Algebraic variational approach to atomic and molecular photoionization cross sections: Removing the energy dependence from the basis

We describe a variational method for calculating photoionization cross sections from a matrix element of the resolvent operator. Scattering boundary conditions are enforced by expanding the resolvent in a basis of square-integrable (L² ) and outgoing wave continuum basis functions. By employing several continuum basis functions, with overlaps defined by a suitable analytic continuation, we can, in a single calculation, express the cross section over a continuous range of energies without explicitly resolving the variational equations at each desired energy. The method is illustrated by calculation of the photoionization cross section of atomic Be in the autoionizing region between the 1s² 2s and 1s² 2p states of Be⁺ .