Equi-g(r) sequence of systems derived from the square-well potential

We introduce the idea of an “equi-g(r) sequence.” This consists of a series of equilibrium many-body systems which have different number densities ρ but share, at a given temperature, the same form of pair correlation function, termed “target g(r).” Each system is defined by a pair potential indexed by ρ as in uρ(r). It is shown that for such a sequence a terminal density ρ⋆ exists, beyond which no physically realizable system can be found. As an illustration we derive explicit values of ρ⋆ for target g(r) that is based on a square-well potential in the limit ρ→0. Possible application of this terminal phenomenon to the investigation into limiting amorphous packing structures of hard spheres is proposed. Virial expansions of uρ(r) and pressure are carried out and compared with the corresponding expressions for imperfect gas. The behaviors of uρ(r) and pressure close to ρ=ρ⋆ are examined as well, and associated exponents extracted when they exist. The distinction between equi-g(r) sequence and the related, recently introduced concept of “iso-g(2) process” is briefly discussed.