Inner and outer radial density functions in many-electron atoms

When any two electrons are considered simultaneously, the radial density function D(r) in many-electron atoms is shown to be rigorously separated into inner D-<(r) and outer D->(r) radial densities. Accordingly, radial properties such as the electron-nucleus attraction energy V-en and the diamagnetic susceptibility chi(d) are the sum of the inner and outer contributions. The electron-electron repulsion energy V-ee has an approximate relation with the minus first moment of the outer density D->(r). For the 102 atoms He through Lr in their ground states, different characteristics of local maxima in the radial densities D-<(r), D->(r), and D(r) are reported based on the numerical Hartree-Fock wave functions. Relative contributions of the inner and outer components to V-en and chi(d) are also discussed for these atoms.