INTEGRAL-EQUATION APPROACH TO THE CALCULATION OF THE POTENTIAL DISTRIBUTION IN A FLUID

If a test particle in a fluid is subject to a scalar field from each molecule of the fluid, the total field experienced by the test particle from N fluid molecules is a random variable whose probability density is often denoted a potential distribution. We develop a general procedure for the calculation of the potential distribution at a real test particle (a molecule of the fluid), based on a generalized, complex pair distribution function. The procedure involves the generalization of integral-equation theory of classical fluids to encompass a system with a complex interaction potential. The mean-spherical approximation for the same problem is studied to motivate a generalized closure of the integral-equation formalism. With this single approximate ingredient, a closed, coupled pair of non-linear integral equations is obtained and their numerical solution is outlined. For the Gaussian approximation, a simplified version of the same procedure can be used to compute the second moment of the distribution without invoking the Kirkwood superposition approximation. The general method is applied to the calculation of the potential distribution in a one-component plasma.