ROBUST SOLUTIONS OF THE YVON-BORN-GREEN EQUATION AT VERY HIGH-DENSITIES .2. LONG-RANGE BEHAVIOR AND SOLUTION MULTIPLICITY

The Yvon-Born-Green equation under the Kirkwood superposition closure is solved for a system of hard spheres at very high densities, using a robust (second-order) convergence routine. In this paper, the range of the pair correlation function solutions is extended to 100 and 200 diameters. The several solutions branches found in an earlier paper (JANGKAMOLKULCHAI, A., GREEN, K. A., and LUKS, K. D., 1989, Molec. Phys., 68, 791) were incompletely mapped. These branches are completed for 50 and 100 diameters up to values of lambda-0 = 4-pi-n-sigma-3 = 20, where the 'close packing' value of lambda-0 is 17.77, and yield multiple results for values of the density parameter-lambda = lambda-0g(2) (1+) on each branch. The interpretation of our results is presented in light of the analysis of solution multiplicity put forth by Lovett for approximate density functional theories.