{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"aa5a78b042bc9734401ad4a0781a1fd333324f0845b901409009dc0137a3f7cd","created":"2026-10-03T07:17:53Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"910322623c7e20964784e90a8923a25e8eb111a2eda0dbd4f6042f85fbebf097","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"identification","assisted_by":[],"external_id":"amo.bound-state-qed.helium-ionization-energy","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"Helium has two electrons, which makes its energy levels harder to compute than hydrogen's, but theory now claims sub-MHz accuracy. The measured binding energy of a long-lived excited state disagrees with this theory by nine standard errors.","posed_since":"","precise":"The measured ionization energy of $\\mathrm{He}\\,(1\\mathrm{s})(2\\mathrm{s})\\,2^{3}\\mathrm{S}_1$ is $1152842742.7082(60)\\,\\mathrm{MHz}$ (Clausen et al 2025), versus the theoretical $1152842742.231(52)\\,\\mathrm{MHz}$ (Patkos, Yerokhin, Pachucki), a $9\\sigma$ difference; a similar $7\\sigma$ deviation affects $2^{1}\\mathrm{S}_0$. Identify whether the error lies in the $\\alpha^{7} m$ QED contribution, higher-order terms, or the experiments.","problem_ref":null,"references":"","settled_by":"An independent complete $\\alpha^{7} m$ calculation for helium singlet and triplet S states, or an independent measurement of the same ionization energy with a different method.","status_note":"The 2025 ETH Zurich Rydberg-series measurement improved precision five-fold and confirmed the discrepancy.","title":"Nine $\\sigma$ discrepancy in the ionization energy of metastable 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