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arXiv · 2009.02474

Relativistic Strong Scott Conjecture: A Short Proof

Rupert L. Frank·Konstantin Merz·Heinz Siedentop
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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.

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Rupert L. Frank, Konstantin Merz, Heinz Siedentop. 2020-09-05. Relativistic Strong Scott Conjecture: A Short Proof. https://doi.org/10.1142/9789811272158_0003

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