Aspects of correlation function realizability

Any pair-correlation function g₂(r) and its associated structure factor S(k) for a many-particle system are trivially constrained by non-negativity conditions: g₂(r)≥0 and S(k)≥0. Unfortunately, no general theory has been available to indicate whether any arbitrary candidate function g₂ that satisfies these two inequalities is actually attainable as the descriptor of short-range order in a specific many-particle system. The work discussed in this paper provides some modest evidence in support of the proposition that only the two non-negativity conditions are required, provided that the particle number density is not too large.