# Pair Distribution Function of a Square-Well Fluid

## TL;DR

This paper investigates the structure of a square-well fluid modeling liquid helium-4 using integral equations, calculating pair distribution functions, energies, and structure factors, and comparing results with experiments.

## Contribution

It introduces a method combining the exact two-atom solution with integral equations to analyze the pair distribution function of a square-well fluid.

## Key findings

- Ground state energy estimated at -4.886 K using PY equation
- Calculated pair distribution function and structure factor agree with experimental data
- Demonstrates effectiveness of integral equation methods for fluid structure analysis

## Abstract

The properties of the ground state of liquid $^4$He are studied using a correlated basis function of the form $\prod_{i<j} \psi(r_{ij})$. Here, $\psi(r)$ is chosen as the exact solution of the Schr\"{o}dinger equation for two $^4$He atoms. A hard-sphere plus an attractive square well is used as the interaction potential between $^4$He atoms. The pair distribution function is calculated using approximate integral methods, namely the Percus-Yevick (PY) equation and Hypernetted Chain (HNC) approximation. The values thus obtained are used to calculate the ground state energy, which is found to be -4.886 K using the PY equation. The liquid structure factor is also obtained using the pair distribution function. The values for the pair distribution function and liquid structure factor are compared with experimental results and earlier theoretical calculations.