Upper estimates for the electronic density in heavy atoms and molecules

Abstract

We derive an upper estimate for the electronic density ${\rho }_{\Psi }(x)$ in heavy atoms and molecules. While not sharp, on the distances $\gtrsim Z^{-1}$ from the nuclei it is still better than the known estimate $C{Z}^3$ ($Z$ is the total charge of the nuclei, $Z\asymp N$ the total number of electrons).