Schrödinger formulation of the nondipole light-matter interaction consistent with relativity

Abstract

An alternative and powerful Schr\odinger-like equation for describing beyond dipole laser-matter interactions and leading relativistic corrections is derived. It is shown that this particular formulation is numerically very efficient with respect to computational effort and convergence rate of the solutions. Furthermore, its nonrelativistic form turns out to be more compatible with relativity than what seems to be the case with the more common formulations of the nonrelativistic light-matter interaction. Moreover, the extension of this interaction form into the relativistic region preserves, to a large extent, the numerical efficiency. In this work, the formulation is applied to study beyond dipole corrections and relativistic corrections in multiphoton ionization of a hydrogen atom in the x-ray regime.