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

TL;DR

This paper presents a method to derive shell model Hamiltonians from density functional theory, incorporating quadrupolar and pairing correlations, and tests it on sd-shell nuclei using different energy density functionals.

Contribution

The authors introduce a procedure to map density functional theory into shell model Hamiltonians with quadrupole and pairing interactions, enabling beyond-mean-field correlation analysis.

Findings

Effective Hamiltonians reproduce correlation energies beyond mean field.

Mass quadrupole operator rescaling is nearly independent of pairing strength.

Method successfully applied to deformed sd-shell nuclei.

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.