A test-particle method for the calculation of the three-particle distribution function of the hard-sphere fluid:: density functional theory and simulation

The three-particle distribution function g((3)) of the homogeneous hard-sphere fluid is studied by means of the test-particle method of Percus. We consider an inhomogeneous situation in which the position of two particles is fixed and the inhomogeneous density profile that arises is related to g((3)). The profile is calculated via Monte Carlo (MC) simulation and density functional theory (DFT). The results of the simulation are compared with standard MC results for the homogeneous fluid in order to check the numerics. The results of DFT are compared with MC data, showing a significant improvement over the well-known superposition approximation of Kirkwood.