Momentum dependence of the symmetry potential and nuclear reactions induced by neutron-rich nuclei at RIA

Effects of the momentum-dependence of the symmetry potential in nuclear reactions induced by neutron-rich nuclei at RIA energies are studied using an isospin- and momentum-dependent transport model. It is found that symmetry potentials with and without the momentum-dependence but corresponding to the same density-dependent symmetry energy $E_{sym}(\rho)$ lead to significantly different predictions on several $E_{sym}(\rho)$-sensitive experimental observables. The momentum-dependence of the symmetry potential is thus critically important for investigating accurately the equation of state (${\rm EOS}$) and novel properties of dense neutron-rich matter at RIA.Comment: Rapid Communication, Phys. Rev. C in pres

A Transport Model for Nuclear Reactions Induced by Radioactive Beams

Major ingredients of an isospin and momentum dependent transport model for nuclear reactions induced by radioactive beams are outlined. Within the IBUU04 version of this model we study several experimental probes of the equation of state of neutron-rich matter, especially the density dependence of the nuclear symmetry energy. Comparing with the recent experimental data from NSCL/MSU on isospin diffusion, we found a nuclear symmetry energy of $)\approx 31.6(\rho /\rho_{0})^{1.05}$ at subnormal densities. Predictions on several observables sensitive to the density dependence of the symmetry energy at supranormal densities accessible at GSI and the planned Rare Isotope Accelerator (RIA) are also made.Comment: 10 pages. Talk given at the 2nd Argonne/MSU/JINA/INT RIA Workshop at MSU, March 9-12, 2005 to be published in the Proceedings by the American Institute of Physic

A schematic model for fragmentation and phase transition in nuclear collisions

We develop here a simple yet versatile model for nuclear fragmentation in heavy ion collisions. The model allows us to calculate thermodynamic properties such as phase transitions as well as the distribution of fragments at disassembly. In spite of its simplicity the model gives very good fit to recent data taken at the Michigan National Superconducting Cyclotron Laboratory. The model is an extension of a lattice gas model which itself has strong overlaps with percolation models which have been used in the past to compare with nuclear fragmentation data.Comment: 12 pages (RevTex), 4 figures (uuencoded ps file), To appear in Phys. Lett.

Effects of momentum-dependent symmetry potential on heavy-ion collisions induced by neutron-rich nuclei

Using an isospin- and momentum-dependent transport model we study effects of the momentum-dependent symmetry potential on heavy-ion collisions induced by neutron-rich nuclei. It is found that symmetry potentials with and without the momentum-dependence but corresponding to the same density-dependent symmetry energy $E_{sym}(\rho)$ lead to significantly different predictions on several $E_{sym}(\rho)$-sensitive experimental observables especially for energetic nucleons. The momentum- and density-dependence of the symmetry potential have to be determined simultaneously in order to extract the $E_{sym}(\rho)$ accurately. The isospin asymmetry of midrapidity nucleons at high transverse momenta is particularly sensitive to the momentum-dependence of the symmetry potential. It is thus very useful for investigating accurately the equation of state of dense neutron-rich matter.Comment: The version to appear in Nucl. Phys. A. A paragraph and a figure on neutron and proton effective masses in neutron-rich matter are adde

Lattice gas model for fragmentation: From Argon on Scandium to Gold on Gold

The recent fragmentation data for central collisions of Gold on Gold are even qualitatively different from those for central collisions of Argon on Scandium. The latter can be fitted with a lattice gas model calculation. Effort is made to understand why the model fails for Gold on Gold. The calculation suggests that the large Coulomb interaction which is operative for the larger system is responsible for this discrepancy. This is demonstrated by mapping the lattice gas model to a molecular dynamics calculation for disassembly. This mapping is quite faithful for Argon on Scandium but deviates strongly for Gold on Gold. The molecular dynamics calculation for disassembly reproduces the characteristics of the fragmentation data for both Gold on Gold and Argon on Scandium.Comment: 13 pages, Revtex, 8 figures in ps files, submitted to Phys. Rev.

A unified description for nuclear equation of state and fragmentation in heavy ion collisions

We propose a model that provides a unified description of nuclear equation of state and fragmentations. The equation of state is evaluated in Bragg-Williams as well as in Bethe-Peierls approximations and compared with that in the mean field theory with Skyrme interactions. The model shows a liquid-gas type phase transition. The nuclear fragment distributions are studied for different densities at finite temperatures. Power law behavior for fragments is observed at critical point. The study of fragment distribution and the second moment $S_2$ shows that the thermal critical point coincides with the percolation point at the critical density. High temperature behavior of the model shows characteristics of chemical equilibrium.Comment: 20 pages in RevTex, 11 figures (uuencoded ps files), to appear in Phys. Rev.

Statistical Models of Nuclear Fragmentation

A method is presented that allows exact calculations of fragment multiplicity distributions for a canonical ensemble of non-interacting clusters. Fragmentation properties are shown to depend on only a few parameters. Fragments are shown to be copiously produced above the transition temperature. At this transition temperature, the calculated multiplicity distributions broaden and become strongly super-Poissonian. This behavior is compared to predictions from a percolation model. A corresponding microcanonical formalism is also presented.Comment: 12 pages, 5 figure

First Order Phase Transition in Intermediate Energy Heavy Ion Collisions

We model the disassembly of an excited nuclear system formed as a result of a heavy ion collision. We find that, as the beam energy in central collisions in varied, the dissociating system crosses a liquid-gas coexistence curve, resulting in a first-order phase transition. Accessible experimental signatures are identified: a peak in specific heat, a power-law yield for composites, and a maximum in the second moment of the yield distribution

Momentum--dependent nuclear mean fields and collective flow in heavy ion collisions

We use the Boltzmann-Uehling-Uhlenbeck model to simulate the dynamical evolution of heavy ion collisions and to compare the effects of two parametrizations of the momentum--dependent nuclear mean field that have identical properties in cold nuclear matter. We compare with recent data on nuclear flow, as characterized by transverse momentum distributions and flow ($F$) variables for symmetric and asymmetric systems. We find that the precise functional dependence of the nuclear mean field on the particle momentum is important. With our approach, we also confirm that the difference between symmetric and asymmetric systems can be used to pin down the density and momentum dependence of the nuclear self consistent one--body potential, independently. All the data can be reproduced very well with a momentum--dependent interaction with compressibility K = 210 MeV.Comment: 15 pages in ReVTeX 3.0; 12 postscript figures uuencoded; McGill/94-1

Comparison of heavy-ion transport simulations: Collision integral in a box

Simulations by transport codes are indispensable to extract valuable physical information from heavy-ion collisions. In order to understand the origins of discrepancies among different widely used transport codes, we compare 15 such codes under controlled conditions of a system confined to a box with periodic boundary, initialized with Fermi-Dirac distributions at saturation density and temperatures of either 0 or 5 MeV. In such calculations, one is able to check separately the different ingredients of a transport code. In this second publication of the code evaluation project, we only consider the two-body collision term; i.e., we perform cascade calculations. When the Pauli blocking is artificially suppressed, the collision rates are found to be consistent for most codes (to within 1 % or better) with analytical results, or completely controlled results of a basic cascade code. In orderto reach that goal, it was necessary to eliminate correlations within the same pair of colliding particles that can be present depending on the adopted collision prescription. In calculations with active Pauli blocking, the blocking probability was found to deviate from the expected reference values. The reason is found in substantial phase-space fluctuations and smearing tied to numerical algorithms and model assumptions in the representation of phase space. This results in the reduction of the blocking probability in most transport codes, so that the simulated system gradually evolves away from the Fermi-Dirac toward a Boltzmann distribution. Since the numerical fluctuations are weaker in the Boltzmann-Uehling-Uhlenbeck codes, the Fermi-Dirac statistics is maintained there for a longer time than in the quantum molecular dynamics codes. As a result of this investigation, we are able to make judgements about the most effective strategies in transport simulations for determining the collision probabilities and the Pauli blocking. Investigation in a similar vein of other ingredients in transport calculations, like the mean-field propagation or the production of nucleon resonances and mesons, will be discussed in the future publications