Variational approximations to exact solutions in shell-model valence spaces: calcium isotopes in the pf-shell

Abstract

We study the performance of self-consistent mean-field and beyond-mean-field approximations in shell-model valence spaces. In particular, Hartree-Fock-Bogolyubov, particle-number variation after projection and projected generator coordinate methods are applied to obtain ground-state and excitation energies for even-even and odd-even Calcium isotopes in the pf-shell. The standard (and non-trivial) KB3G nuclear effective interaction has been used. The comparison with the exact solutions -- provided by the full diagonalization of the Hamiltonian -- shows an outstanding agreement when particle-number and angular-momentum restorations are performed and both quadrupole and neutron-neutron pairing degrees of freedom are explicitly explored as collective coordinates.

14 pages, 10 figures

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Cited by in corpus (15)

• Projection on particle number and angular momentum: Example of triaxial Bogoliubov quasiparticle states
• Beyond-mean-field approaches for nuclear neutrinoless double beta decay in the standard mechanism
• Variational approach with the superposition of the symmetry-restored quasi-particle vacua for nuclear shell-model calculations
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• Application of efficient generator-coordinate subspace-selection algorithm to neutrinoless double-$\beta$ decay
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• 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
• New angular momentum coupling method based on Wigner rotation theory
• Ab initio study in the island of inversion within the two-major-shell valence space