Atomic charge density at the nucleus and inequalities among radial expectation values

A self-consistent study of the function f(r)={ρ}(r)+{ρ}'(r)/(2Z), where {ρ}(r) is the spherically averaged electron density of the ground state of an atom, shows that f(r){≥}0 everywhere. This allows us to obtain several inequalities relating the atomic electronic density at the nucleus {ρ}(0) and atomic radial expectation values 〈r^α〉. In particular, we generalize upper bound found by Hoffmann-Ostenhof, Hoffmann-Ostenhof, and Thirring [J. Phys. B 11, L571 (1978)] to {ρ}(0). We also obtain accurate inequalities between the radial expectation values 〈r^α〉 of atomic systems.