HAL Id: jpa-00221847
https://hal.archives-ouvertes.fr/jpa-00221847
Submitted on 1 Jan 1982
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
EFFECT OF ELECTRIC FIELDS ON AUTOIONIZING RESONANCES
D. Kelleher, G. Lombardi, J. Delpech, J. Weiner
To cite this version:
D. Kelleher, G. Lombardi, J. Delpech, J. Weiner. EFFECT OF ELECTRIC FIELDS ON AU- TOIONIZING RESONANCES. Journal de Physique Colloques, 1982, 43 (C2), pp.C2-439-C2-441.
�10.1051/jphyscol:1982235�. �jpa-00221847�
JOURNAL DE PHYSIQUE
CoZZoque C2, suppZdment a u nO1l, Tome 43, novembre 1982 page C2-439
EFFECT OF ELECTRIC FIELDS ON AUTOIONIZING RESONANCES
D.E. Kelleher, G.G. Lombardi, J.F. ~ e l p e c h * and J.W. Weiner**
National Bureau o f Standards, Washington, D. C. 20234, U . S. A.
* I n s t i t u t d r E Z e c t r o n i q u e FondamentaZe, B6t. 220, U n i v e r s i t d de Paris-Sud, 92 405 Orsay Cedex, France
*
YU n i v e r s i t y o f Maryland, Co ZZege Park, Mary Zand, U . S . A.
We have s t u d i e d t h e e f f e c t of e l e c t r i c f i e l d s on a u t o i o n i z i n g (AI) resonances. We have observed t h e broadening o f a r e l a t i v e l y sharp
A1
resonance by f i e l d m i x i n g w i t h another much broader resonance. The e f f e c t i s analogous t o t h e broadening o f t h e metable 2s i n Hydrogen by f i e l d m i x i n g w i t h t h e 2 ~ . ( ' ) The A1 problem d i f f e r s , however, i n t h a t continua a r e involved, and A1 decay r a t e s (and t h e r e f o r e w i d t h s ) a r e t y p i c a l l y on t h e order o f 10 times l a r g e r than r a d i a t i v e decay r a t e s . 4
We have looked a t doubly e x c i t e d s t a t e s o f Sr, Ca, and Gd which l i e near t o b u t above t h e i o n i z a t i o n l i m i t . I n c o n t r a s t t o t h e f i e l d - i n d u c e d resonances discussed e a r l i e r t h i s conference, we consider resonances which a r e present even a t zero f i e l d , and observe how t h e i r a u t a i o n i z a t i o n r a t e s (widths) change as a f u n c t i o n o f e l e c t r i c f i e l d .
The experiments were performed by l a s e r scanning t h e resonances i n a thermal beam between f i e l d p l a t e s , and d e t e c t i n g t h e r e s u l t i n g i o n s w i t h an e l e c t r o n mu1 t i p 1 ie r . Our experiment i s complementary t o e a r l i e r ones 12y3) which were performed on Rydberg A1 l e v e l s , where changes i n w i d t h were observed a t l e v e l a n t i c r o s s i n g s . The r e s u l t s we r e p o r t here a r e monotonic i n t h e f i e l d
strength. Also, f i r s t order Stark s p l i t t i n g s o f a sharp Feshbach ( A I ) resonance i n
H-
were observed byB
~ n t e t a1 . ( 4 )Our measurements i n Sr were performed on d i s t i n c t l y
non
Rydberg A 1 resonances. Some such "valence" l e v e l s a r e extremely broad, e.g. Sr 4d6p 1 PT, has a w i d t h o f 415 cm-' i n zero f i e l d . ( 5 ) I n our experiment we scanned over a r e l a t i v e l y sharp resonance (1.2 cm-' i n zero f i e l d ) o f opposite p a r i t y , 4656 D2. 1 which f a l l s e n e r g e t i c a l l y i n t h e near wing (E'-E' 2 600 cm-l) o f t h e broad resonance. The increase i n w i d t h o f t h e r e l a t i v e l y narrow D2 resonance became 1 l a r g e enough t o measure a t a f i e l d o f about 50 KV/cm. Over a range o f measure- ments i n Sr from 50 t o 130 KY/cm, a l e a s t squares f i t through t h e data y i e l d s-lo
'
O e 2 , wherer0
i san e l e c t r i c f i e l d induced w i d t h
[rF-rol
= 6.5 x 10 FVlc,,-t h e zero f i e l d w i d t h i n cm-l. We would have l i k e d t o extend t h e measurements t o higher f i e l d strengths, b u t even a t 10 V/cm o u r apparatus tends t o s e l f d e s t r u c t , 5 and a t F > 1.3 x 10 t h e number o f blown amp1 i f i e r s per data p o i n t becomes 5
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982235
JOURNAL DE PHYSIQUE
p r o h i b i t i v e .
We compare t h i s r e s u l t t o a simple bound-bound p e r t u r b a t i o n s m i x i n g model, given by Davis and ~ a c o b s , ( ~ ) which can be w r i t t e n as
r .
1 = d 2 ~ 2r
( E , - E . ) ~ + I - . ~ / ~ j (1
1
J 3
where Ti i s t h e f i e l d induced w i d t h due t o m i x i n g w i t h t h e much broader l e v e l j, d = e < Y i l z I y . > i s t h e d i p o l e c o u p l i n g constant, F represents t h e f i e l d
J
s t r e n g t h and E t h e energy o f t h e c e n t e r o f t h e resonance. T h i s i s j u s t t h e 0 j
q u a d r a t i c Stark expression w i t h t h e smeared energy d i s t r i b u t i o n o f t h e j l e v e l taken approximately i n t o account by using E.+E
+
i r . 1 2 . This zero-order estimate~j J
assume t h e m i x i n g o f Lorentzian ( i n f i n i t e ) p r o f i l e s separated by AE.
.>>r
It I J j' does n o t address such questions as t h e e f f e c t o f t h e f i e l d on t h e shape o f t h e p r o f i l e s , whether t h e energy E should i n c l u d e t h e s h i f t due t o c o n f i g u r a t i o n0 j
i n t e r a c t i o n w i t h t h e continuum, t h e case AEij
5
Tj, o r t h e e f f e c t s o f continuum mixing. These a r e a l l questions which p e r t a i n t o our experiment, and which w i l l be discussed i n an ensuing p u b l i c a t i o n ( f o r an i n i t i a l e f f o r t a t a morefundamental approach t o t h i s problem, see r e f . 7 ) .
Notwithstanding t h e severe l i m i t a t i o n s o f t h e bound-bound p e r t u r b a t i o n model, i t s p r e d i c t i o n s a r e i n reasonable agreement w i t h o u r experimental r e s u l t s .
By comparing our r e s u l t s a t 10 Vlcm w i t h eqn. (1 5 ), we o b t a i n a d i p o l e m a t r i x element d = 21 eao, compared t o a Coulomb approximation value(') o f d = 15 eao.
(Our Froese-Fischer Hartree-Fock code does n o t converge f o r t h e 4d5d D2 s t a t e ) . 1 Of course, improved c a l c u l a t i o n s a r e r e q u i r e d before we can conclude much from t h i s r e l a t i v e l y good agreement. However, these and r e l a t e d r e s u l t s appear t o p o i n t c o n s i s t e n t l y t o a general f e a t u r e o f f i e l d m i x i n g t h a t warrants f u r t h e r t h e o r e t i c a l consideration: bound-bound f i e l d m i x i n g appears t o dominate;
continuum-continuum m i x i n g e f f e c t s have n o t been observed. This conclusion i s c o n s i s t e n t w i t h n u l l r e s u l t s we have obtained f o r o t h e r l i n e s i n Sr and Ca,
(some o f which were s i g n i f i c a n t l y sharper than t h e D2 i n Sr) and w i t h t h e r e s u l t s 1 o f o t h e r
experiment^(^'^'^).
Our q u a l i t a t i v e i n t e r p r e t a t i o n o f t h i s observation may be expressed as f o l l o w s : As Fano p o i n t e d out,(') an A1 resonance may be considered as a s u p e r p o s i t i o n o f d i s c r e t e ("bound") s t a t e s
6,
and continuum s t a t e s qE:YE = aE4 + / b E t q E S d E '
The w i d t h o f t h e resonance i s p r o p o r t i o n a l t o t h e c o n f i g u r a i o n i n t e r a c t i o n
between t h e d i s c r e t e and continuum p a r t s : I ' ~ ) < @ l t l ) $ > l 2 , where H i s t h e Hamiltonian f o r t h e system. I f we t u r n on an e l e c t r i c f i e l d , we w i l l couple s t a t e s o f
opposite p a r i t y . Three types o f c o u p l i n g a r i s e
(a) bound-bound: z l e e >
-
important(b) bound-contin: <4°yelzl@e'o> = zero
( c ) c o n t i n - c o n t i n : <$O
1
z ~ $ ~ >-
no observed e f f e c t sThe bound-bound c o u p l i n g g i v e s r i s e i n lowest o r d e r t o eqn ( 1 ) . The bound- continuum c o u p l i n g i s f o r m a l l y zero because t h e one e l e c t r o n o p e r a t o r "z" cannot couple two s t a t e s t h a t d i f f e r by two e l e c t r o n s (e.g. srx*+sr++e-). The apparently n e g l i g i b l e r o l e o f continuum-continuum c o u p l i n g i s l e s s s t r a i g h t f o r w a r d t o
explain. We n o t e t h a t if one uses a p e r t u r b a t i o n expansion f o r t h e wave f u n c t i o n s i n a f i e l d F:
@ ( o ) ( F ) = + F r<@:ldl@%@i (E-En)-l (za)
and analogous expression f o r @ (such a p e r t u r b a t i o n expansion f o r t h e continua i s thoroughly u n j u s t i f i e d due t o t h e degeneracies i n v o l v e d ) , we o b t a i n :
+ 0(F4) 1%)
and analogous expressions f o r @ ( o ) ( F ) ; where,
re
i s t h e zero f i e l d w i d t h o f t h e (narrower i n our expt.) resonance:re
= 2nlvel2,ve
= < @ e l ~ o l $ e > . The important p o i n t here i s t h a t t h e bound-bound mixing, < @ e ( d Z ~ @ O > i s weighted by t h e l a r g e" w i d t h "
vO,
w h i l e t h e continuum-continuum i s weighted by t h e small "width"ve.
I n our S r experiment, r0/re%350. Unfortunately, t h e v a l i d i t y o f t h i s argument s u f f e r s from t h e i n v a l i d i t y o f the p e r t u r b a t i v e expansion f o r t h e continuum- continuum mixing.
We have a l s o observed e l e c t r i c f i e l d e f f e c t s on t h e Gadolinium A1 resonance c i t e d i n r e f . (10). We observed pronounced f i e l d e f f e c t s a t Fz1.5 volts/cm!
While t h i s resonance i s r e l a t i v e l y i s o l a t e d and c l e a r l y non-Rydbergian, i t appears t o be c o n f i g u r a t i o n mixed w i t h a Rydberg s e r i e s converging t o t h e f i r s t e x c i t e d s t a t e o f ~ d + . More d e t a i l s w i l l be published elsewhere.
References
G. LUders, Z. Naturforschg, 5a, 608 (5950).
R.R. Freeman and G.C. B j o r k l z d , Phys. Rev. L e t t .
40,
118 (1978).K.A. Safinya, J.F. Delpech, T.F. Gallagher, Phys. Rev.
&,
1062 (1980).H.C. Bryant, e t a l . , Phys. Rev. L e t t .
40,
107 (1978). H.C. Bryant, e t a l . , i n "Atomic Physics 7", p. 29, Plenum Press, New York (1981) eds. Kleppner and P i p k i n .W.R. Garton, e t a l . , J. Phys. B
1,
114 (1968).J. Davis and V.L. Jacobs, Phys. Rev.
m,
2017 (1975).D.E. Kelleher, i n "Spectral L i n e Shapes 5", 281, Walter de Gruyter, New York (1 981), ed. B. Wende.
We thank R.R. Freeman f o r p r o v i d i n g us w i t h t h e r e s u l t s o f t h i s c a l c u l a t i o n . U. Fano, Phys. Rev.
124,
1866 (1961).G.I. Bekov, V.S. Letokhov, 0.1. Matveev and V . I . Mishin, JETP L e t t . 28, 283 (1978).
