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.

Virtual and bound states in low-energy positron scattering by atoms and molecules via modified effective range theory

“…, where κ r and κ i are the pole coordinates along the real and imaginary axis, respectively. We found, see table 4, that |κ| almost perfectly correlates with κ determined in other works by fitting equations (3) to theoretical low-energy positron annihilation data (see [27,[30][31][32]). Since theoretical Z eff (k) follows equation (3), the increase in the cross-section for positron direct annihilation with decreasing interaction energy is primarily due to the positron wave function being 'in resonance' with the shallow energy level (for all considered targets).…”

“…In particular, we discuss the validity of the shallow-state energy estimation based only on the value of the scattering length. Moreover, when addressing the effect of dipole polarisability in determining energy levels, we show that the discrepancy between scattering lengths in positron collisions estimated by MERT and from the positron annihilation data (as can be found in [27,[30][31][32]) disappears.…”

“…The latter is frequently used to extrapolate scattering data (such as theoretical phase shifts or experimental cross-sections) towards zero energy to determine the s − wave scattering length (e.g. see [27,[30][31][32]48]). However, the energy range of the applicability (kR * = 1) of equation (10) is much narrower than equation (6).…”

“…Unlike the bound state, the energy of virtual level in positron scattering is hardly ever calculated directly, and its existence is usually postulated when a considerable negative s-wave scattering length (a 0 ) is found (e.g. see [8,[30][31][32]). The energy of the virtual level is then estimated as ma 2…”

“…Alternatively, as theoretical studies indicate, an energy-resolved positron annihilation can also be used to determine a 0 (e.g. see [27,[30][31][32] and their supplemental materials). However, the latter approach may give substantially different values than MERT estimates.…”