Angular-momentum structure of the yrast bands of deformed nuclei

Abstract

We have quantitatively analyzed the wave functions of the low-lying yrast states of deformed, heavy nuclei (specifically ${}^{238}$U and ${}^{168}$Er) given by different models to determine the relative contribution of the valence nucleons to the total angular momentum of the nucleus. In all models, an yrast state is generated, as expected, by collective contributions from both proton and neutron angular momenta. We have also examined the relative contribution of valence nucleons in the normal-parity states and in the abnormal-parity, high-$j$, intruder states to the yrast angular momentum. If the states with definite angular momenta projected from the Nilsson intrinsic state of the nucleus are assumed to provide a good approximation to the structure of the yrast band, the contribution of nucleons in the abnormal-parity states to the yrast angular momentum is shown to be about the same as that of nucleons in the normal-parity states. This result is in marked contrast to the assumption made in two prominent models (pseudo-${\mathrm{SU}}_{3}$ model and its symplectic extension and fermion dynamic symmetric model) that the nucleons in abnormal-parity states, do not, in the first approximation, contribute any angular momentum to the yrast band. We also find that the distribution of angular momenta contained in the intrinsic state of the abnormal-parity nucleons in the ${j}^{n}$ configuration, which does not have any ${\mathrm{SU}}_{3}$ symmetry, is surprisingly similar to the distribution of angular momenta contained in an ${\mathrm{SU}}_{3}$ intrinsic state with the same average value of angular momentum.