Anisotropy in High Energy Nucleus - Nucleus Collisions

The predictions of event anisotropy parameters from transport model RQMD are compared with the recent experimental measurements for 158A GeV Pb+Pb collisions. Using the same model, we study the time evolution of event anisotropy at 2A GeV and 158A GeV for several colliding systems. For the first time, both momentum and configuration space information are studied using the Fourier analysis of the azimuthal angular distribution. We find that, in the model, the initial geometry of the collision plays a dominant role in determining the anisotropy parameters. 1 Event anisotropy, often called flow, has been observed in heavy ion collisions at every laboratory energy [1–9]. It is believed that the information about the equation of state (EOS) can be obtained from the study of flow [10]. Recently, several authors argue that the event shape with respect to the reaction plane may carry the information about pressure created at the early stage of the collision [11–15]. Theoretically, in terms of hydrodynamics, the connection between the EOS and flow is well defined and has been studied extensively for many years. This is especially the case for collisions at beam energy below 15A GeV. (For the latest review of the subject, see Ref. [9,16].) However, it is still not clear whether the experimentally observed event anisotropy is of a dynamic origin (pressure-driven hydroexpansion) or due to shadowing of cold nuclear matter, passing time etc. If the initial geometry of the system plays an important role, the information about the collision dynamics may be obscured. In any case, it seems to be necessary to understand the interplay between these two competing effects. For this purpose, we use the transport model RQMD(v2.3 cascade mode) [17] to study the event anisotropy as a function of the colliding system and beam energy. We also investigate the collision time dependence of the event shapes. In RQMD, the reaction plane is defined by the impact parameter (x direction) and the projectile momentum (z direction). Particle azimuthal distribution with respect to the reaction plane at a given rapidity window can be deconvoluted by the Fourier expansion [24], dN dφ ≈ v 0 (1 + 2v 1 cos(φ) + 2v 2 cos(2φ)) (1) where the first and second Fourier coefficients, v 1 and v 2 , are connected to the directed flow and elliptic flow, respectively [24]. The coefficient v 0 is a normalization constant and φ is defined as the azimuthal …