Bound clusters on top of doubly magic nuclei

TL;DR

This paper derives an effective alpha particle equation for doubly magic nuclei, specifically analyzing $^{212}$Po, and explores how alpha clustering influences nuclear structure beyond traditional shell model descriptions.

Contribution

It introduces a novel approach inspired by the THSR wave function to describe alpha clustering on doubly magic nuclei, incorporating four-particle correlations and analyzing density-dependent state transformations.

Findings

Alpha clustering occurs at low matter densities.

Shell model struggles to describe preformed alpha clusters.

Critical density marks transition from bound to unbound states.

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-R\"{o}pke) 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.