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,...,I_max for a K=0 band and I=K,K+1,...,I_max for a K≠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^HF, then E_I is greater (less) than E_I' for I<I'. A plausible reason why one should use the deformed HF state rather than any other deformed state is also pointed out.