强Scott猜想的证明
Proof of the Strong Scott Conjecture for Chandrasekhar Atoms
摘要：
我们考虑一个原子序数为$Z$的大的中性原子，通过假设色散关系$\sqrt{c^2p^2+c^4}$考虑相对论效应。在保持$Z/c$不变的极限$Z,c\to\infty$下，研究了长度标度$Z^{-1}$上的单粒子基态密度的行为，发现球平均密度和所有单个角动量密度分别收敛于相对论类氢密度.这证明了强斯科特猜想的相对论性原子的推广，并显示，特别是，相对论效应发生在靠近原子核。一路上，我们证明了相对论性类氢密度的上限。
英文摘要：
We consider a large neutral atom of atomic number $Z$, taking relativistic effects into account by assuming the dispersion relation $\sqrt{c^2p^2+c^4}$. 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 and find that the spherically averaged density as well as all individual angular momentum densities separately converge to the relativistic hydrogenic ones. This proves the generalization of the strong Scott conjecture for relativistic atoms and shows, in particular, that relativistic effects occur close to the nucleus. Along the way we prove upper bounds on the relativistic hydrogenic density.
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