Critical Point in the Percus-Yevick Theory

Some consequences of the Percus-Yevick theory are studies in the neighborhood of the critical point for adhesive hard spheres and for the 6:12 potential (truncated at $6\sigma$). It is shown that the Percus-Yevick theory gives rise to classical behavior at the critical point. In particular, it is shown that for the compressibility equation of state the critical exponents $\gamma$ and $\delta$ are 1 and 3, respectively, and for the energy equation of state the critical exponents $\alpha$ and $\beta$ are 0 and ½, respectively. In addition, the behavior of the Percus-Yevick distribution function in the neighborhood of the critical point is examined and it is shown that for the critical isochore the temperature derivative of the distribution function diverges with a critical exponent of ½ which is independent of $\mathcal{r}$ and that for the critical isotherm the distribution function is a linear function of the density for all $\mathcal{r}$.