Soft sphere potential

The soft sphere potential is defined as

${\mathrm{\Phi }}_{12}(r)=\{\begin{array}{ccc}ϵ{(\frac{\sigma }{r})}^n& ;& r\le \sigma \\ 0& ;& r>\sigma \end{array}$

where ${\mathrm{\Phi }}_{12}(r)$ is the intermolecular pair potential between two soft spheres separated by a distance $r:=|{\mathbf{r}}_1-{\mathbf{r}}_2|$, $ϵ$ 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 effectively becomes the high temperature limit of the Lennard-Jones model . If $n\to \mathrm{\infty }$ one has the hard sphere model. For $n\le 3$ no thermodynamically stable phases are found.