TIGHT RIGOROUS BOUNDS TO ATOMIC INFORMATION ENTROPIES

The position-space entropy S(rho) and the momentum-space entropy S(gamma) are two increasingly important quantities in the study of the structure and scattering phenomena of atomic and molecular systems. Here, an information-theoretic method which makes use of the Bialynicki-Birula and Mycielski's inequality is described to find rigorous upper and lower bounds to these two entropies in a com.pact, simple and transparent form. The upper bounds to S(rho) are given in terms of radial expectation values [r(alpha)] and/or the mean logarithmic radii [ln r] and [(ln r)2], whereas the lower bounds depend on the momentum expectation values [p(alpha)] and/or the mean logarithmic momenta [ln p] and [(ln p)2]. Similar bounds to S(gamma) are also shown in a parallel way. A near Hartree-Fock numerical analysis for all atoms with Z less-than-or-equal-to 54 shows that some of these bounds are so tight that they may be used as computational values for the corresponding quantities. The role of the mean logarithmic radius [ln r] and the mean logarithmic momentum [ln p] in the improvement of accuracy of the aforementioned bounds is certainly striking.