arXiv 2603.294822026-03physics.atom-phmath.CAphysics.comp-ph

Thomas-Fermi方程再探：Majorana主题的一种变奏

Thomas-Fermi equation revisited: A variation on a theme by Majorana

Beijing Institute of Technology（北京理工大学）；National University of Singapore（新加坡国立大学）

Berthold-Georg Englert

备注：: Dedicated to Goong Chen on the occasion of his 75th birthday; 16 pages, 4 figures, 4 tables; v2 (18 pages) has an additional section and some minor errors are corrected

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AI总结：

本文回顾Majorana对Thomas-Fermi方程的缩放性质应用方法，重新计算中性原子和弱电离原子解中的积分及其他重要物理量，并与1980年代的数值结果进行比较。

摘要：

Majorana找到了利用Thomas-Fermi方程的缩放性质，将这个二阶微分方程转换为一阶方程的方法。我们探讨了该方法在熟悉中性原子解中的应用，并将其扩展到与弱电离原子相关的解中。各种积分和其他对原子物理重要的量被重新计算，并与1980年代通过更繁琐的数值方法得到的结果进行了比较。

英文摘要：

Majorana found a way to exploit the scaling properties of the Thomas-Fermi equation for converting this second-order differential equation into one of first order. We explore his method for the familiar neutral-atom solution and extend it to the solution that is relevant for weakly ionized atoms. Various integrals and other quantities with importance for atomic physics are recalculated and their values compared with the ones obtained in the 1980s by more tedious numerical procedures.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。