Statistical fluctuations for the fission process on its decent from saddle to scission

We reconsider the importance of statistical fluctuations for fission dynamics beyond the saddle in the light of recent evaluations of transport coefficients for average motion. The size of these fluctuations are estimated by means of the Kramers-Ingold solution for the inverted oscillator, which allows for an inclusion of quantum effects.Comment: 12 pages, Latex, 5 Postscript figures; submitted to PRC e-mail: [email protected] www home page: http://www.physik.tu-muenchen.de/tumphy/e/T36/hofmann.htm

Nuclear fission: The "onset of dissipation" from a microscopic point of view

Semi-analytical expressions are suggested for the temperature dependence of those combinations of transport coefficients which govern the fission process. This is based on experience with numerical calculations within the linear response approach and the locally harmonic approximation. A reduced version of the latter is seen to comply with Kramers' simplified picture of fission. It is argued that for variable inertia his formula has to be generalized, as already required by the need that for overdamped motion the inertia must not appear at all. This situation may already occur above T=2 MeV, where the rate is determined by the Smoluchowski equation. Consequently, comparison with experimental results do not give information on the effective damping rate, as often claimed, but on a special combination of local stiffnesses and the friction coefficient calculated at the barrier.Comment: 31 pages, LaTex, 9 postscript figures; final, more concise version, accepted for publication in PRC, with new arguments about the T-dependence of the inertia; e-mail: [email protected]

Low density instability in a nuclear Fermi liquid drop

The instability of a Fermi-liquid drop with respect to bulk density distortions is considered. It is shown that the presence of the surface strongly reduces the growth rate of the bulk instability of the finite Fermi-liquid drop because of the anomalous dispersion term in the dispersion relation. The instability growth rate is reduced due to the Fermi surface distortions and the relaxation processes. The dependence of the bulk instability on the multipolarity of the particle density fluctuations is demonstrated for two nuclei $^{40}Ca$ and $^{208}Pb$.Comment: 12 pages, latex, 3 ps-figures, submitted to Phys. Rev.

Spinodal decomposition of expanding nuclear matter and multifragmentation

Density fluctuations of expanding nuclear matter are studied within a mean-field model in which fluctuations are generated by an external stochastic field. Fluctuations develop about a mean one-body phase-space density corresponding to a hydrodinamic motion that describes a slow expansion of the system. A fluctuation-dissipation relation suitable for a uniformly expanding medium is obtained and used to constrain the strength of the stochastic field. The distribution of the liquid domains in the spinodal decomposition is derived. Comparison of the related distribution of the fragment size with experimental data on the nuclear multifragmentation is quite satisfactory.Comment: 19 RevTex4 pages, 6 eps figures, to appear in Phys. Rev.

Antisymmetrized molecular dynamics with quantum branching processes for collisions of heavy nuclei

Antisymmetrized molecular dynamics (AMD) with quantum branching processes is reformulated so that it can be applicable to the collisions of heavy nuclei such as Au + Au multifragmentation reactions. The quantum branching process due to the wave packet diffusion effect is treated as a random term in a Langevin-type equation of motion, whose numerical treatment is much easier than the method of the previous papers. Furthermore a new approximation formula, called the triple-loop approximation, is introduced in order to evaluate the Hamiltonian in the equation of motion with much less computation time than the exact calculation. A calculation is performed for the Au + Au central collisions at 150 MeV/nucleon. The result shows that AMD almost reproduces the copious fragment formation in this reaction.Comment: 24 pages, 5 figures embedde

Memory effects on descent from nuclear fission barrier

Non-Markovian transport equations for nuclear large amplitude motion are derived from the collisional kinetic equation. The memory effects are caused by the Fermi surface distortions and depend on the relaxation time. It is shown that the nuclear collective motion and the nuclear fission are influenced strongly by the memory effects at the relaxation time $\tau \geq 5\cdot 10^{-23}{\rm s}$. In particular, the descent of the nucleus from the fission barrier is accompanied by characteristic shape oscillations. The eigenfrequency and the damping of the shape oscillations depend on the contribution of the memory integral in the equations of motion. The shape oscillations disappear at the short relaxation time regime at $\tau \to 0$, which corresponds to the usual Markovian motion in the presence of friction forces. We show that the elastic forces produced by the memory integral lead to a significant delay for the descent of the nucleus from the barrier. Numerical calculations for the nucleus $^{236}$U shows that due to the memory effect the saddle-to-scission time grows by a factor of about 3 with respect to the corresponding saddle-to-scission time obtained in liquid drop model calculations with friction forces.Comment: 22 pages, 8 figures, submitted to Phys. Rev.

Spinodal instabilities within BUU approach

Using a recently developed method for the inclusion of fluctuation in the BUU dynamics, we study the self-consistent propagation of inherent thermal noise of unstable nuclear matter. The large time behaviour of the evolving system exhibits synergism between fluctuation and non-linearities in a universal manner which manifest in the appearance of macroscopic structure in the average description.Comment: 12 pages Revtex. Two figures, uuencoded, are enclosed in a separate fil

Nuclear Multifragmentation in the Non-extensive Statistics - Canonical Formulation

We apply the canonical quantum statistical model of nuclear multifragmentation generalized in the framework of recently proposed Tsallis non-extensive thermostatistics for the description of nuclear multifragmentation process. The test calculation in the system with A=197 nucleons show strong modification of the 'critical' behaviour associated with the nuclear liquid-gas phase transition for small deviations from the conventional Boltzmann-Gibbs statistical mechanics.Comment: 4 pages, 4 figure