No-core configuration-interaction model for the isospin- and angular-momentum-projected states

W. Satula, P. Baczyk, J. Dobaczewski, and M. Konieczka

Date: March 5, 2016

Abstract:

Background

Single-reference density functional theory is very successful in reproducing bulk nuclear properties like binding energies, radii, or quadrupole moments throughout the entire periodic table. Its extension to the multi-reference level allows for restoring symmetries and, in turn, for calculating transition rates.

Purpose

We propose a new variant of the no-core-configuration-interaction (NCCI) model treating properly isospin and rotational symmetries. The model is applicable to any nucleus irrespective of its mass and neutron- and proton-number parity. It properly includes polarization effects caused by an interplay between the long- and short-range forces acting in the atomic nucleus.

Methods

The method is based on solving the Hill-Wheeler-Griffin equation within a model space built of linearly-dependent states having good angular momentum and properly treated isobaric spin. The states are generated by means of the isospin and angular-momentum projection applied to a set of low-lying (multi)particle-(multi)hole deformed Slater determinants calculated using the self-consistent Skyrme-Hartree-Fock approach.

Results

The theory is applied to calculate energy spectra in $N\approx Z$ nuclei that are relevant from the point of view of a study of superallowed Fermi $\beta$-decays. In particular, a new set of the isospin-symmetry-breaking corrections to these decays is given.

Conclusions

It is demonstrated that the NCCI model is capable to capture main features of low-lying energy spectra in light and medium-mass nuclei using relatively small model space and without any local readjustment of its low-energy coupling constants. Its flexibility and a range of applicability makes it an interesting alternative to the conventional nuclear shell model.