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 e
lectron-electron coalescence h(0) = [delta(u)] of a many-electron syst
em are shown in a rigorous manner (i.e., no approximate wave functions
were used). The resulting rigorous inequalities also allow one to bou
nd 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-elec
tron 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 Hyl
leraas wave functions. The accuracy is found to increase, generally, w
ith increasing Z and decreasing order beta of the involved moments.