The HNC and PY integral equations provide the pair distribution functions of the particles in a classical fluid, even for very high coupling strengths.
The CHNC method provides an approximate "escape" from these difficulties, and applies to regimes beyond perturbation theory.
In Robert B. Laughlin's famous Nobel Laureate work on the fractional quantum Hall effect, an HNC equation was used within a classical plasma analogy.
[3] The value of the method lies in its ability to calculate the interacting pair distribution functions g(r) at zero and finite temperatures.
Comparison of the calculated g(r) with results from Quantum Monte Carlo show remarkable agreement, even for very strongly correlated systems.