We propose a unified R-matrix-FLoquct method which can he used to analyse both the multiphoton ionization of a t o m and laser-assisted electron-atom collisions. Our treatment is nompertwhative and can be applied to an arbitrary LII"'II.

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We study the inelastic scattering, accompanied by the transfer of L photons, of fast electrons by hydrogen and helium atoms in the presence of a laser field. A detailed analysis is made of the excitation of the n =2 and n =3 states of atomic hydrogen, and of the 1 'S-2 'S and 1 'S-2 'P transitions in helium. It is shown that the "dressing" effect due to the dipole distortion of the target by the laser field produces important modifications of the cross sections at small momentum transfers for S-S and S-D transitions. However, this dressing effect is reduced in the case of S-P transitions. Our results exhibit qualitative differences from the case of laser-assisted elastic collisions; this is mainly due to the possibility of intermediate resonances in the laser-atom interaction during the collision event.

We study the influence of a laser field on the dynamics of fast (e, 2e) collisions on atomic hydrogen, in the asymmetric coplanar geometry. We find that the triply diA'erential cross sections are strongly dependent on the "dressing" of the atomic target by the laser.PACS numbers: 34.80.Qb, 32.80.t In this Letter, we present a theoretical treatment of fast (e, 2e) reactions in a laser field, and report a number of new results concerning the modifications of the angular distributions of the ejected electrons due to the presence of the laser. In particular, we have found that dramatic changes in the triply differential cross sections (TDCS) can occur because of the "dressing" of the atomic target states by the laser.In order to keep the discussion simple, we shall assume that the laser is treated classically as a spatially homogeneous electric field, linearly polarized and single mode, C(t) =rosin(rut), and that the target consists of atomic hydrogen.The (e,2e) kinematical arrangement which we have selected is the Ehrhardt asymmetric coplanar geometry, ' such that a fast electron of momentum k; is incident on the target, and a fast ("scattered") electron of momentum kg is detected in coincidence with a slow ("ejected") electron of momentum kp, the three momenta k;, kq, and kq being in the same plane. Moreover, the scattering angle 8~of the fast electron is fixed and small, while the angle eg of the slow electron is varied. The reasons for our choice of the Ehrhardt geometry are that (i) at high incident energies most of the (e,2e) collisions occur in this kinematical regime and (ii) accurate experimental and theoretical' results are available in this geometry for the corresponding field-free (e, 2e) reaction e +H(ls)~H++2eRemembering that in the Ehrhardt geometry exchange effects between the projectile and target electrons are small, and that a perturbative treatment of the (direct) interaction between the fast projectile electron and the target atom is justified, 3 4 we start from the first Born ionization S-matrix element, which for the present laser-assisted (e,2e) reaction is given (in atomic units) by ++oo S~"' =i dt(Zg"(ro, t)@g,(ri, t) i I/rol -I/roiZg, (ro, l)@p(rl, t)),where ro and rl are respectively the coordinates of the projectile and target electrons, and rol = i rorl i. The wave functions Xi, , (rp, r) and Zi,"(rp, r) are Volkov wave functions of the form Xi, (ro, t) =(2x) i exp[i(k rok aosincot Ekt)], -where Ek =k /2 and ao =Co/ro, ru being the laser angular frequency.The wave functions @o(rl,t) and @i, , (rl, t) in Eq. (1) are the "dressed" states of the hydrogen atom embedded in the laser field, the first one corresponding to the initial (bound) state and the second one to the final (continuum) state in which a slow electron of momentum kq has been ejected. In what follows we shall consider laser fields such that Co«5x10" V m ' (the atomic unit of field strength). The dressed atomic bound states can then be obtained by use of first-order, time-dependent perturbation theory. In particular, the dr...

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