Laser assisted proton collision on light nuclei at moderate energies

We present analytic angular differential cross section model for laser assisted proton nucleon scattering on a Woods-Saxon optical potential where the nth-order photon absorption is taken into account simultaneously. As a physical example we calculate cross sections for proton - ${}^{12}$C collision at 49 MeV in the laboratory frame where the laser intensity is in the range of $ 10^{7} - 10^{21}$W\mathrm{/}cm$^2$ at optical frequencies. The upper intensity limit is slightly below the relativistic regime.