Generator-coordinate methods with symmetry-restored Hartree-Fock-Bogoliubov wave functions for large-scale shell-model calculations

Abstract

The generator coordinate method (GCM) combined with the projection method is applied to large-scale shell-model calculations. The quadrupole deformation is taken as a generator coordinate and the GCM basis states are prepared by the quadrupole-constrained Hartree-Fock Bogoliubov method with the variation after particle-number projection. The resultant GCM wave function is a linear combination of the angular-momentum and parity projected basis states. We discuss how well the present method approximates the exact solution of the shell-model diagonalization method by the benchmark tests of $^{48}\mathrm{Ca}$, $^{56}\mathrm{Ni}$, and $^{48}\mathrm{Cr}$ in the $pf$-shell model space and those of $^{132}\mathrm{Ba}$ and $^{133}\mathrm{Ba}$ in the $50<N,\phantom{\rule{0.28em}{0ex}}Z<82$ model space.