Hyperfine structure and $(e^{-},e^{+})$-pair annihilation in the muonium-positronium MuPs and positronium hydrides

TL;DR

This paper calculates the hyperfine structure of various positronium hydrides and MuPs systems using precise variational methods, and evaluates key annihilation probabilities and conversion processes within MuPs.

Contribution

It provides highly accurate calculations of hyperfine structures and annihilation probabilities in MuPs and positronium hydrides, advancing understanding of their quantum properties.

Findings

Hyperfine structures accurately determined for multiple positronium hydrides and MuPs.

Probabilities of $(e^{-}, e^{+})$-pair annihilation in MuPs evaluated.

Conversion processes in MuPs quantitatively analyzed.

Abstract

The hyperfine structure of the ground states in a number of positronium hydrides (TPs, DPs, ${}^{1}$HPs) and MuPs ($\mu^{+} e^{-}_2 e^{+}$) is determined with the use of highly accurate variational wave functions. We also evaluate the probabilities of various processes in the MuPs system, including the $(e^{-}, e^{+})$-pair annihilation and its conversion into the charge conjugate system $\mu^{+} e^{-}_2 e^{+} \to \mu^{-} e^{-} e^{+}_2$.