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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*}                           


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