RIGOROUS BOUNDS TO THE ATOMIC IONIZATION-POTENTIAL

Several rigorous upper bounds to the atomic ionization potential epsil on are obtained from the Schrodinger equation for atomic systems. They are expressed in terms of radial expectation values [r(alpha)] and/or the electron density and its second derivative at the nucleus, rho(0) and rho''(0) respectively. A numerical study in a non-relativistic Ha rtree-Fock framework is carried out for some atoms. It is shown that t he accuracy of the relationship among epsilon, rho(0) and rho''(0) is higher than 80% for all atoms studied. An interesting property of the bounds in terms of various (r(alpha)] is that they reach the exact val ue of the ionization potential in a limiting case.