Bounds on the decay of electron densities with screening

Differential inequality techniques are applied in the derivation of the following upper bound for the one-electron density ρ(x) of atomic or molecular systems: √ρ(x)≤C(1+r)^(Z-n+1)√2ε-1e^-√2εr where $r=|x|$, ε is the first ionization potential, n the number of electrons, and Z the nuclear charge (or the sum of nuclear charges in the molecular case). Related bounds on the decay of the k-electron density and the wave function itself are also given. These bounds improve upon previous results [TH-O, MH-O, RA Phys. Rev. A 18, 328 (1978)]. For the ground state of a two-electron atom (ion) we report a lower bound to ρ(x) which exhibits the same functional form as the upper bound. Finally, for this case we give a lower bound to the wave function itself which shows essentially the same decay as the corresponding upper bound.