Potential model for the elastic scattering of electrons by helium at intermediate energies

Abstract

Differential scattering cross section of electrons scattered elastically by helium atoms is computed using a model potential constructed from the Hartree–Fock wavefunction of Roothan, Sachs, and Weiss and a three parameter phenomenological potential to account for the effects of long range polarization effects and nonlocal dynamic effects. The results are in good agreement with the recently published experimental data of Bromberg. The calculated values of the partial wave phase shifts agree with those of Ganas, Dutta, and Green and LaBahn and Callaway for angular momentum in the range 0<l<10 within 5%. Results indicate that the model based on the Hartree–Fock wavefunction and a three parameter polarization potential can predict the scattering cross section at intermediate energies within a few percent of the experimental data. On the basis of the computed cross sections in 200–700 eV range, the approximate effective electron helium interaction potential for the quantum mechanical scattering problem is found to be Ve(r) ?<Φ0‖V(r,r1, r 2) ‖Φ0≳−(0.25+0.31r) e−2.8r−αd(1+e−8r)[r4+(1.3+E/350)4]−1. The forward scattering amplitudes calculated from this model and corrected for electron exchange scattering compare favorably with the results of dispersion relation and eikonal optical model theories.