Shell-model Hamiltonian from self-consistent mean-field model: $N=Z$ nuclei

TL;DR

This paper introduces a method to derive effective shell-model Hamiltonians from self-consistent mean-field models, enabling more accurate and practical nuclear structure calculations for N=Z nuclei.

Contribution

The authors develop a procedure to determine shell-model Hamiltonian parameters directly from Skyrme mean-field models, improving the connection between mean-field and shell-model approaches.

Findings

Energy spectra agree well with experimental data.

The monopole interaction plays a significant role.

Method successfully applied to N=Z nuclei in different shell regions.

Abstract

We propose a procedure to determine the effective nuclear shell-model Hamiltonian in a truncated space from a self-consistent mean-field model, e.g., the Skyrme model. The parameters of pairing plus quadrupole-quadrupole interaction with monopole force are obtained so that the potential energy surface of the Skyrme Hartree-Fock + BCS calculation is reproduced. We test our method for $N=Z$ nuclei in the $fpg$- and $sd$-shell regions. It is shown that the calculated energy spectra with these parameters are in a good agreement with experimental data, in which the importance of the monopole interaction is discussed. This method may represent a practical way of defining the Hamiltonian for general shell-model calculations.