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 $50<N,Z<82$ model space.

• Received 20 March 2021
• Accepted 25 May 2021

DOI:https://doi.org/10.1103/PhysRevC.103.064302