High-order above-threshold ionization: the uniform approximation and the effect of the binding potential

A versatile semiclassical approximation for intense laser-atom processes is presented. This uniform approximation is no more complicated than the frequently-used multi-dimensional saddle-point approximation and far superior, since it applies for all energies, both close to as well as away from classical cutoffs. In the latter case, it reduces to the standard saddle-point approximation. The uniform approximation agrees accurately with numerical evaluations for potentials, for which these are feasible, and constitutes a practicable method of calculation in general. The method is applied to the calculation of high-order above-threshold ionization spectra with various binding potentials: Coulomb, Yukawa, and shell potentials which may model C$_{60}$ molecules or clusters. The shell potentials generate high-order ATI spectra that are more structured and may feature an apparently higher cutoff.