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For shallow potentials with $-1000 MeV\\lesssim V_0 < 0$ the wave functions for the positive-energy states $\\Psi _+(r)$ are dominated by their nucleon component $g(r)$. But for deeper potentials with $V_0 \\lesssim -1500 MeV $ the $\\Psi_+(r)$s begin to have dominant anti-nucleon component $f(r)$. In particular, a special intruder state enters with wave function $\\Psi_{1/2}(r)$ and energy $E_{1/2}$. We have considere"},"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":"1705.00489","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nucl-th","submitted_at":"2017-05-01T12:03:02Z","cross_cats_sorted":[],"title_canon_sha256":"1404ef1321478d7cfdda69a79bd0fbc5a07ca92fd6eb9e518415a911f9f5b9e7","abstract_canon_sha256":"29116d29afe0c43bd38b6feb412875cf1700e7824fac63faa7788f39207f93bc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:51.056052Z","signature_b64":"md9mCFh0Jei38e1tjvSnGI5DTUZSNE3ZtvIgUML1JeZ2CvGs74WLzPYEQpYuvg2JUvnK7h2Cw8d/nqY6jgnOBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c2cf67a9b3a52200e4f7329ecba0d4728212e2266d7f5a817e6c7db86973e671","last_reissued_at":"2026-05-18T00:44:51.055543Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:51.055543Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nucleon-anti-nucleon intruder state of Dirac equation for nucleon in deep scalar potential well","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nucl-th","authors_text":"E. Osnes, S. Shu, T.K. Kuo, T.T.S. Kuo","submitted_at":"2017-05-01T12:03:02Z","abstract_excerpt":"We solve the Dirac radial equation for a nucleon in a scalar Woods-Saxon potential well of depth $V_0$ and radius $r_0$. A sequence of values for the depth and radius are considered. For shallow potentials with $-1000 MeV\\lesssim V_0 < 0$ the wave functions for the positive-energy states $\\Psi _+(r)$ are dominated by their nucleon component $g(r)$. But for deeper potentials with $V_0 \\lesssim -1500 MeV $ the $\\Psi_+(r)$s begin to have dominant anti-nucleon component $f(r)$. In particular, a special intruder state enters with wave function $\\Psi_{1/2}(r)$ and energy $E_{1/2}$. 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