Exact solutions of the nuclear shell-model secular problem: Discrete Non-Orthogonal Shell Model within a Variation After Projection approach
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916924700491776 |
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| author | Dao, Duy Duc Nowacki, Frédéric |
| author_facet | Dao, Duy Duc Nowacki, Frédéric |
| contents | 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 $^{48}$Cr. The resulting discrete non-orthogonal shell model developed in such variation after projection method is further examined in the case of $^{78}$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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09073 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exact solutions of the nuclear shell-model secular problem: Discrete Non-Orthogonal Shell Model within a Variation After Projection approach Dao, Duy Duc Nowacki, Frédéric Nuclear Theory 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 $^{48}$Cr. The resulting discrete non-orthogonal shell model developed in such variation after projection method is further examined in the case of $^{78}$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. |
| title | Exact solutions of the nuclear shell-model secular problem: Discrete Non-Orthogonal Shell Model within a Variation After Projection approach |
| topic | Nuclear Theory |
| url | https://arxiv.org/abs/2507.09073 |