A new division scheme for the pair potential into long-range and short-rang
e parts is presented, which takes account of the dependence on the density
and makes possible the extraction of the bridge function B(r) in the core r
egion. The calculation of the correlation functions is carried out with the
hybridized mean spherical approximation (HMSA). As attested by the compari
son with the simulation results, HMSA used with this potential separation i
s suitable to produce accurate bridge function and pair correlation functio
n for the Lennard-Jones fluid.