Penetrable square well model

The penetrable square well model is given by :

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

where $\Phi _{12}(r)$ is the intermolecular pair potential, $\epsilon _{r}$ is the hight of the repulsive core and $\epsilon _{a}$ is the attractive well depth, $r$ is the distance between site 1 and site 2 $r:=|\mathbf {r} _{1}-\mathbf {r} _{2}|$.