Application of classical formulations of quantum mechanical time-dependent variational principles to the shell and collective models

The pairing off of two-dimensional vortices with opposite orientation and constant strength has its analog in nuclear pairing forces, where the constant vortex strength corresponds to the projection of the angular momentum on the symmetry axis. This occurs as a second-order phase transition for a critical value of the interaction strength. Interactions leading to configurational mixing are analyzed in terms of Euler's equation of an asymmetrical top in the strong coupling limit. The dynamics of pairing forces, configurational mixing, and deformation alignment, due to quadrupole forces and the coupling of the total angular momentum to the intrinsic spin of the odd nucleon, are analyzed by imposing constraints on the coefficients of a quadratic rotational Hamiltonian. Processes leading to deformation alignment give rise to precessional motion of the total angular momentum about the nuclear symmetry axis.