On the basis of a microscopic theory of large-amplitude collective motion, called the adiabatic self-consistent collective coordinate method, we have developed a local quasiparticle RPA (QRPA) to determine microscopically the vibrational and rotational inertial functions appearing in the five-dimensional (5D) quadrupole collective Hamiltonian of the Bohr-Mottelson type.
The local QRPA is a natural extension of the QRPA for small-amplitude vibrations to large-amplitude vibrations, and provides an efficient way of evaluating the inertial functions taking into account the contributions from the time-odd terms that arise in the moving mean field. These contributions are ignored in the widely used Inglis-Belyaev cranking inertial functions. We apply the newly developed microscopic approach to a wide variety of low-frequency quadrupole collective motions including anharmonic vibrations, quantum phase transitions and oblate-prolate shape coexistence/mixing phenomena. Some typical results will be presented including proton-rich Se and Kr isotopes, neutron-rich Mg, Cr isotopes and Gd and Sm isotopes.