NONLINEAR RESONANCE IN THE TIME-DEPENDENT HARTREE-FOCK MANIFOLD

In order to try to open a new scope to explore the mutual dependence b etween the single-Particle and collective modes of motion near to the level crossing region, a general method is developed to investigate th e nonlinear resonant structure of the time-dependent Hartree-Fock (TDH F) manifold, without depending on the adiabatic assumption. By using t he Lie canonical transformation with the Deprit perturbation treatment , in this method, the maximal integrable-form representation of the TD HF manifold is introduced. This representation plays an essential role in exploring the nonlinear resonant structure of the TDHF manifold, w hich characterizes complex topology of the manifold. Aiming at relatin g the nonlinear resonance in the TDHF manifold with the dynamics betwe en the single-particle and collective modes of motion near to the leve l crossing region, structure of the TDHF wave function is investigated . It is clarified that an isolated nonlinear resonant region of the TD HF manifold is characterized by a local constant of motion (dynamical symmetry) and generates a new type of dynamical stable single-Slater-d eterminent states, which is topologically different from the TDHF stat es near the HF ground state, and cannot be reached by the conventional static Hartree-Fock method, constrained Hartree-Fock method, nor the adiabatic TDHF theories. One may expect that the appearance mechanism of the new dynamical stable single-Slater-determinant states gives us a new scope for understanding occurrence mechanism of a variety of col lective sideband structure near to the level crossing region.