Bounds to electron-pair relative and center-of-mass radii in many-electron atoms

When the electron-electron interaction is explicitly considered in many-electron atoms, the average electron radius (r) splits into the inner (r<) and outer (r>) radii. It is shown that the sum and difference of these radii constitute upper and lower bounds, respectively, to the electron-pair relative distance r(12)=(/r1-r2/). An analogous result is also derived for the electron-pair center-of-mass radius (R)=(/r1+r2//2). For the 102 atoms He through Lr in their ground states, the tightness of these bounds is numerically examined at the Hartree-Fock limit level. Good linear correlations are observed between (r12) and (r>), and between (R) and (r>)/2.