Green's-function approach to nonresonance multiphoton absorption in the alkali-metal atoms

An exact Green's function is constructed for the one-electron Schrödinger equation using a central potential obtained from a piecewise linear approximation to $-rV\left(r\right)\mathrm{}$ of Herman and Skillman. With the Green's function two- and three-photon ionization cross sections are calculated for $\mathrm{He}\mathrm{}\left(1s\right)\mathrm{}\left(2s\right)\mathrm{}{}_{}{}^1{}_{}{}^{}S$, ${}_{}{}^3{}_{}{}^{}S$, and the alkali metals, and compared to other calculations and experiments. Resonances in the cross sections occur at model eigenvalues rather than experimental energy levels. It is demonstrated that the resonances can be made to occur at experimental values either by simple shifts in the wavelength scale, by adjusting the ionization energy in the calculation, or by including the eigenvalue differences in a finite sum. However, as these are perturbation-theory calculations and not applicable at very high intensities or on resonance, only the wings of the resonance structure are included in the calculation.