Lower bounds to density-dependent quantities of atoms in terms of logarithmic expectation values

Bounds to different quantities of atomic systems, related in a direct way to the single-particle electron density of the system (such as the kinetic energy, T, the exchange energy in the Dirac-Slater form, Eex, the average radial density, , and the electron density at the nucleus, rho (0)), are given in terms of two radial expectation values of the form and ). The quality of the bounds is numerically studied within the Hartree-Fock framework.