Elliptic flow in heavy ion collisions near the balance energy

The proton elliptic flow in collisions of Ca on Ca at energies from 30 to 100 MeV/nucleon is studied in an isospin-dependent transport model. With increasing incident energy, the elliptic flow shows a transition from positive to negative flow. Its magnitude depends on both the nuclear equation of state (EOS) and the nucleon-nucleon scattering cross section. Different elliptic flows are obtained for a stiff EOS with free nucleon-nucleon cross sections and a soft EOS with reduced nucleon-nucleon cross sections, although both lead to vanishing in-plane transverse flow at the same balance energy. The study of both in-plane and elliptic flows at intermediate energies thus provides a means to extract simultaneously the information on the nuclear equation of state and the nucleon-nucleon scattering cross section in medium. PACS number(s): 25.70.-z, 25.75.Ld, 24.10.Lx Heavy ion collisions provide the possibility to study the properties of nuclear matter in conditions vastly different from that in normal nuclei, such as high density and excitation as well as large difference in the proton and neutron numbers [1–5]. Such knowledge is not only of interest in itself but also useful in understanding astrophysical phenomena such as the properties of the core of compact stars, the evolution of the early universe, and the formation of elements in stellar nucleosynthesis. One observable that has been extensively used for extracting such information from heavy ion collisions is the collective flow of various particles [6–21] (for a recent review, see Refs. [22–25]). For example, the proton flow in heavy ion collisions at 200 MeV/nucleon to 1 GeV/nucleon has been found to be consistent with a soft nuclear equation of state [7,8]. From the kaon flow in heavy ion collisions at 1 to 2 GeV/nucleon, the existence of a weak repulsive kaon potential has been obtained [10]. In heavy ion collisions at energies higher than 2 GeV/nucleon, recent studies of proton flow seem to indicate that there is a softening of nuclear equation of state as the nuclear density and excitation increase [18]. There are also suggestions that particle collective flows at ∗Permanent address: China Institute of Atomic Energy, P. O. Box 275(18), Beijing 102413, China