One- and two-photon ionization cross sections for the negative hydrogen ion ${\mathrm{H}}^{\mathrm{\ensuremath{-}}}$ are evaluated by using a one-electron model where the effective intra-atomic potential energy is assumed to be of a very-short-range character and approximated by a ``spherical \ensuremath{\delta} shell.'' The adjustment of the two parameters involved in the model potential so as to reproduce either the photodetachment energy or the behavior of the one-photon ionization cross section over a substantial range of frequencies beyond the ionization threshold leads to conjecture of a reasonable estimate of the two-photon ionization cross section over the proper range of frequencies of the ionizing field.
A realistic model for resonant two-photon ionization of an atom is developed which can be solved exactly to give the ionization probability as a function of time, photon intensity, and a few atomic parameters. The exact solutions are compared to various commonly used perturbation results in order to ascertain the regions of validity of the perturbation calculations. It is shown that there are combinations of the parameters for which ionization rates cannot accurately describe the correct results, and that one commonly used perturbation development is not generally applicable to resonant two-photon ionization. Extension of the model to
(n+m)-photon ionization having an
m-photon resonance is discussed. The model is applied to two- and three-photon ionization in Cs.