Introduction of the Coulomb dressed potential into atomic scattering

The model of the Coulomb dressed potential is applied to solving the problem of electron scattering for simplifying the calculation in the electrostatic field and the excimer laser field. The introduction and the application of the model are based on the electric dipole approximation, so the contribution of the electric multipole is neglected. In this paper, rigorous analysis and deduction are carried out for the introduction of the dressed Coulomb potential into the laser field. It is found that the introduction of the dressed potential in the fractional form is feasible only when the laser field (not including far ultraviolet field and x-ray) is a weak field, i.e. the quiver radius of the free electron is smaller than the atomic scale. In addition, the necessary analysis is also conducted of the limitation of the application of the Coulomb dressed potential.