Ph. Chomaz

3D stochastic mean-field simulations of the spinodal fragmentation of dilute nuclei

Abstract We study the spinodal decomposition of hot and dilute nuclear systems using a stochastic one-body approach in 3D. The early clusterization process appears dominated by unstable modes with well defined multipolarity and radial structure, which can be related to infinite nuclear matter properties. These instabilities favour primary partitions of the system in nearly equal mass fragments, in association with a lack of small clusters. Finally, we discuss how these features are affected by the final decay of the formed fragments.

Energy correlations as thermodynamical signals for phase transitions in finite systems

Abstract A new method is proposed to extract information on the properties of the possible phase transition occurring in finite systems as multifragmenting atomic nuclei. The average energy of a subsystem is demonstrated to provide a thermometer when data are sorted in total excitation energy bins, while the associated fluctuations are quantitatively related to the heat capacity. A coupled analysis with total energy fluctuations in bins of the partial energy allows us to detect the presence of a phase transition and the associated order. Deformations due to finite size effects and experimental cuts are also discussed.

Quantum Calculation of the Dipole Excitation in Fusion Reactions

The excitation of the giant dipole resonance induced by fusion reaction is studied with N/Z asymmetry in the entrance channel. The time dependent Hartree-Fock solution exhibits a strong dipole vibration which can be associated with a giant vibration along the main axis of the deformed compound nucleus. This dipole motion appears to be nonlinearly coupled to the shape oscillation, leading to a strong modulation of its frequency. These phenomena can be detected in the gamma-ray emission from hot compound nuclei.

Phase transition in an isospin dependent Lattice Gas Model

Abstract The role of isospin as a degree of freedom and as an observable in heavy ion reaction experiments is analyzed in the theoretical framework of an isospin dependent Lattice Gas Model. We show that the critical temperature is only slightly dependent on the isospin asymmetry and finite size effects go in the direction of increasing the τ critical exponent respect to the asymptotic limit of the three dimensional Ising universality class. An interesting signature of the liquid-gas phase transition and a possible observable to localize the multifragmenting system in the T − ρ plane is given by the isotopic composition of fragments. We show that in the coexistence region the vapor fraction is more asymmetric than the liquid fraction and that this signal should not be washed out by secondary decays.

Linear response in stochastic mean-field theories and the onset of instabilities

Abstract We study the small amplitude response of stochastic one-body theories, such as the Boltzmann-Langevin approach. Whereas the two-time correlation function only describes the propagation of fluctuations initially present, the equal-time correlation function is related to the source of stochasticity. For stable systems it yields the Einstein relation, while for unstable systems it determines the growth of the instabilities. These features are illustrated for unstable nuclear matter in two dimensions.

Mechanical and chemical spinodal instabilities in finite quantum systems

Self consistent quantum approaches are used to study the instabilities of finite nuclear systems. The frequencies of multipole density fluctuations are determined as a function of dilution and temperature, for several isotopes. The spinodal region of the phase diagrams is determined and it appears that instabilities are reduced by finite size effects. The role of surface and volume instabilities is discussed. It is indicated that the important chemical effects associated with mechanical disruption may lead to isospin fractionation.

Quantal effects on growth of instabilities in nuclear matter

Abstract The growth rates of unstable modes in nuclear matter are investigated using a quantal dispersion relation. Calculations carried out with a realistic finite range potential show that unstable modes with wave number larger than the Fermi momentum are strongly suppressed, due to the quantal effect, in the mean field evolution. The observed consequence is the shift of the most important modes towards longer wave lengths.

Pre-equilibrium effects on properties of hot giant dipole resonances

Abstract In this article we analyse how the presence of a pre-equilibrium dipole strength can affect the properties of the giant dipole resonance (GDR) built on hot nuclei. We show that a little amount of GDR phonons still excited when the compound nucleus is formed will substantially modify the γ-decay from the giant resonance region. Also on the basis of microscopic calculations of the reaction dynamics we propose to study the effect of the N over Z ratio in the entrance channel. This analysis could bring independent information on the problem of the GDR disappearing at high excitation energy.

First-order phase transitions: equivalence between bimodalities and the Yang–Lee theorem

First order phase transitions in finite systems can be defined through the bimodality of the distribution of the order parameter. This definition is equivalent to the one based on the inverted curvature of the thermodynamic potential. Moreover we show that it is in a one to one correspondence with the Yang Lee theorem in the thermodynamic limit. Bimodality is a necessary and sufficient condition for zeroes of the partition sum in the control intensive variable complex plane to be distributed on a line perpendicular to the real axis with a uniform density, scaling like the number of particles.

Role of anharmonicities and nonlinearities in heavy ion collisions A microscopic approach

Abstract Using a microscopic approach beyond RPA to treat anharmonicities, we mix two-phonon states among themselves and with one-phonon states. We also introduce nonlinear terms in the external field. These nonlinear terms and the anharmonicities are not taken into account in the “standard” multiphonon picture. Within this framework we calculate Coulomb excitation of 208Pb and 40Ca by a 208Pb nucleus at 641 and 1000 MeV/A. We show with different examples the importance of the nonlinearities and anharmonicities for the excitation cross section. We find an increase of 10% for 208Pb and 20% for 40Ca of the excitation cross section corresponding to the energy region of the double giant dipole resonance with respect to the “standard” calculation. We also find important effects in the low-energy region. The predicted cross section in the DGDR region is found to be rather close to the experimental observation.