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

Abstract

A method is presented 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. 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.