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)>=<parallel tor(1)-r(2)parallel to>. An analogous result is also derived for the electron-pair center-of-mass radius <R>=<parallel tor(1)+r(2)parallel to/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 <r(12)> and <r(>)>, and between <R> and <r(>)>/2. (C) 2005 American Institute of Physics.