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\begin{eqnarray*}
E &=& u_{LJ}(r) \qquad r \leq r_s \\
&=& u_{LJ}(r_s) + (r-r_s) u'_{LJ}(r_s) - \frac{1}{6} A_3 (r-r_s)^3 \qquad r_s < r \leq r_c \\
&=& 0 \qquad r > r_c
\end{eqnarray*}
\end{document}