{"paper":{"title":"Relativistic recoil effects to energy levels in a muonic atom: a Grotch-type calculation of the second-order vacuum-polarization contributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.atom-ph","authors_text":"Evgeny Yu. Korzinin, Savely G. Karshenboim, Vladimir G. Ivanov","submitted_at":"2013-11-22T17:15:33Z","abstract_excerpt":"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 unc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.5822","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}