Variation after full projection with triaxially deformed nuclear mean field

Abstract

We implemented a variation after projection (VAP) algorithm based on a triaxially deformed Hartree-Fock-Bogoliubov vacuum state. This is the first projected mean field study that includes all the quantum numbers (except parity), i.e., spin ($J$), isospin ($T$) and mass number ($A$). Systematic VAP calculations with $JTA$-projection have been performed for the even-even $sd$-shell nuclei with the USDB Hamiltonian. All the VAP ground state energies are within 500 keV above the exact shell model values. Our VAP calculations show that the spin projection has two important effects: (1) the spin projection is crucial in achieving good approximation of the full shell model calculation. (2) the intrinsic shapes of the VAP wavefunctions with spin projection are always triaxial, while the Hartree-Fock-Bogoliubov methods likely provide axial intrinsic shapes. Finally, our analysis suggests that one may not be possible to associate an intrinsic shape to an exact shell model wave function.

arXiv comment5 pages,2 figures

References in corpus (15)

• Structure of even-even nuclei using a mapped collective Hamiltonian and the D1S Gogny interaction
• Shape Coexistence and the Effective Nucleon-Nucleon Interaction
• Triaxial Angular Momentum Projection and Configuration Mixing calculations with the Gogny force
• Configuration mixing of angular-momentum projected triaxial relativistic mean-field wave functions
• Configuration mixing of angular-momentum and particle-number projected triaxial HFB states using the Skyrme energy density functional
• Three-dimensional angular momentum projection in relativistic mean-field theory
• Angular momentum projected analysis of Quadrupole Collectivity in \protect(^{30,32,34}Mg\protect) and \protect(^{32,34,36,38}Si\protect) with the Gogny interaction
• Application of the gradient method to Hartree-Fock-Bogoliubov theory
• Description of quadrupole collectivity in N ~ 20 nuclei with techniques beyond the mean field
• Toward extremes of angular momentum: Application of the Pfaffian algorithm in realistic calculations
• Matrix elements of one-body and two-body operators between arbitrary HFB multi-quasiparticle states
• Improved basis selection for the Projected Configuration Interaction method applied to heavy nuclei
• Effective shell model Hamiltonians from density functional theory: quadrupolar and pairing correlations
• Particle-Number Projected Hartree-Fock-Bogoliubov Study with Effective Shell Model Interactions
• A convenient implementation of the overlap between arbitrary Hartree-Fock-Bogoliubov vacua for projection

Cited by in corpus (17)

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• Skyrme-Hartree-Fock-Bogoliubov mass models on a 3D Mesh: Effect of triaxial shape
• Symmetry restoration in the mean-field description of proton-neutron pairing
• Triaxial rigidity of ${}^{166}$Er and its Bohr-model realization
• Symmetry-projected variational calculations with the numerical suite TAURUS I. Variation after particle-number projection
• Projection of angular momentum via linear algebra
• Occupation numbers of spherical orbits in self-consistent beyond-mean-field methods
• Variational approximations to exact solutions in shell-model valence spaces: systematic calculations in the $sd$-shell
• Variation after projection calculations for high-spin states
• New algorithm in the variation after projection calculations for non-yrast nuclear states
• Nucleon-pair truncation of the shell model for medium-heavy nuclei
• A Pfaffian formulation for matrix elements of three-body operators in multiple quasi-particle configurations
• Finite-temperature mean-field approximations for shell model Hamiltonians: the code HF-SHELL
• Finding the best basis states for the variation after projection nuclear wave functions
• Mixing of one-particle-one-hole projected states with the variation after projection wave functions
• Exact solutions of the nuclear shell-model secular problem: Discrete Non-Orthogonal Shell Model within a Variation After Projection approach