ELECTRON CAPTURE BY MULTICHARGED IONS AT eV ENERGIES

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ELECTRON CAPTURE BY MULTICHARGED IONS

AT eV ENERGIES

C. Havener, M. Huq, F. Meyer, R. Phaneuf

To cite this version:

30URNAL DE PHYSIQUE

Colloque Cl., supplement au nO1, Tome

50,

janvier 1989

ELECTRON CAPTURE BY MULTICHARGED IONS AT eV ENERGIES

C.C. HAVENER, M.S. HUQ, F.W. MEYER and R.A. PHANEUF

Oak Ridge National Laboratory, Oak Ridge, TN 3 7 8 3 1 - 6 3 7 2 , U.S.A.

A b s t r a c t

-

A m u l t i c h a r g e d ion-atom merged-beams apparatus has been used i n conjunction w i t h the ORNL-ECR i o n sour.ce t o measure accurate a b s o l u t e e l ectron-capture cross s e c t i o n s i n t h e energy range from below 1 eVlamu t o 1500 eVlamu. Measurements f o r N3+.4+~5+

+

H(D) c o l l i s i o n s i n d i c a t e good agreement w i t h a v a i l a b l e t h e o r e t i c a l calcula- t i o n s . However, measurements w i t h 05+

+

H(D) show an unexpected low-energy behavior which may be a t t r i b u t a b l e t o the ion-induced-dipole a t t r a c t i o n between t h e reactants. Scaled Landau-Zener c a l c u l a t i o n s presented here i d e n t i f y a t r a n s f e r p l u s e x c i t a t i o n channel which has the c o r r e c t energy dependence a t low energies. T h i s f i n d i n g suggests the need f o r a comprehensive Coupled channel c a l c u l a t i o n which would i n c l u d e such pro- d u c t states.

1

-

INTRODUCTION

The i n e l a s t i c process whereby a m u l t i c h a r g e d i o n captures an e l e c t r o n from a n e u t r a l atom i s important i n environments c o n t a i n i n g b o t h h i g h l y charged ions and neutrals. Cross sections f o r t h i s e l e c t r o n - c a p t u r e process a t low energies a r e t y p i c a l l y l a r g e (>10-15 cmz) and selec- t i v e l y populate e x c i t e d s t a t e s o f t h e m u l t i p l y charged ion. Such c o l l i s i o n s , t h e r e f o r e , are important f o r plasmas o f thermonuclear f u s i o n , astrophysics, m u l t i c h a r g e d i o n sources, and the development o f X-ray l a s e r s .

Only v e r y l i m i t e d d a t a a r e a v a i l a b l e f o r e l e c t r o n capture by m u l t i c h a r g e d i o n s c o l l i d i n g w i t h n e u t r a l s i n t h e v e l o c i t y range ( ~ ( 0 . 1 a.u.).

I n

such l o w - v e l o c i t y c o l l i s i o n s , t h e r e l a t i v e nuclear motion between c o l l i s i o n p a r t n e r s i s slow compared t o t h e o r b i t a l motion o f the a c t i v e e l e c t r o n s o f t h e system. E l e c t r o n s o f t h e temporary quasi-molecule formed i n the c o l l i s i o n have s u f f i c i e n t t i m e t o a d j u s t t o the changing i n t e r a t o m i c f i e l d as the n u c l e i approach and separate. Coupled s t a t i o n a r y - s t a t e c a l c u l a t i o n s / 1 , 2 / , w h i l e successful a t h i g h e r energies, do n o t n e c e s s a r i l y g i v e c o n s i s t e n t p r e d i c t i o n s a t lower energies. I n such c a l c u l a t i o n s , t h e i n t e r n u c l e a r motion has g e n e r a l l y been t r e a t e d c l a s s i c a l l y . I t would seem t h a t f u l l quantal c a l c u l a t i o n s 13-51 may be r e q u i r e d f o r accurate p r e d i c t i o n s a t t h e lowest energies, b u t such methods have remained u n t i l r e c e n t l y /6,71 e s s e n t i a l l y untested. At these low energies t h e r e has been s p e c u l a t i o n 13,8/ t h a t t h e ion-induced d i p o l e a t t r a c t i o n between t h e r e a c t a n t s may cause o r b i t i n g t r a j e c t o r i e s 191. Cross s e c t i o n s due t o t h i s process -are p r e d i c t e d c l a s s i c a l l y t o have a l l v dependence a t lower energies.

Cl-8 JOURNAL DE PHYSIQUE

Most o f t h e experimental work on such c o l l i s i o n processes has been based on ion-beam gas-target methods, which have g e n e r a l l y been l i m i t e d t o energies above 100 eV/amu. Some experiments a t lower energies have heen performed by Phaneuf e t a l . I 1 0 1 using a pulsed- laser-produced plasma as a source o f slow m u l t i p l y charged ions. I n t h e 10 t o 100 eV/amu energy regime t h e y found t h a t f o r few-electron systems t h e r e e x i s t s no simple s c a l i n g o f the cross s e c t i o n s w i t h charge o r v e l o c i t y , so t h a t each system must be i n v e s t i g a t e d separately. The s t r o n g i n f l u e n c e o f t h e i o n i c core has been seen i n t h e o r e t i c a l c a l c u l a t i o n s /11,12/ and measurements 1131 o f substate d i s t r i b u t i o n s a t energies l e s s than a few keV1amu.

To address t h e need f o r experimental measurements i n t h i s energy range, an ion-atom merged- beam apparatus has been developed / 6 / a t Oak Ridge N a t i o n a l Laboratory t o measure absolute t o t a l e l e c t r o n capture cross s e c t i o n s f o r m u l t i c h a r g e d i o n s c o l l i d i n g w i t h atomi'c hydrogen i n t h e energy range o f 1 t o 1000 eV/amu.

2

-

EXPERIMENTAL

The merged-beam method i s w e l l s u i t e d f o r such measurements i n t h i s energy range. D e t a i l s a r e presented i n r e f . 6. I n t h i s technique, beams o f n e u t r a l atoms and m u l t i c h a r g e d i o n s each having l a b o r a t o r y energies i n the keV range a r e merged, r e s u l t i n g i n a r e l a t i v e v e l o c i t y o f t h e two beams t h a t can be "tuned" over a l a r g e range. The r e l a t i v e energy i n t h e center-of- mass frame i s g i v e n by

E1 E2 E1 E2 1/2

Erel (eV1amu) =

-

+

- -

2

(-

-) cos 8 "'1 m2 m1 m2

where E i and mi denote t h e energy and mass o f each beam, and 0 i s t h e i r angle o f i n t e r s e c - t i o n . F o r p e r f e c t l y c o l l i n e a r beams, 8=0 and Erel can be made zero f o r Ellml=Eplm2.

F i g u r e 1 i s a s i m p l i f i e d schematic o f t h e apparatus. The m u l t i c h a r g e d i o n beam Xq+ i s merged e l e c t r o s t a t i c a l l y w i t h a n e u t r a l H o r D beam. The merged beams i n t e r a c t i n a f i e l d - f r e e r e g i o n f o r a d i s t a n c e o f 80.8 cm, a f t e r which t h e p r i m a r y beams a r e m a g n e t i c a l l y separated from each o t h e r and from t h e product o r " s i g n a l " H(D)+ ions. The ~ ( 4 - 1 ) + product o f t h e r e a c t i o n i s n o t measured separately, b u t i s c o l l e c t e d t o g e t h e r w i t h t h e primary Xq+ i n a l a r g e Faraday cup. The n e u t r a l beam i n t e n s i t y i s measured by secondary-electron emission from a s t a i n l e s s s t e e l p l a t e , and t h e s i g n a l H+ o r D+ ions a r e recorded by a channel e l e c t r o n m u l t i p l i e r (CEM) operated i n pulse-counting mode. A pure ground-state beam o f H o r D atoms i s produced by passing a 6-9 keV beam o f H- o r D- ions through t h e o p t i c a l c a v i t y o f a 1.06-pm Nd:YAG l a s e r , where up t o 600 W o f continuous power c i r c u l a t e s and t y p i c a l l y 0.5% o f the negative i o n s undergo photodetachment. A n e a r l y p a r a l l e l beam o f H(D) atoms i s produced i n t h e merge-path w i t h a diameter o f 2-4 mn FWHM and an i n t e n s i t y o f 10-20 ( p a r t i c l e ) na. The divergence o f t h i s beam i s t y p i c a l l y l e s s than 0.2". A 50-90 keV, 2-5 pA beam o f X4+ i o n s i s produced by t h e ORNL-ECR w i t h a t y p i c a l l y 6-8 mn FWHM i n t h e merge p a t h and a divergence o f l e s s than 0.5".

ORNL- DWG 88-41570

'CHANNEL ELECTRON MULTIPLIER

Fig. 1. S i m p l i f i e d schematic o f t h e i o n - n e u t r a l merged-beam apparatus.

ORNL-OWG 87- (7478

I

l

I

I

I

I

0 ' 4 0 50 60 70 80 9 0 !OO

05+ BEAM ENERGY ( k e V )

Cl-10 JOURNAL DE PHYSIQUE

An important advantage o f t h e merged-beam technique i s t h e l a r g e d e a m p l i f i c a t i o n o f the i n t e r a c t i o n - e n e r g y u n c e r t a i n t y r e s u l t i n g from t h e energy u n c e r t a i n t i e s i n t h e p r i m a r y beams. I n Fig. 2, t h e slope o f t h e curves i s j u s t AEre1/AE2, where AE2 i s t h e energy u n c e r t a i n t y i n t h e 05+ beam. As Erel decreases, t h e slope decreases, reducing the u n c e r t a i n t y i n Erel. For an estimated u n c e r t a i n t y o f 10 eV i n the n e u t r a l beam energy and 100 eV i n t h e 05+ beam energy, t h e estimated u n c e r t a i n t y due t o each beam i s l e s s than 1 eV1amu a t Ere] = 100 eV1amu and 0.1 eV/amu a t Erel = 1.0 eV1amu.

Another advantage o f t h e merged-beam technique i n low-energy measurements i s t h e p o t e n t i a l l y l a r g e angular c o l l e c t i o n o f t h e r e a c t i o n products. The low energy e l e c t r o n capture c o l l i - sions under study a r e exoergic, and, since b o t h products a r e p o s i t i v e l y charged, they can undergo s i g n i f i c a n t angular s c a t t e r i n g i n the center-of-mass frame 1141. I n t h i s respect t h e merged-beam technique i s i d e a l since t h e angular s c a t t e r i n g i n t h e center-of-mass frame becomes s i g n i f i c a n t l y compressed i n t h e l a b o r a t o r y frame, i n which t h e product i o n s are c o l l e c t e d . The apparatus was designed t o have as l a r g e an angular c o l l e c t i o n as possible. An average angular c o l l e c t i o n i n t h e l a b o r a t o r y frame along t h e 80.8 cm merge p a t h was deter- mined by d e t a i l e d t r a j e c t o r y c a l c u l a t i o n s I 6 1 t o be 1.8'. The r e s u l t a n t angular c o l l e c t i o n i n t h e center-of-mass frame i s shown i n Fig. 3. Note t h a t f o r measurements performed w i t h a 9 keV D beam a t an Erel = 1 eV/amu product t r a j e c t o r i e s w i t h up t o 90' s c a t t e r i n g i n t h e center-of-mass frame a r e c o l l e c t e d .

Electron-capture cross s e c t i o n s a r e determined by measuring t h e r a t e o f H+(D+) product ions produced by t h e beam-beam i n t e r a c t i o n over the merged l e n g t h L. The cross-section value i s c a l c u l a t e d a t each v e l o c i t y from t h e d i r e c t l y measurable q u a n t i t i e s through the equation

ORNL-DWG 87-47477

I 1 1 ' 1 I I I I 1 1 I I l l I 1 I 1

I

A N G U L A R C O L L E C T I O N

I N T H E C E N T E R - O F - M A S S F R A M E

l

where R, 11, and I 2 correspond t o the measured count r a t e , e f f e c t i v e c u r r e n t produced by n e u t r a l p a r t i c l e s , and 05+ c u r r e n t , r e s p e c t i v e l y . The t r u e n e u t r a l " c u r r e n t " i s given by I ~ / Y , Y being t h e measured e f f e c t i v e secondary-electron emission c o e f f i c i e n t f o r t h e n e u t r a l - p a r t i c l e d e t e c t o r . The q u a n t i t y q i s t h e charge s t a t e o f t h e i n c i d e n t ion, e i s t h e elec- t r o n i c charge, and v, i s the r e l a t i v e v e l o c i t y o f t h e two beams, t r a v e l i n g a t v e l o c i t i e s v1 and v2. <F> i s t h e e f f e c t i v e form f a c t o r 161 and i s a measure o f t h e s p a t i a l overlap o f the two beams along t h e merged p a t h L.

To o b t a i n a v a l u e f o r <F>, t h e beam-beam overlap i s measured i n two dimensions a t f o u r d i f - f e r e n t l o c a t i o n s along t h e merged path. Measurements were performed by two mechanical k n i f e - edge scanners and two r o t a t i n g - w i r e monitors, each performing h o r i z o n t a l and v e r t i c a l scans (see r e f . 6). The secondary emission c o e f f i c i e n t f o r t h e n e u t r a l d e t e c t o r was c a l i b r a t e d (a process t a k i n g several hours) i n s i t u and found t o have a s l i g h t dependence on n e u t r a l beam v e l o c i t y and vacuum h i s t o r y . For t y p i c a l o p e r a t i n g c o n d i t i o n s a t an i n t e r a c t i o n energy o f 25 eVlamu f o r 05+

+

D, t h e s i g n a l r a t e , R, i s t y p i c a l l y 100 Hz and must be detected i n the presence o f a background o f 6 kHz. This background i s due t o t h e n e u t r a l beam s t r i p p i n g on background gas. Therefore, vacuum i n t h e merge s e c t i o n had t o be maintained as low as possible, t y p i c a l l y 1-2 X 10-l0 T o r r w i t h beams. To separate the s i g n a l from t h e background,

a two-beam modulation scheme 161 was used. Since t h e s i g n a l r a t e produced by t h e beam-beam i n t e r a c t i o n i s p r o p o r t i o n a l t o t h e r e l a t i v e v e l o c i t y o f t h e beams ( f o r a constant cross s e c t i o n ) , t h e signal-to-background r a t i o determined t h e lowest energies a t which measurements could be made. I f t h e cross section, i n f a c t , a l s o decreases w i t h decreasing energy, measure- ments become more d i f f i c u l t a t lower energies. The lower-energy l i m i t imposed by the apparatus i t s e l f i s approximately 0.2 eV/amu, and i s a consequence o f the f i n i t e angular divergence o f t h e i n t e r a c t i n g beams.

3

-

CROSS-SECTION MEASUREMENTS

The merged-beam apparatus has been used /6,7/ t o measure t o t a l e l e c t r o n capture cross sec- t i o n s f o r 05+ and N3+,4+l5+ c o l l i d i n g w i t h ground s t a t e H(0) i n t h e energy range <1.0 eV/amu t o 21500 eV/amu. The measurements f o r 05+ and N5+ a r e compared t o o t h e r measurements and theory i n Figs. 4 and 5, r e s p e c t i v e l y . The e r r o r bars shown denote t h e - r e l a t i v e u n c e r t a i n t y estimated a t a 90% confidence l e v e l . The t o t a l absolute u n c e r t a i n t y i s i n d i c a t e d by extended e r r o r b a r s on a few p o i n t s i n Fig. 4. For a l l systems s t u d i e d t h e measurements were per- formed a t s u f f i c i e n t l y h i g h Erel t o o v e r l a p w i t h e x i s t i n g experimental measurements. Agree- ment w i t h previous measurements i s shown t o be good, e s p e c i a l l y i n t h e 05+ System (see Fig. 4) where low-energy measurements by Phaneuf e t a l . / l 0 1 extend down t o 80 eV/amu and, thereby, p r o v i d e an extended range o f comparison. These measurements were performed w i t h a l a s e r - i o n source and a hydrogen oven as t a r g e t . I n t h i s energy range t h e r e a r e a l s o two unpublished d a t a p o i n t s by Meyer e t al., measured w i t h t h e ORNL-ECR i o n source and t h e same hydrogen oven (see r e f . 15). The 05+ and the N4+ ions a r e L i - l i k e and, t h e r e f o r e , f r e e o f metastables, a l l o w i n g measurements w i t h these ions t o be d i r e c t l y compared w i t h t h e o r e t i c a l c a l c u l a t i o n s where they e x i s t .

JOURNAL DE PHYSIQUE ORNL-OWG 87-17469R 0 0.4 1.0 1 0 1 0 0 1 0 0 0 40,000 ENERGY [eV/amu] I 1 1 1 1 1 1 1 1 I 1 1 1 1 1 1 1 1 I 1 1 1 1 1 1 1 1 I 1 1 1 1 1 1 1 1 I 1 1 1 1 1 1 1

-

05+ .t H (D)

-

04+

+

H+ (D+)

-

EXPERIMENT THEORY

- o (BEAM-GAS) PHANEUF et al. (82)

----

BOTTCHER AND HElL

-

(BEAM-GAS) MEYER et al. (84) UNPUB. (83), UNPUBLISHED (MERGED-BEAMS) PRESENT RESULTS

---

GARGAUD AND

-

-

McCARROLL (871, UNPUBLISHED -

\

CLASSICAL (ORBITING)-

-

-

-

-

l 1 1 1 1 1 1 1 1 I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 l 1 1 1 1 1 1 1 1 1 1 l 1 l l l l L

Fig. 4. Comparison o f merged-beams data f o r e l e c t r o n capture i n 05+

+

H c o l l i s i o n s w i t h previous measurements and theory. S e l e c t d a t a a r e presented w i t h i n n e r and o u t e r e r r o r bars denoting r e l a t i v e and estimated t o t a l experimental u n c e r t a i n t i e s estimated a t a 90% con- f i d e n c e l e v e l . The energy u n c e r t a i n t y i s denoted by a h o r i z o n t a l b a r a t t h e lowest energy, where t h e u n c e r t a i n t y i s r e l a t i v e l y t h e l a r g e s t . ORNL-DWG 8 8 - 8 5 8 0 I 1 1 1 1 1 1 1 ~ I 1 1 1 11111 I 1 1 1 11111 I 1 1 1 11111 I l l l I l l 1 N ~ +

+

H(D)

-, N ~ +

+

H+(D+)

- _EXPERIMENT Present Results I 1 1 1 1 1 1 1 1 I 1 1 1 1 1 1 1 1 I 1 1 1 1 1 1 1 1 1 ! 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0:)

1

10 100 1000 100 Energy (eV/a

m

U)

ORNL- OWG 87- V468 1 2 0 , I I I _{I I} I I I

I

0

0

0

1 10 4 00 1000 1 l0 l00 1000 ENERGY (eV/amu)

100

-

ALL DATA - - 6 keV H AN0 D DATA

-

40

-

o 6 keV H, FASTER

Fig. 6. Data f o r 05+

+

H(D) c o l l i s i o n s taken under d i f f e r e n t l a b o r a t o r y conditions. (a) A l l data, under a l l c o n d i t i o n s , a r e p l o t t e d and a l i n e i s drawn t o guide t h e eye through the s c a t t e r i n t h e data p o i n t s . The data taken w i t h (b) 6 keV H and D, ( c ) 8 keV D, (d) 9 keV D beams a r e compared w i t h t h e l i n e from (a) representing t h e average o f a l l t h e data.

,

-

20

5

?

0 9 120

*

b-100

80 60 40 20

For measurements below 2 eV/amu t h e sharp increase observed i n 054 i s suggestive o f the l l v dependence p r e d i c t e d by t h e c l a s s i c a l o r b i t i n g model. According t o t h i s model 191, as the i o n and n e u t r a l approach, a d i p o l e i s induced i n t h e n e u t r a l causing an a t t r a c t i v e f o r c e and p o s s i b l e o r b i t i n g t r a j e c t o r i e s . However, as p o i n t e d o u t by Henchman 1171, i t may be inappro- p r i a t e t o a r b i t r a r i l y apply t h i s simple c l a s s i c a l o r b i t i n g p i c t u r e t o electron-capture c o l l i s i o n s , where t h e important curve crossings o f t e n occur a t t o o l a r g e an i n t e r n u c l e a r separation f o r t h e incoming i o n - n e u t r a l p a i r t o sample t h e p o t e n t i a l w e l l caused by the ion-induced d i p o l e .

Measurements 171 f o r c o l l i s i o n s o f

N5+

+

H(D) (see Fig. 5) show good agreement w i t h theore- t i c a l c a l c u l a t i o n s which i n d i c a t e a r i s i n g cross s e c t i o n w i t h decreasing Erel. There i s considerable s c a t t e r i n t h e d a t a t h a t i s b e l i e v e d t o be p r i m a r i l y due t o t h e s h o r t term i n s t a b i l i t i e s o f t h e N5+ beam produced by t h e i o n source. Comparing t h e

N5+

measurements t o t h e 05+ measurements, one sees t h a t even though t h e c a l c u l a t i o n s p r e d i c t t h e same general t r e n d w i t h energy f o r b o t h systems, t h e measured cross s e c t i o n s a r e q u i t e d i f f e r e n t .

- - I I I

0

-

1

1

8 keV 0 DATA - $7 -

-

\.$

"4\p\f\~

-

-

-

.8 keV D, SLOWER - o 8 keV D. FASTER

The merged-beams technique was extended t o o t h e r systems where a d d i t i o n a l comparison could be made. The measurements 171 f o r the N3+

+

H c o l l i s i o n s a r e i n e x c e l l e n t agreement w i t h the t h e o r e t i c a l c a l c u l a t i o n s o f Gargaud and McCarroll 1181, Bienstock e t a l . 1191, Watson and Christensen 151, and McCarroll and Val i r o n 1201. The

Nu+

measurements 171 agree w i t h t h e low energy c a l c u l a t i o n s o f F e i k e r t e t a l . 1211 where o v e r l a p e x i s t s (=l evlamu).

Cl-14 JOURNAL

DE

PHYSIQUE

Having gained a d d i t i o n a l confidence i n the merged-beams technique, we now re-examine t h e 05+ r e s u l t s . A schematic r e p r e s e n t a t i o n o f t h e d i a b a t i c p o t e n t i a l energy curves f o r t h e 05+

+

H c o l l i s i o n system i s presented i n Fig. 7, showing t h e approximate c r o s s i n g distances o f several product channels w i t h the i n c i d e n t channel. I n s p e c t i o n o f t h e energy dependence of Gargaudls 4s and 4p p a r t i a l cross-section c a l c u l a t i o n 1161 shows t h a t t h e decrease observed i n t h e experimental d a t a f o l l o w s t h e c a l c u l a t e d energy dependence f o r t h e 4s cross section. The 4p c o n t r i b u t i o n t o t h e c a l c u l a t e d cross section, which i s dominant a t t h e lower energies, l a c k s t h e c o r r e c t energy dependence t o account f o r t h e experimental data.

I n t h e n e x t s e c t i o n t h e Landau-Zener mpdel w i l l be used t o q u a l i t a t i v e l y i n v e s t i g a t e the dynamics o f e l e c t r o n capture a t low energies, i.e., t o i n v e s t i g a t e t h e r o l e o f t r a j e c t o r y e f f e c t s due t o t h e ion-induced d i p o l e on the e l e c t r o n capture cross section. I d e n t i f i c a t i o n o f f i n a l s t a t e s i s sought whose cross s e c t i o n i s enhanced by t h e ion-induced d i p o l e a t t r a c - t i o n , l e a d i n g t o an energy dependence s i m i l a r t o t h a t observed.

Diabatic Potential

Energy Curves

I l I I l l l

-2.011 I l l I I I I 1 I I

1- 10- luu

Internuclear Separation (a-u.)

Fig. 7. Schematic r e p r e s e n t a t i o n o f t h e d i a b a t i c p o t e n t i a l curves f o r t h e 05+

+

D c o l l i s i o n system showing t h e approximate c r o s s i n g distances (R,) f o r several f i n a l s t a t e s w i t h the i n c i d e n t channel. The shallow w e l l i n t h e i n c i d e n t channel i s caused by t h e a t t r a c t i v e ion- induced d i p o l e p o t e n t i a l .

4

-

LANDAU-ZENER CALCULATIONS WITH CLASSICAL TRAJECTORIES

We have used t h e measured peak i n t h e 05+ Cross s e c t i o n a t 20 eV/amu t o o b t a i n estimates f o r the parameters necessary t o perform Landau-Zener c a l c u l a t i o n s . These c a l c u l a t i o n s include t r a j e c t o r y e f f e c t s due t o t h e ion-induced-dipole a t t r a c t i o n i n t h e i n i t i a l s t a t e .

The capture cross s e c t i o n i s c a l c u l a t e d I 2 2 1 by i n t e g r a t i n g t h e t r a n s i t i o n p r o b a b i l i t y , 2 p ( l - p ) , over t h e impact parameter b,

where p i s t h e Landau-Zener p r o b a b i l i t y and i s given by p = exp

( -

28 h2

A i s t h e energy s p l i t t i n g a t t h e a v o i d e d c r o s s i n g , RC; vr i s t h e r a d i a l component o f t h e c o l l i s i o n v e l o c i t y ; and /Hll~ 1 i s t h e d i f f e r e n c e i n s l o p e s o f t h e d i a b a t i c p o t e n t i a l energy curves a t t h e c r o s s i n g . S i n c e t h e c r o s s i n g s o c c u r a t r e l a t i v e l y l a r g e i n t e r n u c l e a r s e p a r a t i o n s , t h e p o t e n t i a l energy f o r t h e i n i t i a l s t a t e can be approximated by t h a t due t o t h e i o n - i n d u c e d d i p o l e , - a q 2 / ~ ~ , (a i s t h e p o l a r i z a b i l i t y o f H) and t h e f i n a l - s t a t e p o t e n t i a l energy b y ( q - 1 ) l R ( a t o m i c u n i t s ) . A was e s t i m a t e d 1231 f r o m t h e observed maximum i n t h e c r o s s s e c t i o n a t 20 eVIamu and found t o be 6.23 X lO-, a.u. E q u a t i o n s ( 3 ) - ( 4 ) were e v a l u a t e d

w i t h r e a c t a n t t r a j e c t o r i e s w h i c h account f o r t h e i o n - i n d u c e d d i p o l e . T h i s r e s u l t e d i n s t r a i g h t f o r w a r d m o d i f i c a t i o n s t o HI1, ,,,,b and v,.

I n o r d e r t o p e r f o r m c a l c u l a 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 h i c h c r o s s t h e i n i t i a l s t a t e a t d i f f e r e n t i n t e r n u c l e a r s e p a r a t i o n s , a new energy s p l i t t i n g was c a l c u l a t e d u s i n g But1 e r and D a l g a r n o ' s s c a l i n g 1241 and by assuming, as i s shown i n t h e c a l c u l a t i o n s o f Gargaud 1161, t h a t t h e peak i n t h e c r o s s s e c t i o n a t 20 eV1amu i s due t o c a p t u r e t o t h e l s 2 2 s 4 s s t a t e o f 04+ w h i c h has a c r o s s i n g a t = l 0 a.u. By s c a l i n g t h e energy s p l i t t i n g t o t h e i n t e r n u c l e a r s e p a r a t i o n a p p r o p r i a t e f o r t h e 1 ~ ~ f i n a l s t a t e ( = l 2 2 ~ 4 ~ a.u.), t h e Landau-Zener c r o s s sec- t i o n f o r c a p t u r e t o t h e 4p was c a l c u l a t e d and f o u n d t o be c o n s i s t e n t t o t h e r e s u l t s o f Gargaud and M c C a r r o l l 1161. By comparing Landau-Zener c a l c u l a t i o n s w i t h and w i t h o u t t h e p o t e n t i a l due t o i o n - i n d u c e d d i p o l e , t h e e f f e c t due t o c o n s i d e r i n g r e a l i s t i c o r s t r a i g h t - l i n e t r a j e c t o r i e s c o u l d be e s t i m a t e d . I t was f o u n d t h a t f o r c a p t u r e t o t h e 2s4s and 2s4p s t a t e s t h e r e was n e g l i g i b l e c r o s s - s e c t i o n enhancement due t o t h e a t t r a c t i v e p o t e n t i a l a t 1 eVIamu. F i n a l - s t a t e c r o s s s e c t i o n s t h a t a r e enhanced by t r a j e c t o r y e f f e c t s and, t h e r e b y , more l i k e l y t o produce t h e c o r r e c t energy dependence a t low e n e r g i e s w i l l o c c u r a t l o w e r RC t h a n t h a t p o p u l a t i n g 2s4s, where t h e i o n - i n d u c e d d i p o l e a t t r a c t i o n i s s t r o n g e r (see Fig. 7). C r o s s i n g s p o p u l a t i n g n=3 p r o d u c t s t a t e s o c c u r a t i n t e r n u c l e a r s e p a r a t i o n s o f ~ 4 a.u. and, t h e r e f o r e , A a p p r o p r i a t e l y s c a l e d i n c r e a s e s b y a f a c t o r o f =83 r e l a t i v e t o t h a t found f o r t h e 4 s c r o s s i n g . T h i s causes t h e c a l c u l a t e d c r o s s s e c t i o n f o r t h i s s t a t e t o be s h i f t e d t o h i g h e r e n e r g i e s , l e a v i n g n e g l i g i b l e c o n t r i b u t i o n around 1 eVIamu. We n e x t c o n s i d e r s t a t e s such as 1 ~ ~ 2 ~ 3 s w h i c h i n v o l v e c a p t u r e i n t o t h e 3s s t a t e p l u s a core- e x c i t a t i o n (2s-2p), t h e e f f e c t o f t h e e x c i t a t i o n b e i n g a l o w e r i n g o f A by t h e f a c t o r S(Rc) = 0.5e-'.~~c 1241. I n an i n d e p e n d e n t - e l e c t r o n model A can be e s t i m a t e d by a p r o d u c t o f S(Rc) and t h e above R s c a l i n g f o r s i n g l e c a p t u r e 1241. The r e s u l t i s t h a t H12 i s i n c r e a s e d by a f a c t o r o f 1.6 r e l a t i v e t o A f o r c a p t u r e t o ls22s4s. The c a l c u l a t e d c r o s s s e c t i o n s f o r t h i s channel w i t h b o t h r e a l i s t i c and s t r a i g h t - l i n e t r a j e c t o r i e s a r e shown i n F i g . 8. A l s o shown i n t h e f i g u r e a r e t h e Landau-Zener c a l c u l a t i o n s f o r s i n g l e c a p t u r e t o 2s4s i n which t r a j e c - t o r y e f f e c t s were c a l c u l a t e d t o be n e g l i g i b l e . The c r o s s s e c t i o n f o r t r a n s f e r p l u s e x c i t a - t i o n i s 4 0 % o f t h a t due t o 4s a t around 20 eV1amu. I t i s shown t h a t f o r l o w e r e n e r g i e s t h e c a l c u l a t i o n f o r t h e 2p3s f i n a l s t a t e e x h i b i t s t h e measured energy dependence when r e a l i s t i c t r a j e c t o r i e s a r e used.

Of course, f i n d i n g a f i n a l s t a t e w i t h t h e c o r r e c t energy dependence does n o t mean t h a t i t c o n t r i b u t e s s i g n i f i c a n t l y t o t h e t o t a l c r o s s s e c t i o n . A t 20 eVIamu t h e dominant f i n a l s t a t e s ( 4 t ) c r o s s t h e i n i t i a l s t a t e a t r = f10-14 a.u. and t h e r e b y reduce t h e i n i t i a l f l u x r e a c h i n g t h e i n n e r channels. F o r l o w e r e n e r g i e s t h e " r e a c t i o n window" t e n d s t o move toward l a r g e r i n t e r n u c l e a r s e p a r a t i o n s making these c r o s s i n g more a d i a b a t i c , and t h e r e b y even f u r t h e r b l o c k i n g t h e i n i t i a l f l u x f r o m r e a c h i n g t h e i n n e r c r o s s i n g s . To e s t i m a t e t h e t r a n s i t i o n p r o b a b i l i t y t o t h e l s 2 2 p 3 s f i n a l s t a t e i n t h e presence o f t h e 4Q f i n a l s t a t e s c r o s s i n g t h e i n i t i a l channel a t t h e l a r g e r R C ' s , a Multichannel-Landau-Zener t r e a t m e n t (MCLZ) I 2 5 1 i s used r e s u l t i n g i n t h e t o t a l 2p3s t r a n s i t i o n p r o b a b i l i t y

P, , ,

JOURNAL

DE

PHYSIQUE

Single-Channel Landau-Zener Cross Section

100 _{I I I 1 l l I l}

Energy (eVlamu)

F i g . 8. S i n g l e - c h a n n e l Landau-Zener c a l c u l a t i o n s f o r c a p t u r e i n t o t h e l s Z 2 s 4 s and ls22p3s s t a t e s o f O4+. C l a s s i c a l t r a j e c t o r i e s were used which i n c l u d e d e f f e c t s due t o t h e i o n - induced d i p o l e p o t e n t i a l . F o r c a p t u r e t o t h e ls22p3s s t a t e , t h e Landau-Zener c a l c u l a t i o n s w i t h s t r a i g h t l i n e t r a j e c t o r i e s a r e a l s o shown.

where PI,.

.

.p4 a r e t h e Landau-Zener p r o b a b i l i t i e s [Eq. ( 4 ) ] f o r t h e p a r t i c i p a t i n g 4s,4p,4d, and 2p3s p r o d u c t s t a t e s , r e s p e c t i v e l y . I n t e g r a t i o n o f t h i s t r a n s i t i o n p r o b a b i l i t y over impact parameters [see Eq. ( 3 ) ] l e a d s t o an a l m o s t n e g l i g i b l e c o n t r i b u t i o n t o t h e t o t a l cross s e c t i o n below 1 eV/amu. However, o u r t r e a t m e n t h e r e i s o n l y an a p p r o x i m a t i o n t o a more a p p r o p r i a t e c o u p l e d m o l e c u l a r s t a t e c a l c u l a t i o n , where d e t a i l s o f t h e i o n i c c o r e a r e i n c l u d e d .

5

-

SUMMARY

6

-

ACKNOWLEDGMENTS

T h i s r e s e a r c h was sponsored b y t h e D i v i s i o n o f Chemical Sciences, U.S. Department o f Energy, under C o n t r a c t No. DE-AC05-840R21400 w i t h M a r t i n M a r i e t t a Energy Systems, Inc. T h i s research would n o t have been p o s s i b l e w i t h o u t t h e s t a b l e , h i g h - i n t e n s i t y beams o f m u l t i p l y charged i o n s produced b y t h e ORNL-ECR i o n source. We a r e i n d e b t e d t o C. B o t t c h e r and R. K. Janev f o r many f r u i t f u l d i s c u s s i o n s . S p e c i a l thanks a r e due t o M. Gargaud, R. M c C a r r o l l , C. B o t t c h e r , and T. G. H e i l f o r communicating t h e i r t h e o r e t i c a l r e s u l t s p r i o r t o p u b l i c a t i o n .

M. S. Huq was a p p o i n t e d t h r o u g h a Postgraduate Research T r a i n i n g Program, a d m i n i s t e r e d by Oak Ridge ASsociated U n i v e r s i t i e s (ORAU) f o r t h e U.S. Department o f Energy.

7

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