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ELECTRON ”CUSP” SPECTROSCOPY OF THE FORWARD PEAK IN CONTINUUM ELECTRON
CAPTURE AND LOSS IN GASES AND SOLIDS
I. Sellin
To cite this version:
I. Sellin. ELECTRON ”CUSP” SPECTROSCOPY OF THE FORWARD PEAK IN CONTINUUM
ELECTRON CAPTURE AND LOSS IN GASES AND SOLIDS. Journal de Physique Colloques, 1979,
40 (C1), pp.C1-225-C1-235. �10.1051/jphyscol:1979147�. �jpa-00218427�
JOURNAL DE PHYSIQUE Colloque C1, supplkment au n " 2, Tome 40, fkvrier 1979, page C1-225
I.A. S e l l i n
U n i v e r s i t y of Tennessee, Knoxville, Tennessee 37916, Oak Ridge N a t i o n a l Laboratory, Oak Ridge, Tennessee 37830, U.S.A., and Research I n s t i t u t e o f P h y s i c s , S-104 05 Stockholm, Sweden Rlsum'e. Nous d i s c u t o n s l e s r l s u l t a t s de p l u s i e u r s e x p & i e n c e s r e c e n t e s de c o l l i s i o n ion- atome e t i o n - s o l i d e en c e q u i concerne l e p i c en a v a n t dans l a p r o d u c t i o n d l ' e l e c t r o n s du c o n t i n u 2 p a r t i r de l a c a p t u r e e t l a p e r t e de 1 ' L l e c t r o n v e r s l e s ' e t a t s du c o n t i n u centr'es s u r l e p r o j e c t i l e . L ' a c c e n t e s t m i s s u r l a d i s c u s s i o n d e t r o i s e x p l r i e n c e s r'ecentes ef- fectu'ees s u r l e s a c c ' e l e r a t e u r s tandem de ORNL e t BNL. La premi'ere a t r a i t a u d'esaccord e n t r e l a t h l o r i e e t l ' e x p ' e r i e n c e 1 propos d e l a dlpendance en Z du p r o j e c t i l e pour l a c a p t u r e de l ' g l e c t r o n v e r s l e s ' e t a t s du c o n t i n u c e n t r 6 s s u r l e p r o j e c t i l e (ECC) dans l e s c o l l i s i o n s ion-atome. La seconde concerne l a d'ecouverte d'une s t r u c t u r e p'eriodique non- p r L d i t e ( i n t e r f ' e r e n c e ? ) dans l a v o i e de l a p e r t e de 1 " e l e c t r o n (ELC) dans l e s c o l l i s i o n s ion-atome. La troisi'eme concerne l 1 i m P u i s s a n c e des mod'eles ECC e t "wake r i d i n g " 1 repro- d u i r e l e s c a r a c t B r i s t i q u e s du p i c en a v a n t dans l e s c o l l i s i o n s ion-solide.
A b s t r a c t . R e s u l t s of s e v e r a l r e c e n t ion-atom and i o n - s o l i d c o l l i s i o n experiments concerning t h e forward peak i n continuum e l e c t r o n p r o d u c t i o n from e l e c t r o n c a p t u r e and l o s s t o projec- t i l e - c e n t e r e d continuum s t a t e s a r e d i s c u s s e d . Emphasis i s g i v e n t o d i s c u s s i o n of t h r e e re- c e n t experiments c a r r i e d o u t a t t h e ORNI, and BNL tandem a c c e l e r a t o r s . The f i r s t concerns disagreement between t h e o r y and experiment on t h e p r o j e c t i l e Z dependence f o r e l e c t r o n cap- t u r e t o p r o j e c t i l e - c e n t e r e d continuum s t a t e s (ECC) i n ion-atom c o l l i s i o n s . The second con- c e r n s t h e d i s c o v e r y of u n p r e d i c t e d p e r i o d i c ( i n t e r f e r e n c e ? ) s t r u c t u r e i n t h e e l e c t r o n l o s s channel (ELC) i n ion-atom c o l l i s i o n s . The t h i r d concerns f a i l u r e of b o t h ECC and "wake- r i d i n g t ' models of t h e forward peak c h a r a c t e r i s t i c s i n i o n - s o l i d c o l l i s i o n s .
INTRODUCTION
S i n c e t h e p i o n e e r i n g experimental work o f Crooks and Rudd [11 and t h e a s s o c i a t e d t h e o r e t i c a l work of Macek C21 ( a n t i c i p a t e d i n p a r t by Oldham [3]) on e l e c t r o n "cusps" from e l e c t r o n c a p t u r e t o contin- uum s t a t e s (ECC) f o r f a s t p r o t o n s o n He, much theo- r e t i c a l 12-91 and experimental [5,10-251 a t t e n t i o n h a s been devoted t o e l e c t r o n e j e c t i o n from t a r g e t atoms i n t o such p r o j e c t i l e - c e n t e r e d continuum states.
The c h a r a c t e r i s t i c cusp-shaped peak i n t h e e j e c t e d - e l e c t r o n v e l o c i t y d i s t r i b u t i o n , which i s s h a q i l y peaked n e a r t h e p r o j e c t i l e v e l o c i t y , and a l s o sharp- l y peaked i n t h e forward d i r e c t i o n , was i d e n t i f i e d a t n e a r l y t h e same time f o r l i g h t i o n s p a s s i n g t h r u C f o i l s by H a r r i s o n and Lucas [ l o ] . These a u t h o r s have continued such work w i t h o t h e r c o l l a b o r a t o r s i n a s e r i e s o f i n v e s t i g a t i o n s [5,11,19,201 f o r v a r i o u s H, He p r o j e c t i l e s , m o s t l y i n t h i n s o l i d and occasion- a l l y i n gaseous t a r g e t s , a t p r o j e c t i l e e n e r g i e s up t o 1.2 M~V/A. E x t e n s i v e work w i t h b o t h s o l i d and g a s t a r g e t s and H, He p r o j e c t i l e s h a s a l s o been un-
'work s u p p o r t e d i n p a r t by NSF (USA); ONR (USA); by DOE (USA) under c o n t r a c t w i t h Union Carbide Corpo- r a t i o n and A s s o c i a t e d U n i v e r s i t i e s , Inc.; and by t h e Swedish N a t u r a l Science Research Council.
d e r t a k e n by Menendez, Duncan and co-workers [12-171, and w i t h s o l i d t a r g e t s by Heckbach et a l . 1171. The l a t t e r a u t h o r s have w r i t t e n an e x c e l l e n t summary ar t i c l e 1171, whose t i t l e "Do p r e s e n t 'charge t r a n s f e r t o t h e continuum' t h e o r i e s c o r r e c t l y d e s c r i b e t h e p r o d u c t i o n o f v e = v i i n i o n beam-foil c o l l i s i o n s ? "
emphasizes s e v e r a l c o n t r o v e r s i a l disagreements be- tween t h e v a r i o u s d a t a and t h e o r e t i c a l p r e d i c t i o n s .
Chiu, McGowan, and I f i t c h e l l [ 181 have ex- tended t h e work o f Meckbach et aZ. 1171 t o g a s t a r g e t s , and f i n d s u p p o r t f o r a n ECC d e s c r i p t i o n i n gas t a r g e t s , i n o p p o s i t i o n t o a l l e g e d d e f i c i e n c i e s o f such a d e s c r i p t i o n f o r s o l i d t a r g e t s [171. But re- c e n t l y Steckelmacher et a l . have c r i t i c i z e d t h e in- t e r p r e t a t i o n g i v e n t h e d a t a o f Meckbach e t a l . 1171 on i n s t r u m e n t a l r e s o l u t i o n and background t r e a t m e n t grounds, and a r g u e f o r t h e v a l i d i t y of t h e ECC mod- e l f o r t h e s o l i d t a r g e t c a s e a s w e l l , and a g a i n s t t h e r i v a l , s o l i d - s t a t e "wake-riding" d e s c r i p t i o n E8,91. The l a t t e r model c o n s i d e r s t h e p o s s i b i l i t y t h a t e l e c t r o n s may b e t r a p p e d i n a n o s c i l l a t o r y , e- l e c t r o n d e n s i t y f l u c t u a t i o n p o l a r i z a t i o n p o t e n t i a l extending behind and moving w i t h t h e p r o j e c t i l e , fi- n a l l y b e i n g l i b e r a t e d a t t h e e x i t s u r f a c e .
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979147
JOURNAL DE PHYSIQUE As we s h a l l s e e , i n t h e work o f o u r labo-
r a t o r y , which i s d i s t i n c t from a l l p r e v i o u s work by v i r t u e of t h e u s e of f a s t e r , h e a v i e r , b a r e and high- l y i o n i z e d i o n s ( p e r m i t t i n g wide p r o j e c t i l e charge s t a t e v a r i a t i o n ) , we f i n d agreement w i t h n e i t h e r the ECC nor "wake-riding" models f o r t h e s o l i d t a r g e t c a s e [251.
The work of o u r l a b o r a t o r y concerning t h e forward peak was n o t o r i g i n a l l y motivated s o much by i n t r i n s i c i n t e r e s t i n p r o p e r t i e s of t h e forward peak a s by a f a s c i n a t i n g a s s e r t i o n of B o t t c h e r concern- i n g t h e mechanism of many-electron s t r i p p i n g of t a r - g e t atoms by h i g h e r 2, b a r e p r o j e c t i l e s i n s i n g l e ion-atom c o l l i s i o n s [26]. His paper proposes t o ex- p l a i n e v e n t s l i k e t h e simultaneous 1 0 - e l e c t r o n exci- t a t i o n of Ne by b a r e Ar i o n s which we observed i n our l a b o r a t o r y f i v e y e a r s ago 1271 by a p p e a l i n g t o m u l t i p l e e l e c t r o n c a p t u r e t o t h e p r o j e c t i l e - c e n t e r e d
continuum a s t h e dominant mechanism.
Whether h i s a s s e r t i o n i s v a l i d remains an a s y e t e x p e r i m e n t a l l y u n s e t t l e d q u e s t i o n . But a l l t h r e e of o u r i n i t i a l experiments devoted t o t h i s q u e s t i o n have l e d b o t h t o u n a n t i c i p a t e d d i s c o v e r i e s and t o s i g n i f i c a n t d i f f e r e n c e s w i t h t h e o r e t i c a l de- s c r i p t i o n s of t h e forward peak. These t h r e e experi- ments - t o be d i s c u s s e d at some l e n g t h - a r e v e r y much a group e f f o r t w i t h my c o l l e a g u e s Vane, S u t e r , L a u b e r t , E l s t o n , Alton, G r i f f i n , and Thoe, a b l y a i d -
ed by t h e ORNL and BNL tandem a c c e l e r a t o r l a b o r a t o r y s t a f f s . The e x t e n s i v e work of Vane i n h i s p a i n s t a k - i n g d e s i g n , c o n s t r u c t i o n , assembly, t e s t i n g and mo- d i f i c a t i o n of a l l of t h e a p p a r a t u s e x c e p t i n g a n e- l e c t r o n energy a n a l y z e r k i n d l y l e n t u s b y !f.O.Krause of ORNL deserves s p e c i a l mention, a s do t h e e f f o r t s of S u t e r t o understand t h e p e r i o d i c ( i n t e r f e r e n c e ? ) s t r u c t u r e s we have r e c e n t l y d i s c o v e r e d i n t h e wings of t h e forward peak i n e l e c t r o n l o s s t o continuum (ELC) p r o c e s s e s [24],of Laubert who h a s l e d t h e s o l - i d t a r g e t work [25], and E l s t o n and Thoe whose un- sung development of t h e e l e c t r o n i c c o n t r o l and com- puter-based d a t a a c q u i s i t i o n systems used i n o u r work h a s been i n d i s p e n s a b l e . Because a l l t h r e e of
t h e experiments [25,26,27] have l e d t o b o t h new d i s - c o v e r i e s and c h a l l e n g e s t o t h e o r y , and because many e x c e l l e n t reviews of t h e complementary work w i t h H, He p r o j e c i i l e s a r e a v a i l a b l e , e.g. [5,9,17,20], my d i s c u s s i o n w i l l f o c u s on t h e s e p r e v i o u s l y u n r e v i e w ed, complementary r e s u l t s w i t h h e a v i e r and h i g h l y i o n i z e d , f a s t e r p r o j e c t i l e s .
A key f e a t u r e of o u r experimental proce- d u r e i s t h e e a s y i n t e r c h a n g e of s h o r t g a s and t h i n s o l i d t a r g e t s a t t h e same p h y s i c a l p o s i t i o n w i t h a l l a p e r t u r e s i z e s , dimensions, p o s i t i o n s , and oth- e r experimental d e t a i l s u n a l t e r e d . It h a s t h e r e f o r e been p o s s i b l e t o cancel most s y s t e m a t i c a p p a r a t u s e f f e c t s i n comparing g a s and s o l i d t a r g e t r e s u l t s t o f i r s t o r d e r . By using s i n g l e ion-atom c o l l i s i o n t e c h n i q u e s , by u s i n g b a r e and f e w e l e c t r o n i o n s of a p p r e c i a b l y h i g h e r charge t h a n h e r e t o f o r e , by ex- t e n d i n g t h e v e l o c i t y range of measurement appreci- a b l y above t h a t of e a r l i e r experiments, and by study- 'in2 c h a r g e - s t a t e v a r i a t i o n over a n a p p r e c i a b l y wider range t h a n used p r e v i s u s l y , we have t h u s been a b l e t o t e s t e x p e r i m e n t a l l y f e a t u r e s of continuum e l e c - t r o n - c a p t u r e and - l o s s t h e o r i e s which have been in- a c c e s s i b l e i n p r e v i o u s experiments. These somewhat orthogonal t e s t s coraplement r a t h e r t h a n d u ~ l i c a t e e a r l i e r experimental t e s t s , b u t , l i k e them, r a i s e new q u e s t i o n s about s t i l l o t h e r conspicuous d i s a - greements.
Before proceeding w i t h a d e t a i l e d discus- s i o n of methods used and r e s u l t s o b t a i n e d i n t h e t h r e e experiments, a few a d d i t i o n a l c o m e n t s con- c e r n i n g disagreements between t h e o r y and experiment and among experimental r e s u l t s seem worth making.
Notable among t h e s e disagreements a r e t h e following:
F o r s u f f i c i e n t l y l a r g e i o n v e l o c i t y (Vi) and small + -+
p r o j e c t i l e rest-frame e l e c t r o n v e l o c i t y Ive - ~ i 1,
Dettmann, H a r r i s o n , and Lucas [ 5 ] o b t a i n e d t h e d i f - f e r e n t i a l c r o s s - s e c t i o n f o r ECC i n t h e form du/dVe= -+
F ( V i ) f ( l ? e - ? i l ) . Meckbach e t al. 1171 claim t h a t a
-+ -+
v e c t o r f u n c t i o n o f (Ve- Vi) i s needed t o e x p l a i n t h e i r cusp-shape r e s u l t s f o r p r o t o n s on C t a r g e t s , when l o n g i t u d i n a l (2) and t r a n s v e r s e components ($)
+ -+
of V e - V i a r e s e p a r a t e l y scanned, and a s s e r t a t r u e cusp i s n o t observed ( i . e . t h e i r r e s u l t s s u p p o r t the
-+
-+ + -+
view t h a t f(Ve- Vi) remains f i n i t e a s Ve-+V; instead
-+ +
of t a k i n g t h e form Iv, - vi 1 1. Also, t h e p r e d i c t e d dependence of c u s p w i d t h o n beam v e l o c i t y was n o t ob- served, a d i s c r e p a n c y c o r r o b o r a t e d i n t h e independ- e n t measurements of Menendez and co-workers [12-161.
On t h e o t h e r hand, Cranage and Lucas [ I l l f i n d ex-
c e l l e n t agreement w i t h t h e o r e t i c a l cusp shapes f o r
l o n g i t u d i n a l ( e l e c t r o n energy) scans, provided a
l a r g e d i r e c t i o n i z a t i o n background i s f i r s t sub-
t r a c t e d . We have confinned t h e shape r e s u l t s of
Cranage and Lucas f o r 0.7-lfeV/A d+ on Ar c o l l i s i o n s ,
and have f u r t h e r demonstrated Z independence of t h e
cusp shape. But we a r e puzzled t o f i n d much s m a l l e r direct-ionization-background s u b t r a c t i o n s t h a n those of Cranage and Lucas.
Very r e c e n t l y Steckelmacher e t aZ. [20]
have challenged t h e i n t e r p r e t a t i o n of t h e observed V i independence of l o n g i t u d i n a l and a n g u l a r ( t r a n s - v e r s e v e l o c i t y ) cusp w i d t h s observed by Meckbach e t a l . 1171 and Chiu et a l . [ I 8 1 f o r s o l i d C t a r g e t s . T h i s independence had been used [17,181 i n i n f e r r i n g a p o s s i b l e v e c t o r i a l f u n c t i o n a l dependence i n
-+
-+-+ -+
f ( V e - V i ) , a s opposed t o f ( ] v e - v i l ) . A l l a u t h o r s seem t o a g r e e t h a t i n t h e ion-atom c o l l i s i o n c a s e corresponding cusp w i d t h s do s c a l e i n p r o p o r t i o n t o V i , a s p r e d i c t e d t h e o r e t i c a l l y [51. The c h a l l e n g e i s based on e s t i m a t e d , l a r g e peak h e i g h t c o r r e c t i o n s brought a b o u t by s a t u r a t i o n e f f e c t s stemming from f i n i t e a n a l y z e r r e s o l u t i o n v e r y n e a r t h e cusp, and on a n a l l e g e d l y improper background s u b t r a c t i o n prior t o cusp w i d t h e s t i m a t i o n .
The q u e s t i o n of whether and how t o sub- t r a c t backgrounds underneath t h e cusps i s fundamen-
t a l . A convincing argument has been made by Rudd and Macek [28] and s u b s e q u e n t l y by many o t h e r s t h a t no unambiguous background s u b t r a c t i o n of d i r e c t , t a r g e t - c e n t e r e d i o n i z a t i o n e l e c t r o n s from t h o s e due t o p r o j e c t i l e - c e n t e r e d ECC p r o c e s s e s can be made.
Essentially one a r g u e s t h a t e l e c t r o n s r e a c h i n g par- t i c u l a r energylnomentum continuum s t a t e s a r e physi- c a l l y i n d i s t i n g u i s h a b l e , and t h a t which mechanism o p e r a t e s t o produce a s p e c i f i c e l e c t r o n cannot b e decided even i n p r i n c i p l e . I n s u p p o r t i n g t h e ECC model f o r t h e s o l i d t a r g e t c a s e , Steckelmacher e t aZ.
[201 seem t h u s t o make a somewhat v a l i d c r i t i c i s m of t h e peak w i d t h e s t i m a t i o n procedure of lleckbach e t a l . [171 (although a co-author of 1201, Lucas
[ I l l , seems t o have made s i m i l a r background s u b t r a c - t i o n s from time t o time [ I l l ) .
The f i r s t of t h e t h r e e experiments I s h a l l d i s c u s s i n d e t a i l 1231 i s i n disagreement w i t h two d i f f e r e n t c l a s s e s o f t h e o r i e s [2,6] v s . [3,5] concern- i n g t h e p r o j e c t i l e Z dependence o f ECC. The second [24] concerns o u r d i s c o v e r y of i n t e r e s t i n g , p e r i o d i c ( i n t e r f e r e n c e ? ) s t r u c t u r e i n t h e wings o f t h e f o r - ward peak i n th-e ELC channel. The t h i r d r251 con- c e r n s t h e f a i l u r e of b o t h ECC and s o l i d - s t a t e "wake- riding'' models [8,91 t o d e s c r i b e o u r s o l i d t a r g e t r e s u l t s .
SUGGESTED CONNECTIONS BETWEEN ECC. ELC CAPTURE TO HIGH RYDBERG STATES, RADIATIVE RECOMBINATION. AND THE BEAM-FOIL CASCADE PROBLEM
The p r e s e n c e of an abundance o f e l e c t r o n s accompanying a p r o j e c t i l e emergent from a s o l i d t a r - g e t a t n e a r l y t h e same speed and i n n e a r l y t h e same d i r e c t i o n l e a d s one t o s p e c u l a t e concerning t h e pos- s i b l e c o n t r i b u t i o n of such e l e c t r o n s t o long-lived cascades by means of r a d i a t i v e recombination proces- s e s from continuum s t a t e s . Indeed, c a p t u r e t o high Rydberg s t a t e s h a s r e c e i v e d much d i s c u s s i o n i n t h i s and p r e v i o u s conferences i n t h i s s e r i e s . S e v e r a l y e a r s ago Rudd and Phcek 1281 had a l r e a d y emphasized t h e c l o s e connection between e x c i t a t i o n t o o r cap- t u r e i n t o a band of h i g h Rydberg s t a t e s c h a r a c t e r - i z e d by An, and s i m i l a r continuum bands above t h e i o n i z a t i o n l i m i t . As they p o i n t o u t , e j e c t i o n of slow, secondary e l e c t r o n s i s a n a t u r a l c o n t i n u a t i o n of e x c i t a t i o n t o s t a t e s of h i g h p r i n c i p a l quantum numbers, and t h a t t h e e l e c t r o n c a p t u r e p r o c e s s should c o n t i n u e beyond t h e i o n i z a t i o n l i m i t of t h e hydrogen atom i n a smooth, continuous, and u n i n t e r - r u p t e d way. I n t h e i r model, t h e d i f f e r e n t i a l c r o s s s e c t i o n f o r producing e l e c t r o n s w i t h low e n e r g i e s i n t h e r e s t frame of t h e p r o j e c t i l e c o n t a i n s a compo- n e n t g i v e n by d o r / d E ' = 5 i x ( E ' ) , where E' i s t h e e- l e c t r o n energy i n t h e p r o j e c t i l e frame, and a L x ( ~ ' ) i s a slowly v a r y i n g f u n c t i o n of E'. The c o n s t a n t
3;,(Er) n e a r E ' = 0 i s connected w i t h t h e c o n s t a n t
sex i n t h e l / n 3 law f o r e l e c t r o n c a p t u r e r e a c t i o n a c c o r d i n g t o o n ( e x ) = 8,, ~ n / n ~ = Vex AE,"= - oL~(E')AE'.
The replacement of a n / n 3 by AEn i s s p e c i f i c t o t h e Coulomb p o t e n t i a l , and accounts f o r t h e smooth t r a n - s i t i o n r i g h t a c r o s s t h e i o n i z a t i o n l i m i t .
I n r e c e n t y e a r s many l a b o r a t o r i e s includ- i n g o u r own have c a r r i e d o u t s t u d i e s of r a d i a t i v e recombination through r a d i a t i v e e l e c t r o n c a p t u r e by f a s t p r o j e c t i l e s , p r i m a r i l y i n t h e X-ray r e g i o n . G e n e r a l l y t h e d i s c u s s i o n of such experiments h a s c e n t e r e d on c a p t u r e from bound s t a t e s of a t a r g e t atom. Because t h e mechanism of forward peak e l e c - t r o n p r o d u c t i o n i s s o p o o r l y understood, p a r t i c u l a r - l y f o r s o l i d t a r g e t s , I would l i k e t o s u g g e s t t h a t t h e p o s s i b l e r o l e of r a d i a t i v e c a p t u r e of e l e c t r o n s i n t h e forward peak i n r a d i a t i v e recombination b e examined b o t h t h e o r e t i c a l l y and e x p e r i m e n t a l l y a s i t r e l a t e s t o t h e beam-foil cascade problem i n t h e v e r y n e a r f u t u r e .
EXPERIMENTAL METHOD
A schematic diagram of t h e a p p a r a t u s i s
d i s p l a y e d i n F i g . 1. P r o j e c t i l e i o n s from t h e OWL
o r BNL tandem a c c e l e r a t o r t r a v e r s e a t h i n g a s o r in-
t e r c h a n g e a b l e s o l i d t a r g e t o v e r a v e l o c i t y range
JOURNAL DE PHYSIQUE
FIG. 1. - Schematic diagram o f , t h e forward peak e- l e c t r o n spectrometric apparatus. (1) 0.71 mm aper- t u r e ; (2) 0.33 mm a p e r t u r e ; (3) 4 mm long gas c e l l , 2 mm e x i t a p e r t u r e ; ( 4 ) , (5) Inner, o u t e r s p h e r i c a l s e c t o r p l a t e s ; (6) 0.7 e x i t aperture; (7) Negative b i a s e d e l e c t r o n m u l t i p l i e r cone; (8) 7.9 mm Faraday cup s h i e l d i n g aperture; (9) Bias r i n g f o r adjacent Faraday cup; (11) 4.nalyzer housing; (12) Variable entrance a p e r t u r e ; (13) E l e c t r o n m u l t i p l i e r output.
corresponding t o 0.7 - 5 KeV/A. A l l beans a r e c o l l i - mated t o 113 mm diam and k0.025° angular spread, and then t r a v e r s e a 4-m-thick t a r g e t c e l l terminated by
"2-mm a p e r t u r e s ( o r a f o i l t a r g e t centered a t t h e same l o c a t i o n ) . The beam and accompanying e l e c t r o n s then e n t e r along t h e c e n t r a l r a y of a 180' s p h e r i c a l - s e c t o r analyzer of mean r a d i u s 3.8 cm, whose AE/E of 1.4% f u l l width a t half-maximum i s s e t by a 0 . 7 1 - m ~ analyzer e x i t a p e r t u r e , and t h e source dimensions a t t h e c e n t e r of t h e c e l l . The minimally d e f l e c t e d i o n beam passes through a n a p e r t u r e i n t h e l a r g e r - r a d i u s p l a t e of t h e analyzer and i n t o a Faraday cup used f o r beam normalization. Typical g a s p r e s s u r e s of -15 mTcrr a r e e s t a b l i s h e d by a standard feedback- c o n t r o l l e d capacitance-manometer system. Single- c o l l i s i o n conditions and n e g l i g i b l e charge changing a r e e s t a b l i s h e d by extremely l i n e a r p l o t s of i n t e - g r a t e d cusp c r o s s s e c t i o n s versus p r e s s u r e f o r t h e v a r i o u s i o n s and energies. The p l o t i n t e r c e p t s typ- i c a l l y coincide p r e c i s e l y w i t h very small r e s i d u a l cusp c r o s s s e c t i o n s measured a t zero pressure. Spu- r i o u s s i g n a l s from e l e c t r o n l o s s by contaminant beams were r u l e d o u t , a s d e l i b e r a t e changes i n t h e a c c e l e r a t o r vacuum by a decade i n p r e s s u r e produced no n o t i c e a b l e e f f e c t on p r e s s u r e l i n e a r i t y . The f i n e c o l l i m a t i o n guarantees t h a t t h e beam never encoun- t e r s any a p e r t u r e o r s u r f a c e i n t h e gas c e l l o r spec- trometer regions, a s v e r i f i e d by v e r y low spurious s i g n a l s obtained a t zero pressure. Efagnetic f i e l d s
a r e reduced t o < 3 x 1 0 - ~ T over t h e spectrometer vol- ume by t h r e e orthogonal e x t e r n a l c o i l s . Changes i n c o i l c u r r e n t of S 2 0 % produce n e g l i g i b l e changes i n cusp shape and i n t e g r a t e d production c r o s s s e c t i o n s . A sample electron-energy cusp obtained f o r
o'+ t r a v e r s i n g A r a t 30 MeV i s shown i n t h e i n s e t t o Fig. 2, and f o r 40 MeV 08+ i n t h e upper l e f t cor- ner of Fig. 3. Our e x p l o i t a t i o n of an improved sig- nal-to-background r a t i o over t h a t of Cranage and Lucas [11] revealed r i c h s t r u c t u r e i n t h e cuspwings f o r 0" ( b u t n o t f o r 08+), a s d e p i c t e d i n Fig. 3, and a s w i l l be discussed i n a subsequent section.
FIG. 2. - Z and V i dependence of e l e c t r o n c a p t u r e i n t o continuum s t a t e s f o r bare c6+ and 0 8 + ions i n A r a r e shown i n t h e upper p o r t i o n , i n a l o g o versus logE/A power-law p l o t . The lower p o r t i o n shows charge-state v a r i a t i o n d a t a on i n t e g r a t e d c r o s s sec- t i o n s f o r 0"+ - 08+ a t 30 ?lev. The i n s e t shows a cusp f o r 08* i o n s i n A r a t 30 MeV, and has super- posed on it a d-Ar c a l i b r a t i o n cusp (only a repre- s e n t a t i v e small f r a c t i o n of d a t a p o i n t s over t h e peak a r e shown).
It i s of i n t e r e s t t o note a v e r y u s e f u l f e a t u r e of such f a s t e l e c t r o n cusp spectroscopy.
The kinematic transformation between p r o j e c t i l e and
l a b o r a t o r y frames r e s u l t s i n a non-linear b u t high
g a i n a m p l i f i c a t i o n of small energy i n t e r v a l s very
near zero energy i n the p r o j e c t i l e r e s t frame. For
example, t h e 0 t o 100 meV e l e c t r o n k i n e t i c energy in-
t e r v a l i n t h e r e s t frame of a 5 MeV/A p r o j e c t i l e i s
transformed i n t o t h e i n t e r v a l 2743 eV - 2776 eV f o r
zero degree e l e c t r o n s i n t h e l a b o r a t o r y frames f o r
I 1.0 1.4 18 10 1.4 1.8
I I I I I I I I I I I I
ELECTRON ENERGY (KeV)
FIG. 3. - Normalized s p e c t r a f o r e l e c t r o n capture and l o s s t o continuum s t a t e s i n t h e forward direc- t i o n f o r 2.5-MeV/amu 09' and siq+ on A r . Zero-count base l i n e s a r e shown f o r each spectrum. S t a t i s t i c a l e r r o r s a r e about 2 X a t t h e peaks; The "difference"
spectrum i n t h e lower left-hand p o r t i o n of t h e f i g - u r e r e s u l t s from d i r e c t s u b t r a c t i o n of the 05+ from
the 0 4 + normalized data.
an o v e r a l l energy i n t e r v a l a m p l i f i c a t i o n f a c t o r of -330. The a d d i t i o n a l advantage of coping with de- t e c t i o n problems f o r 3 keV e l e c t r o n s r a t h e r than 0.1 eV e l e c t r o n s can s c a r c e l y be overestimated.
The compression of t h e 4a s o l i d angle i n the pro- j e c t i l e frame i n t o a small cone very near the for- ward d i r e c t i o n can a l s o r e p r e s e n t a considerable ad- vantage i n c o l l e c t i n g power f o r a l l the e l e c t r o n s of i n t e r e s t i n some desired energy i n t e r v a l . The corresponding drawbacks a r e , of course, extremely coarse angular r e s o l u t i o n ( i n the p r o j e c t i l e frame), and the peak shape and h e i g h t d i s t o r t i o n discussed by Steckelmacher et aZ. [20] r e s u l t i n g from t h e ef- f e c t s of f i n i t e analyzer energy r e s o l u t i o n f o r very small angular i n t e r v a l s near the forward d i r e c t i o n . Nonetheless, t h e i n h e r e n t high g a i n energy i n t e r v a l a m p l i f i c a t i o n i s a most promising experimental t o o l which remains t o be exploited.
RESULTS CONCERNING ANOMALOUS PROJECTILE Z DEPENDENCE A s i g n i f i c a n t .prediction of t h e theory of Dettmann, Harrison, and Lucas 151 and a l s o t h a t of Macek [2] i s a z 3 dependence f o r do/&, f o r given V i . We did not f i n d t h i s dependence i n the observ- ed cross-section r a t i o (when i n t e g r a t e d between s u i t a b l y s c a l e d , f i x e d , v e l o c i t y l i m i t s ) f o r bare 0" vs c6+ ions t r a v e r s i n g A r gas a t t h e same v e l o c i t y [271. But t h i s r a t i o i s independent of velocity,
j u s t a s p r e d i c t e d . To see where t h e predicted z 3
dependence a r i s e s , we can parametrize our r e s u l t s i n terms of t h e simple a n a l y t i c forms given by Dett- mann et aZ.[5]. Highly s i m i l a r r e s u l t s f o r cusp
shapes and doubly d i f f e r e n t i a l c r o s s s e c t i o n s a r e obtained i n t h e various ECC t h e o r i e s , which d i f f e r mainly i n t h e p o s s i b l e occurrence of i n t e r f e r e n c e
s t r u c t u r e a s i n t h e formulations of Macek and of Band [2,6]. The t h e o r i e s of liacek and Band add sep- a r a t e f i r s t - o r d e r amplitudes f o r d i r e c t i o n i z a t i o n and charge t r a n s f e r , leading i n p r i n c i p l e t o i n t e r - ference, which has been sought b u t not found i n 0.5-MeV/A ~ e + + - ~ e c o l l i s i o n s by llenendez and co- workers [151. The theory of Dettmann, Harrison, and Lucas 151, which i s a second-Born-approximation cal- c u l a t i o n of the charge t r a n s f e r t o the continuum, l e a d s t o a cusp i n c r o s s s e c t i o n such t h a t
where i n second Born approximation
Here Ve, V i , VB, Z , ZT, a B and 8, r e f e r , respective- l y , t o l a b o r a t o r y e l e c t r o n , ion, Bohr v e l o c i t i e s , p r o j e c t i l e and t a r g e t atomic n w b e r s , t h e Bohr ra- d i u s , and the half-angle of a small cone B o over which 'the doubly d i f f e r e n t i a l c r o s s s e c t i o n i s in-
t e g r a t e d t o o.btain da/dve. Of course F(Vi) can be c a l c u l a t e d i n o t h e r approximations, many of which would be expected t o s c a l e l i k e Z2. Hence t h e over- a l l Z 3 f a c t o r a r i s e s from the l i n e a r Z dependence of the f o r e f a c t o r multiplying any form f o r F which s c a l e s a s 2'.
I n t h e upper p o r t i o n of Fig. 2 t h e cusp c r o s s s e c t i o n ( a r b i t r a r y s c a l e ) i n t e g r a t e d over e- l e c t r o n v e l o c i t y between f i x e d b u t scaled v e l o c i t y l i m i t s t o be described i s p l o t t e d f o r bare c6+ and 0 8 + ions versus energy per nucleon, on a l o g o vs.
1ogEIAplot. The p a r a l l e l i s m of t h e curves shown and t h e i r r a t i o d e p i c t both a common v e l o c i t y de- pendence, and a velocity-independent Z dependence.
I n t e g r a t i ~ d 0 ( 8 ~ ) / & , between t h e v e l o c i t y l i m i t s ( 1 -a)Vi and ( l + a ) V i , where a i s a r b i t r a r y b u t con- s i s t e n t l y chosen t o be 0.04, standardizes a f i x e d , s c a l e d , v e l o c i t y - i n t e r v a l region of i n t e g r a t i o n , which s c a l e s a s t h e o r e t i c a l l y p r e d i c t e d by Dettmann, Harrison, and Lucas 151, and minimizes bac~ground and shape c o r r e c t i o n s . D i r e c t l y measured o8+/cSia
r a t i o s a t 1.88 and 2.50 MeV/A a r e approximately
C1-230 JOURNAL DE PHYSIQLE
1.87 *0.08 and 1.94 k0.08, corresponding t o p r e d i c t - ed r a t i o s of 2.37 i f a z3 dependence i s assumed.
The e r r o r b a r s correspond t o range e r r o r s i n measur- ed r a t i o s . E v i d e n t l y t h e r e i s reasonably good a g r e e ment between t h e o r y and experiment concerning cusp shape, b u t unacceptably poor agreement concerning Z dependence.
Following t h e s u g g e s t i o n s of Macek ( p r i v a t e communication) t h a t t h e i n t e g r a t i o n l i m i t s might be too broad, opening t h e p o s s i b i l i t y of a mixed Zpower i n t h e range 2=6 t o 8, we v a r i e d t h e r e g i o n of i n t e - g r a t i o n , b u t f i n d no s y s t e m a t i c change i n t h e power over t h e e n t i r e range a = 0.01 t o 0.04. We have a l s o c a r r i e d o u t a s y e t unpublished measurements f o r deu- t e r o n s and b a r e s i l k + i o n s i n A r a t t h e same v e l o c i - t i e s . The same z ~ . power law ~ ~ ~ i s found t o cor- . ~
r e c t l y p r e d i c t both t h e d+Ar and s i l
4++ A r cross- s e c t i o n s , w i t h i n e r r o r b a r s . The disagreement be- tween t h e o r y and experiment t h u s p e r s i s t s , and e i t h e r c o n s t i t u t e s a fundamental c h a l l e n g e t o t h e o r y o r t o experimenters t o f i n d something wrong w i t h t h e in- t e r p r e t a t i o n of t h e d a t a .
RESULTS CONCERNING OBSERVATION OF PERIODIC (INTER- FERENCE?) STRUCTURE IN THE FORWARD PEAK FROM FAST PROJECTILE ELECTRON LOSS (ELC)
Drepper and Briggs [7] have g i v e n a theory concerning b i n a r y - c o l l i s i o n a l e l e c t r o n l o s s by f a s t p r o j e c t i l e i o n s i n which t h e laboratory-frame d i s - t r i b u t i o n of t h e l a r g e forward e j e c t e d - e l e c t r o n peak d i s p l a y s a v e r y s i m i l a r cusp i n b o t h energy and an-
-+ -+
g l e , c e n t e r e d i n v e l o c i t y n e a r V e = Vion. The theore- t i c a l cusp shape c l o s e l y resembles t h a t p r e d i c t e d i n t h e ECC t h e o r i e s [2,4,5,6] f o r b a r e i o n s . The theo- r i e s of Macek and Band [2,61 r e g a r d i n g ECC d i f f e r i n p r i n c i p l e from t h e o t h e r ECC t h e o r i e s i n t h e p o s s i - b l e o c c u r r e n c e of i n t e r f e r e n c e s t r u c t u r e modifying
t h e shape of t h e observed cusp i n e l e c t r o n energy.
T h i s s t r u c t u r e r e s u l t s from i n t e r f e r e n c e of sepa- r a t e amplitudes f o r d i r e c t i o n i z a t i o n and f o r charge t r a n s f e r to t h e p r o j e c t i l e - c e n t e r e d continuum. While t h e l a t t e r t h e o r i e s a r e f i r s t - o r d e r approximations which o b t a i n separate amplitudes f o r t h e i o n i z a t i o n
and c h a r g e - t r a n s f e r c o n t r i b u t i o n s , t h e former theo- r i e s employ a singze amplitude equal t o t h e second Born amplitude away from t h e forward peak, b u t ex-
-+ +
h i b i t i n g a n enhancement near .Ve=Vion a r i s i n g from t h e u s e of s u i t a b l e Coulomb wave f u n c t i o n s c e n t e r e d on t h e p r o j e c t i l e . Thus t h e l a t t e r ECC t h e o r i e s ad- m i t p o s s i b l e i n t e r f e r e n c e e f f e c t s which a r e most
pronounced when t h e phase of t h e exchange c r o s s sec- t i o n i s varying most r a p i d l y because of Coulomb d i s - t o r t i o n of t h e f i n a l - s t a t e wave f u n c t i o n . The f o r - mer single-amplitude t h e o r i e s , of c o u r s e , l e a d t o no such i n t e r f e r e n c e e f f e c t s .
To o u r knowledge, p r i o r t o o u r paper [24]
t h e r e had been no p r e v i o u s d i s c u s s i o n of p o s s i b l e i n t e r f e r e n c e e f f e c t s i n e l e c t r o n - l o s s p r o c e s s e s , o r of p o s s i b l e i n t e r f e r e n c e between c a p t u r e and l o s s p r o c e s s e s l e a d i n g t o t h e same s o r t of p r o j e c t i l e - c e n t e r e d continuum s t a t e s . S i m i l a r l y t h e r e had been no p r e v i o u s experimental o b s e r v a t i o n of i n t e r f e r e n c e e f f e c t s i n e i t h e r t h e ECC o r t h e electron-loss-to- continuum (ELC) channels. An u n s u c c e s s f u l s e a r c h f o r ECC i n t e r f e r e n c e s t r u c t u r e i n 0.5-M~V/A H++-He col-
l i s i o n s was, however, made by Duncan e t aZ. 1151.
Within e r r o r l i m i t s , o u r more r e c e n t experiments on ECC f o r 1 . 6 - 3.9-MeVlA C, 0 , and S i b a r e i o n s trav- e r s i n g He, Ne, and Ar do n o t e x h i b i t i n t e r f e r e n c e s t r u c t u r e . Menendez e t aZ. 1141 have a l s o performed t h e p r o t o t y p e c h a r g e - s t a t e v a r i a t i o n experiment, i n comparing e l e c t r o n s p e c t r a f o r He+ and He++ on A r , f i n d i n g no s i g n i f i c a n t d i f f e r e n c e s i n t h e cuspshapes.
However, i n experiments w i t h H- p r o j e c t i l e s [7] t h e y o b t a i n e d q u i t e d i f f e r e n t e l e c t r o n s p e c t r a n e a r -+ V e =
=
-fV i and proposed t o e x p l a i n t h e observed s t r u c t u r e a s r e s u l t i n g from two a d d i t i v e p r o c e s s e s , namely s i n g l e and double e l e c t r o n l o s s i n t h e forward d i - r e c t i o n .
I n o u r paper 1241 we r e p o r t e d t h e observa- t i o n of pronounced and unexplained o s c i l l a t o r y struc- t u r e i n t h e wings of t h e ELC forward peak f o r 1.6- 3.9-lIeV/A 0 4 + and ~ i ' " 'I2+ i o n s t r a v e r s i n g Ne and Ar g a s e s . These s t r u c t u r a l f e a t u r e s e x h i b i t no ob-
s e r v a b l e t a r g e t - g a s dependence and show o n l y v e r y weak dependence, p o s s i b l y o f k i n e m a t i c o r i g i n , on p r o j e c t i l e energy i n t h e p r o j e c t i l e r e s t frame.
S i m i l a r b u t much weaker s t r u c t u r e i s observed f o r some 0q+ and ~ i q + p r o j e c t i l e s o t h e r t h a n t h o s e a l - ready l i s t e d b u t no d e t e c t a b l e o s c i l l a t o r y s t r u c - t u r e i s s e e n f o r t h e b a r e i o n s .
F i g u r e 3 shows energy s p e c t r a o b t a i n e d f o r
e l e c t r o n s e m i t t e d i n t h e forward d i r e c t i o n u s i n g a n
argon g a s t a r g e t and s e v e r a l 0q+ and ~ i q + p r o j e c t i l e
i o n s . A l l s p e c t r a d i s p l a y e d a r e f o r p r o j e c t i l e s
having t h e same v e l o c i t y (2.5 MeV/A). Each of t h e
s p e c t r a h a s been normalized t o t h e same peak h e i g h t
and no a n a l y z e r - t r a n s m i s s i o n o r d e t e c t o r - e f f i c i e n c y
c o r r e c t i o n s have been made. The uppermost two spec-
t r a a r e f o r b a r e 0 8 + and si14+ undergoing p u r e ECC.
and e x h i b i t t h e t y p i c a l skewed d i s t r i b u t i o n found p r e v i o u s l y by u s f o r ECC by b a r e i o n s ( a q u a n t i t a - t i v e t h e o r y of t h e skewness i s n o t y e t a v a i l a b l e ) . A much more symmetric, narrower, and a l - most s t r u c t u r e l e s s cusp i s shown f o r 0". The abso-
l u t e y i e l d , d e f i n e d by numerical i n t e g r a t i o n o v e r a f i x e d f r a c t i o n of t h e cusp, i s about 2.2 times g r e a t e r f o r 0" t h a n a s i m i l a r l y d e f i n e d y i e l d f o r 08+. The f r a c t i o n of ECC can be e s t i m a t e d assuming a n e f f e c t i v e i o n charge of Z e f f = q by s c a l i n g t h e known 0 8 + y i e l d by zef '. '. Extension t o lower- charge s t a t e s of t h e ECC c o n t r i b u t i o n e l i m i n a t i o n a c c o r d i n g t o t h i s procedure shows t h a t f o r 1.6-2.5-
>lev/A 0q+ p r o j e c t i l e s t h e ELC y i e l d dominates t h e ECC c o n t r i b u t i o n when L-electrons a r e p r e s e n t . For 0 5 + a t 2.5 MeV/A on Ar t h e ELC y i e l d i s about 4
times t h e ECC c o n t r i b u t i o n . Thus t h e narrower, more symmetric, and t h e r e f o r e s i g n i f i c a n t l y d i f f e r e n t peaks observed f o r 0 5 + , 0 4 + , and 0 3 + a r e i n d i c a t i v e of ELC p r o c e s s e s . We observe a s i m i l a r q u a l i t a t i v e behavior i n peak-shape v a r i a t i o n f o r t h e ~ i q + charge s t a t e s where, f o r q = 11, ELC and ECC c o n t r i b u t i o n s a r e comparable.
The s p e c t r a f o r 0 4 + i n F i g s . 3, 4 show pronounced o s c i l l a t o r y s t r u c t u r e i n b o t h wings of t h e cusp. I n F i g . 3 t h i s s t r u c t u r e h a s been made
V E L O C I T Y ( R . U . )
FIG. 4. - Expanded view of t h e 0 4 + + A r ELC d a t a i n c l u d e d i n Fig. 3, w i t h raw d a t a p o i n t s ( s t a t i s t i - c a l e r r o r s p o i n t s i z e ) . A f i t t e d , s l i g h t l y skewed, cusp-shaped f i t t o t h e d a t a i s a l s o shown, t o g e t h e r w i t h a n o f f - s e t and magnified d i f f e r e n c e curve a t t h e t o p of t h e f i g u r e .
v i r t u a l l y obvious by means of s u b t r a c t i n g t h e n e a r l y symmetric and s t r u c t u r e l e s s peak-normalized 0
5+cusp from t h e 04+ cusp. T h i s 0 4 + - 0 5 + " d i f f e r e n c e " r e s u l t i s shown i n t h e bottom left-hand corner of t h e f i g - u r e , w i t h t h e v e r t i c a l s c a l e expanded by a f a c t o r of 2 f o r c l a r i t y . Well-defined maxima and minima lo- c a t e d n e a r l y syrmnetrically about t h e cusp c e n t e r a r e v i s i b l e . The f i r s t obvious maximum i n t h e " d i f f e r - ence" spectrum i s s e p a r a t e d by , . , 100 eV from t h e cusp c e n t e r i n t h e l a b frame which corresponds t o o n l y - 2 eV i n t h e p r o j e c t i l e frame, demonstrating t h e u t i l i t y of t h e k i n d of n o n l i n e a r electron-energy i n t e r v a l a m p l i f i c a t i o n r e s u l t i n g from p u r e l y kinema- t i c c o n s i d e r a t i o n s d i s c u s s e d above.
By u s e of p r o j e c t i l e s w i t h more t h a n f o u r e l e c t r o n s , f o r example 0 3 + , t h e o s c i l l a t o r y s t r u c - t u r e i s obscured o r eliminated. C h a r a c t e r i s t i c of t h e s e lower-charge s t a t e s i s a narrow c e n t r a l cusp on t o p of a much b r o a d e r d i s t r i b u t i o n , a s shown i n t h e f i g u r e d i r e c t l y above t h e " d i f f e r e n c e " spectrum.
S i m i l a r cusp shapes have been observed f o r t h e same p r o j e c t i l e s a t s e v e r a l beam e n e r g i e s (1.6-3.9 M~V/A) a:ld i n a l l c a s e s t h e s t r o n g e s t o s c i l l a t o r y s t r u c t u r e h a s been e v i d e n t f o r 0'+ p r o j e c t i l e s .
F i g u r e 4 p r o v i d e s a p r e v i o u s l y unpublished, even more g r a p h i c p r e s e n t a t i o n of t h e same d a t a ( s t a t i s t i c a l e r r o r b a r s - p o i n t s i z e ) . Here a f i t t e d cusp-shaped curve h a s been s u b t r a c t e d from t h e d a t a i n v e l o c i t y space a f t e r m u l t i p l y i n g t h e Dettmann et aZ. [51 quoted above by an a d d i t i o n a l f a c t o r
(V,/V;)~ t o account f o r t h e observed asymmetry (P i s a parameter of t h e f i t ) . The d i f f e r e n c e spectrum, o f f - s e t and enhanced by an a r b i t r a r y f a c t o r , i s shown a t t h e t o p of t h e f i g u r e . A p l e a s i n g , symmet- r i c d i f f e r e n c e spectrum i s seen, s t r o n g l y suggestive of a n i n t e r f e r e n c e p a t t e r n . The observed s t r u c t u r a l f e a t u r e s have w i d t h s comparable t o t h e f i n i t e r e s o l u - t i o n ( 1 . 4 Z f u l l w i d t h a t half-maximum) of t h e ana- l y z e r a l o n e , i n d i c a t i n g t h a t t h e s e f e a t u r e s may have w i d t h s which a r e c o n s i d e r a b l y narrower, even i n t h e l a b o r a t o r y frame.
Measurements f o r t h e same p r o j e c t i l e s (oq+
and ~ i q + ) and beam e n e r g i e s b u t w i t h a d i f f e r e n t t a r g e t g a s , neon, r e s u l t i n s p e c t r a having s t r u c t u r - a l f e a t u r e s of d i f f e r e n t amplitude b u t o c c u r r i n g a t t h e same e n e r g i e s a s t h o s e f o r argon, demonstrating a t a r g e t independence of t h e b a s i c phenomenon.
Data o b t a i n e d under p r e c i s e l y t h e same ex-
p e r i m e n t a l c o n d i t i o n s w i t h ~ i q + p r o j e c t i l e s a r e d i s -
played i n t h e right-hand column of Fig. 3. O s c i l l a -
t o r y s t r u c t u r e i n t h e wings s i m i l a r t o t h a t f o r 0 4 +
cl-232 JOURNAL DE PHYSIQUE i s evident. I n c o n t r a s t t o t h e 0 d a t a where strong
o s c i l l a t o r y s t r u c t u r e i s found only f o r the four- e l e c t r o n p r o j e c t i l e , the S i d a t a c l e a r l y show such s t r o n g s t r u c t u r e f o r p r o j e c t i l e s with 2 , 3 , a n d 4 e- l e c t r o n s . For siq+ w i t h q < 10 ( a s f o r 0 3 + ) no c l e a r o s c i l l a t i o n s have been observed. As i n t h e 04' data, t h e energy p o s i t i o n s of the s t r u c t u r a l f e a t u r e s i n t h e p r o j e c t i l e r e s t frame a r e approximately inde- pendent of q , Vi, and t a r g e t gas b u t t h e energy sep- a r a t i o n s of what appear t o be maxima and minima cor- responding t o those of the 0'' s p e c t r a a r e different- l y spaced.
The wide range of charge s t a t e s used f o r
siq+ on A r ( q = 5-14) gives r i s e t o a monotonically decreasing ELC i n t e g r a t e d cusp cross-section (a=0.04) with q , producing a f a c t o r of 10 drop i n going
from q = 5 to q = 11. These y i e l d s have been found t o be weakly dependent on V i , veryfying f o r t h e f i r s t time t h e very r e c e n t p r e d i c t i o n of Briggs and Drepper [71 t h a t i n t h e p r e s e n t v e l o c i t y range and higher, such electron-loss c r o s s s e c t i o n s should tend t o complete v e l o c i t y independence. S i g n i f i c a n t depar- t u r e s (e.g. a f a c t o r of 2 2 over t h e r a n g e 2.5-3.9 MeV/A) from t h i s weak v e l o c i t y dependence s e t i n only f o r q2.11, j u s t i n the range where t h e ELC
c r o s s s e c t i o n s a r e dropping below t h e more s t r o n g l y velocity-depentlent [231 ECC c r o s s s e c t i o n s .
Variation of the a v a i l a b l e experimental parameters (2, q , V i , ZT) has l e a d t o s e v e r a l con- clusions: (1) The "positions" of s t r u c t u r a l maxima and minima i n projectile-rest-frame energy a r e inde- pendent of t a r g e t gas. Thus t h e e f f e c t i s projec- t i l e s p e c i f i c and t h e r e f o r e cannot be described by a molecular model a s a r e some o s c i l l a t o r y phenomena obtained i n ion-atom c o l l i s i o n s . (2) The s t r u c t u r a l
"positions" i n t h e p r o j e c t i l e frame a r e approximate- l y independent of both q and V i , b u t t h e amplitudes of t h e f e a t u r e s a r e s t r o n g l y dependent on q f o r 04'
( l e s s so f o r s i q + ) and weakly dependent on V i . (3) The "positions" a r e dependent on Z1. (4) The s t r u c - t u r e found corresponds t o e l e c t r o n s having energies between 2 and 20 eV i n the p r o j e c t i l e frame. Since no single-electron e x c i t a t i o n of t h e highly ionized p r o j e c t i l e s can lead t o a u t o i o n i z a t i o n i n t h i s energy range, i t i s u n l i k e l y t h a t t h e s t r u c t u r e r e s u l t s from p r o f e c t i l e autoionization.
While a much needed t h e o r e t i c a l i n t e r p r e t a - t i o n of t h e highly reproducible (observed i n hurrd- reds of s p e c t r a ) s t r u c t u r e i s admittedly lacking a t t h i s time, some p o s s i b l e i n t e r p r e t a t i o n s can be en- visioned. The observed o s c i l l a t o r y s t r u c t u r e has
p e r i o d i c i t y , e s p e c i a l l y obvious i n the f a r wings of the ~ i " > l "12+
CUSPS,i n d i c a t i v e of an i n t e r f e r e n c e - based phenomenon. Such s t r u c t u r e might be the r e s u l t of i n t e r f e r e n c e between d i f f e r e n t one-electron tran- s i t i o n channels i n ELC o r i n t e r f e r e n c e of amplitudes f o r multiple-electron e j e c t i o n i n a single-step pro- cess. One can a l s o s p e c u l a t e about multiple-electron t r a n s i t i o n s i n ELC leading t o the observed s t r u c t u r e v a r i a t i o n s . S t r u c t u r e due t o one ELC process might e a s i l y wash o u t t h a t due t o another and y i e l d the observed n o n o s c i l l a t o r y s t r u c t u r e f o r 03+. It i s also p o s s i b l e t h a t multiple-electron l o s s processes might l e a d through c o r r e l a t e d mutual Coulomb repulsion during e j e c t i o n t o s t r u c t u r e s i m i l a r t o t h a t observed f o r 03+ and siq+ (with q 6 10). Though one could a l s o envision t h e p o s s i b l e i n t e r f e r e n c e of single-electron ELC and ECC f o r values of q where ELC and ECC c o n t r i - butions t o t h e t o t a l c r o s s s e c t i o n a r e comparable, one should bear i n mind t h a t t h e strong s t r u c t u r e f o r 0'+ ELC i s observed under conditions where ELC dominates ECC by a f a c t o r
N20.
RESULTS CONCERNING RIVAL ECC AND "WAKE-RIDING"
MODELS FOR COLLISIONS I N SOLIDS
As remarked e a r l i e r , the ease of i n t e r - change of gas and s o l i d t a r g e t s i n our apparatus while leaving a l l o t h e r geometrical and kinematic conditions f i x e d has permitted us t o compare gas and s o l i d t a r g e t r e s u l t s under conditions where most systematic apparatus e f f e c t s cancel t o f i r s t order.
A key parameter f o r comparison of theory and experi- ment i s the f u l l width a t h a l f maximum r of t h e
R,v
l o n g i t u d i n a l e l e c t r o n v e l o c i t y d i s t r i b u t i o n of the e l e c t r o n s emerging i n t h e forward d i r e c t i o n . I n ECC theory 151 I. can be expressed a s = lri 8,, ,
fi,v
where V i i s t h e p r o j e c t i l e v e l o c i t y i n a.u. and g o
h a l f of t h e acceptance angle, i n radians, of t h e
e l e c t r o n v e l o c i t y analyzer. For gaseous t a r g e t s
experimental r e s u l t s a r e g e n e r a l l y c o n s i s t e n t with
t h i s p r e d i c t i o n , a s noted e a r l i e r . As discussed i n
t h e i n t r o d u c t i o n , some a u t h o r s [ 17,181 observe T' s
t h a t a r e e s s e n t i a l l y independent of the v e l o c i t y of
the p r o j e c t i l e . These r e s u l t s a r e a t odds with t h e
ECC p r e d i c t i o n and t h e assumption t h a t t h e " l a s t
t a r g e t layer" i s the source of the continuum elec-
trons. The p r o p e r t i e s of continuum e l e c t r o n s coming
from wake r i d i n g (WR) s t a t e s a r e p r e d i c t e d t o be
s i g n i f i c a n t l y d i f f e r e n t fr.om ECC e l e c t r o n s . The FWHM
of t h e l o n g i t u d i n a l v e l o c i t y d i s t r i b u t i o n f o r wake
r i d i n g e l e c t r o n s can be expressed [8,91, i n a.u.,
a s
( ~ t ~ ~ ) ~ / ~ [-( 4 - 4 9 '"
rWR = 1.67 B'/' -
R ,v
WRes
where w i s t h e m a t e r i a l s p e c i f i c plasma r e s o - Res
nance frequency, B = zff * Cn where z ; ~ ~ i s t h e ef- f e c t i v e c h a r g e of t h e i o n i n t h e medium,
C = exp(-3ny/4w Res ) a c c o u n t s f o r t h e damping of the wake through y ( t h e w i d t h of t h e plasma frequency d i s t r i b u t i o n ) , and r~ = 1-2 i s determined by a cor- r e l a t i o n between t h e wake and t h e wake bound e- l e c t r o n s . I n t h e wake r i d i n g d e s c r i p t i o n o f such e l e c t r o n s t h e J!WZlM i s determined by t h e c h a r a c t e r - i s t i c s of t h e t a r g e t m a t e r i a l (uReS,y) and t h e ef- f e c t i v e charge of t h e ion. It should d e c r e a s e with i n c r e a s i n g p r o j e c t i l e v e l o c i t y i n c o n t r a d i s t i n c t i o n t o t h e ECC p r e d i c t i o n . Our experiment 1251 was de- s i g n e d t o t e s t t h e s e s p e c i f i c p r e d i c t i o n s by u s i n g v a r i o u s t a r g e t s (C, At, Ag, and Au), and l a r g e a t - omic numbers f o r t h e i n c i d e n t i o n s (ZI = 1 t o 28) a t h i g h ~ r o j e c t i l e v e l o c i t i e s (6 t o 14 a . u . ) . These experimental c o n d i t i o n s a r e f a v o r a b l e t o wake f o r - mation d u r i n g passage of t h e i o n through t h e s o l i d . P r e v i o u s experiments w i t h s o l i d t a r g e t s ( s e e Bib- l i o g r a p h y ) were performed a t lower p r o j e c t i l e ve- l o c i t i e s ( 1 - 3 a.u.) where i t may b e q u e s t i o n a b l e i f A w a k e i s formed [8,91. We f i n d t h a t t h e r e a r e d i s t i n c t d i f f e r e n c e s between s o l i d and gaseous t a r g e t s i n agreement w i t h o t h e r experiments, b u t none of t h e p r e d i c t i o n s of t h e wake-riding t h e o r y concerning t h e w i d t h o f t h e l o n g i t u d i n a l v e l o c i t y d i s t r i b u t i o n of convoy e l e c t r o n s a r e borne o u t .
I o n beams ( H : , E, = 2.5 t o 3.86 MeV/A;
0*q E, = 1 t o 3.86 MeV/A; ~ i El + = 1 ~ t o 4.7 MeV/A;
and ~ i El + = 1 ~ t o 2.5 M ~ V / A of 20 pA i n t e n s i t y and v a r i o u s charge s t a t e s were passed through t h i n C , AR, Ag, and Au t a r g e t s .
T y p i c a l d a t a i n Fig. 5 show t h e l o n g i t u - d i n a l e l e c t r o n v e l o c i t y d i s t r i b u t i o n , do/dVe (cor- r e c t e d f o r t h e v a r i a t i o n i n t h e energy a c c e p t a n c e band AEeciEe) f o r 108 MeV si+' i n c i d e n t o n a 100 pg/cm2 Au f o i l ( s o l i d l i n e ) , and t h e normalized v e l o c i t y d i s t r i b u t i o n ( n o r m a l i z a t i o n c o n s t a n t - 3)
f o r 108 MeV Si+13 t r a v e r s i n g 30 mTorr of Ar. The dashed v e r t i c a l . l i n e marks t h e v e l o c i t y of t h e in- c i d e n t p r o j e c t i l e . The v e l o c i t y d i s t r i b u t i o n ob- s e r v e d from a s o l i d t a r g e t was found t o b e inde- pendent of t h e i n c i d e n t s i l i c o n charge s t a t e q
(q = 6 t o 1 4 ) , t h e v e l o c i t y of t h e p r o j e c t i l e , t h e t a r g e t m a t e r i a l , and of t h e t h i c k n e s s of t h e t a r - g e t . Hence t h e s o l i d l i n e marks t h e t y p i c a l
d u
-
dve
K ckts
FIG. 5. - The d i f f e r e n t i a l c r o s s s e c t i o n du/dVe a s a f u n c t i o n of t h e e l e c t r o n v e l o c i t y , Ve, of contin- uum e l e c t r o n s emerging near O0 w i t h r e s p e c t t o t h e i o n beam f o r 108 MeV s i + 1 3 on 30 mTorr Ar g a s and
~ i on 100 pg/cm2 Au f o i l . + ~ The e l e c t r o n energy s c a l e a p p e a r s a t t h e t o p of t h e f i g u r e .
E, ( k e V )
1.6 1.8 2.0 2.2 2.4 2.6
d i s t r i b u t i o n o b t a i n e d w i t h s o l i d t a r g e t s . S i n c e t h e mean e x i t c h a r g e s t a t e from a s o l i d of 108 MeV
~ i i s * 12.9, ~ a d i r e c t comparison between t h e e l e c - t r o n d i s t r i b u t i o n s from t h e g a s and t h e s o l i d can b e made. We n o t e t h a t t h e y a r e d i s t i n c t l y d i f f e r e n t . For gaseous t a r g e t s t h e v e l o c i t y d i s t r i b u t i o n (dash- ed l i n e ) e x h i b i t s a n e g a t i v e skewness ( a n asymmetry towards lower e l e c t r o n v e l o c i t y ) . For s o l i d t a r g e t s t h e v e l o c i t y d i s t r i b u t i o n ( s o l i d l i n e ) i s narrower, a s measured by t h e FWHM, and e x h i b i t s a markedly d i f f e r e n t skewness. T h i s i s a completely unexpect- ed r e s u l t n o t p r e d i c t e d by e i t h e r ECC o r WR theo- r i e s and c a n b e i n d i c a t i v e of t h e d i f f e r e n t proces- s e s of e x c i t a t i o n f o r p r o j e c t i l e s t r a v e r s i n g s o l i d s and g a s e s .
V e l o c i t y d i s t r i b u t i o n s of t h e kind shown i n F i g . 5 were a c q u i r e d f o r t a r g e t s of ~ ( t = 3 0 p g / c u ? ) , AR(t= 50 vg/cm2), A g ( t = LOO pg/cm2) and Au(t = 100 pg/cm2) w i t h t h e a f o r e - m e n t i o n e d i o n s . These thick- n e s s e s were chosen t o p e r m i t s u f f i c i e n t s p a t i a l ex- t e n t f o r wake f o r m a t i o n and c h a r g e e q u i l i b r i u m . We f i n d t h e EWHM of t h e v e l o c i t y d i s t r i b u t i o n i s , with- i n experimental u n c e r t a i n t y , i n s e n s i t i v e t o t h e
18-
I I I I I I
108 MeV ~ i - + ~
I - - +13onAr
16- + 9 0 n Au-
14 - -
12 - -
/
\
.
c 1-234 JOURNAL DE PHYSIQUE
ity range of 8.7 to 12.4 a.u. The = 25 measurements with gaseous targets and 0+8 and si+14 projectiles
incident projectile, its charge state or velocity, E, (MeV/amu)
as well as to the target material and its thick- 0.1 0.5 1.0 2.0 4.0
are represented by the three open points in Fig. 6.
cThe light solid lines in Fig. 6 are the result of
FIG. 6. - The full width at half maximum of the ness. The results of a 80 measurements are summa-
rized in Table I. The uncertainty in each measure- I . 0 - ment is estimated to be f 0.02 a.u., or lo%, aris- 0.9 ing from statistics, background subtraction and in-
strumental resolution. Although distinct trends 0.8 appear, all of the data for solid targets can be
represented, within experimental uncertainty, by 0.7
r
a FWHM r = 0.25 f 0.02 a.u. 1 *v .t ,v Comparison of the experimental results ( a.u.1 0.6;
with ECC theory and WR theory are shown in Fig. 6. 0.5 The dashed line through the origin is the result
of the ECC theory with an acceptance half angle for 0.4
the electron energy analyzer of e o = 1.3". The re- 0.3 sults for gaseous targets (Ne and Ar) with 0+* and
si+14 projectiles are indistinguishable within ex- 0.2 perimental uncertainty (+lo %) and follow the pre-
the WR theory [8,91 for various incident ions, longitudinal electron velocity distribution, rQ,
denote,d by Z1, on an target. The material con-. in a.~., for continuum electrons as a function of the electron velocity Ve. in a.u. The incident oro-
I I I t i I I I 1
- -
-
- \" 1 4 \ \
-
- \i"i- -
/a( - -
- /
/ -
/
stants, qes and constant C, are shown in Table I. jectile energy, in ~ h / i , appears at the top ofA the For C targets, WR theory predicts values of r WR ~ , ~ figure. The dashed line is the ECC prediction. The
solid lines are the predictions of the WR theory that are approximately 213 of those for A%. For Ag for an AL target with the indicated projectiles.
and Au targets WR theory predicts about equal The lowest solid curve marked Ag is the prediction of WR theory for protons incident on Ag. The experi- ues of I? that are approximately 113 the A!Z values. mental data for solids, summarized in Table I. are
0.1 - dicted ECC linear velocity dependence in the veloc- /
. .
The solid curve marked Ag is obtained from the a- represented by the heavy solid line. The open points
WR re resent the gas target (Ne and Ar) results for
bove expression for r ~ , ~ for protons incident on O+g and si+14.
TABLE I
The measured full width at half maximum, r ~ , ~ in a.u. of the longitudinal velocity distribution of contin- uum electrons in the forward direction from thin solid targets. The energy range, in MeV/A, of the inci- dent ions is indicated below the ionic species in parenthesis. The material plasma frequency w ~ in ~ ~ , a.u., and damping constant C, defined in the text, are listed, respectively, in parentheses below the tar- get material. The bottom line lists the mean value of I' for a particular target material.
R,v
.. -'-. .._
,Target Ion --._
l-1.. -
