PHOTODETACHMENT IN MAGNETIC FIELDS

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PHOTODETACHMENT IN MAGNETIC FIELDS

D. Larson, R. Stoneman

To cite this version:

D. Larson, R. Stoneman. PHOTODETACHMENT IN MAGNETIC FIELDS. Journal de Physique

Colloques, 1982, 43 (C2), pp.C2-285-C2-290. �10.1051/jphyscol:1982222�. �jpa-00221833�

Colloque C2, supplément au n°ll, Tome 43, novembre 1982 page C2-285

PHOTODETACHMENT IN MAGNETIC FIELDS

D.J. Larson and R. Stoneman

Department of Physics, University of Virginia, Charlottesville, VA 22901, U.S.A.

Résumé. - Le comportement près du seuil de la section efficace de photodéta- chement des ions atomiques négatifs est décrit et illustré à l'aide des ré- sultats expérimentaux obtenus sur S . L'effet de l'interaction avec l'état final est discuté. La situation est comparée à la photoionisation d'atomes neutres dans un champ magnétique. Des résultats récents, concernant le photo- détachement de l'ion moléculaire SeH dans un champ magnétique sont présentés et commentés.

Abstract. - The behavior of the photodetachment cross section, near threshold, for atomic negative ioris in a magnetic field is described and illustrated with data on photodetachment of electrons from negative sulfur ions. The effect of the final state interaction is discussed and the photodetachment of atomic negative ions in a magnetic field is compared to photoionization of neutral atoms in a magnetic field. New data on the photodetachment cross section of a molecular negative ion, SeH-, in a magnetic field are presented and discussed.

A striking and interesting example of the differences between negative ions and neutral atoms is provided by a comparison of atomic photodetachment in a magnetic field to atomic photoionization in a magnetic field. A description^ which ignores the final state interaction between the neutral atom and the departing electron compares rather well to experimental data on photodetachment from negative sulfur Ions^ while the cross section for photoionization in a magnetic field is obviously strongly influenced by the coulomb attraction between the resulting ion and the departing electron.3 Of course, this situation is also true in the absence of the magnetic field as shown clearly by Wigner many years ago.4>5 He demonstrated that for production of pairs of non-interacting particles the cross section near threshold should vary as k2£+l where k is the relative wave vector and I is the angular momentum in the final state. Final state interactions which fall off faster than r~2, i.e. faster than the centrifugal potential, do not change the shape of the cross section near threshold although they can affect the absolute magnitude and the range over which the asymptotic behavior is valid.-* However

the stronger coulomb potential washes out the effect of the centrifugal potential and produces a cross section which is finite at threshold even for higher angular momenta.

The behavior for negative ions is easily understood in terms of the golden rule which says the cross section is proportional to |<f|v|i>|2p(Ef) where V is the perturbation causing the transition between initial and final states and p(Ef) is

the density of final states. For energies near threshold and distances on the order of the size of the initial bound state, kr « 1 and the free particle final state wavefunctions are proportional to (kr)^-. Since p(Ef) ~ k, the cross section varies as a ~ k2*"+l in agreement with the Wigner prediction. This kind of behavior has been verified in a number of cases.*>

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982222

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A p p l i c a t i o n of a magnetic f i e l d changes t h e f i n a l s t a t e wavefunctions from f r e e p a r t i c l e t o c y c l o t r o n wavefunctions. I f t h e f i e l d i s weak enough, t h e f i n a l s t a t e wavefunction i s n o t modified very much i n t h e r e g i o n of space where i t o v e r l a p s t h e i n i t i a l s t a t e wavefunction. E x p l i c i t l y , s t a r t i n g i n a bound p o r b i t a l we s t i l l f i n d t h a t t h e t r a n s i t i o n m a t r i x element i s independent of energy t o f i r s t o r d e r j u s t a s i n t h e absence of t h e f i e l d . However, t h e d e n s i t y of s t a t e s changes s i g n i f i c a n t l y . By c o n s t r a i n i n g t h e e l e c t r o n t o a s i n g l e c y c l o t r o n o r Landau l e v e l , we have reduced t h e t h r e e dimensional continuum t o a one dimensional continuum. Thus p(Ep) " l / k and 0

-

^{l / k .} Of course, t h e r e i s now an i n f i n i t e number of t h r e s h o l d s corresponding t o t r a n s i t i o n s t o s u c c e s s i v e l y h i g h e r c y c l o t r o n l e v e l s and i n t h e l i m i t where t h e magnetic f i e l d i s t o o s m a l l t o p e r m i t r e s o l u t i o n of t h e i n d i v i d u a l c y c l o t r o n l e v e l s a sum over t h e i n d i v i d u a l c r o s s s e c t i o n s r e c o v e r s t h e Wigner p r e d i c t i o n .

The only experimental d a t a t o d a t e on photodetachment of e l e c t r o n s from atomic n e g a t i v e i o n s i n a magnetic f i e l d i s t h a t o b t a i n e d f o r n e g a t i v e s u l f u r i o n s . l s 2 I n o r d e r t o apply t h e i d e a s of t h e b a s i c d e s c r i p t i o n above t o t h e a c t u a l d a t a , some complications have t o be introduced. F i r s t t h e motion of t h e i o n s i n t h e magnetic f i e l d d u r i n g photodetachment l e a d s t o broadening e f f e c t s from Doppler and motional S t a r k s h i f t s . Second, t h e v a r i o u s Zeeman s u b l e v e l s i n t h e n e g a t i v e i o n and n e u t r a l atom l e a d t o a number of t h r e s h o l d s f o r a s i n g l e c y c l o t r o n l e v e l and t h e s e t h r e s h o l d s need t o be included w i t h a p p r o p r i a t e f r e q u e n c i e s and r e l a t i v e amplitudes. T h i s i s d e s c r i b e d i n d e t a i l i n r e f e r e n c e 1. An example of t h e agreement o b t a i n e d between t h e o r y and experiment i s shown i n F i g u r e 1.

-32.0 0.0 32.0 64.0 96.0

RELATIVE FREQUENCY (GHZ)

F i g u r e 1. Photodetachment d a t a f o r S - i o n s n e a r t h e P312 2 + 'p2 t h r e s h o l d . The f r a c t i o n of i o n s s u r v i v i n g i l l u m i n a t i o n IS p l o t t e d a s a f u n c t i o n of l i g h t frequency (with an a r b i t r a r y z e r o ) . The d a t a shown h e r e a r e f o r l i g h t of 0 p o l a r i z a t i o n a t 1.07 T. The d a t a p o i n t s a r e p l o t t e d t o g e t h e r w i t h a curve p r e d i c t e d by t h e t h e o r y d e s c r i b e d i n t h e t e x t .

The d e s c r i p t i o n o u t l i n e d g i v e s r a t h e r good agreement w i t h photodetachment e x p e r i - ments where motional e f f e c t s add s i g n i f i c a n t broadening. It seems l i k e l y t h a t such a simple d e s c r i p t i o n could f a i l t o produce such good agreement i f t h e

r e s o l u t i o n were n o t l i m i t e d by t h e motional broadening. One obvious omission from

from atomic n e g a t i v e i o n s , t h e r e i s no s i g n i f i c a n t m o d i f i c a t i o n of t h e shape of t h e t h r e s h o l d i n t h e absence of t h e magnetic f i e l d . However, t h e magnetic f i e l d c o n s t r a i n s t h e e l e c t r o n t o remain c l o s e t o t h e atom ( i n two dimensions) and might enhance t h e e f f e c t s of t h e f i n a l s t a t e i n t e r a c t i o n . I n o r d e r t o g e t an i d e a of t h e e f f e c t of t h e f i n a l s t a t e i n t e r a c t i o n , assume t h a t t h e motion of t h e e l e c t r o n i s dominated by t h e magnet@ f i e l d and t h a t t h e electron-atom i n t e r a c t i o n i s g i v e n by a p o t e n t i a l V ( r ) . The e f f e c t of v(?) i n d i r e c t i o n s p e r p e n d i c u l a r t o t h e f i e l d i s assumed t o b e s m a l l and V can be t r e a t e d a s a p e r t u r b a t i o n , b u t f o r motion along t h e f i e l d we must c o n s i d e r t h e e f f e c t of t h e p o t e n t i a l completely and n o t a s a p e r t u r b a t i o n .

Consider t h e c a s e when t h e e l c t r o n i s detached t o t h e ground c y c l o t r o n s t a t e . Following Landau and L i f s h i t z 7 we w r i t e t h e wavefunction a s t h e product of r a d i a l and a x i a l p a r t s

$(?)

= R o 0 ( p ) ~ ( z ) , s u b s t i t u t e i n t h e schr;dinger e q u a t i o n , m u l t i p l y by Roo(p) and i n t e g r a t e over pdp t o o b t a i n

- h2

^{X I '} _{?(z)X = EX}

2m

where E = E

-

1 / 2 4 w and

I f we s t a r t w i t h a 3 dimensional w e l l of depth Vo and range ro << aH, we f i n d a n e f f e c t i v e one dimensional p o t e n t i a l of depth Uo " Vo (r;/a2) where a ~ i s t h e c y c l o t r o n r a d i u s . Thus t h e e f f e c t i v e depth i s reduced by !?h; r a t i o of t h e time t h e e l e c t r o n spends i n t h e w e l l t o theotime i t spends o u t of t h e w e l l . I f we s t a r t w i t h a w e l l a few eV deep and 1A wide, t h e r e i s an e f f e c t i v e w e l l depth on t h e o r d e r of 1 GHz a t 1.0 T. This i s comparable t o t h e motional broadening i n t h e p r e v i o u s experiments. Note t h a t t h e e f f e c t i v e depth i n c r e a s e s l i n e a r l y w i t h a p p l i e d f i e l d .

The p o t e n t i a l w e l l m o d i f i e s i n two ways t h e o t h e r w i s e f r e e e l e c t r o n motion i n one dimension. F i r s t , any one dimensional w e l l , no m a t t e r how shallow, has a t l e a s t one bound s t a t e . Thus applying t h e magnetic f i e l d c r e a t e s a new bound s t a t e . (This r e s u l t i s known7 and i m p l i e s t h e e x i s t e n c e of a bound n e g a t i v e i o n s t a t e

f o r ground s t a t e helium i n t h e presence of a magnetic f i e l d . 8 The ground s t a t e of helium has a n e g a t i v e e l e c t r o n a f f i n i t y i n t h e absence of a magnetic f i e l d ) . U n f o r t u n a t e l y t h e binding, i f r e a l , i s on t h e o r d e r of kHz f o r our e f f e c t i v e poten- t i a l and t h e bound s t a t e would be very d i f f i c u l t t o observe i n t h i s case. A

second e f f e c t of t h e p o t e n t i a l w e l l i s t o reduce t h e s p a t i a l d e n s i t y of t h e continuum s t a t e s i n t h e v i c i n i t y of t h e w e l l f o r e l e c t r o n s n e a r zero energy. This o c c u r s over a range of e n e r g i e s comparable t o t h e w e l l depth and could be observable i n p r e c i s e experiments. C l e a r l y t h i s e f f e c t i s c o r r e l a t e d w i t h t h e presence of t h e bound s t a t e s i n c e w i t h energy r e s o l u t i o n l a r g e compared t o t h e e f f e c t i v e w e l l depth, t h e e f f e c t s of t h e p o t e n t i a l should be unobservable.

I f t h e assumptions i n t h e d i s c u s s i o n above a r e v a l i d , t h e n t h e f i n a l s t a t e i n t e r - a c t i o n could be v i s i b l e i n more p r e c i s e d a t a and would provide a r a r e look a t atomic p h y s i c s i n one dimension. Of c o u r s e a c a r e f u l a n a l y s i s would have t o i n c l u d e a r e a l i s t i c atom-electron i n t e r a c t i o n .

It seems c l e a r t h a t a reasonably good d e s c r i p t i o n of photodetachment from atomic n e g a t i v e i o n s i n a magnetic f i e l d can i g n o r e t h e f i n a l s t a t e i n t e r a c t i o n o r perhaps t r e a t i t i n some p e r t u r b a t i v e f a s h i o n , a t l e a s t f o r magnetic f i e l d s a t t a i n a b l e i n t h e l a b o r a t o r y . However, t h i s i s c l e a r l y n o t t h e c a s e f o r photo- i o n i z a t i o n i n a magnetic f i e l d . The d i f f e r e n c e i s due t o t h e long range c h a r a c t e r of t h e coulomb p d e n t i a l . I f we s t a r t w i t h a v e r y s t r o n g magnetic f i e l d , t h e behavior of t h e photodetachment c r o s s s e c t i o n n e a r t h e t h r e s h o l d w i l l b e

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s u b s t a n t i a l l y i n f l u e n c e d by t h e f i n a l s t a t e i n t e r a c t i o n i f aH i s comparable t o atomic dimensions. I f t h e f i e l d i s reduced and t h u s t h e r a d i u s of t h e c y c l o t r o n o r b i t i s i n c r e a s e d , i t appears t h e magnetic f i e l d e f f e c t s a l o n e w i l l e v e n t u a l l y determine t h e shape of t h e c r o s s s e c t i o n . As t h e magnetic f i e l d i s educed t h e energy of t h e ground c y c l o t r o n l e v e l i s reduced i n p r o p o r t i o n t o l/aH.

5

Since t h e l o n g e s t range i n t e r a c t i o n between t h e n e u t r a l atom and t h e e l e c t r o n f a l l s a t l e a s t a s f a s t a s l l r 3 , t h e magnetic energy w i l l dominate a t s u f f i c i e n t l y s m a l l v a l u e s of magnetic f i e l d . This argument should apply f o r any f i n a l s t a t e i n t e r - a c t i o n s which f a l l o f f f a s t e r t h a n l / r 2 .

This s u g g e s t s t h a t a p a r t i c u l a r l y i n t e r e s t i n g c a s e i n t e r m e d i a t e between atomic p h o t o i o n i z a t i o n and photodetachment from atomic n e g a t i v e i o n s would b e a system where t h e f i n a l s t a t e i n t e r a c t i o n v a r i e d a s l / r 2 . Indeed, even i n t h e absence of a magnetic f i e l d t h i s i s a n i n t e r e s t i n g c a s e s i n c e a s t h e s t r e n g t h of t h e i n t e r a c t i o n i s i n c r e a s e d from z e r o t o a l a r g e v a l u e t h e photodetachment c r o s s s e c t i o n f o r a g i v e n R v a r i e s from t h e Wigner form t o one which i s f i n i t e a t t h r e s h 0 1 and t h e r e f o r e s i m i l a r t o t h a t observed w i t h an a t t r a c t i v e Coulomb i n t e r - actions.' Molecular n e g a t i v e i o n s p r o v i d e c a n d i d a t e s f o r observing t h i s type of behavior due t o t h e i n t e r a c t i o n between t h e molecular d i p o l e moment and t h e e x t r a e l e c t r o n . Indeed, t h r e s h o l d s w i t h o n s e t s s h a r p e r t h a n t h e Wigner p r e d i c t i o n f o r R=O have been r e c e n t l y observed9 i n r o t a t i o n a l l y r e s o l v e d photodetachment from OH- and explained10 i n terms of t h e i n t e r a c t i o n between t h e e l e c t r o n and t h e molecular d i p o l e moment.

We have very r e c e n t l y made measurements on t h e photodetachment of e l e c t r o n s from SeH- i n a magnetic f i e l d of about 1.3T. The b a s i c experimental t e c h n i q u e i s s i m i l a r t o t h a t used f o r measurements on n e g a t i v e s u l f u r ions.2 The SeH- i o n s a r e c r e a t e d by d i s s o c i a t i v e attachment of e l e c t r o n s t o H2Se, s t o r e d i n a Penning i o n t r a p , s u b j e c t e d t o i l l u m i n a t i o n by l i g h t of a s e l e c t e d energy, and counted by measuring t h e c u r r e n t s induced on t h e t r a p e l e c t r o d e s w h i l e d r i v i n g t h e i o n motion. The f r a c t i o n of i o n s s u r v i v i n g i l l u m i n a t i o n by a f i x e d number of photons i s p l o t t e d a s a f u n c t i o n of o p t i c a l frequency. An example of t h e r e s u l t s o b t a i n e d i n t h e p r e s e n t experiments i s shown i n F i g u r e 2. F i v e s e p a r a t e t h r e s h o l d s of t h e

X

X X X

17632 17636 17640 17644 17648 PHOTON ENERGY, C M - I

F i g u r e 2. Photodetachment d a t a f o r SeH- i n t h e v i c i n i t y of a t h r e s h o l d . This d a t a was taken w i t h a r e s o l u t i o n of 0.2 cm-I a t a f i e l d of 1.3 T.

apparent s c a t t e r of d a t a p o i n t s i n F i g u r e 2 i s much l a r g e r t h a n t h e n o i s e l e v e l and i n f a c t is due t o a n o s c i l l a t o r y v a r i a t i o n i n t h e i o n s i g n a l which a p p e a r s g e n e r a l l y i n t h e d a t a . This o s c i l l a t o r y s t r u c t u r e i s shown more c l e a r l y i n F i g u r e 3

17571 17573 17575 17577 17579 PHOTON ENERGY, C M - I

F i g u r e 3. Photodetachment d a t a f o r SeH- i n a f i e l d of 1.3T. This d a t a shows more c l e a r l y t h e o s c i l l a t o r y s t r u c t u r e p r e s e n t i n F i g u r e 2 a s w e l l .

where a f i n e r s c a n was taken i n t h e v i c i n i t y of a n o t h e r t h r e s h o l d . The experimental r e s o l u t i o n f o r t h e s e r e s u l t s i s on t h e o r d e r of 0.2 cm-l. The o s c i l l a t o r y

s t r u c t u r e i s h i g h l y r e p r o d u c i b l e and appears t o be a t o r v e r y c l o s e t o t h e e l e c t r o n c y c l o t r o n frequency.

Whi'le no a n a l y s i s of t h e e f f e c t of a magnetic f i e l d on molecular photodetachment has been c a r r i e d o u t and w h i l e i t i s n o t c l e a r t h a t t h e a n a l y s i s done f o r t h e zero magnetic f i e l d c a s e can be r e a d i l y extended t o included magnetic f i e l d s , i t i s c l e a r from t h e d a t a on SeH- t h a t t h e r e i s a s u b s t a n t i a l e f f e c t due t o t h e magnetic f i e l d . The most s t r i k i n g f e a t u r e of t h e d a t a i s t h e way i n which t h e i o n number o s c i l l a t e s w i t h o u t damping even f a r from a t h r e s h o l d . This i s i n s h a r p c o n t r a s t t o t h e S- c a s e where t h e o s c i l l a t i o n damps our i n a few c y c l e s due t o motional broadening and o v e r l a p i n g Zeeman s p l i t t h r e s h o l d s . It i s p o s s i b l e t h a t o t h e r s o u r c e s f o r t h e o s c i l l a t i o n should be considered, b u t i t is u n l i k e l y t h a t anything o t h e r t h a n d i r e c t i n t e r a c t i o n of t h e d e p a r t i n g e l e c t r o n w i t h t h e magnetic f i e l d could have such a s t r i k i n g e f f e c t i n t h e photodetachment d a t a . D e s p i t e our l i m i t e d understanding of t h e e f f e c t s of a magnetic f i e l d on molecular photodetachment, i t seems c l e a r t h a t i t w i l l prove t o b e an i n t e r e s t i n g and c h a l l e n g i n g problem.

We would l i k e t o thank P. A. Schulz and P. C. Engelking f o r p r e p r i n t s of t h e i r papers. This work was supported i n p a r t by t h e U. S. O f f i c e of Naval Research and by t h e N a t i o n a l Science Foundation.

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