KUNS 1285 Periodic Orbits and New Shell Structure Generated by a Combination of Quadrupole and Octupole Deformations

In this talk, we would like to present a simple model in which a prominent shell structure emerges for a combination of quadrupole and octupole deformations. We shall then discuss the origin of such a new shell structure in terms of the periodic orbits and their bifurcations. Importance of shell effects for the occurrence of reflection-asymmetric deformed shapes have been lively discussed in various region of nuclei [1,2] and also in micro-clusters [3,4]. According to the semi-classical theory, the shell structure, i.e., the oscillating structure in the single-particle level density is generated by classical closed orbits with short periods. Thus, our task is to identify important periodic orbits and study how they are born and how their properties change as function of deformation parameters. This subject is deeply related with the general subjects of quantum chaos; in particular, quantum manifestation of bifurcation phenomena in classical Hamiltonian dynamics. We would like to emphasize that, although “quantum chaos” in the chaotic limit has been much discussed, bifurcation of periodic orbits is characteristic for mixed systems where regular and chaotic motion coexist and remains largely unexplored. Finite quantum systems possessing both quadrupole and octupole deformations are situated in an intermediate region between regular and chaotic systems [5,6], and therefore provide us with a very good opportunity to study, from both theory and experiment, this important subject.