Spline methods for resonances in photoionisation cross sections

Abstract

Spline-based methods for continuum state wavefunctions are evaluated by applying these techniques to the study of the resonance structure in the photoionisation cross section of He, both from the 1s^{2 1}S ground state and the 1s2p ¹P excited state. The Galerkin method is used for obtaining approximate solutions of Schrodinger's equation for a wavefunction defined in terms of a single continuum orbital and a set of bound orbitals. Eigenvectors of interaction matrices for a range of energies are obtained using inverse iteration. This method is an extension of the MCHF method in which the SCF procedure allows bound orbitals to vary with the energy. Photoionisation cross sections, resonance positions and widths are compared with other theories and experiment. Good agreement is obtained, but the studies suggest that 'weakly closed' channels be treated in the same manner as the continuum orbitals, reducing the iterative SCF nature of the calculation and expanding the dimension of the interaction matrices.