Relativistic recoil effects to energy levels in a muonic atom: a Grotch-type calculation of the second-order vacuum-polarization contributions

Abstract

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 ${\alpha }^2(Z\alpha {)}^4{m}^2/M$ 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%.

Submitted to Phys.Rev.A; cross refs are added in v.2&3

References in corpus (4)

• The ${\alpha }^2(Z\alpha {)}^{4}m$ contributions to the Lamb shift and the fine structure in light muonic atoms
• Vacuum polarization in muonic atoms: the Lamb shift at low and medium Z
• Relativistic recoil effects in a muonic atom within a Grotch-type approach: General approach
• Relativistic recoil effects for energy levels in a muonic atom within a Grotch-type approach: An application to the one-loop electronic vacuum polarization

Cited by in corpus (1)

• Relativistic levels of mesic atoms