Calculation of cross sections for multiphoton ionization of complex atoms

Abstract

A method is proposed for solving the equations of perturbation theory appropriate for multiphoton excitation or ionization of complex atoms, and detailed calculations are carried out for two-photon ionization of He. The method consists of writing the wave function for order $N$ as a product of $N\mathrm{th}$- and zeroth-order wave functions for the electron absorbing the photon ("optical" electron) and the remaining electrons ("passive" electrons), respectively, with symmetrization of the spatial wave function appropriate for an eigenfunction of spin. Projection onto the space of the passive electrons then generates an integro-differential equation for the optical electron. The Coulomb Green's function is used to convert this equation into an integral equation, which is solved numerically using a modified version of the noniterative method of solution used extensively in scattering theory. Results obtained with the Hartree-Fock zeroth-order model show good agreement with the results of coupled Hartree-Fock perturbation theory. Results are also obtained ignoring exchange, and the error is observed to be about a factor of 2 over a wide range of frequencies.