Microscopic Study of Non-Linear Collective Motions in Yrast Region of Medium-Heavy Nuclei

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The purpose of the present project is to establish the theoretical framework to renormalize the kinematical and dynamical anharmonicity effects in the yrast region of medium-heavy nuclei, and to analyze the collective motions in both the low and high spin states using this theory.As approaches from the side of low-spin region,1. We analyzed the collective motions in the low-spin region by using the Dyson boson mapping method on the basis of spherical basis vectors.2. We established the theory of the Dyson-type self-consistent-collective-coordinate method, which is, so to say, a dynamical boson expansion theory to renormalize non-linear coupling effects into collective coordinates. Using this theory, we analyzed the shape transition phenomena in the Sm isotopes.As approaches from the side of high-spin region,3. to make a unified description of rotation, vibration and rotation-aligned single-quasiparticle mode, we established a "rotating shell model + RPA + quasiparticle-vibration-rotation coupling model" on the basis of deformed basis vectors.Using this model, we investigated the super-deformed rotational bands, pairing phase transitions, and anomalies of E2-M1 transitions in the quasiparticle-rotation bands in the very high spin states.In order to treat soft-deformation effects, we generalized the boson mapping method to be capable to renormalize higher-order coupling effects, and applied it to the description of unclear wobbling motion.In addition to these, we were successful to develop the computer programs for algebraic manipulation of angular momentum coupling in quantum mechanics. These programs would be very useful in the many fields of quantum physics.