A model-potential method is employed to calculate binding, elastic scattering, and annihilation of positrons for a number of atoms and small nonpolar molecules, namely, Be, Mg, He, Ar, ${\mathrm{H}}_2, {\mathrm{N}}_2, {\mathrm{Cl}}_2$, and ${\mathrm{CH}}_4$. The model potential contains one free parameter for each type of atom within the target. Its values are chosen to reproduce existing ab initio positron-atom binding energies or scattering phase shifts. The calculations are performed using a Gaussian basis for the positron states, and we show how to obtain values of the scattering phase shifts and normalized annihilation rate $Z_{\text{eff}}$ from discrete positive-energy pseudostates. Good agreement between the present results and existing calculations and experimental data, where available, is obtained, including the $Z_{\text{eff}}$ value for ${\mathrm{CH}}_4$, which is strongly enhanced by a low-lying virtual positron state. An exception is the room-temperature value of $Z_{\text{eff}}$ for ${\mathrm{Cl}}_2$, for which the present value is much smaller than the experimental value obtained over 50 years ago. Our calculations predict that among the molecular targets studied, only ${\mathrm{Cl}}_2$ might support a bound state for the positron, with a binding energy of a few meV.

• Received 6 December 2019
• Accepted 14 January 2020

DOI:https://doi.org/10.1103/PhysRevA.101.022702