Collective flow from the intranuclear cascade model.

The phenomenon of collective flow in relativistic heavy ion collisions is studied using the hadronic cascade model ARC. Direct comparison is made to data gathered at the Bevalac, for Au+Au at p = 1 − 2 GeV/c. In contrast to the standard lore about the cascade model, collective flow is well described quantitatively without the need for explicit mean field terms to simulate the nuclear equation of state. Pion collective flow is in the opposite direction to nucleon flow as is that of anti-nucleons and other produced particles. Pion and nucleon flow are predicted at AGS energies also, where, in light of the higher baryon densities achieved, we speculate that equation of state effects may be observable. Collective flow in relativistic heavy ion collisions has long been a subject of interest, since it was felt the phenomenon might carry information about the nuclear matter equation of state. In this letter, we will be concerned only with the so-called ‘Sideward Flow’, which is related to an event-by-event azimuthal asymmetry in the distribution of final state particles. Theories which have been used to describe the heavy ion collisions fall into two broad classes: those based on macroscopic thermodynamical/hydrodynamical considerations, and those which attempt a more microscopic description of the ion–ion collision, for instance by carrying out successive collisions (cascading) of the elementary (hadronic) constituents. Among the microscopic models one can distinguish pure cascade models, which include only the elementary 2or in principle n-body collisions of the constituents. These models take as their main input the experimentally measured cross-sections (and angular distributions) for hadron-hadron σ(hh → X) in free space, and then carry out the ion–ion collision by Monte-Carlo methods. The model, ARC = A Relativistic Cascade, which we will use to discuss flow, is such a pure hadronic cascade model. Additionally, there are microscopic models which include mean field, collective, or inmedium effects in some fashion, as well as treating the elementary hadron–hadron collisions. Both classes of microscopic model presumably simulate semi-classical (relativistic) kinetic theory of the hadron gas in some limit, and these models would then be equivalent to solving transport equations, either Boltzmann-Vlasov, or Boltzmann-Vlasov-Uehling-Uehlenbeck (BUU), depending on whether or not a mean field is included from the outset. In the BUU case, the mean field enters through the gradient of a potential energy, which may be calculated, e.g., from a phenomenological equation of state for nuclear matter. Our treatment of flow using ARC will neglect mean fields entirely, and this is based on the assumption that the mean field U satisfies U ≪ T where T is the typical kinetic energy involved in a hadron–hadron collision within the cascade. For the initial nucleon–nucleon collisions in Au+Au at p = 1.7 GeV/c this is a reasonable assumption, but of course the kinetic energy available in successive collisions cascades down as the ion+ion collision takes place. So, the mean field may not be negligible in late or very soft collisions or for co-moving spectators in the projectile and target. However, a spectator cut is applied to the data and to ARC so as to reject particles having small kinetic energy in the projectile or target frames. We expect therefore that mean field contributions will not be dominant. Indeed, we shall see that ARC, using un-modified free space cross-sections and no mean field is, at least by direct calculation, adequate to the task of describing sideward flow in Au+Au at Bevalac energies. Given the prior extensive success of ARC in predicting and describing inclusive data for heavy ion collisions at AGS energies, our strong theoretical prejudice would then be that mean fields and/or phenomenological equations of state need not be included over this range of energies (1-15 GeV/c). In-medium effects if and when they do arise ought then, in our point of view, to be included by modifying the elementary interactions. Nevertheless, the high baryon densities apparently achieved during massive ion collisions at AGS energies, may still manifest themselves through traditional equation of state effects. Our specific concern will be with the proton-like sideward flow measured at the Bevalac in Au+Au collisions at lab momentum p = 0.96− 1.9 GeV/c. Such data have already been measured using the Plastic Ball spectrometer, and new experiments with better immunity to detector distortions were recently carried out using the EOS time projection chamber; flow results from the EOS collaboration are expected to be available later this year. We anticipate the EOS data by considering forward rapidity data only in our comparisons, as is reasonable given the downstream location of the EOS detector. By proton-like, we mean to say that protons contained in identified outgoing nuclear fragments are counted towards the flow, together with outgoing free protons. We consider proton-like flow, because ARC does not as yet dynamically include the production of nuclear fragments larger than single nucleons. Coalescence calculations for deuterons and tritons from ARC have been carried out at AGS energies, and are in good agreement with data. There is in principle no obstacle to carrying these calculations to lower energy. We calculate sideward flow à la Danielewicz and Odyniec, by first defining a reaction plane for the ion+ion collision, neglecting pions, using the beam direction and a vector defined as a weighted average of outgoing transverse momenta: