Lower bounds on the electronic charge and momentum densities of spherical atoms at the origin

Lower bounds to the electronic charge density of spherical atoms at the origin, ρ(0), are given in terms of the radial expectation values 〈$r^{\alpha }$〉 and the average electron density 〈ρ〉. Similar bounds are also valid in momentum space. Previous results are also improved, and several relationships among ρ(0), the Coulomb energy, and 〈$r^{\alpha }$〉 values have been derived. The quality of the bounds is analytically discussed and numerically studied within the Hartree-Fock framework.