Theoretical studies in photoelectron spectroscopy: Use of angular distribution data to deduce molecular orbital parameters. III. Extraction of effective charge and anisotropy parameters of the molecular orbital from energy dependent measurements of β, the asymmetry parameter of the angular distribution

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Abstract
Formulas are presented for β, the asymmetry parameter of the angular distribution for photoionization, for the ejection of electrons from molecular orbitals of molecules possessing a center of symmetry. Previous studies are indicative that the motion of the ejected electron is dominated by the monopole term of the electron-molecular ion potential expanded about the molecular center of mass when the ratio of the orbital velocity of the bound electron to the velocity of the ejected electron is smaller than about 1:2. Thus the motion of the ejected electron appears to be approaching the limit of motion in a spherically symmetric, screened Coulomb potential. At this limit, β has a form particularly easy to evaluate. We replace the screened Coulomb potential by the Coulomb potential itself, of strength Z, where Z is taken to be an adjustable parameter. We present arguments to justify this approximation based on the condition that at high energies the photoelectric conversion occurs most efficiently in the immediate vicinity of the nuclei such that it can be argued that it is a good approximation to take the zeroth order motion of the ejected electron as motion in the Coulomb potential of strength equal to the full nuclear charge, and to correct for screening effects to first order in the Coulomb-Born series. This procedure provides β in analytic form and thereby facilitates its study as a function of Z, of k, the velocity of the photoelectron, and of the sets {λj} and {ζj}, where these are anisotropy and effective charge parameters, respectively, of the jth-component of the molecular orbital expanded about the center of mass. The theory can be made systematically more accurate by exact numerical or Coulomb-Born solution of the partial wave equations of the ejected electron in the appropriate screened Coulomb potential, eliminating Z as an adjustable parameter.