Nuclear flow excitation function.

We consider the dependence of collective flow on the nuclear surface thickness in a Boltzmann–Uehling–Uhlenbeck transport model of heavy ion collisions. Well defined surfaces are introduced by giving test particles a Gaussian density profile of constant width. Zeros of the flow excitation function are as much influenced by the surface thickness as the nuclear equation of state, and the dependence of this effect is understood in terms of a simple potential scattering model. Realistic calculations must also take into account medium effects for the nucleon–nucleon cross section, and impact parameter averaging. We find that balance energy scales with the mass number as A, where y has a numerical value between 0.35 and 0.5, depending on the assumptions about the in-medium nucleon-nucleon cross section. PACS Indices: 25.70.-z, 02.70.Lq, 21.65.+f Broadly speaking, nuclear collective flow in a heavy ion collision is the deflection of nuclear matter perpendicular to the beam axis during the course of the reaction. Experimentally, one observes that flow disappears at a well defined beam energy [1][5], the so called balance energy EBal, whose value depends on the system and impact parameter range being considered. These zeros in the flow excitation function were predicted by the Boltzmann–Uehling–Uhlenbeck (BUU) transport model [6, 7], and an analysis of scale invariant quantities [8], and may be understood as an overall cancellation of the attractive part of the mean field interaction with repulsive contributions from the mean field and collisional kinetic pressure. Thus, as has been shown explicitly for BUU simulations in Ref. [3], EBal is expected to depend on both the nuclear equation of state and the magnitude of the in–medium nucleon–nucleon cross section. By making a systematic study of the balance energy as a function of the nuclear mass, one therefore hopes to gain insight into these properties. However, other parameters might well influence the balance energy. In particular, we wish to investigate in this note the effect of finite nuclear surface thicknesses and impact parameter variations on EBal. We begin by defining the flow variable to be used here, and point out the importance of obtaining well–defined nuclear surfaces that are independent of the grid size used to compute density gradients. We then show how the strong surface dependence of flow in a Vlasov simulation may be understood in terms of a simple potential scattering model. This dependence persists for full BUU calculations that include a non–zero collision integral. Lastly, we consider the effect on the balance energy when the mass number and impact parameter are varied. To analyze flow quantitatively in experiments one of the main problems that has to be addressed is the determination of the reaction plane (see, for example, Refs. [9]–[11]). In a model calculations, on the other hand, knowledge of the reaction plane immediately allows one to define a flow variable such as the average in–plane transverse momentum 〈wPx〉 = 1 N N