Semi-spheroidal Quantum Harmonic Oscillator
arXiv:0704.0847 · doi:10.1016/j.physleta.2008.06.054
Abstract
A new single-particle shell model is derived by solving the Schrödinger 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