Electron-atom ionising collisions in the presence of a low-frequency laser field

The authors extend the previous treatment of electron-atom scattering in the field of a low-frequency laser to the case of single ionisation. They expand in powers of the laser frequency neglecting second-order terms. They exclude the case in which there are scattering resonances in the absence of the laser and require that the energy of each of the final free electrons by several photon energies above threshold. Their result is similar to the case in which the atom is not ionised as the cross section in the presence of the laser can be expressed in terms of that in the absence of the laser, which slightly shifted initial and final momenta. The ionisation does, however, result in a change of the arguments of the kinematic Bessel function which appears in this kind of problem. The extension of their results to multiple ionisation and to inner-shell photoionisation by X-rays in the presence of a low-frequency laser field is also described.