We investigate the spatial structure of dense square-shoulder fluids. To this end, we derive analytical perturbative solutions of the Ornstein–Zernike equation in the low- and high-temperature limits as expansions around the known hard sphere solutions. We then discuss the suitability of perturbative approaches in relation to the Ornstein–Zernike equation. Our analytical expressions are shown to reproduce reasonably well numerical data in the appropriate regimes.

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Indeed, in most cases, the form of p will depend on T through exponential terms that cannot be Taylor expanded in this regime.

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