{"paper":{"title":"About disposition of energy levels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nucl-th","physics.atm-clus","quant-ph"],"primary_cat":"physics.comp-ph","authors_text":"Evgeny Z. Liverts, Nir Nevo Dinur","submitted_at":"2012-05-20T11:53:14Z","abstract_excerpt":"The unique properties of central potential of the form $-\\beta e^{-r}r^{\\gamma}$ were studied using the recently developed critical parameter technique. The particular cases of $\\gamma=0$ and $\\gamma=-1$ yield, respectively, the exponential and Yukawa potentials widely used in the atomic, molecular and nuclear physics. We found different behavior of the energy levels of this potential for three different ranges of the value of $\\gamma$. For $\\gamma\\geq0$ it was found that the energy of bound states with the same principal quantum number $N$ decreases with increasing angular momentum $\\ell$. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4408","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"}