Gauge-invariant formulation of the adiabatic self-consistent collective coordinate method

Abstract

The adiabatic self-consistent collective coordinate (ASCC) method is a practical micro-scopic theory of large-amplitude collective motion in nuclei with superfluidity. We show that its basic equations are invariant under transformations involving the gauge angle in particle-number space. By virtue of this invariance, a clean separation of the large-amplitude collective motion and the pairing rotational motion can be made, and this allows 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 propose a gauge-fixing prescription that seems most convenient in realistic calculations.