Chaos modified wall formula damping of the surface motion of a cavity undergoing fissionlike shape evolutions

The chaos weighted wall formula developed earlier for systems with partially chaotic single particle motion is applied to large amplitude collective motions similar to those in nuclear fission. Considering an ideal gas in a cavity undergoing fission-like shape evolutions, the irreversible energy transfer to the gas is dynamically calculated and compared with the prediction of the chaos weighted wall formula. We conclude that the chaos weighted wall formula provides a fairly accurate description of one body dissipation in dynamical systems similar to fissioning nuclei. We also find a qualitative similarity between the phenomenological friction in nuclear fission and the chaos weighted wall formula. This provides further evidence for one body nature of the dissipative force acting in a fissioning nucleus.Comment: 8 pages (RevTex), 7 Postscript figures, to appear in Phys.Rev.C., Section I (Introduction) is modified to discuss some other works (138 kb

Chaoticity and Shell Effects in the Nearest-Neighbor Distributions

Statistics of the single-particle levels in a deformed Woods-Saxon potential is analyzed in terms of the Poisson and Wigner nearest-neighbor distributions for several deformations and multipolarities of its surface distortions. We found the significant differences of all the distributions with a fixed value of the angular momentum projection of the particle, more closely to the Wigner distribution, in contrast to the full spectra with Poisson-like behavior. Important shell effects are observed in the nearest neighbor spacing distributions, the larger the smaller deformations of the surface multipolarities.Comment: 10 pages and 9 figure

One-body dissipation and chaotic dynamics in a classical simulation of a nuclear gas

In order to understand the origin of one-body dissipation in nuclei, we analyze the behavior of a gas of classical particles moving in a two-dimensional cavity with nuclear dimensions. This "nuclear" billiard has multipole-deformed walls which undergo periodic shape oscillations. We demonstrate that a single particle Hamiltonian containing coupling terms between the particles' motion and the collective coordinate induces a chaotic dynamics for any multipolarity, independently on the geometry of the billiard. If the coupling terms are switched off the "wall formula" predictions are recovered. We discuss the dissipative behavior of the wall motion and its relation with the order-to-chaos transition in the dynamics of the microscopic degrees of freedom.Comment: 16 pages, 12 postscript figures included, revtex, new version completely revised accepted by Physical Review C and scheduled to appear in the issue of november 199

Invariant Manifolds and Collective Coordinates

We introduce suitable coordinate systems for interacting many-body systems with invariant manifolds. These are Cartesian in coordinate and momentum space and chosen such that several components are identically zero for motion on the invariant manifold. In this sense these coordinates are collective. We make a connection to Zickendraht's collective coordinates and present certain configurations of few-body systems where rotations and vibrations decouple from single-particle motion. These configurations do not depend on details of the interaction.Comment: 15 pages, 2 EPS-figures, uses psfig.st

Kinetic-theory approach to low-energy collective modes in nuclei

Two different solutions of the linearized Vlasov equation for finite systems, characterized by fixed and moving-surface boundary conditions, are discussed in a unified perspective. A condition determining the eigenfrequencies of collective nuclear oscillations, that can be obtained from the moving-surface solution, is studied for isoscalar vibrations of lowest multipolarity. Analytic expressions for the friction and mass parameters related to the low-enegy surface excitations are derived and their value is compared to values given by other models. Both similarities and differences are found with respect to the other approaches, however the close agreement obtained in many cases with one of the other models suggests that, in spite of some important differences, the two approaches are substantially equivalent. The formalism based on the Vlasov equation is more transparent since it leads to analytical expressions that can be a basis for further improvement of the model.Comment: 16 pages, 1 EPS figure, to be published in Nucl. Phys.