A geometrical characteristic of the mixing effect induced by non-Abelian Berry's phase -: Case of nuclear quadrupole system rotating about two axes

A geometrical characteristic of the mixing effect induced by the non-Abelian Berry's phase appearing in a nuclear quadrupole system (I = 3/2) rotating about two axes is examined by using the rotating frame formulation. We show that the geometry-dependent parts of the mixing effect appear in the magnitude of the probability amplitude of the spin states and the rate of non-trivial mixing among these states after one period of motion of the system. These values depend only on the geometrical parameters which determine the trajectory traced by the principal-axis defined as the direction of the symmetry axis of the quadrupolar interaction.