(e,2e) Collisions in the Presence of a Laser Field

Abstract

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...

Laser-assisted coplanar symmetric (e, 2e) triple differential cross sections

“…We see that, even for intense laser fields, the dressing effects of the target are somewhat insignificant at low frequencies. Moreover, our results present an absolute minimum corresponding to the zero of the electronic term (term in brackets in equation (19)) which is dominant in low frequencies. This minimum, located around 44 q = • , corresponds to the compensation between electron-electron and electron-nucleus interactions.…”

“…These rapid oscillations reflect the highly non-perturbative nature of the interaction of the laser field with the free electron. This oscillatory phenomenon can be explained by the changes of the Bessel function, i.e., the sign of the argument of the Bessel function changes depending on the sign of the summation over N coming from equation (19). This behavior can be traced back to the fact that the argument of the Bessel functions, entering the expressions of the amplitudes equations (19) and (20), grows with 0  and varies with the scattering angle.…”

“…This oscillatory phenomenon can be explained by the changes of the Bessel function, i.e., the sign of the argument of the Bessel function changes depending on the sign of the summation over N coming from equation (19). This behavior can be traced back to the fact that the argument of the Bessel functions, entering the expressions of the amplitudes equations (19) and (20), grows with 0  and varies with the scattering angle. Accordingly, at higher field strengths, every other laser parameter being fixed, one explores more zeros of the Bessel functions when varying the scattering angle.…”

“…A simplified description of this process is that of twostep processes in the course of which the atomic electron is first brought into the continuum as a result of the collision, and then exchanges photons with the laser field [3]. When the laser intensity increases, an oscillatory phenomenon is observed which is due to the interference between the terms constituting the dominant electronic amplitude f 1 given by equation (19) and the change of sign of the argument of the Bessel function (see below); (iii) Figure 2 indicates that, for ℓ 0 = , the dressing of the target states does not play a dominant role in the physics of the process. In other words, this result shows that the term f 1 (equation (19)) is dominant in the transition amplitude (equation (18)).…”

“…to enhance or suppress the ionization cross section as per the requirement in a particular physical process. Since the laser field can act as a reservoir of energy and its polarization vector introduces a new axis of symmetry, the laser-assisted ionization cross sections could differ strongly in shape and magnitude from the field-free cross sections as predicted in several theoretical studies on this topic [18][19][20][21][22][23][24].…”