Shapes and Symmetries of Light Nuclei

We demonstrate that the existence of symmetries under the operations $T$, $P_{\exp }(-i\pi J_y)$, and $\left(i\pi J_z\right)$ 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.