Coexistence of regular undamped nuclear dynamics with intrinsic chaoticity.

We study the conditions under which the nucleons inside a deformed nucleus can undergo chaotic motion. To do this we perform self-consistent calculations in semiclassical approximation utilizing a multipole-multipole interaction of the Bohr-Mottelson type for quadrupole and octupole deformations. For the case of harmonic and non-harmonic static potentials, we find that both multipole deformations lead to regular motion of the collective coordinate, the multipole moment of deformation. However, despite this regular collective motion, we observe chaotic single particle dynamics. PACS: 21.10.Ky, 21.10.Re, 21.60.-n, 24.60.Lz The question about the origin of dissipation in collective motion of finite Fermi systems [1] such as atomic nuclei or small metallic clusters is an intriguing and up to now not completely satisfactorily solved problem. For example, the mutual balance of one-body and two-body processes is still a question of debate. For the case of one-body dissipation and friction in nuclear dynamics, Swiatecki and coworkers [2, 3, 4, 5] have developed this picture: particles which move in a shape-deformed container are reflected from the (moving) walls, and due to parts of it having positive curvature (for higher multipole moments) the particles very quickly loose their coherence, thus inducing pseudo-random motion, i.e. heat, into the system. At the same time the shape oscillation is very much slowed down. Blocki et al. [4, 5] consider a purely classical gas of particles contained in a deformed billiard. The only similarity with a Fermi gas comes from the fact that initially the particles’ momenta are distributed within a Fermi sphere. The walls of the container undergo periodic shape oscillations with a frequency much smaller than a typical single particle frequency. In the interior of the container the particles move on linear trajectories. They study the particle kinetic energy increase as a function of time and find that for ellipsoidal shape deformations (l = 2) the particles act as a classical Knudsen gas [6], i.e. the total kinetic energy increase over an entire shape oscillation period is 0. However, for l ≥ 3 the kinetic energy in the single particle