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Hemispheroidal quantum harmonic oscillator

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Aug 2008Embargo end date: 01 Jan 2007Publisher:Elsevier BVJournal:Physics Letters A, volume 372, pages 5,448-5,451 (issn: 0375-9601,

Authors: Andrey V. Solov’yov; R. A. Gherghescu; Dorin N. Poenaru; Walter Greiner;

doi: 10.1016/j.physleta.2008.06.054 , 10.48550/arxiv.0704.0847

arXiv: http://arxiv.org/abs/0704.0847

Hemispheroidal quantum harmonic oscillator

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Abstract

A new single-particle shell model is derived by solving the Schr��dinger equation for a semi-spheroidal potential well. Only the negative parity states of the $Z(z)$ component of the wave function are allowed, so that new magic numbers are obtained for oblate semi-spheroids, semi-sphere and prolate semi-spheroids. The semi-spherical magic numbers are identical with those obtained at the oblate spheroidal superdeformed shape: 2, 6, 14, 26, 44, 68, 100, 140, ... The superdeformed prolate magic numbers of the semi-spheroidal shape are identical with those obtained at the spherical shape of the spheroidal harmonic oscillator: 2, 8, 20, 40, 70, 112, 168 ...

4 pages, 3 figures, 1 table

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FOS: Physical sciences, Physics - Atomic and Molecular Clusters, Atomic and Molecular Clusters (physics.atm-clus)

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