X-ray photoionization in the presence of a bichromatic laser field

X-ray photoionization of hydrogen in the presence of a bichromatic laser field is considered. The expressions for the T matrix and the cross sections for the laser-assisted x-ray photoionization are presented. The initial state is the laser-field-dressed hydrogen-atom ground state, while the final state is the improved Coulomb-Volkov wave. The gauge consistency is ensured by working in the r⋅E gauge. It turns out that the matrix elements (the explicit form of which is given in the Appendix) are much simpler in this case. This enables one to consider the symmetry properties of the T matrix and the cross sections analytically. It was shown that the symmetry (φ+π,π-θ)↔(φ,θ), where φ is the relative phase between the laser-field components and θ is the polar angle of the outgoing electron, is exact in our case. In addition to this, there are approximate symmetries φ↔-φ and φ↔φ+π. All these symmetries, as well as the behavior of the differential and total cross sections as functions of φ, θ, and the number of exchanged photons, are analyzed in numerous examples. The results presented show the possibility of the coherent phase control of the laser-assisted x-ray photoionization process. It was also shown that in the monochromatic case our model gives results that are in good agreement with the results of previous work.