Soft sphere potential

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The soft sphere potential is defined as

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

where $\Phi_{12}\left(r \right)$ is the intermolecular pair potential between two soft spheres separated by a distance $r := |\mathbf{r}_1 - \mathbf{r}_2|$ , $ε$ is the interaction strength and $σ$ 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 ^[1]. If $n\rightarrow \infty$ one has the hard sphere model. For $n \le 3$ no thermodynamically stable phases are found.