A collective model study using the interacting boson model-2 (IBM-2), as well as an approach explicitly treating both the shell-model and collective-model degrees of freedom, i.e., the particle-core coupling model (PCM), are applied to the N=84 isotones ${}_{}{}^{138}{}_{}{}^{}\mathrm{Xe}$ to ${}_{}{}^{146}{}_{}{}^{}\mathrm{Sm}$. A new mapping procedure from the PCM onto the IBM-2 model space is developed in order to more fully understand and discriminate between the shell-model and collective-model parts of the nuclear wave functions, and to study the criteria for which the IBM-2 is a valid approximation to the PCM in the N=84 nuclei. It is shown that the PCM gives the better description of all nuclear properties and that, although an apparently good fit is obtained within the IBM-2, its model space using only s and d bosons is too restricted to provide a comprehensive description of these N=84 nuclei.

• Received 18 May 1992

DOI:https://doi.org/10.1103/PhysRevC.46.1301