Exact solutions of the nuclear shell-model secular problem: Discrete Non-Orthogonal Shell Model within a Variation After Projection approach
Abstract
We investigate the capacity of non-orthogonal many-body expansions in the resolution of the nuclear shell-model secular problem. Exact shell-model solutions are obtained within the variational principle using non-orthogonal 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 non-orthogonal wavefunctions 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 Cr. The resulting discrete non-orthogonal shell model developed in such variation after projection method is further examined in the case of 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 non-orthogonal Slater determinantal wavefunctions to describe the eigensolutions of shell-model Hamiltonians.
Cite
@article{arxiv.2507.09073,
title = {Exact solutions of the nuclear shell-model secular problem: Discrete Non-Orthogonal Shell Model within a Variation After Projection approach},
author = {Duy Duc Dao and Frédéric Nowacki},
journal= {arXiv preprint arXiv:2507.09073},
year = {2025}
}