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Exact solutions of the nuclear shell-model secular problem: Discrete nonorthogonal shell model within a variation-after-projection approach

Duy Duc Dao* and Frédéric Nowacki

  • *Contact author: duc.dao@iphc.cnrs.fr
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Phys. Rev. C 114, 014327 – Published 22 July, 2026

DOI: https://doi.org/10.1103/nkck-ctvd

Abstract

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 Cr48. The resulting discrete nonorthogonal shell model developed in such a variation-after-projection method is further examined in the case of Ni78, 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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Phys. Rev. C 114, 014327– Published 22 July, 2026
  • Received 7 January 2026
  • Accepted 21 May 2026
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