SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 3493-3519, January 2021.
We consider two nonlocal variational models arising in physical contexts. The first is the Thomas--Fermi--Dirac--von Weizsäcker (TFDW) model, introduced in the study of ionization of atoms and molecules, and the second is the liquid drop model with external potential, proposed by Gamow in the context of nuclear structure. It has been observed that the two models exhibit many of the same properties, especially in regard to the existence and nonexistence of minimizers. We show that, under a “sharp interface” scaling of the coefficients, the TFDW energy with constrained mass $\Gamma$-converges to the liquid drop model for a general class of external potentials. Finally, we present some consequences for global minimization of each model.

中文翻译：

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TFDW 能量收敛到液滴模型

SIAM 数学分析杂志，第 53 卷，第 3 期，第 3493-3519 页，2021 年 1 月。
我们考虑了物理环境中出现的两个非局部变分模型。第一个是 Thomas--Fermi--Dirac--von Weizsäcker (TFDW) 模型，在原子和分子的电离研究中引入，第二个是具有外势的液滴模型，由 Gamow 在背景下提出核结构。已经观察到，这两个模型表现出许多相同的属性，特别是关于最小化器的存在和不存在。我们表明，在系数的“锐界面”缩放下，具有约束质量 $\Gamma$ 的 TFDW 能量收敛到一般类型的外部电位的液滴模型。最后，我们提出了每个模型全局最小化的一些结果。