NONLINEAR DYNAMICS AND NUCLEAR COLLECTIVE MOTION

To understand the exceedingly rich structure of the quantum excited st ates in nuclei, the importance of exploring the complex structure of t he time-dependent Hartree-Fock (TDHF) manifold is discussed. It is sho wn that various ideas developed in the general theory of non-linear dy namics (e.g., non-linear resonance, elliptic and hyperbolic fixed poin ts, order-to-chaos transition, etc.,) play a decisive role in obtainin g analytic information on the quantum excited states, provided that th e corresponding TDHF manifold has a simple potential energy surface (P ES) with only one minimum. When the TDHF manifold has a PES with more than two local minima, one is involved into an important problem relat ed with adiabatic versus diabatic collective potentials. The adiabatic collective potential is usually obtained when one numerically solves the constrained Hartree-Fock (CHF) equation within a constraining coor dinate space, which has a limited number of degrees of freedom. To exp lore the dynamical relation between the adiabatic and diabatic single- particle states, one has to analyze the CHF method within the full TDH F manifold, which includes the constraint coordinate space. It turns o ut that the solutions of the CHF equation give many differentiable sur faces in the TDHF manifold. By using the differentiable property of th e CHF solutions in the TDHF manifold, a new method for reaching variou s HF points is discussed.