Shapes and symmetries of light nuclei

Abstract

We demonstrate that the existence of symmetries under the operations T, P_exp(-iπJ_y), and (iπJ_z) in the Hartree-Fock densities of even-even N=Z nuclei follows directly from two indisputable features of any effective shell-model interaction, viz., the general exchange nature and the short range. We show that this implies that one should not expect parity mixing in Hartree-Fock ground state wave functions for these nuclei. Finally, we demonstrate that these same features of the interaction allow us to predict the shapes of the Hartree-Fock densities.