Statistical properties of two interacting soft spheres in a hard spherical pore

The structure and thermodynamics of two soft spheres, whose interactions include the soft repulsion and attraction, confined in a hard spherical pore have been considered. The exact partition function, one-body density, and equation of state have been obtained using the Fourier transform method. The pore-size and potential dependence of the structural and thermodynamic properties have been investigated. The two penetrable square-well spheres shows a negative compressibility of the van der Waals type, which imitates the phase transition of many particle system. The van der Waals instability for two penetrable square-well spheres has been studied.