Ground state hyperfine structure of light muon-electron ions

TL;DR

This paper calculates the hyperfine splitting in light muon-electron ions using analytical perturbation theory, accounting for various quantum corrections, to aid future experimental comparisons.

Contribution

It provides detailed theoretical calculations of hyperfine structure in light muon-electron ions, including multiple quantum corrections, which were not comprehensively addressed before.

Findings

Calculated hyperfine splitting values for specific ions.

Analyzed dependence of corrections on nuclear charge Z.

Provided results for future experimental validation.

Abstract

The ground state hyperfine splitting of light muon-electron ions of lithium, beryllium, boron and helium is calculated on the basis of analytical perturbation theory in terms of small parameters of the fine structure constant and electron-muon mass ratio. The corrections of vacuum polarization, nuclear structure and recoil effects and electron vertex corrections are taken into account. The dependence of the corrections on the nucleus charge Z is studied. The obtained total values of hyperfine splitting intervals can be used for comparison with future experimental data.