Effective interactions between nuclear clusters

TL;DR

This paper investigates the effective interactions between nuclear clusters using a cluster model with local nucleon-nucleon forces, revealing how Pauli blocking and force characteristics influence attraction or repulsion among clusters.

Contribution

It provides a detailed analysis of cluster-cluster interactions, highlighting the roles of force range, strength, and parity in binding and repulsion, and connects these to broader quantum systems.

Findings

$d+d$ interaction is repulsive at all distances.

$ ext{alpha}+ ext{alpha}$ and $t+t$ systems are attractive at intermediate distances.

Increasing the range or strength of the attractive $NN$ force enhances cluster attraction.

Abstract

The effective interactions between two nuclear clusters, $d+d$, $t+t$, and $\alpha+\alpha$, are investigated within a cluster model using local nucleon-nucleon~($NN$) forces. It is shown that the interaction in the spin-aligned $d+d$ system is repulsive for all inter-cluster distances, whereas the $\alpha+\alpha$ and spin-aligned $t+t$ systems are attractive at intermediate distances. The Pauli blocking between identical-nucleon pairs is responsible for the cluster-cluster repulsion and becomes dominant in the shallow binding limit. We demonstrate that two $d$-clusters could be bound if the $NN$ force has nonzero range and is strong enough to form a deeply bound $d$-cluster, or if the $NN$ force has both even-parity and odd-parity attraction. Effective dimer-dimer interactions for general quantum systems of two-component fermions are also discussed in heavy-light mass limit, where one component is much heavier than the other, and their relation to inter-cluster interactions in nuclear systems are discussed. Our findings provide a conceptual foundation for conclusions obtained numerically in the literature, that increasing the range or strength of the local part of the attractive nucleon-nucleon interaction results in a more attractive cluster-cluster interaction.