Periodic-Orbit Bifurcation and Shell Structure in Reflection-Asymmetric Deformed Cavity

Shell structure of the single-particle spectrum for reflection-asymmetric deformed cavity is investigated. Remarkable shell structure emerges for certain combinations of quadrupole and octupole deformations. Semiclassical periodicorbit analysis indicates that bifurcation of equatorial orbits plays an important role in the formation of this new shell structure. Theoretical and experimental exploration of reflection-asymmetric deformed shapes is one of the current topics of interest both in nuclear-structure and micro-cluster physics[1,2,3,4]. In theoretical calculations, various approaches like Hartree-Fock-Bogoliubov methods, microscopicmacroscopic methods and semi-classical methods have been exploited for this aim (see Ref. [1] for a review). Each method possesses merits and demerits, so that it would be desirable to explore the subject with various approaches. A basic motive of the semi-classical periodic-orbit approach[5,6,7] is to understand the origin of shellstructure formation that play decisive role in bringing about symmetry-breaking in the average potential of finite quantum systems like nuclei and microcluster. If we could understand the origin and obtain a global perspective, it would become possible to qualitatively predict where we can expect a particular deformation to appear in the multi-dimensional space spanned by various deformation-parameters and the number of constituents of the system. In the conventional wisdom, shell-structure would be weakened if reflection-asymmetric deformation is added to the spheroidal shape. This is because the system becomes non-integrable when the octupole deformation is added, and because the degeneracy of the periodic-orbits is then reduced. Contrary to this expectation, a significant shell structure was found in Refs. [8,9] to emerge for certain combinations of quadrupole and octupole deformations in the reflection-asymmetric deformed oscillator model. It was pointed out that this shell-structure enhancement is associated with bifurcation of periodic orbits. It would be very important to investigate whether such a mechanism of shell-structure formation is special to the harmonic-oscillator model or possesses more general significance. To explore the possibility that significant shell structure emerges in the single-particle spectra for nonintegrable Hamiltonian, we have carried out an analysis of single-particle motions in the reflectionasymmetric, axially-symmetric deformed cavity by parameterizing the surface as