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Envelope induced ionization dynamics beyond the dipole approximation

When atoms and molecules are ionized by laser pulses of finite duration and increasingly high intensities, the validity of the much used dipole approximation, in which the spatial dependence and magnetic component of the external field are neglected, eventually breaks down. We report that when going beyond the dipole approximation for the description of atoms exposed to ultraviolet light, the spatial dependence of the pulse shape, the envelope, provides the dominant correction, while the spatial dependence of the carrier is negligible. We present a first order beyond-dipole correction to the Hamiltonian which accounts exclusively for nondipole effects stemming from the carrier-envelope of the pulse. We demonstrate by {\it ab initio} calculations for hydrogen that this approximation, which we will refer to as the {\it envelope approximation}, reproduces the full interaction beyond the dipole approximation for absolute and differential observables and proves to be valid for a broad range of high-frequency fields. This is done both for the Schr{ö}dinger and the Dirac equation. Moreover, it is demonstrated that the envelope approximation provides an interaction-term which gives rise to faster numerical convergence in terms of partial waves compared to its exact counterpart.