Convergence of the Nosanow cluster expansion assuming the Wu-Krumhansl correlation function

Abstract

We consider the convergence and energy-bounding properties of the Nosanow cluster expansion in combination with the pair correlation function employed by Wu and Krumhansl. We employ the transfer-integral method and one-dimensional model quantum solid developed by Trickey and Nuttall. The results of our investigation differ somewhat from those of Wu and Krumhansl. Their correlation function yields a minimum value of the cluster approximation to the cohesive energy for the model system which is significantly different from the rigorous variational result. The cluster approximation gives a substantially different best value of the pair function variation parameter than that determined by the transfer integral. The cluster-expansion convergence rates reflect these difficulties. Restriction of the variation of the single-particle functions to a parametrized Gaussian eliminates these discrepancies. Such nonphysical behavior is a priori possible with any choice of pair function.