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When alpha is 0 there will not be a quadrupole contibution and hence there is no orientation wich will lower the energy. If alpha is negative we get the picture given in the slides of the quadrupole contibution. In this case we see that the energy will be lower if the dumbbell if parallel to the z-axis. When alpha is positive the situation is reversed and we will get a lower energy if the dumbbell is in the xy-plane.
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