Higher-order corrections for the dynamic hyperfine structure of muonic atoms

TL;DR

This paper presents a method to accurately calculate higher-order energy corrections in the hyperfine structure of heavy muonic atoms, accounting for electric quadrupole and vacuum polarization effects, relevant for upcoming experimental precision.

Contribution

It introduces a multipole expansion approach for the Uehling potential applicable to any nuclear charge distribution, enabling precise hyperfine structure calculations in muonic atoms.

Findings

Corrections are significant enough to be observed in future experiments.

The method applies to arbitrary nuclear charge distributions.

Calculations for muonic Rhenium and Uranium show notable effects.

Abstract

A method for precise calculation of the energy corrections due to second order electric quadrupole interactions, as well as mixed electric quadrupole-vacuum polarization in the framework of the dynamic hyperfine structure in heavy muonic atoms is presented. For this, a multipole expansion of the Uehling potential is performed. The approach is applicable for an arbitrary nuclear electric charge distribution. By performing these calculations for muonic Rhenium and Uranium using a deformed Fermi distribution, it is shown that both corrections contribute on a level presumably visible in upcoming experiments.