Vertex Correction Contribution to the Decay Rate of Concentration Fluctuations in Binary Liquid Critical Mixtures

Recently, a self-consistent scheme for the mode-mode coupling theory of critical fluctuations was developed by Kawasaki in which the decay rate of concentration fluctuations for a binary critical mixture was obtained in the simplest approximation of ignoring all the vertex corrections. In this paper we calculate the contribution of the simplest vertex corrections. We find that the corrections are 2.44% for $q\ll \kappa$, and 0.40% for $q\gg \kappa$, where $q$ and $\kappa$ are the wave number and the inverse correlation range of concentration fluctuations, respectively.