Phase coherent control in electron-argon scattering in a bichromatic laser field

arXiv:0810.1388v1 [physics.atm-clus] 8 Oct 2008 Phase coherent control in electron-argon scattering in a bichromatic laser field Bin Zhou1 and Shu-Min Li1,2 1Department of Modern Physics, University of Science and Technology of China, P. O. Box 4, Hefei, Anhui 230026, People’s Republic of China. 2Institut f¨ur Theoretische Physik, Univsit¨at Heidelberg, 69120 Heidelberg, Germany. (Dated: November 16, 2018) We study the elastic scattering of atomic argon by a electron in the presence of a bichromatic laser field. The numerical calculation is done in the first Born approximation (FBA) for a simple screening electric potential. With the help of numerical results we explore the dependence of the differential cross sections (DCS) on the relative phase ϕ between the two components of the radiation field and discuss the influence of the number of photons exchanged on the phase-dependence effect. Moreover, we also discuss the numerical results of the DCS for different scattering angles and impact energies. PACS numbers: 34.80.Qb; 32.80.Wr; 34.50.Rk; 34.80.Bm Multiphoton free-free transitions (MFFT) have at- tracted much attention since the pioneering papers by Bunkin and Fedorov [1] and Kroll and Watson [2], and a great deal of work has been devoted to them [3, 4, 5, 6, 7]. As the experimental technology improved, powerful lasers and new kinds of laser fields have been applied to laser-assisted atomic and molecular processes. Due to the significance in dynamic control of the multi- color lasers, the processes they modify received consider- able attentions. By changing the phase difference of the multicolor laser field, we can enhance or modify atomic and molecular processes, which are called phase coher- ent control. There has been much work done in phase coherent control [8, 9, 10, 11, 12, 13, 14, 15, 16, 17], thus the investigation on the phase coherent control of elastic electron-atom collisions in a multicolor laser field becomes a very active research domain. In most of the theoretical work, the laser radiation is treated as a clas- sical radiation filed with a single frequency ω, or some narrow band multi-mode approximation has been em- ployed, yielding better agreement with the experiments by Weigngarshofer [18]. Describing a laser beam by a monochromatic classical background field relies on the argument that in a laser beam the density of radiation quanta is so large that the depletion of this beam by emit- ting or absorbing quanta from it is negligible. If the laser frequency ω and intensity I are sufficiently low so that the excitations of atomic transitions can be neglected, the atomic target can be described by a short range po- tential V (r) and the scattering can be treated in the first Born-approximation, as was done by Bunkin and Fedorov [1]. In this letter, we will investigate the relative phase ϕ dependence of free-free transitions for the electron-argon scattering in the presence of bichromatic laser field. During a laser-assisted electron-impact scattering pro- cess l photons may be exchanged with the laser field. In our work, we consider the free-free transition in argon atom in the presence of a bichromatic laser field, accom- panied by transfer of l photons in the first Born approx- imation (l > 0 for emission and l < 0 for absorption). The laser field is treated classically as a electromagnetic field [19] which is a superposition of two components of frequencies ω and 2ω. The bichromatic laser field is de- scribed as E(t) = E0[sin ωt+sin(2ωt+ϕ)], where E0 is the electric field amplitude vector and the relative phase ϕ can be arbitrarily changed. Atomic units ℏ= m = e = 1 are used throughout. In case the laser is much weak compared with the in- ternal field of an atom (ion), the dressing effect in atom can be neglected, and the target atom is described by a screening potential [20, 21, 22] V (r) = −Z r 2 X i=1 Ai exp(−αir), (1) where r denotes the position of the electron with respect to the nucleus, and Z is the nuclear charge number. For argon, A1 = 2.1912, A2 = −2.8252, α1 = 5.5470, α2 = 4.5687. The scattering matrix for the laser-assisted free-free transition in the first Born approximation reads S(1) fi = −i Z ∞ −∞ dt Z drχ∗ kf (r, t)V (r)χki(r, t), (2) where χkf and χki are the initial and the final states of the electron, described by the Volkov wave function χkf,i(r, t) = exp(ikf,i · r) exp  −iEf,it −i ω2 kf,i · E0 sin ωt  × exp  −i 4ω2 kf,i · E0 sin(2ωt + ϕ)  , (3) where ki,f are the wave vectors of electron in the initial and final states, and Ei,f is the corresponding kinetic energies. With using the potential of Eq.(1) and the wave func- tions of Eq.(3), we obtain S(1) fi = −2πi X l T (1) f,i (l)δ(Ef −Ei + lω). (4) 2 0 60 120 180 240 300 360 10 -10 10 -9 10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 0 60 120 180 240 300 360 10 -10 10 -9 10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 (a) l=0 l=1 l=2 l=3 l=4 DCS (a.u.) (deg) (b) l=-1 l=-2 l=-3 l=-4 DCS (a.u.) (deg) FIG. 1: T

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