N. Ohtsuka

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.

Quantum molecular-dynamics approach to heavy-ion collisions with Brueckner G-matrix cross sections

Abstract We calculate the nucleon-nucleon cross section in the nuclear medium with the Brueckner G -matrix and apply it in the quantum molecular-dynamics (QMD) approach to the C-C and Nb-Nb reactions. QMD describes successfully the many-body dynamics of heavy-ion collisions using so far an isotropic NN cross section of 40 mb. Comparing the momentum transfer in transverse and longitudinal direction and the number of emitted particles calculated with the G -matrix cross section and the isotropic cross section, we find for these inclusive data only minor differences between the results in the C-C case but larger ones in the Nb-Nb case. A good agreement is obtained with the experimental double-differential cross section for charged-particle emission in the C-C reaction at E lab =84MeV/nucleon.

Real and imaginary parts of the microscopic optical potential between nuclei in the sudden and adiabatic approximation and its application to medium energy 12C-12C scattering☆

Abstract Real and imaginary parts of the optical potential between two nuclei have been calculated from the realistic two-nucleon interaction of Reid using the approach of Faessler and collaborators but with the following modifications: (a) A surface curvature term proportional to the square of the gradient of the density has been added to the energy density functional and the parameters are determined so as to reproduce the binding energies and rms radii of nuclei considered and (b) in addition to the sudden approximation, an adiabatic situation is also considered. Whereas, in the sudden approximation the density of the composite system is obtained by adding the densities of the two colliding nuclei, in the adiabatic approximation, the maximum density in the composite system is limited to the saturation value while conserving the nucleon number. Although the real part of the potential is in the center quite different in these two approximations, the cross sections are not. The real and imaginary parts of the optical potential are calculated for the nuclear pairs 12C+12C, 16O+16O, 40Ca+40Ca and 208Pb+208Pb for relative momenta per nucleon kr = 0 and 1 fm−1. Elastic, inelastic and reaction cross sections are calculated for 12C+12C scattering at Elab = 300, 360 and 1016 MeV using the calculated potential and coupling the elastic channel to the 2+ at 4.44 MeV and 3− at 9.64 MeV, and compared with the experimental data. The agreement with the data at 1016 MeV is satisfactory and the theory can also reproduce the general trend of the angular distributions at 300 and 360 MeV but the calculated values at larger angles overestimate the data. The energy dependence and the magnitude of the observed reaction cross section are well reproduced by the theory.

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.

Intermediate-energy heavy ion collisions with G matrix potentials and cross-sections

Abstract We present the first quantum molecular dynamics calculations of heavy-ion collisions in which the effective nucleon-nucleon potential and the nucleon-nucleon cross sections in a medium are consistently calculated in the Brueckner theory from the basic Reid soft-core potential. The strong momentum dependence of the Brueckner G -matrix yields a quite different time evolution of heavy-ion collisions as compared with that obtained via Skyrme potentials adjusted to nuclear matter properties and the optical potential. In the calculation of Nb+Nb collisions at 400 MeV/u, we find that the transverse momentum transfer is much larger than that obtained with the hard Skyrme potential, although the compressibility ( K = 182MeV) is even lower than that of the soft Skyrme potential ( K = 200MeV). This raises questions about the possibility of uniquely determining the parameters of the nuclear equation of state from heavy-ion collisions at intermediate energies. The momentum transfer has two physically quite different reasons: the strong momentum dependence of the G -matrix potential causes a strong transverse momentum very early in the time evolution of the reaction, i.e. before the system is compressed. Additional transverse momentum is transferred in the compression phase, similar to observations for Skyrme-like potentials. The momentum transfer in the second process is about that of the soft Skyrme potential, which is not unexpected because the compressibilities are similar and in both calculations about the same density is reached.

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.

Lorentz-covariant description of intermediate energy heavy-ion reactions in relativistic quantum molecular dynamics☆

Abstract We study the consequence of the Lorentz-covariant treatment in describing heavy-ion reactions by comparing the results of the fully covariant and those of the non-covariant quantum molecular dynamics approach. As examples 12 C 12 C collisions at laboratory energies 84, 800 and 2100 MeV/ A and 40 Ca 40 Ca at 1050 MeV/ A have been calculated in both approaches. The difference in the results for experimental cross section (inclusive proton and pion spectra) calculated in the two approaches is very small. For high energies, however, we find a significant difference in the time evolution of the maximum density and the number of NN collisions in 12 C 12 C collisions and the directed transverse momentum in 40 Ca 40 Ca collisions. This difference between the results of a Lorentz-covariant and a non-covariant treatment is much larger than that between the results with hard and soft equations of state.

Relativistic versus nonrelativistic quantum molecular dynamics

Abstract One of the most successful models to describe heavy ion reactions on the microscopic level is the Quantum Molecular Dynamics (QMD). At relativistic energies a covariant generalization of this model, the Relativistic Quantum Molecular Dynamics (RQMD), is available. We compare results concerning the time evolution of the phase space and particle production obtained by both methods at the intermediate energy range looking for relativistic effects in heavy ion collisions at these energies.

Microscopic study of thermal properties of the nuclear matter formed in heavy-ion collisions☆

Abstract The hot Thomas-Fermi formalism, generalized for the case of two interpenetrating pieces of nuclear matter, is applied to investigate thermal properties (the local temperature and entropy) of the nonequilibrium nuclear matter formed during the time evolution of heavy-ion collisions at intermediate energies. Simulations of 20 Ne+ 20 Ne, 40 Ca+ 40 Ca and 93 Nb+ 93 Nb collisions at E lab = 100−400 MeV/u are performed within the framework of the quantum molecular dynamics approach. The sensitivity of thermal properties to the nuclear equation of state as well as their connection with some other dynamic observables are discussed. The anisotropic effects of the nonequilibrium phase space distribution on the thermalization process and the energy- and impact-parameter-dependence of the calculated thermal quantities during the reaction time are studied in detail.

Photon production in heavy-ion collisions and nuclear equation of state

Abstract Photon-production cross sections in 12 C + 12 C, 40 Ca + 40 Ca and 93 Nb + 93 Nb collisions at E lab = 84 and 200 Me V are calculated within the framework of the quantum molecula dynamics approach. The sensitivity of the photon-production cross section to the different types of nuclear equation of state and the momentum dependence in the in-medium NN interaction is studied in detail. Although we found some difference between the soft and hard equation of state in the calculated photon-production cross section, it is suppressed strongly by the momentum dependence in the interaction. There is a sizeable difference between the results calculated with or without taking into account the momentum dependence in the in-medium interaction. The time dependence of the production of the high-energy photons arising from incoherent pn collisions is also studied. The heavier the masses of colliding nuclei, the more number of energetic photons are produced after the system reaches the maximum density, at the expansion stage. Therefore, the photon-production data for heavy colliding nuclei might provide sc me information on the in-medium NN interaction during the time evolution of the heavy-ion reaction.