Study of the Neutron-Proton Correlations in the Shell Model

A shell-model treatment is given for the spectra of the nuclei where there are two protons and two neutrons outside a doubly closed shell. The only restriction is that like-nucleons are required to occupy the same angular momentum state. In addition to this general wave function, more restricted wave functions also are investigated, viz., the pairing wave function (as least one pair of like nucleons is coupled to zero angular momentum) which contain no $n-p$ correlations; the quartetting wave function (two unlike nucleons are first coupled to the maximum angular momentum, then the two pairs are coupled to $I$, the nuclear angular momentum) which does contain $n-p$ correlations; and a superposition of pairing and quartetting wave functions. Results for ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ti}$, ${}_{}{}^{64}{}_{}{}^{}\mathrm{Zn}$, and ${}_{}{}^{204}{}_{}{}^{}\mathrm{Hg}$ are given. The ground states are reproduced quite well by the pairing wave function; it seems, however, to fail for the excited states. The overlap between the general and the quartetting wave function is quite large. Finally, results are also given for the pairing force, which has only a $T=1\mathrm{}$ component.