INTERELECTRONIC MOMENTS OF ATOMIC SYSTEMS

The electron-pair density I(u) of an atomic system, u being the intere lectronic vector r12, may be completely characterized by means of the moments (u9), q>-3, defined as [u(q)]=integral u(q)I(u)u=4pi integral- infinity/0 u(q+2)h(u)du, where h(u) is the spherical average of I(u). These interelectronic quantities are basic elements in the study of th e electron-electron correlation problem. Here it is analytically shown how a moment of a given order q is bounded from below in terms of mom ents with orders higher than or lower than q. To do that, the so-calle d extended-correlation cusp condition [i.e., h (u) - h'(u) greater-tha n-or-equal-to 0 for u greater-than-or-equal-to 0], recently found for various atomic systems in a variational Hylleraas-type framework, is u sed. The lower bounds turn out to be often very accurate.