Gauge-Invariant Formulation of Adiabatic Self-Consistent Collective Coordinate Method

The adiabatic self-consistent collective coordinate (ASCC) method is a practical microscopic theory of large-amplitude collective motions in nuclei with superfluidity. We show that its basic equations are invariant against transformations involving the gauge angle in the particle-number space. By virtue of this invariance, a clean separation between the large-amplitude collective motion and the pairing rotational motion can be achieved, enabling us to restore the particle-number symmetry broken by the Hartree-Fock-Bogoliubov (HFB) approximation. We formulate the ASCC method explicitly in a gauge-invariant form. In solving the ASCC equations, it is necessary to fix the gauge. Applying this new formulation to the multi-O(4) model, we compare different gauge-fixing procedures and demonstrate that calculations using different gauges indeed yield the same results for gauge-invariant quantities, such as the collective path and quantum spectra. We suggest a gauge-fixing prescription that seems most convenient in realistic calculations.Comment: 27 pages, 7 figures, submitted to Prog. Theor. Phy

Effects of Time-Odd Components in Mean Field on Large Amplitude Collective Dynamics

We apply the adiabatic self-consistent collective coordinate (ASCC) method to the multi-O(4) model and study collective mass (inertia function) of the many-body tunneling motion. Comparing results with those of the exact diagonalization, we show that the ASCC method succeeds in describing gradual change of excitation spectra from an anharmonic vibration about the spherical shape to a doublet pattern associated with a deformed double-well potential possessing the oblate-prolate symmetry. The collective mass is significantly increased by the quadrupole-pairing contribution to time-odd components of the moving mean field. In contrast, the cranking (Inglis-Belyaev) mass based on the constrained mean field, which ignores the time-odd components, is smaller than the ASCC mass and fails to reproduce the exact spectra.Comment: 32 pages, 9 figure

Microscopic description of large-amplitude shape-mixing dynamics with local QRPA inertial functions

We introduce a microscopic approach to derive all the inertial functions in the five-dimensional quadrupole collective Hamiltonian. Local normal modes are evaluated on the constrained mean field in the quasiparticle random-phase approximation in order to derive the inertial functions. The collective Hamiltonians for neutron-rich Mg isotopes are determined with use of this approach, and the shape coexistence/mixing around the N = 20 region is analyzed.Comment: 6 pages, 2 figures, Talk given at International Symposium New Faces of Atomic Nuclei, Okinawa, Japan, Nov. 15-17, 201