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ELECTRON-ATOM-PHOTON INTERACTIONS IN A LASER FIELD
B. Bederson, B. Jaduszliwer, G. Shen, J.-L. Cai
To cite this version:
B. Bederson, B. Jaduszliwer, G. Shen, J.-L. Cai. ELECTRON-ATOM-PHOTON INTERAC- TIONS IN A LASER FIELD. Journal de Physique Colloques, 1985, 46 (C1), pp.C1-241-C1-248.
�10.1051/jphyscol:1985123�. �jpa-00224495�
JOURNAL DE PHYSIQUE
Colloque C1, suppl6ment au nO1, Tome 46, janvier 1985 page C1-241
ELECTRON-ATOM-PHOTON INTERACTIONS IN A LASER FIELD
B. Bederson, B. Jaduszliwer, G.F. Shen and J.-L. Cai New York University, NY
10003,U.S.A.
Resume - Nous etudions actuellement la diffusion df61ectrons aux energies basses et intermediaires par des atomes de sodium dans un champ laser. La methode experimentale est prGsent&e, en portant particulihrement attention au recul atomique consecutif 5 l'absorption resonnante de photons. On donne les sections efficaces totales pour les atomes de sodium dans l'etat 3
2P.
Abstract - We are currently studying the scattering of low and intermediate energy electrons by sodium atoms in a laser field. The experimental method is discussed, with particular attention to atomic recoil after resonant photon absorption. Total scattering cross sections by
3 2 ~sodium atoms are presented.
In this paper we will discuss the experiments being conducted in the New York University Atomic Beams Laboratory, which involve the scattering of low and intermediate energ-j electrons by alkali atoms in ground and laser-excited states.
The principal goals of this research are, 1) to effect as close a comparison of ab-initio calculations for simple few-body systems with experiment as possible,
2)to reduce the collision experiment to a determination of separate observables, e.g., direct and exchange scattering amplitudes, selected angular momentum orientations, relative phases of scattering matrix elements, etc., using state selection and analysis, 3) to obtain reliable absolute cross sections for these, without requiring normalization to theory or other experiments, 4) to achieve sufficient redundancy in these state-sensitive cross section measurements to overdetermine scattering amplitudes, permitting detailed scrutiny of time- independent collision theory, 5) to use the laser as a tool in state-preparation and analysis for both fine and hyperfine states, as well as short-lived
electronically excited states,
6 )to look for direct intense-field effects on electron-atom collisions, and finally, 7) to study the atom-laser interaction itself.
From the point of view of this work, therefore, electron-atom scattering in the presence of laser interactions can be considered to be a natural extension of field-free scattering, which makes it possible to perform better collision experiments, but which do not add any intrinsically new physical processes to the two-body scattering problem. In 6) above, this of course changes; however generally speaking very strong fields are required. On the other hand, even when the laser field is not "strong", it is necessary to understand the laser-atom interaction in order to obtain absolute excited-state cross sections. This last point will be discussed more fully later. We will touch on all six items noted above in the present paper, concentrating of course on items
6 ,7 and we will attempt to show how they relate to one another.
We consider "one-electron" atoms, such as the alkalis or atomic hydrogen, and refer the reader to the literature for discussing of collision theory and details of previous work1. For electron scattering by alkali atoms, "close coupling"
calculations have been extremely successful in predicting behavior of ground-state
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985123
C1-242 JOURNAL DE PHYSIQUE
csllision cross sections. This is in part due, of course, to the relatively simple nature of the interaction, in which electron-correlation only plays a role through (cooperative) core polarization effects. In addition, because of the large (and spherical) core shielding, close-coupling convergence is extremely rapid, particularly with respect to optically-connected electric dipole-type matrix elements. Accordingly these systems can serve as stringent test cases for comparison of theory and experiment.
The experimental work described here has been performed using variations of the atomic beam "recoil" technique2, wherein observation of the scattering is made on the "heavy" partner, i.e. the atom, rather than the electron. The method possesses the intrinsic advantages that (1) it is possible to directly observe
change in the atomic magnetic quantum number, caused either by spin-exchange or by angular momentum projection changes; (2) absolute values of cross sections can be obtained, without need for knowledge of the atomic beam density;
( 3 )laser-excited atoms can be spatially separated, using photon-recoil, from unexcited atoms enabling determination of absolute excited-state cross sections.
The work discussed herein was performed on a new atomic beams apparatus, which is described briefly below. Mutually orthogonal rectangular electron, atom and laser beams intersect in an interaction volume; the (ground-state) atom beam is velocity- and hyperfine-state-selected by a tunable hexapole electromagnet.
It is recoil-scattered by both electron and laser beams. After travelling through a field-free "drift regionu 3 m long its spatial dispersion is analyzed by a surface ionization detector of square cross sectional area, capable of displacement in two dimensions. Fig. 1 shows a schematic view of the experi- mental setup.
SINGLE-MODE RING
DYE
Fig.
ELECTRON
1: Schematic view of the experimental setup.
DETECTOR, MASS SPECTROMETER
It is helpful to present some qualitative estimates of recoil angles and displacements, since these determine the angular and energy resolution of the measurements. The "order-of-magnitude" angular deflection j, of the atomic beam by electron scattering is
where mv, MV are the electron and atom momenta respectively. If U is the
electron energy in ev, for a thermal sodium beam, $8 0.02 fi radians which trans- lates into a displacement
". 6 ~ 5cm in our apparatus. For a 1 eV electron, this corresponds to about 30 beam widths, or, effectively, an average angular resolu- tion of 3 ' in the electron polar scattering angle.
The atomic photon recoil angle per resonantly absorbed photon, a . , is
which is approximately 3x10-~ rads for a thermal sodium beam, corresponding to a displacement of 9x10-~ cm. Characteristically our atom beam emits perhaps 250 to 500 spontaneous photons in the interaction volume, so that the net photon recoil produces atom beam deflections of 3 to 6 cm, i-e., of the same order of magnitude as electron recoil.
Scattering experiments can usually be performed in either the "scattering- out" or "scattering-in" mode. Scattering-out generally implies measurement of a '!totaln cross section, and scattering-in of a differential cross section, although analysis can be considerably more difficult when the cross section possesses sharp angular dependence, as is the case for small-angle scattering of polarizable atoms, such as excited-state alkali atoms.
As a "best-case" total (scattering-out) cross section, we show in Fig. 2 our data for total cross sections for scattering of low energy electrons by ground- state (32~,) sodium3r4. These are "absolute", given directly by the formula
2
where (AI/I)atom is the relative scattering-out atomic signal, h a beam geometry factor and Ie the electron number current. Also shown in Fig. 2 is a 4-state close-coupling calculation by Moores and or cross^. The agreement is extremely good, and is indicative of the success of such calculations for one-electron atoms, as noted above.
The experimental configuration with the laser on is shown in Fig. 3. The atom, the electron and laser beams travel in the y,
zand -x directions respectively. A square collimator, 0.1 x 0.1 mm, placed upstream at the interaction volume defines the atom beam cross sectional area. The detector, which can translate in the x-z plane, would observe an undeflected square gaussian beam shape of about
. 5cm FWHM. The curve in Fig. 3 shows the photon- recoiled atom beam. To a first order of approximation atoms deflected a distance d in the -x direction have experienced a net absorption of n photons from the laser field in the interaction volume, given by
The relation between d and f, the fractional population of excited-state atoms in the interaction volume, is
where
T , Tare the time spent by an atom possessing speed V in the interaction volume, an2 the mean atomic lifetime respectively. To obtain a total excited state cross section, the detector is displaced in the -x direction to a position x
=-d, and a conventional scattering-out experiment is now ~ e r f o n e d . The
"effective" cross section observed in this case is a weighted average of ground
and excited state cross sections
0, aex, (in the "weak field" case, where no
coherence effects occur) , given byg
C1-244
JOURNAL DE PHYSIQUE
400
- 300
-5
'2- c
.-
C 0 01 Ucn
m
200
cn 0
2
100
1 3 5
Energy (eV)
LAST- --
+
-K
BEAM
I /
Fig. 2: Total cross sections for the scattering of electrons by Na
( 3 28) atoms.
Squares: Kasdan et a1.3; dots:
Jaduszliwer et a l e 4 ; curve:
Moores and
orc cross^.
Fig. 3:
Experimental
configuration.
Eq. 4 is used to obtain f and Eq. 5 to find uex, assuming og has been determinedby a conventional on-axis scattering-out ex~eriment with the laser off. In Fig. 4 we show combined earlier published and recent unpublished results for the cross section for electron scattering by 3 ' ~ ~ ~ ~ . In the data up to 6eV, the optical excitation was performed using linearly polarized light; a strong magnetic field was aligned parallel to the electron beam and accordingly m
=3/2, and mL
=+1.
J
ENERGY ( eV )
Fig. 4: Total cross sections for the scattering of electrons by ~ a ( 3 ~ ~ ) atoms. Dots:
Jaduszliwer et a ~ . ~ ; square: this work.
The 10 eV point was obtained in weak magnetic field, using circular polarized light. Transforming to the
+zaxis (electron beam direction) the atomic beam can be shown to be aligned, with magnetic quantum state weights l(m~
=-11, 2 ( m ~
=0) and l(mL
=+I). The "total" cross sections obtained for 3'~ using the partla1 elastic 3P-3P and inelastic 3P-3S, 3P-3D and 3P-4s cross sections calculated by Moore et a1.6 are not directly comparable to our measurements because they are averaged over J and mJ. The calculations were only made to 5 eV; no other calculations exist, to our knowledge, for higher energies.
In applying Eqs 1-5, we have not taken a number of possibly significant
factors into account, in analyzing the photon-recoiled atom beam. These factors
include the influence of the atom beam shape, the laser spatial distribution, the
atom beam velocity distribution, power broadening and optical pumping, cumulative
first-order -doppler detuning, ponderomotive ef fects7, and photon statistics8. In
a first step of a more detailed study which is currently in progress, we have
been measuring the atomic beam deflection pattern as a function of various laser
Cl-246 JOURNAL DE PHYSIQUE
o p e r a t i n g parameters, i n c l u d i n g power, s p a t i a l d i s t r i b u t i o n , o r i e n t a t i o n , e t c . I n F i g . 5 we show a s e r i e s o f atom d e f l e c t i o n p a t t e r n s taken a t s e v e r a l d i f f e r e n t l a s e r powers. The v e l o c i t y r e s o l u t i o n w i t h t h e magnetic hexapole o p e r a t i n g i s V/AV
2
4 (FWHM); t h e hexapole s e l e c t s t h e F = 2, mF = 2 , 1, 0 , -1 h y p e r f i n e s t a t e s . A l l of t h e s e s t a t e s can be e x c i t e d without o p t i c a l pumping by c i r c u l a r l y p o l a r i z e d l i g h t s e t f o r F=2 + F=3 r e s o n a n t t r a n s i t i o n s .Fig. 5: ( a ) Atomic beam v e r t i c a l p r o f i l e , and l a s e r - d e f l e c t e d p r o f i l e s w i t h nominal l a s e r power, ( b ) 25 mW, ( c ) 50 mW,
(dl
100mw,
( e ) 200 mW, ( f ) 300 mW and ( g ) 500 mW.D e t e c t o r i s downstream of i n t e r a c t i o n r e g i o n .
The peak o f t h e 500 mW curve ( 4 cm from t h e beam a x i s ) corresponds t o f = 0.3.
The i n t e g r a t e d a r e a s under a l l c u r v e s a r e t h e same t o w i t h i n a b o u t 5 % , i n d i c a t i n g t h a t we a r e accounting f o r e s s e n t i a l l y a l l r e c o i l - s c ' a t t e r e d atoms, a t a l l power l e v e l s . The d i s p e r s i o n , which i n c r e a s e s with i n c r e a s i n g power,
i s
a t t r i b u t a b l e p r i m a r i l y t o t h e r e s i d u a l atomic beam v e l o c i t y spread. The d e f l e c t i o n p a t t e r n s s a t u r a t e with i n c r e a s i n g l a s e r power, due t o a combination of f i r s t - o r d e r Doppler d e t u n i n g and power broadening. F i g . 6 shows a p l o t of t h e most probabled e f l e c t i o n v s . l a s e r power, f o r a ? a r t i c u l a r s e t o f l a s e r beam geometry
parameters. For comparison, i n F i g . 7, we show a l a s e r d e f l e c t e d atom beam curve w i t h o u t s t a t e and v e l o c i t y s e l e c t i o n . T h i s c l e a r l y shows a ) t h e l a c k of
e x c i t a t i o n of t h e
3/5
of t h e beam which i s i n t h e F = 1 g r o u n d - s t a t e , and b ) t h e v e r y l a r g e s p a t i a l d i s p e r s i o n caused by a Maxwellian v e l o c i t y d i s t r i b u t i o n . The c r o s s s e c t i o n s themselves a r e e s s e n t i a l l y power-independent, o v e r t h e range of power l e v e l s o f t h e p r e s e n t experiment9.We a r e c u r r e n t l y extending o u r t o t a l c r o s s s e c t i o n measurements t o h i g h e r e n e r g i e s (up t o 2 5 eV); a l s o , measurements a r e i n p r o g r e s s on d i f f e r e n t i a l e l a s t i c 3P
-
3P, and d i f f e r e n t i a l " s u p e r e l a s t i c " 3P-
3s c r o s s s e c t i o n s . T h i s l a t t e r i s t h e t i m e - r e ~ r s e r e a c t i o n t o t h e 3s-
3P e x c i t a t i o n , performed u s i n g s t a t e a n a l y s i s of t h e e x c i t a t i o n p r o d u c t s l O .T h i s work i s supported by t h e ~ a t i o n a l Science Foundation.
We thank D r . Richard Dang and D r . P h y l l i s Weiss f o r t h e i r c o n t r i b u t i o n s i n t h e e a r l y phases of t h e s e experiments, and g r a t e f u l l y acknowledge t h e s u p p o r t o f D r . Dang by t h e James Arthur Fund.
