Clusters in systems as diverse as metal atoms, virus proteins, noble gases, and nucleons have properties that depend sensitively on the number of constituent particles. Certain numbers are termed 'magic' because they grant the system with closed shells and exceptional stability. To this point, magic number clusters have been exclusively found with attractive interactions as present between atoms. Here we show that magic number clusters exist in a confined soft matter system with negligible interactions. Colloidal particles in an emulsion droplet spontaneously organize into a series of clusters with precisely defined shell structures. Crucially, free energy calculations demonstrate that colloidal clusters with magic numbers possess higher thermodynamic stability than those off magic numbers. A complex kinetic pathway is responsible for the efficiency of this system in finding its minimum free energy configuration. Targeting similar magic number states is a strategy towards unique configurations in finite self-organizing systems across the scales.

中文翻译：

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幻数胶体簇是最小的自由能结构。

诸如金属原子，病毒蛋白，稀有气体和核子之类的系统中的簇具有敏感地取决于组成粒子数量的特性。某些数字被称为“魔术”，因为它们使系统具有封闭的外壳和出色的稳定性。至此，已经发现魔数簇具有原子间存在的有吸引力的相互作用。在这里，我们证明了魔术数簇存在于有限的软物质系统中，相互作用可忽略不计。乳液液滴中的胶体粒子自发地组织为一系列具有精确定义的壳结构的簇。至关重要的是，自由能计算表明具有魔术数的胶体团簇比具有魔术数的胶体团簇具有更高的热力学稳定性。复杂的动力学路径是该系统寻找最小自由能构型的效率的原因。针对相似的魔术数字状态，是一种在整个规模的有限自组织系统中实现独特配置的策略。