Spheroidal analysis of the angular distribution of Auger electrons emitted by homonuclear diatomic molecules

Procedures for calculating the angular distribution of Auger electrons emitted by homonuclear diatomic molecules are presented. The calculation is performed in prolate spheroidal coordinates. A two-center effective potential is introduced to simplify the Schrödinger equation for an electron moving under the influence of the nuclei and other electrons. The effective potential is expressed by having equal fixed effective charges on each nucleus. The wave functions for the bound-state molecular orbitals and those for the Auger electron are obtained by solving the Schrödinger equation in which the appropriate experimental energies are used as the eigenvalues. The transition moments and the angular distribution of the Auger electron in the molecular frame are obtained by numerical integrations. For a specific Auger transition process, the distribution function is expressed in terms of the absolute square of a coherent sum of prolate spheroidal functions. In order to compare the predicted distribution function to our experimental results, corrections due to the rotation of the molecular ions during the course of dissociation are made.