Nuclear clusters bound to doubly magic nuclei: The case of 212Po

An effective alpha-particle equation is derived for cases where an alpha particle is bound to a doubly magic nucleus. As an example, we consider Po-212 with the alpha on top of the Pb-208 core. We consider the core nucleus infinitely heavy, so that the alpha particle moves with respect to a fixed center; that is, recoil effects are neglected. The fully quantal solution of the problem is discussed. The approach is inspired by the Tohsaki-Horiuchi-Schuck-Ropke wave function concept that has been successfully applied to light nuclei. Shell-model calculations are improved by including four-particle (alpha-like) correlations that are of relevance when the matter density becomes low. In the region where the alpha-like cluster penetrates the core nucleus, the intrinsic bound-state wave function transforms at a critical density into an unbound four-nucleon shell-model state. Exploratory calculations for Po-212 are presented. Such preformed cluster states are very difficult to describe with shell-model calculations. Reasons for the different physics behavior of an alpha-like cluster with respect to a deuteron-like cluster are discussed.