Nuclear Collective Motion Within the O( N−1) Invariant Dynamics

Assuming an O( N − 1) symmetry for the interaction term in the N-body Hamiltonian we find a closed subsystem of equations describing the collective motion in a classical way. When studying, in the group geometric way, the mutual correspondency of O( N − 1) invariant approach with the Sp(6, R) collective model we find that the nucleons move along trajectories determined by an effective one-body time-dependent harmonic potential being a function of the collective variables. The relation between the equations for the collective motion and the system of equations found elsewhere for the second-order moments of the Wigner distribution function is discussed. A class of stationary solutions to the collective equations of motion leads to the cranking model with the selfconsistency relations depending on the O( N − 1) scalar part of the potential.