  We find the first three (even) structure factor moments for a (non-quantum)
one-component Jellium made of particles living in three dimensions and
interacting with a Coulomb pair-potential plus a short-range term with either a
finite range or decaying exponentially fast at large distances. Starting from
the hierarchical Born-Green-Yvon equations we show that they are all form
invariant respect to the addition of the short-range term. We discuss the
relevance of the present study to interpret the failure of the moment sum-rules
of ionic-liquids at criticality.
