A semi-classical, microscopic model for nuclear collective rotation plus RPA

Collective rotation and vibration of deformed nuclei are described semiclassically but microscopically by first transforming the time-dependent Schrodinger equation to a rotating frame, while preserving time-reversal invariance, and then applying a variational method. The rotating-frame axes are chosen to coincide with the principal axes of the expectation of an arbitrary, symmetric second-rank tensor operator Gamma. It is shown that the equations derived for the rotational and vibrational motions decouple completely due to the rotational invariance of the Hamiltonian and diagonality of the expectation of Gamma in the rotating frame. The equations describing the vibration reduce to those of the RPA. The equation describing the rotation generalizes that of the conventional cranking model (CM). The predicted rotation moment of inertia is shown to reduce to that of the CM for special types of particle interactions.