{"paper":{"title":"Gravitational Tensor-Monopole Moment of Hydrogen Atom To Order ${\\cal O}(\\alpha)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nucl-ex","nucl-th"],"primary_cat":"hep-ph","authors_text":"Xiangdong Ji, Yizhuang Liu","submitted_at":"2022-08-09T20:18:23Z","abstract_excerpt":"We calculate the gravitational tensor-monopole moment of the momentum-current density $T^{ij}$ in the ground state of the hydrogen atom to order ${\\cal O}(\\alpha)$ in quantum electrodynamics (QED). The result is \\begin{align} \\tau_H/\\tau_0 - 1 = \\frac{4\\alpha}{3\\pi}\\left(\\ln\\alpha^2-0.028\\right) \\nonumber \\end{align} where $\\tau_0= \\hbar^2/4m_e$ is the leading-order moment. The physics of the next-to-leading-order correction is similar to that of the famous Lamb shift for energy levels."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.05029","kind":"arxiv","version":2},"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/2208.05029/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"}