Stability and hyperfine structure of the four- and five-body muon-atomic clusters $a^{+} b^{+} \mu^{-} e^{-}$ and $a^{+} b^{+} \mu^{-} e^{-} e^{-}$

TL;DR

This study demonstrates the stability and analyzes the hyperfine structure of specific four- and five-body muonic atomic clusters containing electrons, muons, and hydrogen isotopes, using accurate variational calculations.

Contribution

It provides the first detailed stability analysis and hyperfine structure calculations for these complex five-body ions and four-body muonic quasi-atoms.

Findings

Five-body ions are stable based on variational calculations.

Hyperfine structure splittings are determined for ground states.

Properties of these muonic clusters are characterized comprehensively.

Abstract

Based on the results of accurate variational calculations we demonstrate stability of the five-body negatively charged ions $a^{+} b^{+} \mu^{-} e^{-} e^{-}$. Each of these five-body ions contains two electrons $e^{-}$, one negatively charged muon $\mu^{-}$ and two nuclei of the hydrogen isotopes $a, b = (p, d, t)$. The bound state properties of these five-body ions, including their hyperfine structure, are briefly discussed. We also investigate the hyperfine structure of the ground states of the four-body muonic quasi-atoms $a^{+} b^{+} \mu^{-} e^{-}$. In particular, we determine the hyperfine structure splittings for the ground state of the four-body muonic quasi-atoms: $p^{+} d^{+} \mu^{-} e^{-}$ and $p^{+} t^{+} \mu^{-} e^{-}$.