Semi-spheroidal Quantum Harmonic Oscillator
Atomic and Molecular Clusters
2009-11-13 v1
Abstract
A new single-particle shell model is derived by solving the Schr\"odinger equation for a semi-spheroidal potential well. Only the negative parity states of the 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 ...
Cite
@article{arxiv.0704.0847,
title = {Semi-spheroidal Quantum Harmonic Oscillator},
author = {D. N. Poenaru and R. A. Gherghescu and A. V. Solov'yov and W. Greiner},
journal= {arXiv preprint arXiv:0704.0847},
year = {2009}
}
Comments
4 pages, 3 figures, 1 table