Virial Expansion of the Solution of the Kirkwood Integral Equation for the Radial Distribution Function of a Fluid

摘要

The solutiongK(r) of the Kirkwood integral equation for the radial distribution function of a fluid is expressed as a series in the density. This series is compared with the virial expansion of the exact radial distribution functiong(r). It is shown that the termg2(r) proportional to the square of the density in the expansion ofgK(r) differs from the corresponding term in the expansion ofg(r). For the special case of hardhyphen;sphere particlesg2K(r) is computed and used to obtain two approximations to the fourth virial coefficient of the equation of state. These results are compared with corresponding results for an approximate Kirkwood equation and for the Bornhyphen;Greenhyphen;Yvon and Percushyphen;Yevick integral equations. The best agreement with exact theory is obtained from the Percushyphen;Yevick equation; the poorest from the Kirkwood equation and the approximate Kirkwood equation.