The motion of a nucleus with an intrinsic multiple moment, in particular an intrinsic hexadecapole (16 poles) moment in external electrostatic multiple (triple) field gradients, is studied from a classical point of view. It is shown that in the classical approximation the angular-momentum vector of a nucleus with an intrinsic hexadecapole moment may precess about the direction of greatest triple field gradient. The formulation of the theory can be generalized to the higher-order multipole cases. For the hexadecapole case, the classical precession frequencies are found to be related to the quantum mechanical dipole transition frequencies.

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