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

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