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

TL;DR

This paper investigates the bound state properties, annihilation rates, and hyperfine structure of various four-body positronium hydrides using advanced numerical methods, providing new insights into their quantum characteristics.

Contribution

The study introduces detailed numerical calculations of bound states, annihilation rates, and hyperfine splitting for multiple four-body positronium hydrides, employing exponential variational expansions.

Findings

Determined bound state energies and properties of several positronium hydrides.

Calculated annihilation rates for different four-body systems.

Evaluated hyperfine structure splittings with high accuracy.

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.