Many-body theory calculations of positron scattering and annihilation in noble-gas atoms via the solution of Bethe–Salpeter equations using the Gaussian-basis code EXCITON+

Abstract

Scattering phase shifts and annihilation rates for low-energy positrons interacting with noble gas atoms are calculated ab initio using many-body theory implemented in the Gaussian-orbital code EXCITON+. Specifically, we construct the positron–atom correlation potential (self-energy) as the sum of three classes of infinite series describing the screened polarization, virtual positronium formation, and positron-hole repulsion found via the solution of Bethe–Salpeter equations for the two-particle propagators. The normalization of the continuum states is determined using the shifted pseudostates method [A. R. Swann and G. F. Gribakin, Phys. Rev. A 101, 022702 (2020)]. Comparison with the previous sophisticated B-spline many-body approach, which is restricted to atoms [J. Ludlow, D. G. Green, and G. F. Gribakin, Phys. Rev. A 90, 032712 (2014)], validates the EXCITON+ code, which can be used for multicentered targets including molecules, clusters, and condensed matter. Moreover, the relative effects of higher-order diagrams are quantified. It is found that the screening of the electron–positron Coulomb interaction represented by the infinite ring-diagram series (random-phase approximation) is compensated effectively by the additional electron-hole attraction corrections to it (the Bethe–Salpeter equation approximation) and that the use of the screened Coulomb interaction (screened at BSE level) in place of the bare Coulomb interaction in the virtual positronium and positron-hole ladder diagrams has negligible effect on both the phase shifts and Zeff. Our scattering length for Ne and Kr is in improved agreement with the convergent close-coupling result, and for Ar, the scattering length is in better agreement with the experiment compared with the previous B-spline many-body approach.