MolecularK-shell photoionization cross sections in the relaxed-core Hartree-Fock approximation

The relaxed-core Hartree-Fock (RCHF) approach to the calculation of K-shell photoionization cross sections is analyzed and applied to K-shell single-hole ionization in CO. A direct method based on the Schwinger variational principle and single-center-expansion techniques is used to generate the continuum orbitals associated with the motion of the photoelectron in the direct and exchange potential of the relaxed ion. A method is presented for evaluating the N-electron transition moment, a step that has posed a considerable computational obstacle due to the lack of orthogonality between the frozen and relaxed orbitals in the initial and final N-electron states, respectively. Besides being very practical and efficient, this formulation establishes the distinction between the ‘‘direct’’ and ‘‘conjugate’’ part of the transition moment, introducing bound-free dipole and overlap integrals, respectively. Whereas for large photoelectron energies the conjugate terms can be neglected, they become important near threshold, contributing, for example, up to 30% to the 1s cross sections in CO. An analysis by means of low-order perturbation theory shows that the RCHF model correctly describes the effect of ionic relaxation, that is, essentially the screening of the 1s hole by the valence electrons. As a consequence the ${\sigma }^{\mathrm{*}}$ shape resonance is substantially shifted to higher energy and broadened compared with the frozen-core Hartree-Fock picture where the more attractive unscreened 1s-hole potentials are used. The remaining discrepancies with the experimental results are attributed to the neglect of target polarization in the RCHF model.