Variational approximations to exact solutions in shell-model valence spaces: systematic calculations in the $sd$-shell

Abstract

We study the ability of variational approaches based on self-consistent mean-field and beyond-mean-field methods to reproduce exact energies and electromagnetic properties of the nuclei defined within the $sd$-shell valence space using the non-trivial USD Hamiltonian. In particular, Hartree-Fock-Bogoliubov (HFB), variation after particle-number projection (VAPNP) and projected generator coordinate methods (PGCM) are compared to exact solutions {obtained by} the full diagonalization of the Hamiltonian. We analyze the role played by the proton-neutron ($pn$) mixing as well as the quadrupole and pairing degrees of freedom (including both isoscalar and isovector channels) in the description of the spectra of even-even, even-odd and odd-odd nuclei in the whole $sd$-shell.

arXiv comment16 pages; 16 figures

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Cited by in corpus (7)

• Beyond-mean-field approaches for nuclear neutrinoless double beta decay in the standard mechanism
• Nuclear states projected from a pair condensate
• Multireference covariant density-functional theory for the low-lying states of odd-mass nuclei
• Symmetry-projected variational calculations with the numerical suite TAURUS II. Configuration mixing of symmetry-projected reference states
• Optimization of the number of intrinsic states included in the discrete Generator Coordinate Method
• Exact solutions of the nuclear shell-model secular problem: Discrete Non-Orthogonal Shell Model within a Variation After Projection approach
• Mean-field approximation on steroids: exact description of the deuteron