Ground state hyperfine structure in muonic lithium ions

TL;DR

This paper calculates the hyperfine splitting in muonic lithium ions using perturbation theory, including various quantum corrections, providing precise theoretical predictions for future experimental comparison.

Contribution

It presents detailed calculations of hyperfine splitting in muonic lithium ions incorporating vacuum polarization, vertex, nuclear structure, and recoil corrections, which are novel for these systems.

Findings

Calculated hyperfine splittings: 21572.16 MHz and 14152.56 MHz for Li-6; 21733.06 MHz and 13994.35 MHz for Li-7.

Results serve as reliable estimates for future experimental validation.

Includes comprehensive quantum corrections in the theoretical model.

Abstract

On the basis of perturbation theory in fine structure constant alpha and the ratio of electron to muon masses we calculate one-loop vacuum polarization, electron vertex corrections, nuclear structure and recoil corrections to hyperfine splitting of the ground state in muonic lithium ions $(\mu\ e\ ^6_3Li)^+$ and $(\mu\ e\ ^7_3Li)^+$. We obtain total results for the ground state small hyperfine splittings in $(\mu\ e\ ^6_3Li)^+$ $\Delta\nu_1=21572.16$ MHz and $\Delta\nu_2=14152.56$ MHz and in $(\mu\ e\ ^7_3Li)^+$ $\Delta\nu_1=21733.06$ MHz and $\Delta\nu_2=13994.35$ MHz which can be considered as a reliable estimate for a comparison with future experimental data.