Abstract

A molecular dynamics simulation of a system of massive charged particles on a compensating homogeneous background confined by a spherical surface has been carried out. A crystallized cluster is a set of nested spherical shells of almost the same structure and a core. It is shown that cluster melting is a combination of shell and core melting. It is found that the values of the Coulomb coupling parameter Γ corresponding to these two types of melting do not depend on the cluster size. Methods for determining Γ based on the Wigner–Seitz cell model are discussed. It is shown that the estimate based on the root-mean-square deviation of a particle from the center of its cell is unreliable due to the self-diffusion of particles. A relation is proposed that defines Γ in terms of the root-mean-square velocity and acceleration of the particle and does not include the root-mean-square deviation of the particle from its average position. It is shown that this relation is satisfied with high accuracy not only for the crystallized, but also for the liquid state. Thus, it has been demonstrated that the Wigner–Seitz cell model is applicable to the strongly inhomogeneous system under consideration.

中文翻译：

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维格纳-塞茨盒近似与库仑簇的相关性

摘要

对球面限制的补偿均匀背景上的大量带电粒子系统进行了分子动力学模拟。结晶团簇是一组具有几乎相同结构和核心的嵌套球壳。结果表明，团簇熔化是壳熔化和芯熔化的结合。发现这两种熔化类型对应的库仑耦合参数Г的值并不依赖于团簇尺寸。讨论了基于 Wigner-Seitz 盒模型确定 Γ 的方法。结果表明，由于粒子的自扩散，基于粒子与其细胞中心的均方根偏差的估计是不可靠的。提出了一种关系式，该关系式根据粒子的均方根速度和加速度来定义 Γ，并且不包括粒子与其平均位置的均方根偏差。结果表明，这种关系不仅对于结晶态而且对于液态都满足高精度。因此，已经证明维格纳-塞茨盒模型适用于所考虑的强非均匀系统。