NEW BOUNDS FOR THE ATOMIC CHARGE AND MOMENTUM DENSITIES AT THE ORIGIN

The "Stieltjes moment problem" technique together with the positivity and monotonic decreasing properties of the electronic density of an atom is used to find new and more accurate lower bounds for the charge density at the nucleus and the momentum density at the origin, in terms of radial and momentum expectation values, respectively. Bounds depending on two and three expectation values are given explicitly and a Hartree-Fock study of their quality is carried out. Also, the behavior of the new bounds at large Z's is discussed. The Stieltjes technique allows to find lower bounds of better accuracy by including expectation values of higher order.