{"paper":{"title":"Antiprotonic atoms with nonperturbative inclusion of vacuum polarization and finite nuclear mass","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"physics.atom-ph","authors_text":"K. Pachucki, V. Patk\\'o\\v{s}","submitted_at":"2025-09-09T13:38:45Z","abstract_excerpt":"We demonstrate that energy levels of excited states in a hydrogenic system consisting of an arbitrary nucleus and an antiproton can be calculated within the framework of nonrelativistic quantum electrodynamics, even for a large nuclear charge $Z$. It is because for rotational states the expansion parameter is $Z\\,\\alpha/n$. The main advantage of this approach is the possibility of exact inclusion of the finite nuclear mass, which we achieve up to the $(Z\\,\\alpha)^6$ order. In addition, we include unperturbatively the one-loop and two-loop electron vacuum polarization (evp) potentials in the no"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.07738","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.07738/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}