Hyperfine Structure of S-States in Muonic Helium Ion

TL;DR

This paper calculates high-order corrections to the hyperfine structure of muonic helium ion's S-states, providing precise theoretical values to compare with future experiments and test quantum electrodynamics.

Contribution

It presents the first detailed calculation of alpha^5 and alpha^6 order corrections to hyperfine splittings in muonic helium ion, including various physical effects.

Findings

Hyperfine splitting for 1S state: -1334.56 meV

Hyperfine splitting for 2S state: -166.62 meV

Hyperfine interval Delta_{12} = 1.64 meV

Abstract

Corrections of orders alpha^5 and alpha^6 are calculated in the hyperfine splittings of 1S and 2S - energy levels in the ion of muonic helium. The electron vacuum polarization effects, the nuclear structure corrections and recoil corrections are taken into account. The obtained numerical values of the hyperfine splittings -1334.56 meV (1S state), -166.62 meV (2S state) can be considered as a reliable estimate for the comparison with the future experimental data. The hyperfine splitting interval Delta_{12}=(8 Delta E^{hfs}(2S)- Delta E^{hfs}(1S)) = 1.64 meV can be used for the check of quantum electrodynamics.