# Inhomogeneous fluid of penetrable-spheres: application of the random phase approximation

## TL;DR

This paper applies the random phase approximation (RPA) to inhomogeneous fluids of penetrable-spheres, exploring its accuracy and limitations across different interaction regimes and component scenarios.

## Contribution

It extends the RPA application to penetrable-spheres, analyzing its effectiveness in weak and strong coupling limits for one- and two-component fluids.

## Key findings

- RPA's accuracy varies with interaction strength
- Weak-coupling limit shows good RPA performance
- Cancellation of mean-field contributions in two-component fluids

## Abstract

The focus of the present work is the application of the random phase approximation (RPA), derived for inhomogeneous fluids [Frydel and Ma, Phys. Rev. E 93, 062112 (2016)], to penetrable-spheres. As penetrable-spheres transform into hard-spheres with increasing interactions, they provide an interesting case for exploring the RPA, its shortcomings, and limitations, the weak- versus the strong-coupling limit. Two scenarios taken up by the present study are a one-component and a two-component fluid with symmetric interactions. In the latter case, the mean-field contributions cancel out and any contributions from particle interactions are accounted for by correlations. The accuracy of the RPA for this case is the result of a somewhat lucky cancellation of errors.