{"paper":{"title":"New recursion relations of matrix elements of $r^\\lambda$ and $\\beta r^\\lambda$ between relativistic hydrogenic eigenstates","license":"","headline":"","cross_cats":["physics.chem-ph"],"primary_cat":"physics.atom-ph","authors_text":"A. L. Salas-Brito, H. N. N\\'u\\~nez-Y\\'epez, R. P. Mart\\'inez-y-Romero","submitted_at":"2003-04-12T00:43:57Z","abstract_excerpt":"We determine exact recurrence relations which help in the evaluation of matrix elements of powers of the radial coordinate between Dirac relativistic hydrogenic eigenstates. The power $\\lambda$ can be any complex number as long as the corresponding term vanishes faster than $r^{-1}$ as $r \\to \\infty$. These formulas allow determining recursively any matrix element of radial powers --$r^\\lambda$ or $\\beta r^\\lambda$, $\\beta$ is a Dirac matrix-- in terms of the two previous consecutive elements. The results are useful in relativistic atomic calculations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"physics/0304049","kind":"arxiv","version":1},"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"}