Bound state properties, positron annihilation and hyperfine structure of the four-body positronium hydrides

Abstract

Bound state properties of the ground (bound) ${}^{1}S(L=0)-$state(s) in the four-body positronium hydrides ${}^1$HPs, ${}^2$HPs (DPs), ${}^3$HPs (TPs) and MuPs are determined and investigated. By using numerical data from our computations of these four-body systems we have determined a number of different annihilation rates for each of these positronium hydrides and evaluated the hyperfine structure splitting. The properties of the ground (bound) states in the four-body exitonic ${}^M{h}^{+}{e}_2^{-}{e}^{+}$ complexes, where $M\ge 1$ and $M\le 1$, have also been evaluated numerically. The neutral four-body systems ${}^M{h}^{+}{e}_2^{-}{e}^{+}$ with $M\gg 1$ are similar to the HPs hydrides. In particular, each of these states has only one bound state. We also discuss applications of the exponential and semi-exponential variational expansions for accurate, bound state computations of the four-body positronium hydrides.

This version approximately corresponds to the final (journal) version published in: Journal of Molecular Physics, {\bf 120}(1), e2019337 (2022) (doi.org/10.1080/00268976.2021.2019337 ). In any case I recommend you to read the final/journal version of this paper