Multiphoton detachment of H- is considered. An accurate one-electron m
odel, which reproduces precisely the known H- detachment energy and th
e low-energy e-H(1s) elastic-scattering phase shifts, is developed. Ge
neralized cross sections, based on lowest-nonvanishing-order perturbat
ion theory, are evaluated by an accurate and efficient numerical algor
ithm for the solution of the associated set of inhomogeneous different
ial equations. Two- to eight-photon detachment cross sections are dete
rmined and compared with a recent one-electron model and two-electron
ab initio calculations. It appears that the present study provides con
sistent results with an accuracy for higher-order (n > 3) photon-detac
hment cross sections comparable to that of lower orders (n = 2,3). Ave
rage detachment rates for linearly polarized light are calculated and
compared with recent experimental measurements. It is found that, for
higher-order photon detachment, the rates for circular polarization ar
e small in comparison with the rates for linear polarization.