{"paper":{"title":"The Spherical Tensor Gradient Operator","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Ernst Joachim Weniger","submitted_at":"2005-05-06T08:06:15Z","abstract_excerpt":"The spherical tensor gradient operator ${\\mathcal{Y}}_{\\ell}^{m} (\\nabla)$, which is obtained by replacing the Cartesian components of $\\bm{r}$ by the Cartesian components of $\\nabla$ in the regular solid harmonic ${\\mathcal{Y}}_{\\ell}^{m} (\\bm{r})$, is an irreducible spherical tensor of rank $\\ell$. Accordingly, its application to a scalar function produces an irreducible spherical tensor of rank $\\ell$. Thus, it is in principle sufficient to consider only multicenter integrals of scalar functions: Higher angular momentum states can be generated by differentiation with respect to the nuclear "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0505018","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math-ph/0505018/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"}