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 ${}^{48}$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.

References in corpus (20)

• The Shell Model as Unified View of Nuclear Structure
• Thick-Restart Block Lanczos Method for Large-Scale Shell-Model Calculations
• ${}^{78}$Ni revealed as a doubly magic stronghold against nuclear deformation
• Shape Coexistence in 78 Ni and the new Island of Inversion
• Symmetry restoration in mean-field approaches
• Factorization in large-scale many-body calculations
• The Neutron-Rich Edge of the Nuclear Landscape. Experiment and Theory
• Nilsson-SU3 selfconsistency in heavy N=Z nuclei
• Variational approach with the superposition of the symmetry-restored quasi-particle vacua for nuclear shell-model calculations
• Variation after full projection with triaxially deformed nuclear mean field
• Variational approximations to exact solutions in shell-model valence spaces: calcium isotopes in the pf-shell
• Angular Momentum Projected Configuration Interaction with Realistic Hamiltonians
• Description of nuclear systems with a self-consistent configuration-mixing approach. I: Theory, algorithm, and application to the ${}^{12}$C test nucleus
• Variational approximations to exact solutions in shell-model valence spaces: systematic calculations in the $sd$-shell
• Description of nuclear systems with a self-consistent configuration-mixing approach. II: Application to structure and reactions in even-even sd-shell nuclei
• Efficient computation of Hamiltonian matrix elements between non-orthogonal Slater determinants
• Improved basis selection for the Projected Configuration Interaction method applied to heavy nuclei
• Further evidence for shape coexistence in ${}^{79}$Zn${}^m$ near doubly-magic ${}^{78}$Ni
• An extension of the generator coordinate method with basis optimization
• New algorithm in the variation after projection calculations for non-yrast nuclear states