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 intercluster 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 intercluster 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.

中文翻译：

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核群之间的有效相互作用

两个核群之间的有效相互作用， $d+d， Ť+Ť$， 和 $\alpha +\alpha$，是在使用局部核仁-核仁（$ññ$） 势力。结果表明，自旋排列中的相互作用$d+d$ 系统对所有群集间距离都具有排斥性，而 $\alpha +\alpha$ 并旋转对齐 $Ť+Ť$系统在中距离时很有吸引力。相同核子对之间的Pauli阻滞负责簇-簇排斥，并在浅结合极限中占主导地位。我们证明了两个$d$ 如果 $ññ$ 力具有非零范围，并且足够强大以形成深度约束 $d$ 集群，或者 $ññ$力具有偶数奇偶吸引和奇数奇偶吸引。还讨论了重组分轻质极限下两组分费米子一般量子系统的有效二聚体-二聚体相互作用，其中一个组分比另一组分重得多，并讨论了它们与核系统中簇间相互作用的关系。我们的发现为从文献中数字得出的结论提供了概念基础，即增加有吸引力的核子-核子相互作用的局部范围或强度会导致更有吸引力的簇-簇相互作用。