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 $r:=|\mathbf {r} _{1}-\mathbf {r} _{2}|$, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \epsilon } is the interaction strength and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n\rightarrow \infty} one has the hard sphere model. For Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n \le 3} no thermodynamically stable phases are found.