Microscopic study of Collective Excitetior Spectra in Heavy Unstable Nuclei taking into account arbitrary deformations and pairing correlation

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1. By means of the symmetry-unrestricted cranked Skyrme-HF method, we have made a systematic calculation for superdeformed and hyperdeformed rotational bands in N=Z nuclei around ^<40>Ca and neutron-rich Sulfur isotopes. On the basis of the selfconsistent RPA calculations, we have suggested that strongly collective soft ~ octupole vibrations may be built on top of the superdeformed and hyperdeformed states.2. Using the symmetry-unrestricted Skyrme-HF-Bogoliubov method, we have theoretically explored exotic shapes in proton-rich N=Z nuclei in the A=60-80 region, and suggested appearance of triangular and tetrahedral deformations in ^<68>Se and ^<80>Zr, respectively.3. We have applied the adiabatic self-consistent collective coordinate method to the oblate-prolate shape coexistence phenomena in nuclei around ^<68>Se and ^<72>Kr, and succeeded in selfconsistently extracting the collective paths connecting the oblate and prolate local minima.4. On the basis of the quasiparticle RPA in the rotating frame, we have investigated microscopic structure of the wobbling modes discovered in recent experiments, and shown that alignment of quasiparticles due to rapid rotation plays an essential role for the appearance of these modes.5. We have developed a new semi-classical trace formula capable of treating periodic-orbit bifurcations in spheroidal cavities, and shown that the bifurcation of 3-dimensional periodic orbits plays an essential role for the appearance of superdeformed shell structure.