Shell-model Hamiltonians from Density Functional Theory

Abstract

The density functional theory of nuclear structure provides a many-particle wave function that is useful for static properties, but an extension of the theory is necessary to describe correlation effects or other dynamic properties. Here we propose a procedure to extend the theory by mapping the properties of the self-consistent mean-field Hamiltonian onto an effective shell-model Hamiltonian with two-body interactions. In this initial study, we consider the sd-shell nuclei Ne-20, Mg-24, Si-28, and Ar-36. Our first application is in the framework of the USD shell-model Hamiltonian, using its mean-field approximation to construct an effective Hamiltonian and partially recover correlation effects. We find that more than half of the correlation energy is due to the quadrupole interaction. We then follow a similar procedure but using the SLy4 Skyrme energy functional as our starting point and truncating the space to the spherical $sd$ shell. The constructed shell-model Hamiltonian is found to satisfy minimal consistency requirements to reproduce the properties of the mean-field solution. The quadrupolar correlation energies computed with the mapped Hamiltonian are reasonable compared with those computed by other methods.

14 pages and 10 figures

References in corpus (10)

• Axially Deformed Solution of the Skyrme-Hartree-Fock-Bogolyubov Equations using The Transformed Harmonic Oscillator Basis. The program HFBTHO (v1.66p)
• 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
• Particle-Number Reprojection in the Shell Model Monte Carlo Method: Application to Nuclear Level Densities
• Fitting theories of nuclear binding energies
• Nuclear level statistics: extending the shell model theory to higher temperatures
• Demonstration of the auxiliary-field Monte Carlo approach for sd-shell nuclei
• Systematics of quadrupolar correlation energies
• RPA vs. exact shell-model correlation energies

Cited by in corpus (7)

• Microscopic nuclear structure models and methods : Chiral symmetry, Wobbling motion and $\gamma -$bands
• Mixing of quasiparticle excitations and gamma-vibrations in transitional nuclei
• Angular Momentum Projected Configuration Interaction with Realistic Hamiltonians
• Extended triaxial projected shell model approach for odd-neutron nuclei
• Effective shell model Hamiltonians from density functional theory: quadrupolar and pairing correlations
• Nuclear spectra from low-energy interactions
• Shell-model Hamiltonian from self-consistent mean-field model: $N=Z$ nuclei