We present a class of closures specifically designed to satisfy the zero-separation theorems for the correlation functions y(r) (the cavity function), gamma(r)=h(r)-C(r) (the indirect correlation), and B(r) (the bridge function) at coincidence r=0 for soft-sphere pair potentials. The rationale is to ensue the correct behavior of these correlation functions inside the core r

Keywords:DIRECTIONAL ATTRACTIVE FORCES;THERMODYNAMIC PERTURBATION-THEORY;INTEGRAL-EQUATIONS;CLASSICAL FLUIDS;SIMPLE LIQUIDS;HARD-SPHERES;MIXTURES;STATE;POLYMERIZATION;SIMULATION