Bound-state expansion method for calculating resonance and nonresonance contributions to continuum processes: Theoretical development and application to the photoionization of helium and the hydrogen negative ion

Abstract

A unified method for calculating both resonance and continuum contributions to photoionization cross sections by bound-state techniques is developed. The stationary scattering wave function for the atomic system is expanded in a subspace of discrete functions which is large enough to be nearly complete for the region near the nucleus involved in the photoionization process. Some of the functions in the subspace are selected by root-stabilization techniques to be accurate representations of the resonances while others represent continuum functions. The expression for the cross section is derived from the Fano treatment of autoionizing states. The accuracy of the method is demonstrated by the calculation of cross sections for photoionization of the ground state $1{}_{}{}^1{}_{}{}^{}S$ of the hydrogen negative ion and the helium atom, and for the metastable $2{}_{}{}^1{}_{}{}^{}S$ state of helium at energies in the continuum and through the resonance $2{}_{}{}^1{}_{}{}^{}S-\left(2s2p\right)\mathrm{}{}_{}{}^1{}_{}{}^{}P$ transition.