# 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
nuclei that are relevant from the point of view of a
study of superallowed Fermi -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.

Jacek Dobaczewski
2016-03-05