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\documentstyle[12pt]{article}
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\begin{document}
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$$
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E=-\frac{Umin}{2} \left[ 1+Cos(\theta-\theta_0) \right]
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$$
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\end{document}
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\documentstyle[12pt]{article}
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\begin{document}
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$$
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E=-Umin \frac{Exp(-a U(\theta,\theta_0))-1\right}{Exp(a)-1}\quad\mbox{with}\quad
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U(\theta,\theta_0)=0.5 \left(-cos[\theta-\theta_0]-1 \right)
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$$
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\end{document}
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\documentclass[12pt]{article}
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\begin{document}
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$$
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E = \frac{Umin}{(r_0-r_c)^2} \left[ (r-r_0)^2-(r_c-r_0)^2 \right]
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$$
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\end{document}
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\documentclass[12pt]{article}
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\begin{document}
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$$
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E = \frac{Umin}{(r_0-r_c)^2} \left[ (r-r_0)^2-(r_c-r_0)^2 \right]
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$$
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\end{document}
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\documentstyle[12pt]{article}
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\begin{document}
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$$
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E=-Umin \frac{Exp(-a U(\theta,\theta_0))-1\right}{Exp(a)-1}\quad\mbox{with}\quad
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U(\theta,\theta_0)=0.5 \left(-cos[\theta-\theta_0]-1 \right)
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$$
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\end{document}
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