Soft sphere potential

The soft sphere potential is defined as

$\Phi _{12}\left(r\right)=\left\{{\begin{array}{lll}\epsilon \left({\frac {\sigma }{r}}\right)^{n}&;&r\leq \sigma \\0&;&r>\sigma \end{array}}\right.$

where $\Phi _{12}\left(r\right)$ is the intermolecular pair potential between two soft spheres separated by a distance $r:=|\mathbf {r} _{1}-\mathbf {r} _{2}|$, $\epsilon$is the interaction strength and $\sigma$ is the diameter of the sphere. Frequently the value of $n$ is taken to be 12, thus the model becomes the high temperature limit of the Lennard-Jones model .