Effects on observables of the singularity in the multiphoton free-free dipole matrix elements

Analysis and calculations on the H atom based on the state-specific expansion approach (SSEA) to the solution of the time-dependent Schrodinger equation (TDSE), show that observables such as high order above threshold ionization (An) and related photoelectron angular distributions (PADS) are strongly dependent on multiphoton couplings in the continuum. In turn, the magnitude of these couplings depend crucially on the on-energy shell singularity of the free-free dipole matrix elements resulting from the asymptotic boundary condition of the energy-normalized scattering functions. Although it is unclear to what extent spatial grid methods account for this singularity accurately, it is certain that expansion methods using some type of box-normalized (finite-range) basis sets cannot handle it, thereby becoming intrinsically inadequate, especially as the field strength increases. This conclusion is supported by our numerical results.