Penetrable sphere model

The penetrable sphere model is given by :

${\mathrm{\Phi }}_{12}(r)=\{\begin{array}{ccc}ϵ& ;& r<\sigma \\ 0& ;& r\ge \sigma \end{array}$

where ${\mathrm{\Phi }}_{12}(r)$ is the intermolecular pair potential, $ϵ$ 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 $n\to \mathrm{\infty }$. In the limit $ϵ\to \mathrm{\infty }$ one has the hard sphere model.