Penetrable sphere model

The penetrable sphere model is given by :

$\Phi _{12}\left(r\right)=\left\{{\begin{array}{ccc}\epsilon &;&r<\sigma \\0&;&r\geq \sigma \end{array}}\right.$

where $\Phi _{12}(r)$ is the intermolecular pair potential, $\epsilon$ is the hight of the repulsive core, $r$ is the distance between site 1 and site 2 $r:=|\mathbf {r} _{1}-\mathbf {r} _{2}|$ and $\sigma$ is the radius of the core. Note: an earlier, different, penetrable sphere model was proposed, but is now known as the Widom-Rowlinson model. This model can be seen as the limiting case of the Gaussian overlap model where $n\rightarrow \infty$. In the limit $\epsilon \rightarrow \infty$ one has the hard sphere model.