A Singularity in the First-order PY Equation for a Square Well Fluid

TL;DR

This paper demonstrates that the first-order Percus-Yevick equation for a one-dimensional square well fluid exhibits a singularity, independent of well width or depth, revealing fundamental limitations in the perturbative approach.

Contribution

It provides an analytical solution showing singular behavior in the first-order PY equation for a 1D square well fluid, highlighting intrinsic mathematical constraints.

Findings

Singularity occurs in the inverse isothermal compressibility

Well width and depth do not influence the singularity location

Analysis is specifically for a one-dimensional system

Abstract

It is shown that a nearest nieghbor Square Well (SW) potential leads to singular behavior in first order. A solution of the first-order perturbative PY equation for an attractive nearest neighbor square well of width less than the core diameter reveals singular behavior. Neither the width of the well nor the depth of the well affects the location of the singularity in the inverse isothermal compressibility. The analysis is carried out in one dimension.