LASERS IN CROSSED BEAM EXPERIMENTS

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LASERS IN CROSSED BEAM EXPERIMENTS

J. Baudon

To cite this version:

J. Baudon. LASERS IN CROSSED BEAM EXPERIMENTS. Journal de Physique Colloques, 1985, 46 (C1), pp.C1-25-C1-36. �10.1051/jphyscol:1985103�. �jpa-00224472�

JOURNAL DE PHYSIQUE

Colloque C I , supplement au n ° l , Tome 46, Janvier 1985 page C l - 2 5

LASERS IN CROSSED BEAM EXPERIMENTS

J . Baudon

Laboratoire de Physique des Lasers, Université Paris-Word, Avenue J.B. Clément, 93430 Villetaneuse, France

Résume

On examine les diverses utilisations possibles du laser dans des expériences de collision en jets croisés. L'exposé est limité aux collisions de faible énergie (quelques dizaines de meV) entre atomes excités et atomes ou molécules. Le premier rôle que peut jouer le laser dans ces expériences est celui de sélecteur, permet- tant aussi bien la préparation de l'état initial que l'analyse de l'état final, qu il s agisse d un niveau atomique bien défini (radiatif ou mëtastable), d'une classe de vitesse, d'un sous-niveau Zeeman. Dans ces applications, le laser n'agit par sur la collision elle même. Il n'en va plus de même aux puissances élevées et à des fréquences décalées par rapport aux fréquences atomiques. Quelques sugges- tions sont faites sur les possibilités d'étudier, en jets croisés, ces collisions assistées par laser.

Abstract

Different possible uses of lasers in crossed beam experiments are examined. The scope is limited to low energy collisions (few tens of meV) between excited atoms and atoms or molecules. The first role of the laser in this kind of experiments is that of a selector, allowing either the preparation of the incoming channel or the analysis of the outcoming one, by selecting one definite atomic level (radiative or metastable), one class of velocities, one magnetic sublevel. In all these appli- cations, the laser does not act on the collision process itself. The situation is quite different at high laser powers and frequencies detuned with respect to atomic frequencies. Some suggestions are made about the feasability of crossed beam stu- dies of these laser-assisted collisions.

The goal in crossed beam experiments is to prepare as well as possible the initial momenta of the collision partners, or equivalently, the relative velocityv and the initial direction in the center-of-mass frame ( 9r M = 0)- According to the species under investigation, and to the financial support, one may use either mono- kinetic (supersonic) beams, or thermal beams plus velocity selector, or pulsed thermal beams plus a time-of-flight analysis. The collision energy is varied either by heating or cooling, or by selecting variable times of flight, or by changing the relative angle between the two beams. In this type of experiments the laser can be used in two different ways : (i) as a tool to complete and improve the prepara-

tion or the analysis of the collision partners, with no appreciable effect on the collision itself : (ii) as a mean to change the nature of the collision process.

I - LASERS AS SELECTORS

Except for ground state species, the internal state of the collision partners before and after the collision is generally not controlled in simple crossed beam experiments. The first possible role of the laser is to act as a selector, or an

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985103

CI-26 JOURNAL DE PHYSIQUE

a n a l y z e r , of s t a t e s and e v e n t u a l l y a l s o of t h e v e l o c i t e s . These u s e s of l a s e r l i g h t a r e summarized i n f i g . 1.

c r o s s e d beams

e-multi.

" 5 2

TOF

I I

one s t a t e I L.I.F.

l a s e r

one V I l a s e r

I L.I. d i s s o c i a t i o n ,

Mselection-1 V s e l e c t i o n (Oc)

Fig. 1 - L a s e r s a s s e l e c t o r s

T h e l a s e r can be used t o produce and s e l e c t r a d i a t i v e s t a t e s - t h e l a s e r beam i s s e n t d i r e c t l y i n t o t h e c o l l i s i o n volume -, o r t o depopulate s e l e c t i v e l y long l i v e d

(e.g. m e t a s t a b l e ) l e v e l s b e f o r e t h e c o l l i s i o n volume. T h e s e s e l e c t i o n p r o p e r t i e s can obviously be used a s w e l l i n t h e a n a l y s i s of t h e f i n a l s t a t e ( c f . f o r i n s t a n c e t h e l a s e r induced f l u o r e s c e n c e method). Good o p t i c a l pumping c o n d i t i o n s g e n e r a l l y r e - q u i r e :

( i ) a continuous t u n a b l e l a s e r 1ocked.on an atomic l i n e ,

! i i ) a s u f f i c e n t l y high power, t o g e t a s t a t i o n n a r y pumping regime, b u t , i n some c a s e s , n o t too high, t o avoid u n d e s i r a b l e s a t u r a t i o n e f f e c t s ,

( i i i ) a convenient c h o i c e of t h e e x c i t a t i o n scheme.

1.1 - P o p u l a t i o n , or d e p o p u l a t i o n , of a s p e c i f i c s t a t e

a ) R a d i a t i v e l e v e l s of a l k a l i atoms ( o r a l k a l i n e - e a r t h s ) a r e p o p u l a t e d d i r e c t l y from ground s t a t e s . Many experiments of t h i s kind have been performed t o s t u d y e x c i t e d atom o r ground s t a t e atom c o l l i s i o n s a t thermal e n e r g i e s . We s h a l l come back t o t h i s c a s e when c o n s i d e r i n g t h e M-selection. Other experiments havebeen devoted t o e x c i t e d alkali-on-molecule c o l l i s i o n s , f o r i n s t a n c e :

* *

- f i n e s t r u c t u r e t r a n s i t i o n i n K ( 4 P ) , o r Rb (5P) + H o r D

2 2

c o l l i s i o n s [ l l . O n e o r i g i n a l i t y of t h i s experiment c o n s i s t s i n t h a t t h e r o t a t i o n a l t e m p e r a t u r e i s v a r i e d by seeding t h e H2(D2) s u p e r s o n i c beam w i t h h e a v i e r atoms, such a s argon (Trot i s e s t i m a t e d from t h e energy balance between t h e d i f f e r e n t degrees of freedom).

- e n e r g y t r a n s f e r ( e l e c t r o n i c t o v i b r a t i o n a l ) i n Na*(3p) on t r i a t o m i c molecule (C02, N20) c o l l i s i o n [ 2 ] ; t h e f i n a l r e l a t i v e e n e r g y E '

CM i s o b t a i n e d a t each s c a t t e r i n g a n g l e by means of a v e l o c i t y s e l e c t o r s e t i n f r o n t of t h e a l k a l i - a t o m d e t e c t o r , and t h e d o u b l y - d i f f e r e n t i a l c r o s s s e c t i o n d 2 o / (dE' dO ) i s measured.

CM' CM

- r e a c t i v e s c a t t e r i n g e x p e r i m e n t s , u s i n g a "simple" ( b u t d i f f e r e n t i a l ) mass a n a l y s i s , e.g. f o r t h e r e a c t i o n s :

(Here no i n f o r m a t i o n i s o b t a i n e d a b o u t t h e i n t e r n a l s t a t e of t h e p r o d u c t ) , o r t h e l a s e r induced f l u o r e s c e n c e method, a s i n :

F + I X +IF(v) + X( 2 P 3 r 2 , I / 2 ] 9 where X i s halogen [ 41 ;

h e r e r e l a t i v e t o t a l c r o s s s e c t i o n s a r e o b t a i n e d f o r e a c h v a l u e of v , i n t h e r a n g e 0 - 16. The same method h a s been used f o r t h e r e a c t i o n s :

*

C s (7P312,112) + H2 ⁺ C s H + H [51 ; a f i r s t l a s e r i s used t o popula- t e CS* and a second one a n a l y s e s t h e i n t e r n a l s t a t e of p r o d u c t .

- c o l l i s i o n between two e x c i t e d a l k a l i - a t o m s [61.

b) upper r a d i a t i v e l e v e l s c a n be o b t a i n e d s t a r t i n g from a m e t a s t a b l e l e v e l . T h i s i s t y p i c a l l y t h e c a s e f o r r a r e g a s atoms. For i n s t a n c e , t h e Hornbeck- Molnar p r o c e s s :

He*(5P) + He( 1 So) + ~ e+ ie

h a s been r e c e n t l y s t u d i e d [ 7 ] . E x c i t e d helium atoms a r e produced w i t h i n a m e t a s t a b l e (2 S)He 3 beam by a f r e q u e n c y doubled CW dye l a s e r ; a b o u t 10 mW a r e o b t a i n e d a t A = 294.5nm, by u s i n g a n i n t r a - c a v i t y ADA d o u b l e r c r y s t a l .

Of c o u r s e upper l e v e l s ( e . g . Rydberg s t a t e s ) c a n be a l s o p o p u l a t e d from a r a d i a t i v e l e v e l , by means of a second l a s e r beam.

c ) A s p e c i f i c m e t a s t a b l e s t a t e c a n b e d e p o p u l a t e d b e f o r e t h e c o l l i s i o n volume and a l s o e v e n t u a l l y b e f o r e t h e m e t a s t a b l e atom d e t e c t o r . T h i s method h a s b e e n used mainly f o r r a r e g a s atoms [ a ] . For p r a c t i c a l r e a s o n s ( s p e c t r a l r a n g e ) , t h e n e o n atom i s h e r e t h e i d e a l one. For example, v e r y d e t a i l e d s t u d i e s of N ~ * ( ~ s , ~ P ) - He

0 and N ~ * ( ~ S , ~ P ~ ) - Ne c o l l i s i o n s have been performed [91. I t i s noteworthy t h a t t h e l a s e r s e l e c t o r i s i s o t o p e s e l e c t i v e ; t h i s g i v e s a v e r y e a s y way t o s e p a r e t h e ex- change p r o c e s s from t h e d i r e c t one, which h e l p s t o c l a r i f y t h e e x p e r i m e n t a l t e s t on t h e p o t e n t i a l e n e r g y c u r v e s , e s p e c i a l l y i n c a s e s where many m o l e c u l a r s t a t e s a r e involved ( e . g . f o r t h e 3 ~ 2 l e v e l ) [ l o ] .

C1-28 J O U R N A L D E PHYSIQUE

1 . 2 - V e l o c i t y s e l e c t i o n

When t h e a t o m i c beam i s w e l l - c o l l i m a t e d b u t h a s a wide v e l o c i t y d i s t r i b u t i o n ( t h e r m a l beam), t h e Doppler e f f e c t a l l o w s t o pump s e l e c t i v e l y a narrow band of v e l o - c i t y . T h i s t e c h n i q u e i s p a r t i c u l a r y u s e f u l when t h e second beam i s monokinetic.

For r a d i a t i v e s t a t e s ( a l k a l i atoms) t h i s l a s e r v e l o c i t y s e l e c t i o n p r o v i d e s a p u r e l y o p t i c a l method t o measure e l a s t i c o r i n e l a s t i c 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 [ I l l

-f

( s e e f i g . 2) : a f i r s t c o l l i n e a r l a s e r beam (w ) s e l e c t s one v e l o c i t y vA w i t h i n t h e e x c i t e d atom beam ; i f t h e i n i t i a l v e l o c i t y vg of t h e second p a r t n e r i s u n i q u e , t h e + i n i t i a l r e l a t i v e v e l o c i t y v -+ i s t h e n w e l l d e f i n e d ; a second l a s e r beam (w ) , indu-

2

c i n g a t r a n s i t i o n from t h e e x c i t e d s t a t e ( e ) of A t o a n upper e x c i t e d s t a t e ( e ) ,

+ ¹ -f 2

and c o l l i n e a r t o v s e l e c t s a d e f i n i t e v a l u e of t h e p r o j e c t i o n of v of t h e r '

f i n a l v e l o c i t y , i . e . a d e f i n i t e v a l u e of t h e CM s c a t t e r i n g a n g l e . An i n e l a s t i c c o l - l i s i o n c a n be s t u d i e d a s w e l l by t u n i n g t h e second l a s e r on a t r a n s i t i o n s t a r t i n g from a n o t h e r s t a t e ( e V l ) of A a f t e r t h e c o l l i s i o n . The o b s e r v a t i o n i s made via t h e f l u o r e s c e n c e (w ) from ( e ).

f 2

F i g 2 - O p t i c a l measurements s of a D.C.S

A v e l o c i t y s e l e c t i o n can be a c h i e v e d a l s o f o r a m e t a s t a b l e l e v e l , by depopula- t i n g a narrow v e l o c i t y band. F i g . 3 shows t h e t i m e - o f - f l i g h t d i s t r i b u t i o n of a me- t a s t a b l e ( 3 s , 3 P )Ne beam. A l a s e r , tuned on t h e 1sl3p2 - 2p6 t r a n s i t i o n (1=614.3nm)

0,2

and t h e n c o n v e n i e n t l y s h i f t e d , b u r n s a h o l e i n t h e d i s t r i b u t i o n , s p e c i f i c a l l y f o r 3~ l e v e l and 2 0 ~ e i s o t o p e [ l l ] . Owing t o t h e l o n g a q u i s i t i o n t i m e s ( h o u r s ) r e q u i r e d

2

i n d i f f e r e n t i a l measurements, t h e l a s e r f r e q u e n c y n e e d s t o be c a r e f u l l y s t a b i l i z e d . I n t h e p r e s e n t c a s e , a CW dye l a s e r i s l o c k e d on a s a t u r a t e d a b s o r p t i o n l i n e s h i f t e d by a magnetic f i e l d 1121. Up t o now, t h e r e s o l u t i o n of t h i s "negative" v e l o c i t y s e l e c t o r i s e s s e n t i a l l y l i m i t e d by t h e a n g u l a r a p e r t u r e of t h e a t o m i c beam (Av :: 8 0

t o 100 m/s).

chopper

l a s e r -

N

e *

t o f (ms)

F i g 3 - Laser v e l o c i t y s e l e c t i o n i n a Ne* m e t a s t a b l e beam.

1.3 - Magnetic s u b l e v e l s e l e c t i o n

Up t o now i t has been i m p l i c i t l y supposed t h a t no p o l a r i z a t i o n e f f e c t o c c u r s . Notice t h a t t h i s i s n o t n e c e s s a r i l y a " n a t u r a l " c a s e , because of t h e s t r o n g p o l a r i - z a t i o n of t h e l a s e r l i g h t , and one has sometimes t o t a k e c a r e t o e l i m i n a t e p o l a r i - z a t i o n e f f e c t s . On a n o t h e r hand, a magnetic s u b l e v e l s e l e c t i o n (M - s e l e c t i o n ) i s v e r y u s e f u l , a t l e a s t when i t i s completely c o n t r o l l e d .

I n low energy c o l l i s i o n s r a t h e r complex p r o c e s s e s may occur a t l a r g e i n t e r - n u c l e a r d i s t a n c e s ( R

>

"good" molecular b a s i s . The M - s e l e c t i o n of i n i t i a l and f i n a l s t a t e s o f f e r s a n i n t e r e s t i n g way t o i n v e s t i g a t e e x p e r i m e n t a l l y t h e s e i n t r i c a t e long range e f f e c t s .

To understand how t h e l a s e r M - s e l e c t i o n o p e r a t e s , one h a s t o c o n s i d e r w i t h a t t e n t i o n t h e r e f e r e n c e q u a n t i z a t i o n a x i s . For sake of c l a r i f y we s h a l l c o n s i d e r

1 1

molecular s t a t e s d i s s o c i a t i n g a t i n f i n i t e R i n t o A X ( P) + B ( S ) ( s e e f i g . 4 ) . When AB i s an h e t e r o n u c l e a r system, t h r e e molecular s t a t e s have t h i s d i s s o c i a -

..

t i o n l i m i t : .K+, 71-, 1, f o r which t h e componant on R of t h e e l e c t r o n i c a n g u l a r momen- tum i s

..

^-

i

A pure s t a t e prepared along zi(e.g.

..

I

..

h o l d s when f i n e s t r u c t u r e , and h y p e r f i n e s t r u c t u r e e x i s t .

JOURNAL DE PHYSIQUE

long range c o u p l i n g s

r e f e r e n c e a x i s

I I

,

-

F i g 4 - M-selection i n a A ( ~ P ) + B( 1 S) c o l l i s i o n

a ) examples f o r r a d i a t i v e l e v e l s ...

- By choosing d i f f e r e n t e x c i t a t i o n schemes ( d i r e c t i o n s of atom and l a s e r beams, p o l a r i z a t i o n , e x t e r n a l magnetic f i e l d ) i t i s p o s s i b l e t o s t u d y a given p r o c e s s ( e l a s t i c o r i n e l a s t i c ) w i t h d i f f e r e n t s u p e r p o s i t i o n s of incoming channels.

The r e l a t i v e c o n t r i b u t i o n s of d i f f e r e n t incoming molecular s t a t e s (and consequently of d i f f e r e n t t y p e s of coupling) t o t h e a p p a r e n t t o t a l c r o s s s e c t i o n f o r t h e f i n e s t r u c t u r e t r a n s i t i o n :

K ( ~ P ~ / ~ ) + r a r e gas X + K(4P1/2) ⁺ X

have been s t u d i e d by t h i s way [13], choosing d i f f e r e n t e x c i t a t i o n schemes, such a s : ( i ) a wide-band l a s e r (0,lA) l i n e a r l y p o l a r i z e d , w i t h a magnetic f i e l d p e r p e n d i c u l a r t o t h e c o l l i s i o n plane, ( i i ) a narrow-band l a s e r (51MHz) c i r c u l a r y p o l a r i z e d . This a l l o w s a measurement of two q u a n t i t i e s :

a s f u n c t i o n s of energy (0.07 t d 0.4 eV), from which t h e r e l a t i v e c o n t r i b u t i o n s of s t a t e s A n3/2 2

a n d B C 1 1 2 a r e d e r i v e d .

- From t h e d i f f e r e n t i a l view p o i n t , a s p e c t a c u l a r e f f e c t of M-selec- t i o n has been found by Diiren [ I 4 1 : when e x c i t e d potassium atoms KX(4 P) a r e 2 prepared by a a+ l a s e r l i g h t ( r e f e r e d t o 2 p e r p e n d i c u l a r t o t h e i n i t i a l v e l o c i t y

i

plane) and then c o l l i d e with e.g. K atoms, a r i g h t - l e f t assymetry i s observed i n 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 , and t h e d i f f e r e n c e between + B and - 0 s c a t t e r e d i n t e n - s i t i e s o s c i l l a t e w i t h 8.

- I n atom-diatom c o l l i s i o n s , t h e i n i t i a l a n g u l a r momentum of t h e e x c i - t e d atom, and a p a r t of t h e r e l a t i v e a n g u l a r momentum can b e t r a n s f e r e d t o t h e

A

molecule. A M-selection w i t h r e s p e c t t o t h e q u a n t i z a t i o n a x i s zi p e r p e n d i c u l a r t o t h e c o l l i s i o n p l a n e , w e l l d e f i n e d i n a d i f f e r e n t i a l e x p e r i m e n t , a l l o w s a d i r e c t s t u d y of t h e s e a n g u l a r momentum t r a n s f e r s , f o r i n s t a n c e i n Na*(3P) + N2 o r H2 c o l l i s i o n s [IS].

b) examples f o r m e t a s t a b l e l e v e l s ...

- A l a s e r M-selection i s p o s s i b l e a l s o w i t h m e t a s t a b l e l e v e l s by a s u i t a b l e c h o i c e of t h e o p t i c a l t r a n s i t i o n , p o l a r i z a t i o n and e x t e r n a l magnetic f i e l d .

3 3 3

For i n s t a n c e , f o r Ne*( P 2 ) , one c a n u s e t h e Zeeman s p l i t t i n g s between 3 s P 2 - 3 p P2 l i n e s t o s e p a r a t e d i f f e r e n t v a l u e s of MJ.

T h i s method h a s been a p p l i e d r e c e n t l y by H. Haberland s g 109 1 t o Ne* - Ne c o l l i s i o n s . An i m p o r t a n t a d v a n t a g e of m e t a s t a b l e atoms i s t h a t t h i s p r e p a r a t i o n i s made b e f o r e t h e c o l l i s i o n volume. T h e r e f o r e i t i s p o s s i b l e , by means of a n appro- p r i a t e magnetic f i e l d (B) +

,.

I*

" a d i a b a t i c a 1 l y " m e a n s h e r e t h a t t h e time e v o l u t i o n of B s e e n by t h e moving atom i s show w i t h r e s p e c t t o t h e p r e c e s s i o n p e r i o d , s o t h a t t h e p r o j e c t i o n of t h e a n g u l a r

,L

momentum a l o n g B i s a c o n s t a n t . The same t e c h n i q u e may be u s e d t o t r a n f o r m a d i a -

,.

,.

b a t i c a k l y Rf I n t o z f . F i n a l l y p r e p a r a t i o n and a n a l y s i s a r e r e f e r e d t o t h e m o l e c u l a r a x i s , which g i v e s a v e r y d i r e c t view of t h e r o t a t i o n a l c o u p l i n g e f f e c t s : f o r an i n f i n i t e l y slow r e l a t i v e motion, t h e e l e c t r o n i c a n g u l a r momentum would be " a t t a c h e d "

A A

t o R and a p u r e M-state would be o b s e r v e a l o n g Rf ; i n f a c t t h e r o t a t i o n of R i s n o t a d i a b a t i c and a combination of f i n a l M-states i s observed. I t may be n o t i c e d t h a t s u c h a measurement i s e x t r e m e l y s e n s i t i v e : s t r o n g d e p o l a r i z i n g e f f e c t s a r e observed even f o r v e r y s m a l l c o u p l i n g s ; hence t h e y do n o t n e c e s s a r i l y imply t h a t m o l e c u l a r p o t e n t i a l s o b t a i n e d 2 non M - s e l e c t i v e measurements a r e wrong.

- Another way t o a c h i e v e t h e M-selection f o r m e t a s t a b l e a t o m s c o n s i s t s i n ;sing t h e Doppler v e l o c i t y s e l e c t i o n d e s c r i b e d i n p a r a g r a p h 1.2. I f t h e o p t i c a l pumping t a k e s p l a c e w i t h i n a magnetic f i e l d , w i t h a f i x e d l a s e r f r e q u e n c y , e a c h Zeeman component g i v e s a h o l e i n t h e v e l o c i t y d i s t r i b u t i o n , a t a d e f i n i t e v a l u e of t h e v e l o c i t y . F i g . 5 shows t h e h o l e g r o f i l e o b t a i n e d i n neon, w i t h a IT p o l a r i z a t i o n w i t h r e s p e c t t o t h e magnetic f i e l d ( B : 480 G) ; t h e a n g l e between Ne* beam a n d l a s e r beam i s 30° ; t h e s o l i d l i n e s c o r r e s p o n d t o t h e t h e o r e t i c a l Zeeman spectrum. For a d e m o n s t r a t i v e purpose t h e e x p e r i m e n t a l c o n d i t i o n s have been a r r a n g e d i n s u c h a way t h a t t h e whole spectrum l i e s w i t h i n t h e v e l o c i t y d i s t r i b u t i o n . Obviously i t i s p r e f e r a b l e t o i n c r e a s e t h e magnitude of B s o t h a t j u s t one component remains i n t h e d i s t r i b u t i o n .

J O U R N A L DE PHYSIQUE

h o l e (%)

l a s e r

I

F i g 5 - Laser M-selection i n a ~ e * m e t a s t a b l e beam

I1 - LASER ASSISTED COLLISIONS

When t h e c o l l i s 6 o n volume i s i r r a d i a t e d by a h i g h power l a s e r beam, which f r e - quency i s more o r l e s s detuned w i t h r e s p e c t t o atomic f r e q u e n c i e s , t h e c o l l i s i o n p r o - c e s s i s n o l o n g e r i n d e p e n d e n t o f t h e i n t e r a c t i o n w i t h t h e e l e c t r o m a g n e t i c (EM) f i e l d . A s shown i n f i g . 6 t h e "main" l a s e r , c h a r a c t e r i z e d by i t s power ( o r e l e c t r i c f i e l d amplitude and d e t u n i n g (A), a c t s during t h e c o l l i s i o n i t s e l f . A s i n d i c a t e d

6 0 )

a n o t h e r l a s e r can be used a s a s e l e c t o r .

I

I

Fig 6 - L a s e r - a s s i s t e d c o l l i s i o n

To g e t a c o r r e c t formulation of t h e problem, one h a s t o c o n s i d e r a s a whole both c o l l i s i o n partners.A,B i n t e r a c t i n g by V, t h e EM f i e l d and t h e i n t e r a c t i o n v between A(or B) and t h e EM f i e l d , i . e . t o c o n s i d e r t h e hamiltonian :

H = h + h + h + V + v

A B R

h a r e t h e i n t e r n a l hamiltonians of A , B , \ i s t h a t of t h e EM f i e l d . A t given c o l - A , B

l i s i o n energy and impact parameter t h e c h a r a c t e r i s t i c time f o r V i s t h e c o l l i s i o n time T

.

The hamiltonian h + hR + v i s t h a t of t h e d r e s s e d atom, whereas i n t h e A(or B)

Born-Oppenheimer approximation, h + h + V d e s c r i b e s t h e quasimolecule AB. The main

A B

t h e o r e t i c a l problem h e r e i s t o e s t a b l i s h some preeminence among t h e v a r i o u s terms contained i n V , and v , i n o t h e r words t o c o n s t r u c t what we might c a l l "dressed Hund's cases". Obviously t h e problem becomes s e r i o u s - a n d i n t e r e s t i n g - f o r l a s e r powers l a r g e enough t o g i v e Q ' - T -1

.

Let us t u r n now t o t h e experiment view p o i n t , and more s p e c i f i c a l l y t o crossed beam experiments. One knowns t h e d i f f i c u l t i e s encountered i n studying l a s e r - a s s i s t e d c o l l i s i o n s i n c e l l e x p e r i m e n t s , and t h e high powers g e n r a l l y r e q u i r e d t o a t t a i n t h e high i n t e n s i t y l i m i t . Therefore toimagine crossed beam experiments i n t h i s f i e l d might seem r a t h e r u t o p i c s i n c e c o l l i s i o n a l e v e n t s i n t h i s type of experiment come from r a r e encounters between atoms belonging t o two d e n s i t y media. However c r o s s e d beams a r e n o t n e c e s s a r i l y a pure inconvenience : s t a t e - s e l e c t i o n s which a r e p o s s i b l e i n such experiments can a l l o w a s e p a r a t i o n of t h e i n v e s t i g a t e d p r o c e s s from many o t h e r unuseful ones. Nevertheless one h a s t o choose c a r e f u l l y t h e s t u d i e d c a s e and t o r e s p e c t some g e n e r a l requirements :

( i ) use low e n e r g i e s ( i . e . l a r g e c o l l i s i o n times and l a r g e d i s t a n c e s )

( i i ) use e x c i t e d s p e c i e s ( p o t e n t i a l curves a r e c l o s e , c o u p l i n g more e f f i c i e n t ) , w i t h long l i f e t i m e s .

( i i i ) s t u d y long-range i n e l a s t i c p r o c e s s e s , i n v o l v i n g d i p o l e t r a n s i t i o n s , ( i v ) choose a l a s e r a s s i s t e d p r o c e s s easy t o be c h a r a c t e r i z e d ,

( v ) use a s u f f i c i e n t l y high i n t e n s i t y t o g e t n' 2 r c -1

A s e n s i t i v e method t o d e t e c t even small c o l l i s i o n a l l a s e r e f f e c t s c o n s i s t s i n using i n t e r f e r e n c e s between c o h e r e n t s c a t t e r i n g amplitudes. A s an example, l e t u s c o n s i d e r a c o l l i s i o n between two e q u a l Z atoms A , A 1 ; A ' i s i n i t i a l l y i n i t s ground- s t a t e ( 0 ) whereas A i s i n a long-lived e x c i t e d s t a t e (1) ( m e t a s t a b l e o r Rydberg).

The l a s e r frequency i s s l i g h t l y detuned w i t h r e s p e c t t o an allowed t r a n s i t i o n , from s t a t e (1) t o an upper e x c i t e d s t a t e ( 2 ) , t h e l i f e t i m e of which i s l a r g e compared t o Q e T 1 and t o t h e t r a n s i t t&me T of A a c r o s s t h e l a s e r beam.

I f t h e l a s e r i n t e n s i t y i s low (avr-' i s much l a r g e r than t h e d u r a t i o n T~ of a c o l l i s i o n ) , t h e c o l l i s i o n p r o c e s s i s completely decoupled from t h e l a s e r i n t e r a c t i o n : a l i n e a r time dependent s u p e r p o s i t i o n of s t a t e s (1) and ( 2 ) evolves w i t h i n t h e l a s e r beam up t o a time t- " j u s t " b e f o r e t h e c o l l i s i o h time t ( b u t i n f a c t = - - f o r t h e c o l l i s i o n i t s e l f ) . I n t h e time i n t e r v a l t- c , t: ( j u s t a f t e r c o l l i s i o n ) , t h e adequate d e s c r i p t i o n i s t h e molecular one. The e v o l u t i o n of t h e system i s governed by poten- t i a l s 1 2 ( s e e f i g . 7) and t h e l a s e r has no a p p r e c i a b l e e f f e c t d u r i n g t h a t t i m e .

u,g' u,g

C 1-34 JOURNAL D E PHYSIQUE

The outcoming c o l l i s i o n a l s t a t e i s then a l i n e a r combination of atomic s t a t e s A'

0 )

A1,2 A'1,2, A. (quasi-resonant e x c i t a t i o n t r a n s f e r ) . A s t h e l a s e r induces t r a n - s i t i o n 1-2 f o r A o n l y , t h e f i n a l ( t = T) p o p u l a t i o n i n A1 t a k e s t h e following from :

where r e a l q u a n t i t i e s C , p and 0 depend on moduli and r e l a t i v e phaseshift of t h e d i r e c t s c a t t e r i n g amplitudes :

Fig 7

-

A t h i g h l a s e r i n t e n s i t y ( r " R'-I), t h e l a s e r e f f e c t can no l o n g e r be n e g l e c t e d w i t h i n t h e ime i n t e r n a l t- +

t c , f o r atoms A

and

4 - s t a t e problem (4 standard molecular s t a t e s I g , 2u ; l U , Z g , coupled by t h e r a d i a - t i o n f i e l d , o r 4 d r e s s e d molecular s t a t e s ) . The f i n a l r e s u l t on / a l ( ~ )

l 2

Another example of a laser-modified i n t e r f e r e n c e e f f e c t i s given by an asymme- t r i c c o l l i s i o n A + B, i n which one of t h e two atoms has an i n t e r n a l a n g u l a r momentum,

1 1 1

f o r i n s t a n c e : A(1, S) + B( S ) , combined w i t h A(2, 'P) + B ( S ) , by means of a l a s e r s l i g h t y detuned w i t h r e s p e c t t o t h e 1, - ^2, 'P t r a n s i t i o n . A t low l a s e r i n t e n s i t y and f o r a l i n e a r p o l a r i z a t i o n p a r a l l e l t o t h e i n i t i a l d i r e c t i o n R of t h e i n t e r -

i

n u c l e a r a x i s , t h e incoming c o l l i s i o n a l s t a t e (t = t-) i s a l i n e a r combination of

1 1 1

s t a t e s A ( ~ , ' S ) , B ( S) and A(2, P o ) , B( S). From theCmolecular viewpoint,' t h e atomic g r o u n d s t a t e i s connected t o a C s t a t e whereas t h e e x c i t e d one i s connected t o C( 1 Po)

and fl( 1 P ) s t a t e s . T h e r e f o r e , i f a long-range II-C r o t a t i o n a l c o u p l i n g i s p r e s e n t , + 1

t h e outcoming ( t = t +) c o l l i s i o n a l s t a t e t a k e s t h e form :

a l ( t c ) f l lls> * a 2 ( t c ) A=o,tl

'

1

1- c

b e c a u s e of t h e r o t a t i o n of R, any component l p would have a p r o j e c t i o n o n t o M = 0 h

a l o n g S ) . Consequently t h e f i n a l g r o u n d s t a t e p o p u l a t i o n c o n t a i n s a n i n t e r f e r e n c e term depending on I f l

,

/

To c o n c l u d e a b o u t t h e f e a s a b i l i t y of such a s s i s t e d c r o s s e d beam e x p e r i m e n t s , l e t u s p o i n t o u t a promizing e x p e r i m e n t a l method developped r e c e n t l y by P i l l e t e t a l [ 1 6 ] . The b a s i c i d e a i s t o u s e t r a n s i t i o n s between h i g h n (n

-

Because o f t h e v e r y l a r g e v a l u e s t a k e n by t h e d i p o l e moments, t h e s o - c a l l e d h i g h - i n t e n s i t y regime i s a c c e s s i b l e w i t h q u i t e r e a s o n a b l e microwave powers (few w/cmL) ; t h e long l i f e t i m e of s u c h s t a t e s i s a l s o a n a b v i o u s a d v a n t a g e of t h e method.

REFERENCES

[ I ] J. C u v e l l i e r , J.M. Mestdagh, M. F e r r a y , P.de P u j o and J. B e r l a n d e , X I 1 1 t h ICPEAC, B e r l i n 1983, p. 603.

[2] G. J a m i e s o n , C.P. S c h u l z , H.U. T i t t e s , I V H e r t e l , X I 1 1 t h ICPEAC, B e r l i n 1983, p. 601.

[ 3 ] H. Schmidt, M.F. Vernon, P.S. Weiss, M.H. Covinsky, Y.T. Lee, X I 1 1 t h ICPEAC, B e r l i n 1983, p. 642.

t41 T. T r i c k 1 and J. Wanner, J. Chem. Phys. 78, 6091 (1983)

[51 C. Crbpin, J.L. Picqub, G. Rahmat, J. VergSs, R. V e t t e r and F.X. Gadea, M. P B l i s s i e r , F. Spiegelmann, J.P. M a l r i e u , l o e Colloque s u r l a Physique d e s

C o l l i s i o n s atomiques e t S l e c t r o n i q u e s , A u s s o i s (France) 1984.

161 J. Weiner, J. Boulner, J. K e l l e r and R. Bonanno, X I 1 1 t h ICPEAC, B e r l i n 1983, p. 327.

[ 7 ] A. P e s n e l l e , S. Runge and G. Watel, X I 1 1 t h ICPEAC, B e r l i n 1983, p. 325.

[81 H . Haberland, Y.T. Lee and P.E. S i s k a , Adv. Chem. Phys. 47, 487 (1981).

C 1-36 JOURNAL DE PHYSIQUE

[ 9 ] Ch. Bender, W. Beyer, H. H a b e r l a n d , D. Hausamann and H.P. Ludescher, t h i s i s s u e . [ l o ] W. Beyer, H. Haberland, D. Hausamann, X I 1 1 t h ICPEAC, B e r l i n , p . 344.

[ I 1 1 V. B o c v a r s k i , J. R o b e r t , I. Colomb d e Daunant, J. R e i n h a r d t , J. Baudon, M.Dumont and Ch. Lerminiaux, l o e C o l l o q u e s u r l a P h y s i q u e d e s C o l l i s i o n s a t o m i q u e s e t g l e c t r o n i q u e s , A u s s o i s ( F r a n c e ) 1984, p . 98.

[ 1 2 ] M. Dumont, J. P h y s i q u e L e t t . 41, ^E 2 7 5 (1980).

[13] J.M. Mestdagh, J. P a s c a l e , X I 1 1 t h ICPEAC, B e r l i n 1983, p. 341.

J.M. Mestdagh, J. B e r l a n d e , P. d e P u j o , J. C u v e l l i e r , A. B i n e t , Z. Phys. A,

3, 3 (1982).

[14] R. Duren, E. H a s s e l b r i n k and H. T i s c h e r , X I 1 1 t h ICPEAC, B e r l i n 1983, p. 343.

[15] G. Jamieson, W. R e i l a n d , C.P. S c h u l z , H.U. T i t t e s and I.V. H e r t e l , X I 1 1 t h ICPEAC, B e r l i n 1983, p. 600.

[ I 6 1 P. P i l l e t , R. Kachru, N.H. Tran, W.W. Smith and T.F. G a l l a g h e r , XIIT t h ICPEAC, B e r l i n 1983, p. 698.