X-RAY-ATOM SCATTERING IN THE PRESENCE OF A LASER FIELD

We consider x-ray-hydrogen atom scattering in the presence of a monoch romatic linearly polarized laser field. The S matrix of this process i s presented and an expression for the differential cross section (DCS) is derived. We show that the time-dependent Wentzel-Kramers-Brillouin approximation can be applied to the present problem. The presented nu merical results for the DCS as a function of the number n of photons e xchanged with the laser field show a characteristic behavior. The numb er n can only be even. For n = 0, +/-2 we have pronounced maxima in th e DCS, followed by sharp minima at n=+/-4. After that, Eve have a plat eau that is different for negative and positive values of n. The plate au for negative Values of n is much more extended than for the positiv e ones. The structure of the plateau and the positions of the minima a nd maxima of the DCS do not depend on the laser field intensity, while the height of the plateaus strongly depends on it. We also analyze th e dependence of the matrix elements of the x-ray spectra on the incide nt x-ray photon energies by using bath the saddle-point method and the numerical evaluation, and we show that the shape and position of the plateau are determined by the simple relation n (h) over bar omega=I-0 -(h) over bar omega(K). This condition connects the number of absorbed or emitted laser field photons n, the laser field photon energy Aw, t he atomic ionization potential I-0, and the energy of the incident x-r ay photon (h) over bar omega K.