{"paper":{"title":"Jacobi Coordinates on Hyper-tori and Geometric Factors in the Volume Dependencies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nucl-th","authors_text":"Hang Yu","submitted_at":"2025-11-10T05:39:47Z","abstract_excerpt":"We derive the volume dependence of bound states from a cluster-cluster picture with nucleon degrees of freedom. A constant factor called the ``geometric factor'' appears in the generalization from point-like particles to clusters. We show that this factor becomes explicit and correct when the underlying overlap integral is evaluated directly in the original many-body space. We achieve this by constructing Jacobi coordinates on the lattice under the periodic boundary. The derivation requires only the interaction \\textit{between} the clusters to be short-ranged, with the non-perturbative Coulomb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.06726","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2511.06726/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"}