B. Remaud

Semi-classical dynamics of heavy-ion reactions

Abstract We present a semi-classical approach of the heavy-ion collision theory in the intermediate energy domain (10–100 MeV incident kinetic energy per nucleon) based on the Vlasov equation and its extension — the Landau-Vlasov equation — when the residual interaction is accounted for through a collision kernel. We use the coherent state set as an overcomplete basis for the decomposition of the nuclear phase-space distributions. We show that the uniform repartition of coherent states in phase space provides semi-classical descriptions of nuclei at equilibrium which are the correct initial conditions of the Vlasov and Landau-Vlasov dynamical equations. In the slab geometry, we compare the results of the Vlasov equation with those of the TDHF theory for the crossing of a potential barrier and the collision of two slabs. We present sample results of three-dimensional calculations of heavy-ion collisions with a Skyrme self-consistent interaction and inclusion of the Coulomb interaction; the individual collisions being described by the Uehling-Uhlenbeck kernel. These calculations illustrate the incomplete fusion process for central collisions at 27 MeV/u incident energy and the onset of an abrasion-like process for more peripheral collisions at 35 MeV/u.

Fluctuations in one-body dynamics☆

Abstract With a view towards nuclear dynamics at intermediate energies, we develop a transport treatment for systems whose reduced one-body phase-space density exhibits a markovian time evolution. A moment expansion of the corresponding Fokker-Planck equation leads to closed equations for the temporal evolution of the ensemble average of the phase-space occupancy f( r, p ) and its correlation function. The general properties of the associated relaxation processes are illustrated and the utility of the formulation for studies of nuclear collisions is discussed.

Semiclassical and Phase Space Approaches to Dynamic and Collisional Problems of Nuclei

Abstract This article summarises recent work on the semiclassical (Thomas-Fermi like) treatment of nuclear correlations and dynamical problems. After a short outline of the general technique the nucleon-nucleus optical potential in the doorway approximation (2p-1h and 2h-1p intermediate states) is treated. The imaginary part serves to calculate the energy dependent correction to the real part. The level density parameter, occupation numbers, and the mean free path are discussed. The semiclassical treatment of the nuclear response function is given in detail. Applications to inelastic electron scattering in the quasi-elastic peak region are presented. Analogously, inelastic proton scattering is calculated. Because of the surface absorption this reaction excites the surface response. The imaginary part of the single-particle (hole) potential in the evaluation of the response function introduces a 2p-2h spreading. The missing charge in the longitudinal response is reduced but not all experimental puzzles can be explained. The experience gained in the description of phenomena close to equilibrium serves to construct solutions of the Landau-Vlasov ( alias Vlasov-Uehling-Uhlenbeck) equation for the description of non-equilibrium processes encountered in heavy ion reactions.

A study of the disintegration of highly excited nuclei with the Vlasov-Uehling-Uhlenbeck equation

Abstract The disintegration of hot and/or compressed nuclei is studied using (i) the Vlasov equation (VE) with imposed spherical symmetry, (ii) the VE in three dimensions (3D) and (iii) the VE in three dimensions supplemented by the Uehling-Uhlenbeck collision term (VUU). We find that case (ii) is slightly more unstable with respect to disintegration compared to case (i) whereas (iii) tends to make nuclei more stable. In all cases the thermal energies (15–20 MeV per nucleon) needed to totally disintegrate a nucleus seem to be higher than those found in static and hydrodynamic calculation. On the contrary, compressional energy very much helps disintegration. Some comments on the introduction of fluctuations and corresponding fragmentation are added.

Semiclassical approaches to proton emission in intermediate-energy heavy-ion reactions

Abstract Semiclassical approaches are proposed for studying the transition between one- and two-body processes in intermediate-energy heavy-ion collisions. The Landau-Vlasov equation is used as a transport equation for nucleons in the nuclear matter. We apply our formalism to the fast proton ejection. On the one hand, the effects of the nucleon-nucleon collisions are studied for particles which travel through the nucleus cores. On the other hand, inertial emission turns out to be an important proton-emission mechanism. Our results conflict with the interpretation of the proton spectra in terms of moving sources. Reasonable agreement with the experimental data are found without reference to any thermal equilibrium.

Nuclear dynamics with the (finite-range) Gogny force: Flow effects

Abstract We introduce for the first time the effective finite-range interaction of Gogny in the semi-classical description of heavy-ion reactions based on the Landau-Vlasov equation. The characteristics of the flow for heavy-ion collisions are studied as functions on the incident energy, the impact parameter and the mass number. The Gogny force reproduces the energy dependence of the real optical potential up to 200 MeV; we show that this energy dependence increases the flow and reproduces the values obtained with stiff local Skyrme forces. These results demonstrate the need of a proper account of the momentum dependence of the nuclear force, to extract informations on the nuclear equation of state, from high-energy heavy-ion collisions.

Fast fission phenomenon, deep inelastic reactions and compound nucleus formation described within a dynamical macroscopic model

Abstract We present a dynamical model to describe dissipative heavy ion reactions. It treats explicitly the relative motion of the two ions, the mass asymmetry of the system and the projection of the isospin of each ion. The deformations, which are induced during the collision, are simulated with a time-dependent interaction potential. This is done by a time-dependent transition between a sudden interaction potential in the entrance channel and an adiabatic potential in the exit channel. The model allows us to compute the compound-nucleus cross section and multidifferential cross sections for deep inelastic reactions. In addition, for some systems, and under certain conditions which are discussed in detail, a new dissipative heavy ion collision appears: fast-fission phenomenon which has intermediate properties between deep inelastic and compound nucleus reactions. The calculated properties concerning fast fission are compared with experimental results and reproduce some of those which could not be understood as belonging to deep inelastic or compound-nucleus reactions.

Semi-classical kinetic approaches of heavy-ion dynamics

Abstract A semi-classical kinetic equation tor the study of transport phenomena in nuclei is presented ; it allows the analysis of the balance between mean field and individual collisions in heavy reactions at intermediate energies. The role of collisions in the onset of various regimes of reactions is discussed. The semi-classical equation gives insights on the microscopic mechanisms of energy equilibration. Strong limitations to the excitation energy available for particle evaporation are predicted in agreement with observed trends. The role of compression modes is underlined in particular as regard to nuclear multifragmentation.

Coulomb instability in collisions between very heavy nuclei around 30 MeV per nucleon

Abstract Simulations, based on the Landau-Vlasov model, of central collisions ( b =0−3 fm) between very heavy nuclei around 30 MeV per nucleon reveal the occurence of the Coulomb instability as already predicted by static calculations of hot nuclei a few years ago. The Coulomb instability shows itself in the formation of unstable bubbles.

Compressional effects in heavy ion collisions. Spinodal decomposition and thermal energy saturation

Abstract Using a kinetic equation (the Landau-Vlasov equation), and analysis of the balance between thermal and collective energies is performed for heavy-ion collisions in the 20–100 MeV/u bombarrding energy range. We show how the initially available energy is shared between thermal and compression degrees of freedom. Compression may in turn drive the nuclear system into the spinodal region. The sensitivity of the amplitude and frequency of the monopole oscillation to the nuclear incompressibility modulus is discussed.