{"paper":{"title":"Multipole characteristics of the open-shell electron eigenstates","license":"","headline":"","cross_cats":["physics.atom-ph"],"primary_cat":"physics.chem-ph","authors_text":"((1) Institute of Low Temperature, (2) Institute of Physics, Jacek Mulak (1), Maciej Mulak (2), Polish Academy of Sciences, Structure Research, Wroclaw University of Technology)","submitted_at":"2007-12-27T12:50:05Z","abstract_excerpt":"The second moment of the sublevels within the initial state | \\alpha SLJ > which constitutes a natural and adequate measure of the crystal-field (CF) effect can be redefined as sigma^{2}=1/(2J+1)\\sum_{k} S_{k}^{2} A_{k}^{2}, where S_{k}=[1/(2k+1)\\sum_{q}|B_{kq}|^2]^{1/2} is the so-called 2^{k}-pole CF strength, whereas A_{k}= < \\alpha SLJ||C^{(k)}||\\alpha SLJ > the reduced matrix element of the k-rank spherical tensor operator. Therefore, the CF effect depends on the sum of products of the two factors representing the identical multipole components of two different charge distributions. The te"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.4227","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"}