S.W. Huang

The role of the Δ (1920) resonance for kaon production in heavy ion collisions

Abstract The long mean free path of K+ mesons in nuclear matter this particle a suitable messenger for the dynamics of nucleus-nucleus reactions at intermediate energies (100 MeV to 3 GeV per nucleon). A prerequisite for this is the knowledge of the elementary production cross sections πN→∑K. Here these cross sections are studied for the first time with the explicit inclusion of the relevant baryon resonances up to 2 GeV as intermediate states. The baryon resonances - N(1710)I(J P ) = 1 2 ( 1 2 + ), N(1720) 1 2 ( 3 2 + ) and Δ(1920) 3 2 ( 3 2 + ) - are taken into account coherently in the calculations of the πN→∑K process. Also K ∗ (892) 1 2 (1 − ) vector meson exchange is included. It is shown that the total cross sections for different channels of the πN→∑K reactions, i.e. π+p→∑+K+, π−p→∑−K+, π+n→∑0K+ (π−p→∑−K+) and π0p→∑0K+ differ not only by absolute values but also by their energy dependence. This shape differences are due to the mixture of the isospin I = 3 2 Δ(1920) with isospin I = 1 2 nucleon resonances. However, this I = 3 2 resonance does not give a contribution to the πN → λK reactions. So the shapes of the total cross sections πN → λK for different isospin projections are the same. In spite of this, such cross sections averaged over different isospin projections in the same multiplet are often used for studies of kaon production in heavy ion collisions. Here we give an explicit separate parametrization of the cross sections for each channel πN → ∑K, which are calculated in this work.

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.

Resonance model of pi Delta to YK for kaon production in heavy-ion collisions

The elementary production cross sections pi Delta to YK (Y= Sigma , Lambda ) and pi N to YK are needed to describe kaon production in heavy-ion collisions. The pi N to YK reactions were studied previously by a resonance model. The model can explain quite well the experimental data obtained by us. In this article, the total cross sections pi Delta to YK at intermediate energies (from the kaon production threshold to 3 GeV of pi Delta centre-of-mass energy) are calculated for the first time using the same resonance model. The resonances, N(1710)I(JP)= 1/2 ( 1/2 +) and N(1720) 1/2 (3/2+) for the pi Delta to Sigma K reactions, and N(1650) 1/2 ( 1/2 -) N(1710) 1/2 ( 1/2 +) and N(1720) 1/2 (3/2+) for the pi Delta to Lambda K reactions are taken into account coherently as the intermediate states in the calculations. Also, t-channel K*(892) 1/2 (1-) vector-meson exchange is included. The results show that K*(892) exchange is negligible for the pi Delta to Sigma K reactions, whereas this meson does not contribute to the pi Delta to Lambda K reactions. Furthermore, the pi Delta to YK contributions to kaon production in heavy-ion collisions are not only non-negligible but also very different from the pi N to YK reactions. An argument valid for pi N to YK cannot be extended to pi Delta to YK reactions. Therefore, cross sections for pi Delta to YK correctly including the different isospins must be calculated for inclusion in simulation codes for kaon production in heavy-ion collisions, where no experimental data are available. Parametrizations of the total cross sections pi Delta to YK for kaon production in heavy-ion collisions are given based on this work.

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.

Consequences of a covariant description of heavy ion reactions at intermediate-energies

Heavy-ion collisions at intermediate energies are studied by using a new relativistic quantum molecular dynamics (RQMD) code, which is a covariant generalization of the quantum molecular dynamics (QMD) approach. We show that this new implementation is able to produce the same results in the nonrelativistic limit (i.e., 50 MeV/nucleon) as the noncovariant QMD. Such a comparison is not available in the literature. At higher energies (i.e., 1.5 GeV/nucleon and 2 GeV/nucleon) RQMD and QMD give different results in respect to the time evolution of the phase space, for example for the directed transverse flow. These differences show that consequences of a covarient description of heavy-ion reactions within the framework of RQMD exist even at intermediate energies.

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.

Kaon production in nucleus-nucleus collisions: Equation of state, momentum dependence and relativistic effects☆

Abstract We investigate the production of K + mesons in nucleus-nucleus collisions from 700 MeV/ A to 2500 MeV/ A within a fully Lorentz covariant (RQMD) and a non-covariant (QMD) quantum molecular dynamics. A Skyrme-type mean field is employed in the classical Hamilton equations of motion. The parameters of this potential are adjusted so that we have two different equations of state: a soft one with incompressibility K =200 MeV and a hard one with K =380 MeV. In the QMD we include also a phenomenological momentum dependence in the in-medium nucleon-nucleon (NN) interaction. A parametrized cross section is used for K + production in elementary baryon-baryon collisions (B 1 +B 2 →B+Y+K + ). We make detailed comparisons among the theoretical results obtained in the QMD and RQMD, with different nuclear equations of state, with and without the momentum dependence in the NN interaction and with different parametrizations for the elementary cross section. The theoretical K + production cross sections obtained in the RQMD are in good agreement with available experimental data for 20 Ne+NaF at 2100 MeV/ A and 28 Si+ 28 Si at 2000 MeV/ A , except for the high momentum tail of the kaon spectrum.

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.

Antikaon and antiproton production in nucleus-nucleus collisions with relativistic quantum molecular dynamics

Abstract In this paper we study the antikaon and antiproton productions in nucleus-nucleus collisions at intermediate bombarding energies. Relativistic quantum molecular dynamics (RQMD) is used to simulate dynamical evolution of nuclear reactions and generate stochastic baryon-baryon collisions where antikaons and antiprotons might be produced. The antikaons and antiprotons are assumed to be created predominantly in processes such as B 1 + B 2 → N + N + K + K and B 1 + B 2 → N + N + p + p . We compare our results obtained with different nuclear equations of state, with and without the absorption of antikaons and antiprotons by surrounding the nucleons; and different parametrizations for the elementary production cross section in the baryon-baryon collision. The theoretical results are also compared with the available experimental data.