Pair Distribution Function of a Square-Well Fluid

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.