An analytic model of electron-oxygen elastic scattering in the 1-500-eV range

Abstract

The spatial distribution of electron energy deposition has become important in astrophysics, atmospheric radiation, fusion, and laser physics. To calculate this distribution requires a detailed specification of the elastic differential cross sections at all energies involved in the degradation process. To satisfy this need in the particular case of electrons slowing down in atomic oxygen we have adopted a strategy which gives realistic angular distributions with reasonable computational costs. First, we establish an analytic independent particle model for O− which has the form of a double Yukawa function with parameters adjusted to simulate an average Hartree-Fock potential and to yield the exact electron affinity. Next, we use an optical model code to calculate at a widely spaced sample of energies the phase shifts for the lower partial waves and a sample of the higher partial waves. We fit these phase shifts with an analytic formula arising from the Born approximation with a simple additional term to satisfy Levinson's theorem for the case of s and p waves which have bound states. By adjusting the parameters of this function to the sample of optical model phase shifts we obtain a precise and economical (12 parameters) analytic description of all optical model phase shifts at all energies. Using these phase shifts and the usual Legendre polynomial representation we can generate the differential cross section for any desired energy and angle. The saving of computation time with respect to the complete use of the optical model program should make it possible to input realistic quantum mechanical results into electron transport calculations. Other possible applications of our analytic method are discussed.