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$$ 
  E = -0.5 K R_0^2  \ln \left[ 1 - \left(\frac{r}{R_0}\right)^2\right] +
  4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - 
    \left(\frac{\sigma}{r}\right)^6 \right] + \epsilon
$$

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