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We also show that the radius of a two-dimensional neutral atom is unbounded when $Z\\to \\infty$, which is contrary to the expected behavior of three-dimensional atoms."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1102.4229","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-02-21T13:58:26Z","cross_cats_sorted":["math.MP","math.SP"],"title_canon_sha256":"b02e73bb5228a0605581168ab20f231db0b28c515f6727ec77fd7d3d4153ccf3","abstract_canon_sha256":"e6da664174bd8c3a21ff5db7085730f94612ec480a0abed3e550992a8b54200f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:19:54.571980Z","signature_b64":"fQMIC+icmJE3OlbMpB4ViTA7arQ/omVzLi5nMm2/Hx1mugnvjBYacWJfNkezGgvEmSIWRLwXT+Y5NKiwoAtgDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36e72fdd570396a8eaf59d0ebb690d32919769b5f55aae31e83f20cafc8c5b01","last_reissued_at":"2026-05-18T04:19:54.571280Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:19:54.571280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotics for Two-dimensional Atoms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Fabian Portmann, Jan Philip Solovej, Phan Thanh Nam","submitted_at":"2011-02-21T13:58:26Z","abstract_excerpt":"We prove that the ground state energy of an atom confined to two dimensions with an infinitely heavy nucleus of charge $Z>0$ and $N$ quantum electrons of charge -1 is $E(N,Z)=-{1/2}Z^2\\ln Z+(E^{\\TF}(\\lambda)+{1/2}c^{\\rm H})Z^2+o(Z^2)$ when $Z\\to \\infty$ and $N/Z\\to \\lambda$, where $E^{\\TF}(\\lambda)$ is given by a Thomas-Fermi type variational problem and $c^{\\rm H}\\approx -2.2339$ is an explicit constant. 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