This aspect will be treated by applying the Hamilton
equations of motion
to the point particles modeling the nucleons with spin, moving in the deformed
Woods-Saxon potential. We intend to investigate the role of the diffusivity
of the nuclear potential as a chaos-generating factor, together with the
spin-orbit interaction and the effect of the exotic deformations such as
exotic octupole deformations of various symmetries, and super- and
hyper-deformations. We will calculate the Lyapunov exponents and perform
the analysis of the time-averages of physical observables in order to
investigate the effect of symmetries on the "stronger or weaker" manifestations
of classical chaos on particles moving in the nuclear-type realistic
potentials.
Within the similar approach we are going to introduce a model of a two-body
residual interaction (of the pairing type) and compare the effect of such
an interaction with the realistic interaction strength on the chaotic properties
of the classical trajectories. In such a way the relative importance of the
typical
"chaos generating nuclear mechanisms" such as: diffusivity and deformation of
the central nuclear potential, varying intensity of the nuclear spin-orbit
effect and the two-body pairing forces will be estimated.
The above purely classical tests will be compared to the
analogous tests
obtained with the help of the Schrödinger equation with the hamiltonian
of exactly the same properties (form of the potential, types of deformations,
symmetries, spin-orbit strengths).