RADIAL-DISTRIBUTION FUNCTION FOR HARD DISKS FROM THE BGY2 THEORY

The Born-Green-Yvon (BGY) hierarchy of equations is truncated by using the Fisher-Kopeliovich approximation for the quadruplet distribution function. The resulting BGY2 equations are solved for hard disks at five different densities. For comparison purposes, the radial distribution functions g(r) from three first-order theories [the BGY1, the Percus-Yevick (PY1), and the convolution-hypernetted-chain (CHNC1) theories] and the Monte Carlo (MC) g(r) are also obtained. At densities less than 47% of the close-packed density, the BGY2 g(r) gives the best agreement with the MC data. At higher densities the BGY2 g(r) agrees well with the MC g(r) at short distances (r≤1.7σ: σ = disk diameter), but the PY1 g(r) appears to be better at larger distances. The results at larger distances are somewhat ambiguous on account of the numerical uncertainties associated with the BGY2 solutions. The pressures predicted from the BGY2 theory are virtually identical to the MC values, demonstrating a rapid convergence of the BGY hierarchy. © 1979 American Institute of Physics.