13 research outputs found
Conditions for equivalence of Statistical Ensembles in Nuclear Multifragmentation
Statistical models based on canonical and grand canonical ensembles are
extensively used to study intermediate energy heavy ion collisions. The
underlying physical assumption behind canonical and grand canonical models is
fundamentally different, and in principle agree only in the thermodynamical
limit when the number of particles become infinite. Nevertheless, we show that
these models are equivalent in the sense that they predict similar results if
certain conditions are met even for finite nuclei. In particular, the results
converge when nuclear multifragmentation leads to the formation of
predominantly nucleons and low mass clusters. The conditions under which the
equivalence holds are amenable to present day experiments.Comment: 5 pages, 5 figure
Effect of secondary decay on isoscaling: Results from the canonical thermodynamical model
The projectile fragmentation reactions using beams
at 140 MeV/n on targets are studied using the canonical
thermodynamical model coupled with an evaporation code. The isoscaling property
of the fragments produced is studied using both the primary and the secondary
fragments and it is observed that the secondary fragments also respect
isoscaling though the isoscaling parameters and changes. The
temperature needed to reproduce experimental data with the secondary fragments
is less than that needed with the primary ones. The canonical model coupled
with the evaporation code successfully explains the experimental data for
isoscaling for the projectile fragmentation reactions
Comparison of heavy-ion transport simulations: Collision integral with pions and Δ resonances in a box
We compare ten transport codes for a system confined in a box, aiming at
improved handling of the production of resonances and pions, which is
indispensable for constraining high-density symmetry energy from observables
such as the yield ratio in heavy-ion collisions. The system in a
box is initialized with nucleons at saturation density and at 60 MeV
temperature. The reactions and
are implemented, but the Pauli blocking and the
mean-field potential are deactivated in the present comparison. Results are
compared to those from the two reference cases of a chemically equilibrated
ideal gas mixture and of the rate equation. In the results of the numbers of
and , deviations from the reference values are observed in many
codes, and they depend significantly on the size of the time step. These
deviations are tied to different ways in ordering the sequence of collisions
and decays, that take place in the same time step. Better agreements are seen
in the reaction rates and the number ratios among the isospin species of
and . These are, however, affected by the correlations, which are
absent in the Boltzmann equation, but are induced by the way particle
scatterings are treated in transport calculations. The uncertainty in the
transport-code predictions of the ratio for the system
initialized at n/p = 1.5, after letting the existing resonances decay,
is found to be within a few percent, which is sufficiently small so that it
does not strongly impact constraining the high-density symmetry energy from
heavy-ion collisions. Most of the sources of uncertainties have been
understood, and individual codes may be further improved. This investigation
will be extended in the future to heavy-ion collisions to ensure the problems
identified here remain under control.Comment: 36 pages, 27 figures; a new Fig. 21 and revised results from some
codes, achieving improved and consistent understandin
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
Comparison of heavy-ion transport simulations: Mean-field dynamics in a box
Within the transport model evaluation project (TMEP) of simulations for heavy-ion collisions, the mean-field response is examined here. Specifically, zero-sound propagation is considered for neutron-proton symmetric matter enclosed in a periodic box, at zero temperature and around normal density. The results of several transport codes belonging to two families (BUU-like and QMD-like) are compared among each other and to exact calculations. For BUU-like codes, employing the test particle method, the results depend on the combination of the number of test particles and the spread of the profile functions that weight integration over space. These parameters can be properly adapted to give a good reproduction of the analytical zero-sound features. QMD-like codes, using molecular dynamics methods, are characterized by large damping effects, attributable to the fluctuations inherent in their phase-space representation. Moreover, for a given nuclear effective interaction, they generally lead to slower density oscillations, as compared to BUU-like codes. The latter problem is mitigated in the more recent lattice formulation of some of the QMD codes. The significance of these results for the description of real heavy-ion collisions is discussed