Effective shell model Hamiltonians from density functional theory: quadrupolar and pairing correlations

Abstract

We describe a procedure for mapping a self-consistent mean-field theory (also known as density functional theory) into a shell model Hamiltonian that includes quadrupole-quadrupole and monopole pairing interactions in a truncated space. We test our method in the deformed N=Z sd-shell nuclei Ne-20, Mg-24 and Ar-36, starting from the Hartree-Fock plus BCS approximation of the USD shell model interaction. A similar procedure is then followed using the SLy4 Skyrme energy density functional in the particle-hole channel plus a zero-range density-dependent force in the pairing channel. Using the ground-state solution of this density functional theory at the Hartree-Fock plus BCS level, an effective shell model Hamiltonian is constructed. We use this mapped Hamiltonian to extract quadrupolar and pairing correlation energies beyond the mean field approximation. The rescaling of the mass quadrupole operator in the truncated shell model space is found to be almost independent of the coupling strength used in the pairing channel of the underlying mean-field theory.

15 pages, 5 figures

References in corpus (21)

• Spectroscopy of discrete energy levels in ultrasmall metallic grains
• Shell model study of the isobaric chains A=50, A=51 and A=52
• Monte Carlo evaluation of path integrals for the nuclear shell model
• Correlations beyond the mean field in Magnesium isotopes: Angular momentum projection and configuration mixing
• Global study of quadrupole correlation effects
• Practical solution to the Monte Carlo sign problem: Realistic calculations of 54Fe
• Total and Parity-Projected Level Densities of Iron-Region Nuclei in the Auxiliary Fields Monte Carlo Shell Model
• Configuration mixing of angular momentum projected self-consistent mean-field states for neutron-deficient Pb isotopes
• 3D Solution of Hartree-Fock-Bogoliubov Equations for Drip-Line Nuclei
• Full pf shell study of A = 47 and A = 49 nuclei
• Particle-Number Reprojection in the Shell Model Monte Carlo Method: Application to Nuclear Level Densities
• 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
• Fitting theories of nuclear binding energies
• Nuclear level statistics: extending the shell model theory to higher temperatures
• Systematics of quadrupolar correlation energies
• Properties of the predicted super-deformed band in ^{32}S
• Global study of the spectroscopic properties of the first 2+ state in even-even nuclei
• Beyond mean-field description of the low-lying spectrum of 16O
• RPA vs. exact shell-model correlation energies
• Shell-model Hamiltonians from Density Functional Theory
• Thermal Signatures of Pairing Correlations in Nuclei and Nanoparticles

Cited by in corpus (10)

• Application of the gradient method to Hartree-Fock-Bogoliubov theory
• Collective structural evolution in neutron-rich Yb, Hf, W, Os and Pt isotopes
• Microscopic nuclear structure models and methods : Chiral symmetry, Wobbling motion and $\gamma -$bands
• Mixing of quasiparticle excitations and gamma-vibrations in transitional nuclei
• Variation after full projection with triaxially deformed nuclear mean field
• Angular Momentum Projected Configuration Interaction with Realistic Hamiltonians
• Extended triaxial projected shell model approach for odd-neutron nuclei
• Configuration interaction relativistic Hartree-Fock model
• Shell-model Hamiltonian from self-consistent mean-field model: $N=Z$ nuclei
• Many-Body Approximations in the sd-Shell Sandbox