We investigate the capacity of nonorthogonal many-body expansions in the resolution of the nuclear shell-model secular problem. Exact shell-model solutions are obtained within the variational principle using nonorthogonal Slater determinants as the variational ansatz. These results numerically prove the realization of the Broeckhove-Deumens theorem on the existence of a discrete set of nonorthogonal wave functions that exactly span the full shell-model space for low-lying states of interest. With the angular-momentum variation after projection, pairing correlations are shown to be fully captured by Slater determinants as exemplified in the backbending phenomenon occurred in ${}^{48}\mathrm{Cr}$. The resulting discrete nonorthogonal shell model developed in such a variation-after-projection method is further examined in the case of ${}^{78}\mathrm{Ni}$, an exotic doubly magic nucleus at the edge of currently feasible diagonalization limits. Its ground state binding energy is shown to converge to a lower value than the largest large-scale shell-model diagonalization ever done by the conventional tridiagonal Lanczos method, revealing an outstanding performance of nonorthogonal Slater determinantal wave functions to describe the eigensolutions of shell-model Hamiltonians.

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• Energy levels
• Nuclear structure & decays
• Nuclear many-body theory
• Shell model