Exotic Deformations in Heavy Unstable Nuclei

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1. High-spin yrast structure of ィイD132ィエD1 S was investigated by means of the cranked Skyrme-Hartree-Fock method in the three-dimensional Cartcsian-mesh representation without imposing restrictions on spatial symmetrics. The result suggests that 1) a crossover from the superdeformed to the hyperdeformed-like configurations takes place on the yrast line at angular momentum I 【similar or equal】 24, which corresponds to the "band termination" point in the cranked harmonic-oscillator model, and 2) non-axial octupole deformations of the YィイD231ィエD2 type play an important role in the yrast states in the range 5 【less than or equal】 I 【less than or equal】 13.2. We have constructed a new computer program of Cranked Skyrme-Hartree-Fock-Bogoliubov method for nuclear structure calculation, which is based on 3D Cartesianmesh representation and which selfconsistently takes into account pairing correlations including continuum states. A new feature of this program is that no restrictions on spatial … More symmetries are imposed. With the use of this program, we have investigated exotic shapes in proton-rich N=Z nuclei in the A=60-80 region and found a non-axial octupole (triangular) shape in ィイD168ィエD1Se.3. We have derived an analytical trace formula for the level density of the two-dimensional elliptic billiard using an improved stationary phase method. The result is a continuous function of the deformation parameter (eccentricity) through all bifurcation points of the short diameter orbit and its repetitions, and possesses the correct limit of the circular billiard at zero eccentricity. Away from the circular limit and the bifurcations, it reduces to the usual (extended) Gutzwiller trace formula which for the leading-order families of periodic orbits is identical to the result of Berry and Tabor. We find enhancement of the amplitudes near the common bifurcation points of both short-diameter and hyperbolic orbits. The calculated semiclassical level densities and shell energies are in good agreement with the quantum mechanical ones. Less