AUTHOR=Hofierka J. , Rawlins C. M. , Cunningham B. , Waide D. T. , Green D. G. 

TITLE=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+

JOURNAL=Frontiers in Physics

VOLUME=Volume 11 - 2023

YEAR=2023

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2023.1227652

DOI=10.3389/fphy.2023.1227652

ISSN=2296-424X

ABSTRACT=Scattering phase shifts and annihilation rates for low-energy positrons interacting with noble-gas atoms are calculated \emph{ab initio} using many-body theory implemented in the Gaussian-orbital code {\tt 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 solution of Bethe-Salpeter equations for the two-particle propagators. The normalisation 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 {\tt EXCITON+} code, which can be used for multicentred 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 Z$_{\rm eff}$. Our scattering length for Ne and Kr are in improved agreement with the Convergent Close Coupling result, and for Ar the scattering length is in better agreement with experiment compared with the previous B-spline many-body approach.