{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:ZUJ5V2DFOD3QJUZE5CLVU7UDEV","short_pith_number":"pith:ZUJ5V2DF","schema_version":"1.0","canonical_sha256":"cd13dae86570f704d324e8975a7e832554c46aec441abbb4225efba12ac110ff","source":{"kind":"arxiv","id":"nucl-th/0612003","version":2},"attestation_state":"computed","paper":{"title":"Empirical formula for the excitation energies of the first $2^+$ and $3^-$ states in even-even nuclei","license":"","headline":"","cross_cats":[],"primary_cat":"nucl-th","authors_text":"Dongwoo Cha, Eunja Ha","submitted_at":"2006-12-02T07:05:58Z","abstract_excerpt":"We report empirical findings that a simple formula in terms of the mass number $A$, the valence proton number $N_p$, and the valence neutron number $N_n$ can describe the essential trends of excitation energies $E_x$ of the first $2^+$ and $3^-$ states in even-even nuclei throughout the periodic table. The formula reads as $E_x = \\alpha A^{-\\beta} + \\exp (- \\lambda N_p) + \\exp (- \\lambda N_n)$. The parameter $\\beta$ in the first term is determined by the mass number $A$ dependence of the bottom contour line of the excitation energy systematics. The other two parameters $\\alpha$ and $\\lambda$ a"},"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":"nucl-th/0612003","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"nucl-th","submitted_at":"2006-12-02T07:05:58Z","cross_cats_sorted":[],"title_canon_sha256":"cc6c0bced11067b85ab1ccea293c60165900b11e5862080ee5ef8735a120d590","abstract_canon_sha256":"d03e5d4fac45e3776170cb2cabaa8b97222d36257f08bd8e7552077267747fab"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:12.952998Z","signature_b64":"4vU7tUmK18rzK9BwAawRUpOE6L48CXWEb1Wneu3IeJ0p2Xk4ZKebCRAWtuj7Kp2VuRRheJfoDYA4qjrGniQUCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cd13dae86570f704d324e8975a7e832554c46aec441abbb4225efba12ac110ff","last_reissued_at":"2026-05-18T01:38:12.952347Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:12.952347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Empirical formula for the excitation energies of the first $2^+$ and $3^-$ states in even-even nuclei","license":"","headline":"","cross_cats":[],"primary_cat":"nucl-th","authors_text":"Dongwoo Cha, Eunja Ha","submitted_at":"2006-12-02T07:05:58Z","abstract_excerpt":"We report empirical findings that a simple formula in terms of the mass number $A$, the valence proton number $N_p$, and the valence neutron number $N_n$ can describe the essential trends of excitation energies $E_x$ of the first $2^+$ and $3^-$ states in even-even nuclei throughout the periodic table. The formula reads as $E_x = \\alpha A^{-\\beta} + \\exp (- \\lambda N_p) + \\exp (- \\lambda N_n)$. The parameter $\\beta$ in the first term is determined by the mass number $A$ dependence of the bottom contour line of the excitation energy systematics. The other two parameters $\\alpha$ and $\\lambda$ a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nucl-th/0612003","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"nucl-th/0612003","created_at":"2026-05-18T01:38:12.952445+00:00"},{"alias_kind":"arxiv_version","alias_value":"nucl-th/0612003v2","created_at":"2026-05-18T01:38:12.952445+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nucl-th/0612003","created_at":"2026-05-18T01:38:12.952445+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZUJ5V2DFOD3Q","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZUJ5V2DFOD3QJUZE","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZUJ5V2DF","created_at":"2026-05-18T12:25:54.717736+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZUJ5V2DFOD3QJUZE5CLVU7UDEV","json":"https://pith.science/pith/ZUJ5V2DFOD3QJUZE5CLVU7UDEV.json","graph_json":"https://pith.science/api/pith-number/ZUJ5V2DFOD3QJUZE5CLVU7UDEV/graph.json","events_json":"https://pith.science/api/pith-number/ZUJ5V2DFOD3QJUZE5CLVU7UDEV/events.json","paper":"https://pith.science/paper/ZUJ5V2DF"},"agent_actions":{"view_html":"https://pith.science/pith/ZUJ5V2DFOD3QJUZE5CLVU7UDEV","download_json":"https://pith.science/pith/ZUJ5V2DFOD3QJUZE5CLVU7UDEV.json","view_paper":"https://pith.science/paper/ZUJ5V2DF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=nucl-th/0612003&json=true","fetch_graph":"https://pith.science/api/pith-number/ZUJ5V2DFOD3QJUZE5CLVU7UDEV/graph.json","fetch_events":"https://pith.science/api/pith-number/ZUJ5V2DFOD3QJUZE5CLVU7UDEV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZUJ5V2DFOD3QJUZE5CLVU7UDEV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZUJ5V2DFOD3QJUZE5CLVU7UDEV/action/storage_attestation","attest_author":"https://pith.science/pith/ZUJ5V2DFOD3QJUZE5CLVU7UDEV/action/author_attestation","sign_citation":"https://pith.science/pith/ZUJ5V2DFOD3QJUZE5CLVU7UDEV/action/citation_signature","submit_replication":"https://pith.science/pith/ZUJ5V2DFOD3QJUZE5CLVU7UDEV/action/replication_record"}},"created_at":"2026-05-18T01:38:12.952445+00:00","updated_at":"2026-05-18T01:38:12.952445+00:00"}