{"paper":{"title":"On the Excess Charge Problem of Atoms","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.FA","math.MP","math.SP","physics.atom-ph"],"primary_cat":"math-ph","authors_text":"Dirk Hundertmark, Marvin Raimund Schulz, Nikolaos Pattakos","submitted_at":"2025-04-25T16:54:13Z","abstract_excerpt":"This paper establishes new bounds on the maximum number of electrons $ N_c(Z) $ that an atom with nuclear charge $Z$ can bind. Specifically, we show that \\begin{equation*}\n  N_c(Z) < 1.1185Z + O(Z^{1/3}) \\end{equation*} with an explicit bound on the lower order term $O(Z^{1/3})$. This result improves long--standing bounds by Lieb and Nam obtained in 1984, respectively 2012. Our bounds show the fundamental difference between fermionic and bosonic atoms for finite $Z$ since for bosonic atoms it is known that $\\lim N_c(Z)/Z = t_c \\approx 1.21$ in the limit of large nuclear charges $Z$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.18487","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/2504.18487/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"}