Hemispheroidal quantum harmonic oscillator

A deformed single-particle shell model is derived for a hemispheroidal potential well. Only the negative parity states of the Z(z) component of the wave function are allowed, so new magic numbers are obtained. The influence of a term proportional to l² in the Hamiltonian is investigated. The maximum degeneracy is reached at a superdeformed hemispheroidal prolate shape whose magic numbers are identical with those obtained at the spherical shape of the spheroidal harmonic oscillator. This remarkable property suggests an increased stability of such a distorted shape of deposited clusters when the planar surface remains opaque.