Two-body Dissipation Research Articles

Dynamic chaos and stability of a weakly open Bose-Einstein condensate in a double-well trap

We investigate the dynamics of a weakly open Bose-Einstein condensate with attractive interaction in a magneto-optical double-well trap. A set of time-dependent ordinary differential equations describing the complex dynamics are derived by using a two-mode approximation. The stability of the stationary solution is analyzed and some stability regions on the parameter space are displayed. In the symmetric well case, the numerical calculations reveal that by adjusting the feeding from the nonequilibrium thermal cloud or the two-body dissipation rate, the system could transit among the periodic motions, chaotic self-trapping states of the Lorenz model, and the steady states with the zero relative atomic population or with the macroscopic quantum self-trapping (MQST). In the asymmetric well case, we find the periodic orbit being a stable two-sided limited cycle with MQST. The results are in good agreement with that of the direct numerical simulations to the Gross-Pitaevskii equation.

Dynamical mean-field study of strongly interacting Bose–Einstein condensate

The experimental results of 85Rb Bose–Einstein condensates are analyzed within the mean-field approximation with time-dependent two-body interaction and dissipation due to three-body recombination. We found that the magnitude of the dissipation is consistent with the three-body theory for longer rise times. However, for shorter rise times, it occurs an enhancement of this parameter, consistent with a coherent dimer formation.

Reaction dynamics and hot nuclei formation in the36Ar+98Moreaction at37AMeVstudied through light charged particle andγ-ray emission

Central and mid-central collisions which lead to the formation of a heavy residue in the 37A MeV ${}^{36}\mathrm{Ar}{+}^{98}$Mo reaction have been studied with the MEDEA multidetector array coupled to a Parallel Plate Avalanche Counter. The dependence of the high energy gamma ray and light charged particle production as a function of the linear momentum transferred to the fused system has been studied. The unique potentialities of the MEDEA detector have made it possible to follow the evolution of the reaction dynamics from the pre-equilibrium stage to the formation of a heavy compound nucleus. The analysis of the correlation between the most energetic photons and protons shows how both of them are mainly produced in the most energetic primary nucleon-nucleon collisions. The multiplicity of high energy ${(E}_{\ensuremath{\gamma}}>30\mathrm{MeV})$ $\ensuremath{\gamma}$ rays has been found to increase with the linear momentum transfer, showing the dominance of two-body dissipation in the transfer mechanism and giving a tool to correlate the momentum transfer with the centrality of the collision. Light charged particle kinetic energy spectra show how in these collisions, compound systems with excitation energies of more than $3A\mathrm{MeV}$ and temperature up to 7 MeV are formed. The experimental findings are compared with Boltzmann-Nordheim-Vlasov calculations. A scenario is found where the nucleus-nucleus interaction starts with two-body nucleon-nucleon collisions in the overlap region of nuclear densities. These collisions give rise to the production of high energy nucleons and $\ensuremath{\gamma}$ rays, and play a fundamental role in the energy transfer from the relative motion to internal excitation of the quasiprojectile and the target.

Langevin description of the charge distribution of fragments originating from the fission of excited nuclei

The charge distribution of fragments originatingfrom the fission of the 236U compound nucleus is calculated within a stochastic approach based on Langevin equations. The elongation coordinate, the neck-thickness coordinate, and the charge-asymmetry coordinate are chosen as collective variables. The friction parameter of the charge mode is calculated on the basis of two nuclear-viscosity mechanisms, that of one-body and that of two-body dissipation. It is shown that the Langevin approach is applicable to studying isobaric distributions. In addition, the charge distribution in question is studied as a function of the excitation energy of the compound nucleus and as a function of the coefficient of two-body viscosity.

Dynamics of Bose–Einstein condensed atoms with attractive two-body interaction and three-body dissipation

Dynamics of Bose–Einstein condensed atoms with attractive two-body interaction and three-body dissipation

Production and decay of excited quasiprojectiles in peripheral and semiperipheral35Cl+197Aureactions in Fermi energy domain

The peripheral and semiperipheral reactions in ${}^{35}\mathrm{Cl}{+}^{197}\mathrm{Au}$ have been studied at 30 and 43 MeV/nucleon. The nonequilibrium $\ensuremath{\alpha}$ and IMF components have been observed in the experiment. The fraction of nonequilibrium emission decreases with an increase in the atomic number of the projectilelike fragments but, for a given projectilelike fragment, it increases with the charge of the emitted particles. The characteristics of quasiprojectiles reconstructed from their decay products reveal several features reminiscent of damped reactions at lower bombarding energies. The atomic number and deflection angle of projectilelike fragments depend strongly on their kinetic energy or dissipated energy. At 30 MeV/nucleon, the experimental data can be explained by a deep inelastic transfer model. One-body dissipation is still the main mechanism for the energy and angular momentum dissipation. However, at 43 MeV/nucleon, deep inelastic transfer models can predict only the experimental tendency. Two-body dissipation plays a more important role at higher incident energies. The similarity observed in the decay product distributions, as a function of excitation energy, suggests that the excited quasiprojectiles formed in binary collisions might approach thermal equilibrium for both incident energies. The decay products have been analyzed with sequential-binary and simultaneous-disassembly statistical decay models. Both statistical models are able to provide good agreement with the experimental observables except for the mean kinetic energy of the products.

Impact parameter dependence of linear momentum transfer and the role of two-body dissipation mechanisms in heavy ion collisions around the Fermi energy

High energy γ-rays ( E γ >35 MeV) have been measured in coincidence with heavy residues emitted in reactions induced by a 37 MeV/u 36Ar beam on a 98Mo target. The γ-ray yield increases strongly with increasing linear momentum transfer indicating the importance of two-body collisions in the transfer mechanism. The high energy γ-ray multiplicity has been used to correlate the linear momentum transfer to the impact parameter. This correlation is compared to dynamical BNV simulations to show the essential role of two body nucleon-nucleon collisions at these bombarding energies.

Giant resonances built on highly excited states: A test-ground for nuclear dynamics

We show that from a study of collective motions built on highly excited states we can extract important information on open problems in structure and dynamics: 1. i) Competition between one-and two-body dissipation and relative temperature dependence 2. ii) Transition in the nature of nuclear collective motions: from pure quantum to classical sound waves 3. iii) Pre-equilibrium effects: the “dynamical” dipole in charge asymmetric entrance channels.

Determination of nuclear friction in strongly damped reactions from prescission neutron multiplicities.

Nonfusion, fissionlike reactions in collisions of four heavy systems (well below the fusion extra-push energy threshold), for which Hinde and co-workers had measured the prescission neutron multiplicities, have been analyzed in terms of the deterministic dynamic model of Feldmeier coupled to a time-dependent statistical cascade calculation. In order to reproduce the measured prescission multiplicities and the observed (nearly symmetric) mass divisions, the energy dissipation must be dramatically changed with regard to the standard one-body dissipation: In the entrance channel, in the process of forming a composite system, the energy dissipation has to be reduced to at least half of the one-body dissipation strength (${\mathit{k}}_{\mathit{s}}^{\mathrm{in}}$\ensuremath{\le}0.5), and in the exit channel (from a mononucleus shape to scission) it must be increased by a factor ranging for the studied reactions from ${\mathit{k}}_{\mathit{s}}^{\mathrm{out}}$=4 to ${\mathit{k}}_{\mathit{s}}^{\mathrm{out}}$=12. These results are compared with the temperature dependence of the friction coefficient, recently deduced by Hofman, Back, and Paul from data on the prescission giant dipole resonance emission in fusion-fission reactions. The combined picture of the temperature dependence of the friction coefficient, for both fusion-fission and nonfusion reactions, may indicate the onset of strong two-body dissipation already at a nuclear temperature of about 2 MeV. \textcopyright{} 1996 The American Physical Society.

Collective friction coefficients in the relaxation time approximation.

Within the framework of the relaxation time approximation we have computed two components of the friction coefficient for various single-particle potentials and have found that the nondiagonal component of the friction coefficient depends generally on the diffuseness of the potential. The diagonal component of friction, which is related to the two-body dissipation mechanism, was found to be unreasonably large in these computations, especially for small temperatures. \textcopyright{} 1996 The American Physical Society.

The many facets of giant resonances at high excitation energies

We show that from a study of collective motions built on highly excited states we can extract important information on open problems in nuclear structure and dynamics: 1. i)Competition between one- and two-body dissipation, 2. ii) Effects of correlations and related density fluctuations, 3. iii) Transition in the nature of nuclear collective motions: from pure quantum to classical sound waves, 4. iv) Pre-equilibrium effects: the “dynamical” dipole in charge asymmetric entrance channels, 5. v) Fusion hindrance from dynamical instabilities. We try also to discuss the relevance of new, more exclusive, experiments and of a larger systematics.

Importance of one- and two-body dissipation at intermediate energies studied by hard photons.

Hard photons were measured in coincidence with projectilelike fragments in peripheral reactions of Ar-36 + Tb-159 at E/A = 44 MeV. The probability for hard photon production was found to scale linearly with the transferred mass and to depend on the direction of the transfer, thus indicating the relative importance of one- and two-body dissipation in peripheral reactions.

The GDR as clock for fission dynamics in hot actinide nuclei

GDR γ-rays emission in competition with fission by hot compound nuclei is used to to determine characteristic time scales for the fission process which are translated into nuclear dissipation coefficients for collective mass flow. Systematic studies in nuclei from Thorium to Rutherfordium were used to extract separately friction coefficients of compound nuclear fission inside the saddle and from the saddle to the scission point. Above a marked excitation energy threshold between 60 and 80 MeV dissipation is large and equal to full one body dissipation on the outside, possibly even larger inside the saddle. Below this energy dissipation appears to be small. The time scale for quasifission is shown to be ∼ 5 × 10 −21 s, about 1 6 of that of CN fission. The time scale for deep inelastic scattering is too fast to see GDR decay from the colliding system. We compare these results with global models for one- and two-body nuclear dissipation.

Damping of giant resonances in hot nuclei.

The effect of one- and two-body dissipation on the damping of giant dipole resonances (GDR's) is studied in a semiclassical approach solving a Vlasov equation with a collision relaxation time. The latter is microscopically evaluated from the equilibration of a distorted momentum distribution in a kinetic approach. Temperature effects are introduced in the initial distribution function and in Pauli blocking rearrangement in the path to equilibration. Particle emission is also computed in the same microscopic picture. Without free parameters a good agreement with data is obtained for GDR's on the ground state. For collective vibration built on excited states we get a dramatic increase of the widths due to the enhancement of nucleon-nucleon (NN) collisions. The saturation observed in some experiments is explained as due to the competition of particle evaporation which cools down the system. The transition to first-sound modes is ruled out for the persistence of long-nucleon mean free paths at relatively high temperatures.

Kinetic approach to the damping of giant quadrupole resonances.

The effect of one- and two-body dissipation on the damping of giant quadrupole resonances is studied in a semiclassic approach solving a Vlasov equation with a collisional relaxation time. The latter is microscopically evaluated from the equilibration of a distorted momentum distribution in a kinetic approach. Important effects from energy and angle dependent nucleon-nucleon (NN) cross sections and from the time variation of Pauli blocking are stressed. Once these points are suitably treated, a good agreement with the experimental systematics is obtained from the use of a free NN cross section.

Collision times in a viscoelastic description of nuclei with a diffuse-surface nuclear density

We investigate the fluiddynamical description of nuclear motion induced by the variational procedure in the presence of one- and two-body dissipation. The equation of motion for the scaling field is established for an abnormal parity mode in a nucleus with a Wood-Saxon density. The local relaxation time can be computed as a function of the distance to the nuclear center, as well as the two-body viscosity. The hydrodynamical and the viscoelastic regimes are specifically examined. It is found that the later appears more appropriate to fit the energy, frequency and time scales of actual nuclei.

On the relaxation-time approximation for the two-body dissipation in HI collisions

In several previous publications the author has treated two-body collisions between the nucléons (the two-body dissipation) encountered in heavy-ion collisions by a relaxation-time approximation. This approximation is here tested against the calculations of Danielewicz in which he studied the dynamics of two slabs of nuclear matter (two Fermi spheres in momentum space) colliding with the NN interactions parameterized to fit NN cross sections. The relaxation-time approximation is found to be in good agreement especially with quantum-dynamical calculations.

Incomplete linear momentum transfer in nuclear reactions: An interplay between one-body and two-body dissipation

An explanation for the experimentally observed linear momentum transfer in light- and heavy-ion induced reactions is propounded by simple geometrical considerations in momentum space. We display explicity the transition from one-body to two-body dissipation. We obtain a surprising agreement with the experiments over the whole measured energy range.

Dissipation in nucleus-nucleus collisions: A model study of two colliding Fermi gases

This paper deals with the mechanism of one- and two-body dissipations in nucleus-nucleus collisions. The average energy transferred to nuclear excitations is calculated using a time-dependent density matrix approach with lowest-order approximations. Considering the nuclei as Fermi gases, and using a gaussian-type NN interaction as the basic perturbation, simplified expressions are obtained for energy dissipations. These expressions are quite instructive to follow a number of interesting aspects of one- and two-body dissipations. It is theoretically observed that the memory time for the two-body dissipation is significantly smaller than that of one-body dissipation. A threshold-type dependence of the transferred energy on the relative velocity between the two nuclei is also observed. This threshold velocity is found to be related with the intrinsic nucleon kinetic energy for two-body dissipation and with the nuclear size for the one-body case. This observation further suggests that the total dissipated energy is shared between the two nuclei approximately in the ratio of their masses. The physical origin of these observations is also explained. Numerical calculations further illustrate some characteristic features of one- and two-body dissipations.

Unified theory of dissipation mechanisms in nuclear systems

An extension of the HF approximation is presented, which involves one-body and two-body dissipation in a unified manner. To accomplish this we assume that the two-particle effective interaction contains a random part and use a diagrammatic technique to derive an approximate equation for the average single-particle propagator. In the extreme one-body regime, randomization of particle motions is produced by random fluctuations of the self-consistent potential. In general, additional randomization is supplied by a collision term of the usual type and a mixed term which couples collisions to fluctuations. Neglecting the collision term, the equation of motion for the one-body density can be put in a form similar to Balian and Vénéroni's ETDHF equation.