Upper Estimates for Electronic Density in Heavy Atoms and Molecules

We derive an upper estimate for 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 $CZ^3$ ($Z$ is the total charge of the nuclei, $Z\asymp N$ the total number of electrons).