Properties of the Projected Spectra for Finite Nuclei

Abstract

The general features of the expressions useful for numerical calculations of the projected deformed Hartree-Fock (HF) spectra for finite nuclei are investigated. It is proved that the projected deformed HF wave-function gives the possible nuclear spins as $I=0,2,4,\dots{},{I}_{max}$ for a $K=0$ band and $I=K,K+1,\dots{},{I}_{max}$ for a $K\ensuremath{\ne}0$ band. It is further proved that if the energy ${E}_{I=K}$ of the projected $I=K$ state is greater (less) than the HF energy $E_{K}^{}{}_{}{}^{\mathrm{HF}}$, then ${E}_{I}$ is greater (less) than $E_{I}^{}{}_{}{}^{\ensuremath{'}}$ for $I<{I}^{\ensuremath{'}}$. A plausible reason why one should use the deformed HF state rather than any other deformed state is also pointed out.