Complex Cluster Integrals for an Augmented Gaussian Gas

摘要

It has been shown by Montroll, Berlin, and Hart that complex cluster integrals can be evaluated very easily if the actual Ursellhyphen;Mayerffunction is replaced by a Gaussian. The possibility of using a more realistic function was suggested by the same authors. We have carried out the actual calculation of the cluster integrals for four particles and determined the dependence of the parameters on the temperature. It is shown that the integration problem is reduced to the evaluation of higher derivatives of the so called graph determinant. The method can also be used to calculate the effective interaction between two articulation points of a complicated cluster. The importance of the nonring diagrams is stressed by some numerical estimates of discrepancy between actual condensation and the divergence of the ring series.