Implementation of the external complex scaling method in spheroidal coordinates: Impact ionization of molecular hydrogen

Abstract

We develop an ab initio procedure based on the driven Schr\odinger equation formalism and the external complex scaling method for the determination of the multifold differential cross sections of the single and double ionization of molecular hydrogen by single photon and fast electron impact. We take advantage of the separability of the two-center Schrodinger equation in prolate spheroidal coordinates in the numerical calculation of the two-electron two-center wave function of the initial and final states of the target. After having verified our procedure by reproducing existing confirmed triple differential cross sections of the $(e,2e)$ ionization of ${\text{H}}_{2}$, we have extended our calculation to the double ionization of ${\text{H}}_{2}$. Our results on double photoionization agree with existing experimental results. We observe in the mean time a small difference with respect to the absolute results obtained by similar ab initio calculations using spherical bases. For the case of the double ionization by fast electron impact for which very few experimental results exist, our results confirm the existing disagreement between the theoretical results and the unique experimental one in the case of $(e,3\text{\ensuremath{-}}1e)$. This we think makes it clear that for $(e,3e)$ the introduction of the higher terms of the Born series for mean energy electron-impact regime is necessary.