Abstract
The multiply differential cross section of the dissociative ionization of ${\mathrm{H}}_{2}^{+}$ by fast (2 keV) electron impact is determined theoretically using a two-center continuum wave function constructed using the exact solutions of the separable two-center Schr\odinger equation in prolate spheroidal coordinates for the slow (50 eV) ejected electron. The comparison of the results to those obtained by approximate approaches, like those using an effective center Coulomb wave or Pluvinage-type two-center wave or the wave packet evolution approach, shows the limits of these approximate methods. Additionally, the variation of the sevenfold differential cross section, which corresponds to the ionization of aligned molecules, reveals interesting mechanisms and gives some insight into the optimal conditions for the dissociative ionization of more complex diatomic targets.
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