%0 Journal Article
%T Relativistic recoil effects to energy levels in a muonic atom: a Grotch-type calculation of the second-order vacuum-polarization contributions
%A Savely G. Karshenboim
%A Evgeny Yu. Korzinin
%A Vladimir G. Ivanov
%J Physics
%D 2013
%I arXiv
%R 10.1103/PhysRevA.89.032129
%X Adjusting a previously developed Grotch-type approach to a perturbative calculation of the electronic vacuum-polarization effects in muonic atoms, we find here the two-loop vacuum polarization relativistic recoil correction of order $\alpha^2(Z\alpha)^4m^2/M$ in light muonic atoms. The result is in perfect agreement with the one previously obtained within the Breit-type approach. We also discuss here simple approximations of the irreducible part of the two-loop vacuum-polarization dispersion density, which was applied to test our calculations and can be useful for other evaluations with an uncertainty better than 1%.
%U http://arxiv.org/abs/1311.5822v3