Grid-based methods for diatomic quantum scattering problems. III. Double photoionization of molecular hydrogen in prolate spheroidal coordinates

Our previously developed finite-element discrete-variable representation in prolate spheroidal coordinates is extended to two-electron systems with a study of double ionization of H2 with fixed nuclei. Particular attention is paid to the development of fast and accurate methods for treating the electron-electron interaction. The use of exterior complex scaling in the implementation offers a simple way of enforcing Coulomb boundary conditions for the electronic double continuum. While the angular distributions calculated in this study are found to be completely consistent with our earlier treatments that employed single-center expansions in spherical coordinates, we find that the magnitude of the integrated cross sections are sensitive to small changes in the initial-state wave function. The present formulation offers significant advantages with respect to convergence and efficiency and opens the way to calculations on more complicated diatomic targets.