BOUNDS TO SOME LOCAL ELECTRON-PAIR PROPERTIES WITH APPLICATION TO 2-ELECTRON IONS

New bounds to the maximum characteristics u(max) and h(max) = h (u(max)) of the spherically averaged electron-pair density h(u) and to the electron-electron coalescence h(0) = [delta(u)] of a many-electron system are shown in a rigorous manner (i.e., no approximate wave functions were used). The resulting rigorous inequalities also allow one to bound a given interelectronic moment [u(beta)] from above and from below. In particular, an interesting inequality is obtained for the electron-electron repulsion energy E(ee) of an N-electron system: 2pih(0)u(max)2 less-than-or-equal-to E(ee) less-than-or-equal-to 3N(N-1)/4u(max). For completeness, just to have an idea of the worth of these results, some of the rigorous inequalities are numerically studied for two-electron ions with nuclear charge Z = 1, 2, 3, 4, 5, and 10 using a highly accurate electron-pair density h(u) constructed from the 204-term Hylleraas wave functions. The accuracy is found to increase, generally, with increasing Z and decreasing order beta of the involved moments.