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To study shape fluctuations of nuclei in transitional regions, the collective Hamiltonian method has often been employed. We intend to construct the quadrupole collective Hamiltonian with the collective inertial functions given by the local quasiparticle random-phase approximation (QRPA) based on the Skyrme energy density functional. For this purpose, we first construct a practical framework of Skyrme QRPA for triaxial nuclear shapes with the finite amplitude method (FAM). We show quadrupole strength functions for a triaxial superfluid nucleus 188Os and the Thouless-Valatin rotational moment of inertia by the local FAM-QRPA for 106Pd.
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