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

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