Exact Solution of the First-Order Perturbed Percus-Yevick Equation for Arbitrary Pair Potentials (Classic Reprint)

Exact first‑order insight into how small tail forces reshape core correlations

This book develops a method to extend the Percus–Yevick equation, solved exactly for hard cores, to include a tail potential of arbitrary range. It shows how a first‑order perturbation leads to explicit formulas for the direct correlation function inside the core and the pair correlation function outside it. The approach blends distribution‑function theory with practical solutions, and it ties the results to known models like Debye–Hückel and Yukawa tails. The work also illustrates how linear responses emerge when tail effects are added and tests these ideas against exact statistical mechanics.

In this edition, you’ll see the step‑by‑step reduction of the perturbed equation to a solvable form, the construction of S‑neighbor representations, and the way boundary conditions at the hard core are used to determine constants of integration. The content connects abstract theory to explicit models, including a simple application to the glue model of Baxter and a discussion of when linear behavior appears in tails. Readers with a background in statistical mechanics or liquid‑state theory will gain a concrete toolkit for analyzing how long‑range interactions alter core structure.

• Derivation of the first‑order direct correlation function inside the hard core and the first‑order pair correlation outside.
• Reduction of the perturbed equation to a fourth‑order differential form with clear boundary conditions.
• Examples that connect to Debye–Hückel, Yukawa, double Yukawa, and power‑law tail potentials.
• Discussion of linearity in tail models and conditions for first‑order phase behavior.

Ideal for readers of advanced statistical mechanics and liquid‑state theory who want a rigorous yet practical path from the hard‑core Percus–Yevick solution to perturbed, long‑range interacting systems.