Dao T. Khoa

Generalized folding model for elastic and inelastic nucleus–nucleus scattering using realistic density dependent nucleon–nucleon interaction

Abstract A generalized double-folding model for elastic and inelastic nucleus–nucleus scattering is presented. It is designed to accommodate effective nucleon–nucleon (NN) interactions that depend upon the density of nuclear matter in which the two nucleons are immersed. A recently parametrized density dependent M3Y interaction, based on the G-matrix elements of the Paris NN potential, has been used in the present folding calculation. The effects of knock-on exchange of the interacting nucleon pair are included in an accurate local approximation. Examples of the application of this model to study the refractive elastic and inelastic scattering data of 12 C+ 12 C and α+58,60Ni systems are presented. A detailed comparison of the use of deformed optical potential (DP) and microscopic folded potential in the analysis of inelastic scattering has shown that the use of DP fails to reproduce the inelastic 12 C+ 12 C scattering data measured over a wide angular range, which covers both the diffractive and refractive regions. The use of the DP model also significantly underestimates the nuclear deformation lengths of the quadrupole and octupole excitations under study.

Study of diffractive and refractive structure in the elastic 16O+16O scattering at incident energies ranging from 124 to 1120 MeV

Abstract The experimental data on elastic 16 O + 16 O scattering at incident energies ranging from 124 to 1120 MeV have been analyzed within the standard optical model (OM), using either the phenomenological (Woods-Saxon squared) potential or that calculated within the double-folding model for the real part of the optical potential. Structure of the elastic cross sections at smallest scattering angles was found to be of a pure diffractive nature, which enabled a consistent check of the absolute normalization of the elastic data under study. The OM analysis shows unambiguously the evolution of the refractive scattering pattern in the 16 O + 16 O system over this energy range. The large angle region of the data is dominated by the refractive far-side scattering. The oscillating Airy structure can be consistently described by a set of optical potentials with the real part given by the folding model and a weak absorptive imaginary potential.

Refractive alpha-nucleus scattering: a probe for the incompressibility of cold nuclear matter

Refractive α-nucleus scattering observed at intermediate energies is of great help in determining the α-nucleus potential at small distances, where the overlap density is large. A systematic folding analysis of the elastic α+12C, 40Ca and 90Zr scattering data at Elab = 59.1–172.5 MeV has been performed using effective density dependent NN interactions based on the G-matrix elements of the Reid- and Paris NN potentials. The new interactions consistently reproduce the saturation properties of cold nuclear matter and generate, at the same time, different values of the nuclear incompressibility K. With the existing refractive scattering patterns, it is possible to conclude from our folding analysis that a nuclear incompressibility K ⋍ 220 ± 50 MeV is the most realistic one.

A nuclear matter study using the density dependent M3Y interaction

Abstract The basic nuclear matter properties are calculated within the standard Hartree-Fock scheme using a Michigan version of the in-medium NN interaction (the so-called M3Y interaction). Due to the attractive character of the M3Y interaction, the saturation requirement for the nuclear matter is not fulfilled and the nuclear matter generated with this interaction is unstable against collapse. This necessitates the introduction of an appropriate density dependence into the original M3Y interaction. Our density dependent versions of the M3Y interaction consistently reproduce the equilibrium density and binding energy of the normal nuclear matter as well as the microscopic results (obtained by Jeukenne, Lejeune and Mahaux) for the nucleon optical potential. They can be used in the folding model to calculate the nucleon-nucleus and nucleus-nucleus potentials. A possible study of the cold nuclear equation of state through heavy-ion scattering, which is based on the use of the new interaction to calculate the heavy-ion optical potential, is also discussed.

In-medium effects in the description of heavy-ion collisions with realistic NN interactions☆

Abstract The simulations of 40Ca + 40Ca and 93Nb + 93Nb collisions at Elab = 400 MeV/u have been performed within the quantum molecular dynamics approach using both the phenomenological Skyrme forces and the Brueckner G-matrix potential as the in-medium NN interaction. The influence of the density and momentum dependence of the interaction on the time evolution of heavy-ion collisions is studied in detail. We found that the momentum dependence of the in-medium interaction strongly affects the density and temperature of the nuclear matter formed during collisions. Most of the results obtained for different observables are shown to be more sensitive to the momentum dependence of the interaction than to the nuclear equation of state. The strong repulsive G-matrix potential acting between nucleons with large relative momenta in the low-density region leads to an appreciably larger transverse momentum transfer and a smaller number of NN collisions compared with those obtained using the Skyrme potentials. Results obtained with the medium-dependent G-matrix NN cross section and those obtained with the phenomenological NN cross section parametrized by Cugnon et al. for the collision term are also compared.

New results for reaction cross sections of intermediate energy α-particles on targets from 9Be to 208Pb

Abstract Reaction cross sections for α -particles have been measured for 9 Be, 12 C, 16 O, 28 Si, 40 Ca, 58,60 Ni, 112,116,120,124 Sn, and 208 Pb at 117.2, 163.9 and 192.4 MeV and for the lighter nuclei also at 69.6 MeV. The results are compared with predictions from optical model calculations using phenomenological, global and double-folded optical potentials. Comparisons are also made with predictions using the Glauber model approach suggested by Bertsch, Brown and Sagawa.

In Medium Effects in description of Heavy Ion Collisions

Abstract The simulations of 40Ca + 40Ca and 93Nb + 93Nb collisions at Elab = 400 MeV/u have been performed within the quantum molecular dynamics approach using both the phenomenological Skyrme forces and the Brueckner G-matrix potential as the in-medium NN interaction. The influence of the density and momentum dependence of the interaction on the time evolution of heavy-ion collisions is studied in detail. We found that the momentum dependence of the in-medium interaction strongly affects the density and temperature of the nuclear matter formed during collisions. Most of the results obtained for different observables are shown to be more sensitive to the momentum dependence of the interaction than to the nuclear equation of state. The strong repulsive G-matrix potential acting between nucleons with large relative momenta in the low-density region leads to an appreciably larger transverse momentum transfer and a smaller number of NN collisions compared with those obtained using the Skyrme potentials. Results obtained with the medium-dependent G-matrix NN cross section and those obtained with the phenomenological NN cross section parametrized by Cugnon et al. for the collision term are also compared.

Nuclear rainbow scattering and nucleus–nucleus potential

Elastic scattering of α-particles and some tightly bound light nuclei has shown the pattern of rainbow scattering at medium energies, which is due to the refraction of the incident wave by a strongly attractive nucleus–nucleus potential. This review gives an introduction to the physics of the nuclear rainbow based essentially on the optical model description of the elastic scattering. Since the realistic nucleus–nucleus optical potential (OP) is the key to explore this interesting process, an overview of the main methods used to determine the nucleus–nucleus OP is presented. Given the fact that the absorption in a rainbow system is much weaker than that usually observed in elastic heavy-ion scattering, the observed rainbow patterns were shown to be linked directly to the density overlap of the two nuclei penetrating each other in the elastic channel, with a total density reaching up to twice the nuclear matter saturation density ρ0. For the calculation of the nucleus–nucleus OP in the double-folding model, a realistic density dependence has been introduced into the effective M3Y interaction which is based originally on the G-matrix elements of the Reid and Paris nucleon–nucleon (NN) potentials. Most of the elastic rainbow scattering data were found to be best described by a deep real OP like the folded potential given by this density-dependent M3Y interaction. Within the Hartree–Fock formalism, the same NN interaction gives consistently a soft equation of state of cold nuclear matter which has an incompressibility constant K≈ 230–260 MeV. Our folding analysis of numerous rainbow systems has shown that the elastic α-nucleus and nucleus–nucleus refractive rainbow scattering is indeed a very helpful experiment for the determination of the realistic K value. The refractive rainbow-like structures observed in other quasi-elastic scattering reactions have also been discussed. Some evidences for the refractive effect in the elastic scattering of unstable nuclei are presented and perspectives for future studies are discussed.

Subthreshold K+ production in 1GeV/u 197Au + 197Au collisions

Abstract We calculate the K + -production cross section in 197 Au+ 197 Au collisions at 1 GeV/u in the framework of quantum molecular dynamics (QMD). The Skyrme potentials, with parameters chosen to generate the soft and hard nuclear equations of state, are used in the propagation of nucleons within QMD. Our calculations show that the kaons are produced from an earlier stage of the collisions and mainly through a two-step process. Theoretical predictions with the soft equation of state are in good agreement with the experimental data from SIS at GSI. The results for soft and hard equations of state differ by approximately a factor 2 to 3.

Temperature-dependent mean field and its effect on heavy-ion reactions

Abstract Temperature-dependent mean field potentials of nucleons are obtained by solving the Bethe-Goldstone equation for a realistic force in nuclear matter at finite temperature. For a more efficient utilization of these potentials in studying the heavy-ion reactions using a transport theory, the density and temperature dependence of these potentials is parametrized in a Skyrme type form. These parametrized temperature-dependent potentials are implemented in quantum molecular dynamics. The temperature during the simulations is deduced using a hot Thomas-Fermi approach generalized for the case of two interpenetrating pieces of nuclear matter. First of all, we show that our formalism works well in the nuclear matter limit. In order to study the effect of temperature dependence in the mean-field potential in heavy-ion reactions, the reactions 40 Ca+ 40 Ca and 93 Nb+ 93 Nb are simulated using both a finite temperature-dependent potential and a temperature-independent (i.e. zero temperature) potential. Our detailed investigation shows that the temperature dependence of the mean field affects the heavy-ion reaction dynamics to a significant amount. These effects are stronger in case of heavier nuclei and are of the same order as the differences between the usual “soft” and “hard” equation of state. An analytical parametrization of the temperature dependence of the self-consistent field is given in a Skyrme type form.