Joseph Cugnon

New potentialities of the Liege intranuclear cascade (INCL) model for reactions induced by nucleons and light charged particles

ege intranuclear cascade (INC) model for the description of spallation reactions is presented in detail. Compared to the standard version (INCL4.2), it incorporates several new features, the most important of which are: (i) the inclusion of cluster production through a dynamical phase space coalescence model, (ii) the Coulomb deflection for entering and outgoing charged particles, (iii) the improvement of the treatment of Pauli blocking and of soft collisions, (iv) the introduction of experimental threshold values for the emission of particles, (v) the improvement of pion dynamics, (vi) a detailed procedure for the treatment of light-cluster-induced reactions taking care of the effects of binding energy of the nucleons inside the incident cluster and of the possible fusion reaction at low energy. Performances of the new model concerning nucleoninduced reactions are illustrated by a comparison with experimental data covering total reaction cross sections, neutron, proton, pion, and composite double-differential cross-sections, neutron multiplicities, residue mass and charge distributions, and residue recoil velocity distributions. Whenever necessary, the INCL4.6 model is coupled to the ABLA07 de-excitation model and the respective merits of the two models are then tentatively disentangled. Good agreement is generally obtained in the 200 MeV to 2 GeV range. Below 200 MeV and down to a few tens of MeV, the total reaction cross section is well reproduced and differential cross sections are reasonably well described. The model is also tested for light-ion induced reactions at low energy, below 100 MeV incident energy per nucleon. Beyond presenting the update of the INCL4.2 model, attention has been paid to applications of the new model to three topics for which some particular aspects are discussed for the first time. The first topic is the production of clusters heavier than alpha particle. It is shown that the energy spectra of these produced clusters are consistent with coalescence. The second topic regards the longitudinal residue recoil velocity and its fluctuations. Excellent results are obtained for these quantities. It addition, it is shown that the distributions of these quantities display typical random-walk characteristics, at least for not-too-large mass losses. They are interpreted as a direct consequence of the independence of successive binary collisions occurring during the cascade process. The last topic concerns the total reaction cross section and the residue-production cross sections for low-energy incident light ions. It is shown that our new model can give a rather satisfactory account of these cross sections, offering so an alternative to fusion models and the advantage of a single model for the progressive change from fusion to pre-equilibrium mechanisms.

Improved Intranuclear Cascade Model for Nucleon-Nucleus Interactions

Abstract The intranuclear cascade (INC) plus evaporation model for nucleon-nucleus interactions in the 200 MeV–1.2 GeV range is revisited. The standard Liege INC model supplemented by the Dresner evaporation-fission model is used and shown to give a good overall agreement with experimental data, basically neutron double differential cross-sections and residue mass spectra. Small systematic discrepancies are identified and shown to correspond to the single scattering contribution. Improvements of the INC model, linked with in-medium cross-sections, refraction of particles at the nuclear surface, treatment of the Pauli blocking, description of nuclear surface, collision mode and hadronisation time are discussed. The problem of the stopping time at which the cascade model gives place to the evaporation model is examined in detail. The introduction of a pre-equilibrium step, intermediate between the cascade and evaporation steps is investigated and shown to bring no significant improvement of the predictions. The production of composites and of intermediate mass fragments is shortly studied, with the help of the standard model, of the three step model mentioned above and of a cascade plus percolation model.

PION PRODUCTION IN CENTRAL HIGH-ENERGY NUCLEAR COLLISIONS

Abstract A model for pion production is studied in the context of a cascade calculation. The pions are produced through Δ-resonances which are allowed to decay. The emitted pions are assumed to interact with the other nucleons by forming new Δ -resonances. The time evolution of the pion and Δ-population is studied; it is found that Δs are always more numerous than pions during the sequence of baryon-baryon collisions. The spectrum of the pions is in considerably better agreement with experiment than the one obtained with frozen Δ-isobars. The presence of Δ-resonances appears to be important for the cooling of the pion system. The pion multiplicity is found to deviate from a Poisson distribution. The pion yield is overestimated by at least 25%; this result is discussed within the framework of conventional dynamics.

Hot nuclear matter in an extended Brueckner approach

Abstract The properties of cold and hot nuclear matter are studied in the frame of the Brueckner theory, extended to finite temperature. The basic task is the evaluation of the two-hole line diagram using the Paris potential supplemented by the introduction of three-body forces, coming from the exchange of π and ρ mesons. The latter have an important saturating effect, but not sufficient to reach correct saturation. The latter is achieved by a phenomenological treatment. The properties of hot nuclear matter, for temperatures around 10 MeV, are investigated. Particular attention is paid to one-body properties. The density and temperature dependence of many quantities, like the single-particle energy spectrum, the optical potential, the effective mass, the non-locality of the single-particle field, the mean free path, is displayed and analyzed. The relative importance of the temperature dependence of the g -matrix and of phase space is investigated, especially in relation with the imaginary part of the optical potential and the mean free path. The temperature dependence of the effective mass is particularly studied. It is shown that the peak due to the so-called core polarization effect disappears rapidly as the matter is heated. The evaluation of the entropy and of the level density parameter a , which are closely related, is discussed, and the failure of the Hartree-Fock approach to reproduce the value of a correctly is explained. Two-body properties are also investigated. The temperature and density dependence of the two-body correlations are displayed. Particular attention is paid to the temperature dependence of the effective interaction. The latter is exhibited in a simple manner. It is shown that the effective force felt by low-energy nucleons does not change by more than a few percent when the temperature goes from 0 to 10 MeV. For high-energy nucleons, the change may be as large as ten percent.

Superfluidity in neutron matter and nuclear matter with realistic interactions

Abstract The 1S0 superfluidity of neutron matter and nuclear matter is studied by solving the gap equation exactly for two realistic nuclear potentials, namely the Paris and the Argonne v14 potential. For neutron matter, the predicted domain of superfluidity is very close to previous results, whereas differences appear in the predicted value of the maximum gap. The results are, however, very close to each other for the two potentials mentioned above. The role of the large momentum component is underlined and the accuracy of several approximations is discussed. The temperature dependence is exhibited. For nuclear matter, the superfluidity disappears at smaller density. The gap is rather small for equilibrium density. The condensation energy estimated through a local-density approximation is dominated by the surface contribution. The definition of the pairing interaction is discussed and an illustrative calculation for an effective interaction is presented.

Medium Polarization Effects on Neutron Matter Superfluidity

Abstract We solve the 1 S 0 gap equation for neutron matter using an effective interaction based on the Argonne V 14 potential that includes effects of the polarization (RPA) graphs. We find a substantial reduction of the gap, and a slight extension of the domain of superfluidity to larger densities. We demonstrate the inadequacy of using the weak coupling approximation.

Nuclear mean field with correlations at finite temperature

Abstract Zero and finite temperature contributions of ground state correlations to the nuclear mean field are studied in nuclear matter at normal density. The framework is the nonrelativistic hole line expansion with the Paris potential as the bare NN interaction. For different temperatures we calculate single particle properties including correlation contributions in the self-consistent determination of the single-particle energies. We evaluate the nucleon effective mass and the energy mass. Their temperature dependence is studied and related to that of the level density parameter. We also calculate the momentum distribution of nucleons and discuss its behaviour at large momenta. In the present approach the spectral function and the lifetime of hole state can be obtained directly. We present our first results and analyze them briefly. Finally, we examine the important aspects of the conserving character of the approximations made in the course of this study.

Proton-nucleus interaction at high energy

Abstract The interaction of high energy protons (between 100 MeV and 20 GeV incident energy) with nuclei is studied in the frame of an intranuclear cascade (INC) model. Particular attention is paid to the energy loss of the projectile and on the emission patterns. It is shown that, in general, the incident proton has left the nucleus before the emission process starts. The latter proceeds first on a rather short time scale and involves fast particles. Progressively the emission rate slows down and the ejected particles are less rapid. The target mass, energy and impact parameter dependences of the energy loss is displayed. As a by-product, we calculate the nuclear stopping power. We investigate the fluctuations in the number of primary collisions, i.e. those suffered by the incoming nucleon, and in the energy loss. Fluctuations in the number of ejectiles are also studied as well as the relationship between primary collisions and the number of fast (grey) particles. The latter number is tentatively related with the number of site vacancies in percolation models. The entropy created inside the target is also calculated. It is shown that the representative point of the system in the (internal energy, entropy) plane spends a relatively long time in the coexistence zone and even in the instability zone corresponding to gas-liquid transition. Implications for these two models of fragmentation are discussed. A preliminary comparison with energy loss measurements in the 3–4 GeV/ c range is performed.

Proton and neutron superfluidity in neutron star matter

Abstract The 3 P 2 neutron superfluidity and the 1 S 0 proton superfluidity in neutron star matter are investigated by solving the gap equation exactly for a realistic nucleon-nucleon potential, namely the Argonne v 14 potential. For the 3 P 2 case, our results point to a nearly isotropic pairing function, in close analogy with the rigorous result obtained by Balian and Werthamer for S = 1 pairing without J -dependence. The proton abundance and the 1 S 0 proton gap are calculated and their relationship with the symmetry energy is discussed.

Global variables and the dynamics of relativistic nucleus-nucleus collisions

Abstract Various global variables providing a simple description of high multiplicity events are reviewed. Many of them are calculated in the framework of an intra-nuclear cascade model, which describes the collision process as a series of binary on-shell relativistic baryon-baryon collisions and which includes inelasticity through the production of Δ-resonances. The calculations are first made for the Ar + KCl system at 0.8 GeV/A, with global variables including either all the nucleons or only the participant nucleons. The shape and the orientation of the ellipsoid of sphericity are particularly investigated. For both cases, on the average, the large axis of the ellipsoid is found to point in the beam direction. This result is discussed in comparison with hydrodynamics predictions and in relation with the mean free path. A kind of small “bounce-off effect” is detected for intermediate impact parameters. The possibility of extracting the value of the impact parameter b from the value of a global variable is shown to depend upon the variation of this variable with b and upon the fluctuation of the global variable for a given impact parameter. A quality factor is denned to quantify this possibility. No current global variable seems to be more appropriate than the number of participant nucleons for the impact parameter selection. The physical origin of the fluctuations inside the intranuclear cascade model is discussed and the possibility of extracting useful information on the dynamics of the system from the fluctuations is pointed out. The energy dependence of our results is discussed. Some results of the calculations at 250 and 400 MeV/A are also presented for the same system Ar + KC1.