Relativistic Strong Scott Conjecture: A Short Proof

R. Frank, Konstantin Merz, H. Siedentop
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引用次数: 5

Abstract

We consider heavy neutral atoms of atomic number $Z$ modeled with kinetic energy $(c^2p^2+c^4)^{1/2}-c^2$ used already by Chandrasekhar. We study the behavior of the one-particle ground state density on the length scale $Z^{-1}$ in the limit $Z,c\to\infty$ keeping $Z/c$ fixed. We give a short proof of a recent result by the authors and Barry Simon showing the convergence of the density to the relativistic hydrogenic density on this scale.
相对论强斯科特猜想:一个简短的证明
我们考虑原子序数为$Z$的重中性原子,用钱德拉塞卡已经使用过的动能$(c^2p^2+c^4)^{1/2}-c^2$来建模。在保持$Z/c$固定的极限$Z,c\to\infty$下,我们研究了单粒子基态密度在长度尺度$Z^{-1}$上的行为。我们给出了作者和Barry Simon最近的一个结果的简短证明,该结果表明密度在这个尺度上收敛于相对论性的氢密度。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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