Empirical model for three-quasiparticle states

An empirical model is proposed for three-quasiparticle states (3qp) which is based on the experimental data of one- and two-quasiparticle states in neighboring nuclei. Calculations have been performed for 3qp states in ${}_{}{}^{163}{}_{}{}^{}\mathrm{Er}$, ${}_{}{}^{175}{}_{}{}^{}\mathrm{Lu}$, and ${}_{}{}^{177}{}_{}{}^{}\mathrm{Lu}$ to check the validity of the model. The ordering of the levels in a given 3qp quadruplet is correctly reproduced in all nuclei. Two strong rules are proposed for (nnp) or (ppn) configurations according to which the highest-lying member of a given quadruplet always has a spin combination in which the spins of like particles are parallel while those of unlike particles are antiparallel and the state having all three spins in the same direction cannot lie lowest in energy. For (nnn) or (ppp) configurations, however, the state having all three spins in the same direction will be the highest in energy.