Influence of momentum-dependent interactions on balance energy and mass dependence⋆

We aim to understand the role of momentum-dependent interactions in transverse flow as well as in its disappearance. For the present study, central collisions involving masses between 24 and 394 are considered. We find that the momentum-dependent interactions have different impact in lighter colliding nuclei compared to heavier colliding nuclei. In lighter nuclei, the contribution of the mean field towards flow is smaller compared to heavier nuclei where binary nucleon-nucleon collisions dominate the scene. The inclusion of momentum-dependent interactions also explains the energy of the vanishing flow in the ¹²C + ¹²C reaction which otherwise was not possible with the static hard equation of state. An excellent agreement of our theoretical attempt is found for balance energy with experimental data throughout the periodic table.     

What is the physics behind the 3He–4He anomaly?

We show that coalescence of nucleons emitted prior to thermalization in highly excited nuclei can explain the anomaly of kinetic energies of helium clusters. A new coalescence algorithm has been included in the statistical approach to nuclear reactions formerly used to describe intermediate mass fragment production. Received: 24 September 1999 / Revised version: 22 November 1999     

III. A stochastic two-stage reaction model for heavy-ion collisions

We propose a two-stage, stochastic model of heavy-ion reactions. Nucleons becoming participants by mean-field effects or by nucleon-nucleon interactions are transferred to definite final states, creating a PLF, a TLF, clusters, or escaping to continuum. Nucleon transfer probabilities are governed by state densities. In this way different hot particle sources are created which afterwards decay by particle emission. Received: 12 March 2001 / Accepted: 20 June 2001     

Evolution of the fusion cross-section for light systems at intermediate energies

Ar + Ni and Ni + Ni collisions are investigated between 32 and around 100A MeV incident energy with the 4π multidetector INDRA. Fusion cross-sections are found to decrease from ∼ 180mb at 32A MeV to zero above 50A MeV. Other experimental results, for light systems, are compared. Moreover, theoretical works are discussed and fusion cross-sections, calculated from two dynamical simulations based on nuclear Boltzmann equation (Boltzmann-Nordheim-Vlasov and Landau-Vlasov models), are also compared to experimental results.     

Prompt ternary break-up in 32S+59Co and 32S+63Cu reactions at 5.6 A · MeV

Final states indicating the presence in the reaction of three-body fragmentation processes has been observed in ³²S+⁵⁹Co and ³²S+⁶³Cu dissipative collisions at 5.6 A · MeV. Besides the already observed sequential binary process, data analysis reveals the presence of prompt ternary break-up of the composite system. Indications on the system configuration at the scission have been deduced by analyzing the event shape in the momentum phase space. The decay appears to occur in a collinear configuration, one of the produced fragments originating from the neck which connects the other two. In spite of the large energy dissipation, structure effects in the charge partition seem to affect part of events. Received: 3 July 1998 / Revised version: 15 October 1999     

Challenges in nuclear dynamics and thermodynamics

The purpose and contents of this topical issue, Dynamics and Thermodynamics with Nuclear Degrees of Freedom, which grew out of a series of workshops in the years 2004 and 2005, are introduced. The central topics are the nuclear density functional, nuclear multi-fragmentation, and nuclear phase transitions.     

Thermal and chemical equilibrium for vaporizing sources

Vaporized sources produced in collisions between ³⁶Ar and ⁵⁸Ni at 95 MeV per nucleon have been detected with the multidetector INDRA. Complete information concerning the deexcitation properties of quasi-projectiles, including second moments of chemical composition, is compared to a quantum statistical model describing a gas of fermions and bosons in thermal and chemical equilibrium. Inclusions in the calculation of all known discrete levels of nuclear species which deexcite into light particles and of a final state excluded volume interaction are found decisive to very well reproduce the experimental data, which strongly supports that thermodynamical equilibrium was achieved at freeze-out for such sources. Received: 6 April 1999     

Jets of nuclear matter in He-A T inelastic collisions at 4.5 A GeV/c

The problem of the nuclear matter jets in nucleus-nucleus collisions at 4.5 A GeV/c is discussed. The global analysis of experimental data, namely the sphericity tensor, is used to evidence such jets. The experimental results are compared with those obtained in the same collisions for hydrodynamic flow and thrust. The experiments have been performed in the frame of the SKM 200 Collaboration from JINR Dubna. Received: 20 March 1997 / Revised version: 20 July 1997     

A semiclassical formula for the reaction cross-section of heavy ions

We discuss an improvement to the expression for the heavy-ion reaction cross-section proposed long ago by Karol (P.J. Karol, Phys. Rev. C 11, 1203 (1975)) which describes the two-ion interaction through the nucleon-nucleon collisions in their overlap region when they come into contact. This improvement consists in considering the limitations due to the Pauli principle, which at low incident energies forbids many nucleon interactions, and in including a Coulomb factor. The final expression for which we also propose a new parametrization reproduces satisfactorily the known reaction cross-sections for many ion combinations using a global set of parameters. A decomposition of the reaction cross-section into the contributions of peripheral interactions, as a function of the impact parameter, is also discussed.     

Freeze-out volume in multifragmentation --Dynamical simulations

Stochastic mean-field simulations for multifragmenting sources at the same excitation energy per nucleon have been performed. The freeze-out volume, a concept which needs to be precisely defined in this dynamical approach, was shown to increase as a function of three parameters: freeze-out instant, fragment multiplicity and system size.     

The case of RIB at intermediate energies: Isospin effects on nuclear dynamics

In the reaction dynamics of intermediate-energy radioactive beams we can probe highly asymmetric nuclear matter in compressed as well as dilute phases. In this report some predictions are presented, based on analytical results as well as on reaction simulations. We suggest a series of experiments with RIB aimed to shed light on isospin properties of nuclear interactions in the medium. Received: 1 May 2001 / Accepted: 4 December 2001     

Energy and angular momentum sharing in dissipative collisions

Primary and secondary masses of heavy reaction products have been deduced from kinematics and E-ToF measurements, respectively, for the direct and reverse collisions of ⁹³Nb and ¹¹⁶Sn at 25 AMeV. Light charged particles have also been measured in coincidence with the heavy fragments. Direct experimental evidence of the correlation of energy-sharing with net mass transfer has been found using information from both the heavy fragments and the light charged particles. The ratio of hydrogen and helium multiplicities points to a further correlation of angular momentum sharing with net mass transfer. Received: 18 September 2000 / Accepted: 2 December 2000     

Electromagnetic form factors of the nucleon

Dynamical and thermal characterizations of excited nuclear systems produced during the collisions between two heavy ions at intermediate incident energies are presented by means of a review of experimental and theoretical work performed in the last two decades. Intensity interferometry, applied to both charged particles (light particles and intermediate mass fragments) and to uncharged radiation (gamma rays and neutrons) has provided relevant information about the space-time properties of nuclear reactions. The volume, lifetime, density and relative chronology of particle emission from decaying nuclear sources have been extensively explored and have provided valuable information about the dynamics of heavy-ion collisions. Similar correlation techniques applied to coincidences between light particles and complex fragments are also presented as a tool to determine the internal excitation energy of excited primary fragments as it appears in secondary-decay phenomena.     

Complete and incomplete fusion in reactions of 7Li + 56Fe at E(7Li) = 50 and 68 MeV from analysis of recoil range and light-particle measurements

Excitation functions for the production of eight radioactive products of the reactions of ⁷Li on ⁵⁶Fe have been measured up to E(⁷ Li) = 89 MeV. Recoil range distributions for these products, together with inclusive proton, deuteron, triton and alpha spectra, have been measured at energies of 50 and 68 MeV. The α, t and d spectra show characteristic “break-up” components at forward angles, while the recoil distributions show evidence of complete fusion and incomplete-fusion process ⁵⁶Fe( ⁷Li,α) ⁵⁹Co ^* . A parallel study on ⁵⁵Mn shows some evidences of the ( ⁷Li,t) incomplete-fusion process, but the cross-section for this process is significantly less than for the triton fusion process. The recoil distributions can be reproduced on the assumption that essentially all the observed break-up fragments are in fact associated with incomplete fusion, but uncertainties in normalisation leave open the possibility of a significant contribution of pure break-up. A diffraction model of the ( ⁷Li,α) transfer process reproduces the observed break-up α spectra with some success. Received: 29 March 2001 / Accepted: 12 November 2001     

Two-proton small-angle correlations in central heavy-ion collisions: A beam-energy- and system-size-dependent study

Small-angle correlations of pairs of protons emitted in central collisions of Ca + Ca, Ru + Ru and Au + Au at beam energies from 400 to 1500MeV per nucleon are investigated with the FOPI detector system at SIS/GSI Darmstadt. Dependences on system size and beam energy are presented which extend the experimental data basis of pp correlations in the SIS energy range substantially. The size of the proton-emitting source is estimated by comparing the experimental data with the output of a final-state interaction model which utilizes either static Gaussian sources or the one-body phase-space distribution of protons provided by the BUU transport approach. The trends in the experimental data, i.e. system size and beam energy dependences, are well reproduced by this hybrid model. However, the pp correlation function is found rather insensitive to the stiffness of the equation of state entering the transport model calculations.     

Multifractal critical thermodynamics in nucleus-nucleus collisions

Critical points approach in the frames of multifractal thermodynamics is suggested to interpret the experimental data on nuclear multifragmentation which come from interactions in nuclear emulsion (in which ¹⁹⁷ ₇₉Au₁₁₈ nuclei of energy ∼1 GeV/nucleon break up into fragments) and from the charge distributions of projectile fragments in sulphur (³²S) fragmentation at 200 GeV/nucleon. It is also shown that multifragmentation after macro-solids collisions exhibits properties analogous to those observed in the nuclear multifragmentation experiments. Received: 19 October 1999     

Emission order of light particles and light fragments from hot nuclei followed by binary fission

Emission orders of light charged particles and Li fragments from highly excited fissioning nuclei in the reaction of ⁴⁰Ar+¹⁹⁷Au at E _beam /A=25 MeV have been studied by measuring difference velocity distributions of two correlated particles at small relative angles in coincidence with two fission fragments. By comparing the data with three-body trajectory calculations, we found that high velocity deuterons are emitted prior to high velocity Li fragments but low velocity deuterons are emitted after low velocity Li fragments. On the other hand, no preferential emission was observed among light particles, such as protons and deuterons. Furthermore, the emission orders are found to depend only weakly on the mass asymmetry of fission fragments. Received: 3 June 1997 / Revised version: 23 July 1997     

Isospin effects on squeeze-out flow in heavy-ion collisions

The squeeze-out flow in reactions of ¹²⁴Sn + ¹²⁴Sn and ¹²⁴Ba + ¹²⁴Ba at different incident energies for different impact parameters is investigated by means of an isospin-dependent quantum molecular dynamics model. For the first time, it is found that the more neutron-rich system (¹²⁴Sn + ¹²⁴Sn) exhibits weaker squeeze-out flow. This isospin dependence of the squeeze-out flow is shown to mainly result from the isospin dependence of nucleon-nucleon cross-section and the symmetry energy. Received: 14 March 2000 / Accepted: 29 September 2000