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Submitted on 1 Jan 1982
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COMMENT ON THE SPACE TRANSLATION METHOD AS USED IN LASER-ASSISTED
COLLISION PROBLEMS
G. Ferrante, C. Leone
To cite this version:
G. Ferrante, C. Leone. COMMENT ON THE SPACE TRANSLATION METHOD AS USED IN
LASER-ASSISTED COLLISION PROBLEMS. Journal de Physique Colloques, 1982, 43 (C2), pp.C2-
433-C2-434. �10.1051/jphyscol:1982233�. �jpa-00221845�
JOURNAL DE PHYSIQUE
CoZZoque C2, supple'ment au n o l l , Tome 43, novembre 1982 page
C2-433COMMENT ON THE SPACE TRANSLATION METHOD AS USED IN LASER-ASSISTED COLLISION PROBLEMS+
G. Ferrante and C. ~ e o n e *
I s t i t u t o di Fisica d e l l ' U n i v e r s i t d , Via Archirafi
36,90123 Palerrno, I t a l y
" ~ s t i t u t o d i Fisica de Z Za Faco Ztd d i Ingegneria, Parco d'orZeans, 901 28, I t a l y
The Space Translation Method ( S T M ) was introduced in ato- mic physics in recent years by Hennebergerl to deal satisfactori- ly with the problem of the interaction of intense light fields with atoms and molecules, for which conventional perturbation theo- ry i s inadequate. Essentially the method consists of a time-depen- dent unitary transformation to an accelerated frame o f reference, which was already known in quantum electrodynamics 2
.
Considering hydrogen atoms as an example, the effect of this transformation is to remove from the appropriate Schroedinger equation the(e/mc)p.A(t) interaction between the e.m. field and the atomic elez-
5
tron, and to change the static electron-nucleus interaction V ( r ) into a time-dependent, displaced potential V ( _ r
+ 5
(t)) withbeing the classical displacement of a free electron from its center of oscillation in a radiation field.
The displaced potential may be separated into a static and a time-dependent part
both being dependent on the laser field parameters.
As the unitarily transformed equations can not be solved exactly, the Henneberger's original proposal was to determine nu- merically approximate eigenstates and eigenvalues of the "dressed"
Hamiltonian
and then proceed with a conventional time-dependent perturbation theory treatment to perturbe with v (r,t) the dressed eigenstates of H 1
0' The STM is used to study, among others, laser modificati-
ons of the spectra of isolated atoms, multiphoton ionization, la- ser-assisted particle-atom collisions and laser-assisted x-ray pho- toeffect. So far, however, none has fully and rigorously carried out the Henneberger's original proposal. Instead, several incomple- te or simplified treatments are available, which not rarely produ-
+partially supported by GNSM-CNR and CRRNSM
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982233
C2-434 JOURNAL DE PHYSIQUE
ce ambiguous and puzzling results, in disagreement with those of more conventional treatments. This is particularly true in laser- assisted collision processes, where, sometimes, the STM fails to predict multiphoton processes', or effects due to free particle-field interaction. Some of the observed discrepancies due to the se of S T M h a v e b e e n discussed and clarified by Lambropoulos et al.
'5 ,
Ehlotzky4 and Ferrante et a15. This Comment, instead, is concerned with the use of STM in laser-assisted collision problems. Remin- ding fundamental properties of the unitary transformations, it can be shown that if the unitary transformations,which are the essence of the STM, are performed properly, the STM gives essentially the same results as the more conventional treatments. The basic idea of this Comment is that any simplification of unitarily transfor- med operators adopted for solving the equations amounts to change the unitary operators, accomplishing the transformation. Accor- dingly, one must look for approximate new unitary transformations which when performed on the original equations yield the simplified transformed equations and/or operators. If this procedure is con- sistently carried out o n all the operators and wavefunctions of the collision problems, disagreement generally disappears. Detai- led analysis concerninq inelastic laser-assisted electron-hydrogen collisions shows that any manipulation of the transformed atomic electron-nucleus interaction V (
r
+ o ( (t)) requires significant changes into the wavefunctions and the interaction operators ente- ring the S-matrix element, if one wants to ensure the necessary equivalence with the untransformed equations.References
1. W.C. Henneberger, Phys. Rev. Lett.
21,
838 (1968).2. H . A . Kramers, Rapport et Discussions, Solvay Congress ( Stoop
Brdssels, 1948 1 .
3. P. Lambropoulos, E.A. Power and T. Thirunamachandran,Phys Rev.
A14, 1910 (1976).
-
4. F. Ehlotzky, Opt. Comm.
140 ,
130 (1982).5 . G. Ferrante, E. Fiordilino and C. Leone: Laser-Assisted X-Ray
Photoeffect and the Space Translation Method. Phys. Lett.,
( in press 1 .
