i d e s u s i n g f o i l s mounted w i t h t h e i r s u r f a c e p e r p e n d i c u l a r t o t h e beam a x i s , f o i l s t i l t e d up t o 45O were a l s o used. I n F i g . 1 a r e shown s e c t i o n s o f s p e c t r o g r a m s o b t a i n e d w i t h 4 MeV c a r b o n p r o j e c t i l e s and t i l t e d f o i l s . The i n t e n s i t i e s o f most o f t h e s p e c t r a l l i n e s depend c l e a r l y on t h e f o i l tilt a n g l e , i n d i c a t i n g t h e p r e s e n c e o f s u r f a c e e f f e c t s , b e c a u s e t h e i n t e r i o r o f a n amorphous f o i l i s n o t changed by t i l t i n g t h e f o i l .

h 343 nm. 6-7

' " ' 1 " 10 ' 1 " 1 M

PROJECTILE ENERGY. LAB SYSTEM. MeV

F i g . 2

-

R e l a t i v e p o p u l a t i o n o f t h e n = 7 l e v e l i n C V I , O V I , NeVI and SVI v e r s u s t h e p r o j e c t i l e e n e r g y i n t h e l a b o r a t o r y system [61.

p r o j e c t i l e energy f o r v a r i o u s , f i v e t i m e s i o n i z e d e l e m e n t s . T h i s i s a t r a n s i t i o n between n = 7 and n = 6 l e v e l s . The upper l e v e l s and a l s o t h e lower l e v e l s of t h a t t r a n s i t i o n have e s s e n t i a l l y t h e same term v a l u e s f o r a l l f i v e t i m e s i o n i z e d e l e m e n t s ,

though t h e number o f c o r e e l e c t r o n s change

E z

Z

W w i t h t h e e l e m e n t . I n SVI o n l y t h e v a l e n c e

+

r

-

s h e l l h a s undergone i o n i z a t i o n , b u t b o t h

t h e K and L s h e l l s a r e completed, and t h i s produces t h e s h a r p i n c r e a s e o f i n t e n s i t y a l r e a d y a t low p r o j e c t i l e energy. C o n t r a r y t o t h i s , i n C V I t h e t r a n s i t i o n i n v o l v e s a

260 270 280 340 350 360

WAVELENGTH, nm d o u b l e e x c i t a t i o n o f t h e K s h e l l , which F i g . 1

-

S e c t i o n s of o p t i c a l s p e c t r a

o b t a i n e d w i t h 4 MeV c a r b o n p r o j e c t i l e s and f o i l tilt a n g l e s o f

oO,

30° and 45O.

E x c i t a t i o n o f a p r o j e c t i l e c o r e o f mean d i a m e t e r s u b s t a n t i a l l y s m a l l e r t h a n t h e a v e r a g e d i s t a n c e between two c a r b o n atoms w i l l , on t h e o t h e r hand, mainly happen i n o n e of t h e r a t h e r few v i o l e n t c o l l i s i o n s between t h e p r o j e c t i l e a n d a f o i l atom. Such p r o c e s s e s t a k e p a l c e d u r i n g t h e p a s s a g e t h r o u g h t h e f o i l .

The j u s t i f i c a t i o n o f a d i v i s i o n i n t o a coke and a n o u t e r atom i s exempli- f i e d i n F i g . 2 , i n which e x c i t a t i o n of t h e A343 nm t r a n s i t i o n i s shown v e r s u s t h e

e x p l a i n s why t h e C V I i n t e n s i t y maximum o c c u r s a t a p r o j e c t i l e e n e r g y o f approxima- t e l y 1 5 MeV. Oxygen and neon f a l l i n

between s u l f u r and c a r b o n from o b v i o u s r e a s o n s .

Whereas e q u i l i b r i u m n o r m a l l y i s r e a c h e d even w i t h t h e t h i n n e s t f o i l s a v a i l a b l e , t h e s i t u a t i o n i s n o t s o a t v e r y h i g h p r o j e c t i l e energy. D i e t r i c h e t a l . C71 have o b s e r v e d c o n s i d e r a b l e changes i n i n t e n s i t y f o r B e - l i k e i r o n l i n e s a t a p r o j e c t i l e e n e r g y of 491 MeV, when changing t h e f o i l t h i c k n e s s from 40 pg/cm2 t o 2 0 6 pg/cm 2

.

Thus, a t such h i g h p r o j e c t i l e e n e r g i e s , t h e f o i l t h i c k n e s s a p p e a r s a s a n e a s i l y c h a n g a b l e e x p e r i m e n t a l p a r a m e t e r .

LEVEL POPULATION AS A FUNCTION OF THE

PROJECTILE ENERGY, UNTILTED AND TILTED

F O I L S

It h a s o f t e n been found e x p e r i - m e n t a l l y t h a t d i f f e r e n t l e v e l s of t h e same c h a r g e s t a t e and a l s o w i t h same c o r e c o n f i g u r a t i o n have p r o p o r t i o n a l e x c i t a t i o n

f u n c t i o n s [ 4 , 8 ] ( w i t h a n e x c i t a t i o n

f u n c t i o n we u n d e r s t a n d t h e raw photon y i e l d normalized t o t h e same amount o f incoming p a r t i c l e s , p l o t t e d v e r s u s t h e p r o j e c t i l e e n e r g y ) . T h i s i s a n i m p o r t a n t f i n d i n g , s i n c e it c a n b e used f o r c h a r g e - s t a t e c l a s s i f i c a t i o n o f new s p e c t r a l l i n e s .

S i n c e t h e f i n a l a r r a n g e m e n t o f o u t e r e l e c t r o n s happens a s t h e p r o j e c t i l e l e a v e s t h e f o i l , t h e beam-f o i l e x c i t a t i o n p r o c e s s c a n b e r e g a r d e d a s , a m u l t i -

e l e c t r o n pick-up from t h e back o f t h e f o i l .

~t i s t h e r e f o r e t e m p t i n g

-

i n a s e a r c h f o r a q u a l i t a t i v e e x p l a n a t i o n o f t h e above- mentioned f a c t

-

t o s e e , whether p a r t o f

t h e r e s u l t s from e l e c t r o n pick-up t h e o r y i n \ a t o m i c c o l l i s i o n s c a n be t a k e n o v e r by t h e beam-foil model.

Nikolaev [ 9 ] c a l c u l a t e d c h a r g e - exchange p r o b a b i l i t i e s f o r f a s t p r o t o n s i n v a r i o u s g a s e s , u s i n g a s e m i - e m p i r i c a l v a r i a n t o f t h e Brinkman-Kramers a p p r o x i - mation

[ l o ] .

He o b t a i n e d a s u r p r i s i n g l y good agreement w i t h e x p e r i m e n t a l d a t a . I t i s found [ 9 ] t h a t f o r p r o t o n s e l e c t r o n c a p t u r e i n t o d i f f e r e n t e x c i t e d l e v e l s w i t h a l m o s t e q u a l b i n d i n g e n e r g i e s w i l l change s i m i l a r l y w i t h t h e p r o j e c t i l e v e l o c i t y . T h i s a l s o h o l d s f o r c a p t u r e i n t o l e v e l s w i t h d i f f e r e n t b i n d i n g e n e r g i e s , a s soon a s t h e s q u a r e of t h e momentum change of t h e c a u g h t e l e c t r o n i s somewhat l a r g e r t h a n t h e b i n d i n g e n e r g y o f t h e e l e c t r o n i n i t s f i n a l s t a t e .

A simi1.ar r e s u i t i s found i n -Ref.

1111, namely t h a t f o r l a r g e p r o j e c t i l e v e l o c i t i e s o r f o r l a r g e v a l u e s o f t h e p r i n c i p a l quantum number o f t h e f i n a l s t a t e , c r o s s s e c t i o n s f o r d i f f e r e n t f i n a l s t a t e s w i l l have t h e same p r o j e c t i l e energy dependence i n t h e Brinkman-Kramers l i m i t [ l o ] .

Theory based upon t h e Brinkman- Kramers a p p r o x i m a t i o n g i v e s t h u s t o Some e x t e n t a n e x p l a n a t i o n o f t h e e m p i r i c a l f i n d i n g t h a t beam-foil e x c i t a t i o n f u n c t i o n s f o r d i f f e r e n t l e v e l s of t h e same c h a r g e s t a t e and w i t h t h e same c o r e c o n f i g u r a t i o n

( i . e . l e v e l s of t h e same v a r i e t y ) a r e a l m o s t p r o p o r t i o n a l . One may e x p e c t t h e p r o p o r t i o n a l i t y t o d i s a p p e a r a t low p r o j e c t i l e v e l o c i t i e s . We have o b s e r v e d t h i s f o r some l e v e l s i n MqII and ZnI, s e e t h e s e p r o c e e d i n g s . However, t h e p r o p o r t i o - n a l i t y a p p l i e s t o a l m o s t a l l p r a c t i c a l c a s e s and c o n t i n u e s t o p r o j e c t i l e e n e r g i e s which a r e c l e a r l y below t h e v a l i d i t y r e g i o n f o r t h e o r y based on t h e Brinkman-Kramers approxima t i o n .

~t i s found f o r c a r b o n , t h a t s p e c t r a l l i n e s f o r d i f f e r e n t l e v e l s o f t h e same v a r i e t y , a s d e f i n e d above, showed t h e same r e l a t i v e change of i n t e n s i t y when t i l t i n g t h e f o i l . Thus,. t h e above-mentioned p r o p o r t i o n a l i t y f o r e x c i t a t i o n f u n c t i o n s a l s o a p p l y w i t h t i l t e d f o i l s , s e e t h e s e p r o c e e d i n g s . When t h e f o i l i s t i l t e d , t h e t i m e t h a t t h e p r o j e c t i l e i n t e r a c t s with. t h e back o f t h e f o i l i s i n c r e a s e d , and t h i s may l e a d t o a l a r g e r p r o b a b i l i t y f o r e l e c t r o n pick-up a t t h e back o f t h e f o i l . The change o f s p e c t r a l l i n e i n t e n s i t y w i t h f o i l t i l t a n g l e may have p r a c t i c a l a p p l i c a t i o n s . T i l t i n g t h e f o i l may ( i ) d e p r e s s a n unwanted l i n e b l e n d i n g a l i n e o f i n t e r e s t , ( i i ) g u i d e i n c h a r g e - s t a t e c l a s s i f i c a t i o n o f new l i n e s , l i k e t h e method o f s t u d y i n g t h e hhange o f photon y i e l d v e r s u s t h e p r o j e c t i l e e n e r g y ,

(iii) a c t a s an a r t i f i c i a l way o f e x t e n d - i n g a c c e l e r a t o r e n e r g i e s towards l o v e r e n e r g i e s ( a s a n example, we mention t h a t a t 7 MeV no C I I l i n e s were o b s e r v e d w i t h u n t i l t e d f o i l s , whereas a few l i n e s o c c u r e d w i t h f o i l s t i l t e d 30° and 45O )

,

( i v ) enhance t h e p o p u l a t i o n o f m u l t i p l y e x c i t e d l e v e l s a t medium t o h i g h p r o j e c - t i l e e n e r g i e s ; t h e h i g h e r p r o j e c t i l e energy w i l l c a u s e l a r g e r amounts of c o r e e x c i t a t i o n s , and t i l t i n g t h e f o i l may i n c r e a s e t h e e l e c t r o n pick-up i n t o t h e o u t e r atom.

JOURNAL DE PHYSIQUE

The g r o u p i n g o f l e v e l s i n t o

v a r i e t i e s i s i l l u s t r a t e d i n F i g . 3 , i n which r e l a t i v e p o p u l a t i o n f u n c t i o n s ( i . e . c u r v e s showing t h e r e l a t i v e p o p u l a t i o n o f s p e c i f i e d l e v e l s v e r s u s t h e p r o j e c t i l e e n e r g y ) f o r some C I I l e v e l s a r e shown. A s c a n b e s e e n

A2831 nrn C I I 2r13p b 3 9 2 0 n m C l l 2s''~

h 251 2 nm C l i 2p'

t-CAR80N FMl OPTlCAL DAlA

F i g . 3

-

R e l a t i v e l e v e l p o p u l a t i o n Curves f o r some C I I t e r m s , s e e a l s o e l s e w h e r e t h e s e p r o c e e d i n g s . t h e p o p u l a t i o n c u r v e s f o r C I I l e v e l s o f c o n f i g u r a t i o n l s 2 2 s 2 n l ( t o p ) a r e v e r y f l a t , t h e c u r v e s f o r t h e l e v e l s of

c o n f i g u r a t i o n l s 2 2 s n l n ' l ' a r e s l o w l y r i s i n g , and t h e l s 2 2p3 ( bottom ) i s more s t e e p l y r i s i n g . S i m i l a r l y f o r C I I I , i t i s found t h a t t h e l s 2 2p2 c u r v e i s s t e e p e r t h a n t h e l s 2 2 s n l c u r v e s . Thus one s e e s how t h e number o f 2 s v a c a n c i e s i n f l u e n c e s t h e s h a p e o f t h e p o p u l a t i o n c u r v e s . I t must h e r e b e remembered, t h a t a l l of t h e C I I l e v e l s o f F i g . 3 a r e c l o s e t o g e t h e r i n e x c i t a t i o n e n e r g y , s o t h a t t h e change o f s l o p e s a s - s e e n i n F i g . 3 i s n o t c a u s e d by d i f f e r e n c e s i n e x c i t a t i o n e n e r g y , a s d i s c u s s e d above f o r MgII and ZnI l e v e l s . I n f a c t , t h e C I I 2p3 t e r m ( bottom ) h a s e x c i t a t i o n e n e r g y below a l l o t h e r upper l e v e l s o f t h e t r a n s i t i o n s g i v e n i n F i g . 3 , e x c e p t f o r t h e 2 s 2 3p term ( t o p )

.

The f u l l c u r v e s shown i n F i g . 3 r e s u l t e d from t h e i n d e p e n d e n t - e l e c t r o n model f o r beam-foil p r o c e s s e s 1121

.

The model t r e a t s t h e r e s u l t a n t c o r e , o u t e r s h e l l e x c i t a t i o n s a s i n d e p e n d e n t p r o c e s s e d , u s i n g o n e p a r a m e t e r f o r t h e o u t e r - s h e l l e l e c t r o n s , and one p a r a m e t e r f o r ' i n n e r s h e l l which may undergo i o n i z a t i o n 1121.

P o p u l a t i o n c u r v e s a r e e x p r e s s e d a s p r o d u c t s o f b i n o m i a l d i s t r i b u t i o n s , we s h a l l n o t r e p e a t t h e e q u a t i o n s h e r e .

The model c a n f o r c a r b o n r e p r o d u c e t h e s h a p e s o f p o p u l a t i o n c u r v e s o f n i n e v a r i e t i e s , by u s e o f o n l y t h r e e p a r a m e t e r s , s e e t h e s e p r o c e e d i n g s .

The model s a y s n o t h i n g a b o u t t h e a b s o l u t e p o p u l a t i o n o f a s p e c i f i c s u b s t a t e o r l e v e l , b u t p r e d i c t s o n l y t h e a b s o l u t e v a l u e o f t h e t o t a l p o p u l a t i o n o f e a c h v a r i e t y o f an e l e m e n t . Charge s t a t e d i s t r i b u t i o n measurements y i e l d i n a p r e c i s e way t h a t s o r t o f i n f o r m a t i o n , a s l o n g a s c o r e e x c i t a t i o n s do n o t happen, and a l s o a u t o i o n i z a t i o n d o e s n o t t a k e p l a c e , s e e Ref. [ 1 2 ] . I n F i g . 4 a r e compared c h a r g e - s t a t e d a t a [ I 3 1 f o r s u l f u r w i t h o p t i c a l d a t a [14] and a model f i t 1131.

The agreement i s good, and we n o t e t h u s t h a t f o r s u l f u r t h e model r e p r o d u c e s 5 s e t s o f a b s o l u t e c u r v e s ( t h e c h a r g e - s t a t e

d i s t r i b u t i o n s ) t o g e t h e r w i t h 5 s e t s o f r e l a t i v e , o p t i c a l c u r v e s by n o t more t h a n o n e p a r a m e t e r , s i n c e no c o r e e x c i t a t i o n s t a k e p l a c e .

LEVEL POPULATION AS FUNCTIONS OF THE FINAL TERM QUANTUM NUMBERS

I n F i g . 5 a r e shown r e l a t i v e beam-foil l e v e l p o p u l a t i o n s f o r d i f f e r e n t l e v e l s o f t h e same Rydberg s e r i e s v e r s u s t h e p r i n c i p a l quantum number n o f t h e e x c i t e d l e v e l . The l e v e l p o p u l a t i o n

-

³

d e c r e a s e s i n a l l c a s e s ,as n ( f o r He1 and C I V ) o r s t e e p e r .

S i n c e t h e p o p u l a t i o n o f Rydberg s t a t e s happens as t h e p r o j e c t i l e l e a v e s t h e f o i l , i t i s r e a s o n a b l e t o e x p e c t t h a t R y d b e r g - s t a t e p o p u l a t i o n s w i l l b e i n f l u e n - ced by t h e form o f t h e e l e c t r o n i c wave f u n c t i o n s i n t h e v i c i n i t y o f t h e p r o j e c t i l e n u c l e u s , from t h e t i m e o f emergence and u n t i l t h e atom i s c o m p l e t e l y f r e e . I t i s

\

^CARBON

0

-

C3 Y

Y 0 CL

9 U CHARGE STATE DATA

0 OPTICAL DATA MODEL

0 200 4 0 0 600

EMERGENT BEAM ENERGY, keV

F i g . 4

-

C h a r g e - s t a t e d i s t r i b u t i o n s and o p t i c a l beam-foil p o p u l a t i o n c u r v e s f o r s u l f u r .

w e l l known [15] t h a t , f o r d i f f e r e n t mem- b e r s o f t h e same a t o m i c Rydberg s e r i e s , t h e i n n e r p a r t s o f t h e i r wave f u n c t i o n s a r e p r o p o r t i o n a l , t h e p r o p o r t i o n a l i t y

f a c t o r b e i n g n'3'2. T h i s e x p l a i n s

-

cum g r a n o s a Z i s

-

why t h e term p o p u l a t i o n w i t h i n t h e same t e r m s e r i e s g o e s

a s y m p t o t i c a l l y a s n-3, a s found e x p e r i - m e n t a l l y f o r He1 l e v e l s and C I V l e v e l s , b e c a u s e t h e p o p u l a t i o n . p r o b a b i l i t y i s p r o p o r t i o n a l t o t h e s q u a r e o f t h e ampli- t u d e o f t h e wave f u n c t i o n .

We n o t e t h a t t h e r e i s a h i g h d e g r e e o f a n a l o g y i n t h e r e l a t i v e t e r m p o p u l a t i o n a s a f u n c t i o n o f n f o r beam- f o i l e x c i t a t i o n s and f o r ion-atom

c o l l i s i o n s C161. A l s o , s i n c e t h e a m p l i t u d e o f a helium t r i p l e t wave f u n c t i o n i s s m a l l e r t h a n t h e a m p l i t u d e o f t h e

c o r r e s p o n d i n g s i n g l e t wave f u n c t i o n [171, t h e above a,rgument e x p l a i n s why t h e r a t i o o f t h e p o p u l a t i o n o f a t r i p l e t t o t h a t

-

^{3 PRINCIPAL 5 DYNIUM 7 9 1 1 NUMBER. n}

F i g . 5

-

R e l a t i v e l e v e l p o p u l a t i o n s a s f u n c t i o n s o f t h e p r i n c i p a l quantum number n.

o f t h e c o r r e s p o n d i n g s i n g l e t i s s m a l l e r t h a n 3 , a s o b s e r v e d f o r h e l i u m - l i k e s p e c i e s [ 4 , 1 8 ] .

We o b s e r v e , however, from F i g . 5 t h a t f o r L i I and f o r hydrogen t h e l e v e l

-

³

p o p u l a t i o n d e c r e a s e s more r a p i d l y t h a n n

.

I n F i g . 6 a r e shown examples o f r e l a t i v e l e v e l p o p u l a t i o n s a s a f u n c t i o n o f t h e o r b i t a l a n g u l a r momentum quantum

ORBITAL ANGULAR MOMENTUM QUANTUM NUMBER

F i g . 6

-

R e l a t i v e beam-foil l e v e l popu- l a t i o n s v e r s u s t h e o r b i t a l a n g u l a r momentum quantum number.

JOURNAL DE PHYSIQUE

* Ng I1 IOOkeV

.

^{C IY} &MeV, n.6 Fe YII 1 5 MeV

1c6

ORBITAL ANGULAR MOMENTUM QUANTUM NUMBER. I

F i g . 7

-

R e l a t i v e b e a m - f o i l l e v e l p o p u l a - t i o n s v e r s u s t h e o r b i t a l a n g u l a r momentum quantum number.

number L f o r l e v e l s w i t h f i x e d n. F u r t h e r examples a r e g i v e n i n F i g . 7 , i n which d a t a f o r F e V I I [ 1 9 ] a r e i n c l u d e d . I t i s s e e n t h a t t h e r e l a t i v e l e v e l p o p u l a t i o n f o r l e v e l s o f t h e same p r i n c i p a l quantum number i n c r e a s e s w i t h t h e o r b i t a l a n g u l a r momentum quantum number e x c e p t f o r a

s u p e r i m p o s e d p e a k i n g i n p o p u l a t i o n f o r p l e v e l s . T h i s i s d i f f e r e n t from ion-atom c o l l i s i o n s , w h e r e t h e c r o s s s e c t i o n s peak f o r d l e v e l s a t low t o medium p r o j e c - t i l e e n e r g y [ l l ] , a n d g r a d u a l l y s h i f t t o p and l a t e r t o s l e v e l s w i t h i n c r e a s i n g p r o j e c t i l e e n e r g y .

T h e r e i s a t p r e s e n t no c l e a r u n d e r s t a n d i n g o f t h e t r e n d s s e e n i n F i g s . 6 and 7.

ACKNOWLEDGEMENTS

Most o f t h e e x p e r i m e n t a l works p r e s e n t e d h e r e h a v e b e e n done a t t h e R e s e a r c h I n s t i t u t e f o r P h y s i c s , Stockholm, o r a t t h e I n s t i t u t e f o r P h y s i c s , ~ n i v e r s i k y o f q r h u s . The a u t h o r w a n t s t o t h a n k t h e two I n s t i t u t e s f o r t h e i r g r e a t h o s p i t a l i - t i e s . A l s o , economic s u p p o r t from t h e Nordic ~ c c e l e r a t o r Committee and t h e D a n i s h N a t u r a l R e s e a r c h S c i e n c e F o u n d a t i o n i s g r e a t l y a p p r e c i a t e d .

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