We present a non-relativistic analytic quantum mechanical model to calculate angular differential cross-sections for laser-assisted proton nucleon scattering on a Woods–Saxon optical potential where the nth-order photon absorption is taken into account simultaneously. With this novel description we can integrate two well-established fields, namely low-energy nuclear physics and multi-photon processes together. As a physical example we calculate cross-sections for proton–12C collision at 49 MeV in the laboratory frame in various realistic laser fields. We consider optical Ti:sapphire and X-ray lasers with intensities which are available in existing laser facilities or in the future ELI or X-FEL.
