Lowest energy configurations double ring

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    ErwinVanBuylaere
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    -For alpha>0: lowest energy configuration is when the dumbbell is parallel to the z-axis (theta = 0 or theta = pi)
    -For alpha=0: any configurations yields the same energy
    -for alpha<0: lowest energy configuration is when the dumbbell is perpendicular to the z-axis (theta = ± pi/2)

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