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\begin{eqnarray*}
\phi\left(r\right) & = & 4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - 
                       \left(\frac{\sigma}{r}\right)^6 \right] \\
E\left(r\right) & = & \phi\left(r\right)  - \phi\left(R_c\right) - \left(r - R_c\right) \left.\frac{d\phi}{d r} \right|_{r=R_c}       \qquad r < R_c 
\end{eqnarray*}                           

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