Variation after parity projection calculation with the Skyrme interaction for light nuclei

Abstract

A self-consistent calculation with variation after parity projection is proposed to study both ground and excited states of light nuclei. This procedure provides description of the ground state incorporating some correlation effects, and self-consistent solutions for the excited states of negative parity. For flexible description of nuclear shapes, single particle orbitals are represented on a uniform grid in the three-dimensional Cartesian coordinates. The angular momentum projection is performed after variation to calculate rotational spectra. To demonstrate the usefulness of the method, results are shown for two $N=Z$ nuclei, $^{20}\mathrm{Ne}$ and $^{12}\mathrm{C}$, for which clustering correlations are known to be important. In the $^{20}\mathrm{Ne}$ nucleus, both cluster-like and shell-model-like states are described simultaneously in the present framework. For $^{12}\mathrm{C}$ nucleus, the appearance of three-alpha clustering correlation in the ground state is investigated in relation to the strength of the two-body spin-orbit interaction.