For alpha<0 the lowest energy configuration is reached for the dumb-bell in the xy-plane making a 90 degree angle with the z-axis. For alpha > 0 the lowest energy configuration is reached for the dumb-bell parallel to the z-axis. For alpha = 0 we reach the lowest energy configuration for every orientation of the dumb-bell. (This is all ofcourse when only looking at the quadrupole corrections and no possible higherorder corrections.)