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The penetrable-sphere fluid in the high-temperature, high-density limit

We consider a fluid of $d$-dimensional spherical particles interacting via a pair potential $ϕ(r)$ which takes a finite value $ε$ if the two spheres are overlapped ($r<σ$) and 0 otherwise. This penetrable-sphere model has been proposed to describe the effective interaction of micelles in a solvent. We derive the structural and thermodynamic functions in the limit where the reduced temperature $k_BT/ε$ and density $ρσ^d$ tend to infinity, their ratio being kept finite. The fluid exhibits a spinodal instability at a certain maximum scaled density where the correlation length diverges and a crystalline phase appears, even in the one-dimensional model. By using a simple free-volume theory for the solid phase of the model, the fluid-solid phase transition is located.