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Ionization of atomic hydrogen by protons in the presence of a laser field

The ionization of atomic hydrogen by protons in the presence of a laser background is studied. We describe the initial and final states of the proton by plane waves, the state of the target by a dressed wavefunction obtained by time-dependent theory in the soft-photon approximation, and the state of the ejected electron by a two-centre Coulomb function modulated in time by the laser field in the same way as a plane wave. The laser-modified double differential cross sections for a geometry of laser polarization parallel to the incident cross section of the proton are calculated and compared with the laser-free results. For each small electron ejection angle, a critical point is found in the electron energy spectrum, behind which the cross section is notably enhanced.