Semiclassical interpretation of the gross-shell structure in deformed nuclei

An analysis of the classical closed orbits in the infinitely deep elongated ellipsoidal well is given with respect to their relevance to the gross-shell structure of the single-particle spectra in deformed nuclei. It is shown that the deformed-shape gross-shells responsible for the ground state deformations, as well as those responsible for the fission intermediate states, find a reasonable explanation in terms of the semiclassical three-dimensional quantization involving the planar orbits in the axis-of-symmetry plane and the simplest three-dimensional orbits which appear at large distortions. The former are found important for the ground state shapes. The results are also compared with the harmonic oscillator model.