Multi-Particle Azimuthal Collective Correlations In Heavy Ion Collisions At AGS Energies

One of the main goals of heavy ion collisions is to study nuclear matter under ex-treme conditions of high temperatures and high densities, i.e. to learn more about thenuclear equation of state. Collective ?ow of the nuclear matter in high energy heavy ioncollisions is a multi-particle collective motion and it is very sensitive to the maximumcompression reached in the early phase of a heavy ion reaction and hence can providean important probe for the nuclear equation of state. At GeV energies, due to the finitenumber of particles in an event, one can put many events together for the ?ow analyses toreduce the effects of statistical ?uctuations. However, much important information maybe lost in the averaging process. In this dissertation, we simulate the reactions of Au+Aucollisions using RQMD model to investigate multi-particle azimuthal collective correla-tions between the directed and elliptic ?ow in an event, explore formation mechanism ofthe elliptic ?ow, and study the time evolution of elliptic ?ow and the space-momentumcorrelations during the process of the collisions.The commonly used method of determining the collective ?ow of the estimated reac-tion plane is introduced. The directed and elliptic ?ow based on the method as a functionof the impact parameter, the incident energy and the transverse momentum of the finalstate particles are analyzed in Au+Au collisions at AGS energies simulated with RQMDmodel. The formation mechanism of the collective ?ow is also discussed. The calculatedresults by the estimated reaction plane can reproduce to some extent the real values in themodel. Without determining the estimated reaction plane, the multi-particle azimuthalcollective correlation between the directed and elliptic ?ow in an event can describe thecollectivity of nuclear matter in heavy ion collisions, and multi-particle azimuthal corre-lation function is established.A variable of multi-particle anisotropy to characterize the strength of multi-particlecollective correlation is introduced, and it can also re?ect the relative orientation betweenthe directed and elliptic flow. We use multi-particle azimuthal correlation function to an-alyze the multi-particle collective correlations between the nucleons and nucleons, andbetween the nucleons and pions as a function of the impact parameter, the incident en-ergy in Au+Au collisions at AGS energies. Our results show that the variable of multi- particle anisotropy can well describe the collectivity of the nuclear matter. We divide theevents into different groups according to the multi-particle collective correlations to over-come the finite numbers of particles in an event at GeV energies. The results in differentgroups show that the final anisotropy in the momentum space is correlated with the initialanisotropy in coordinate space in Au+Au collisions at AGS energies, and there are clearspace-momentum correlations during the whole dynamical evolution of the system.At AGS energies, elliptic flow is affected by the mean field, two body collisionsand the shadowing effects of the spectator regions, etc. We calculate the elliptic flow ofnucleons and pions as a function of the impact parameter, the incident energy and thetransverse momentum of the final state particles in Au+Au collisions with and withoutthe spectator regions at AGS energies. The results show that the shadowing effects ofthe spectator regions on the elliptic ?ow of nucleons and pions are obvious in Au+Aucollisions at AGS energies. The shadowing effects decrease with the increasing incidentenergy and increase with the increasing impact parameter. The shadowing effects of thespectator regions on the elliptic ?ow in the large transverse momentum region are moreobvious.