Simple method for obtaining exact nonrelativistic formulas for two-photon (n, l, m) continuum dipole transitions for hydrogenic atoms.

The Kramers-Heisenberg matrix element for two-photon transitions between a bound (n, l, m) state and a continuum is obtained in terms of the Coulomb Green's function matrix element for the ground-state ? continuum transition. The number of the F(1) Appell functions involved is minimized. The analytical results for the ns ? continuum transitions are given, and both the resonant behavior and the transparency region of the two-photon cross section are predicted.