Bound clusters on top of doubly magic nuclei

Abstract

An effective $\alpha$ particle equation is derived for cases where an $\alpha$ particle is formed on top of a doubly magic nucleus. As an example, we consider ${}^{212}$Po with the $\alpha$ on top of the ${}^{208}$ Pb core. We will consider the core nucleus infinitely heavy, so that the $\alpha$ particle moves with respect to a fixed center, i.e., recoil effects are neglected. The fully quantal solution of the problem is discussed. The approach is inspired by the THSR (Tohsaki-Horiuchi-Schuck-Röpke) 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 ${}^{212}$Po are presented. Such preformed cluster states are only hardly described by shell model calculations. Reasons for different physics behavior of an $\alpha$-like cluster with respect to a deuteron-like cluster are discussed.

24 pages, 5 figures

References in corpus (2)

• Light nuclei quasiparticle energy shift in hot and dense nuclear matter
• Many Body Approach for Quartet Condensation in Strong Coupling

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• Clustering in nuclear environment
• Signatures of an $\alpha$ + core structure in ${}^{44}$Ti + ${}^{44}$Ti collisions at $\sqrt{s_{NN}}=5.02$ TeV by a multiphase transport model
• Three-Dimensional Approach Applied to Quasi-stationary States of Deformed $\alpha$-Emitters
• Pairing versus quarteting coherence length