Elastic scattering of low‐energy positrons by bound silicon and germanium

Elastic scattering differential and total cross sections for low‐energy positron collisions with bound silicon and germanium atoms have been computed using partial wave analysis with static and polarization potentials. The calculations are performed at incident positron energies ranging from 0.2 to 500 eV. For each impact energy, an appropriate number of phase shifts are obtained by numerically integrating the radial wave equation to ensure convergence of the scattering amplitude. A simple parametrization of the total cross section in terms of the screened Rutherford cross section is also presented for use in Monte Carlo codes. Due, in part, to the lack of reliable experimental data, relatively little theoretical work has been done to calculate the inelastic and elastic differential cross sections (DCS) and total cross sections (TCS) for positron scattering. Most of the measurements were made on noble gases where it is observed that low‐energy positrons exhibit a Ramsauer–Townsend (RT) minimum for helium, neon, and possibly argon (for electrons, the RT minimum occurs for heavier noble gases).^1,2 Calculations of the positron TCS for these atoms agree with the observations. The RT effect has also been identified in a number of other free atoms and molecules for electrons.^3,4 Recently, Meredith et al. computed the electron elastic scattering cross sections in solid silicon and germanium.⁵ In this work we calculate the DCS and TCS for positrons elastically scattered by silicon and germanium atoms which are bound in an amorphous solid using partial waves and the optical model. The results are presented for incident positron energies ranging from 0.2 to 500 eV. Simple fits to each TCS are given for use in Monte Carlo scattering simulations. For the static potential V_S, Salvat and Parellada used Dirac–Hartree–Fock–Slater (DHFS) calculations to accurately fit analytic screening functions for atoms.⁶ They also imposed Wigner–Seitz boundary conditions (WSBC) on their wave functions to simulate atoms bound in a solid. The functional form of the static potential is (in atomic units)