Elliptic flow: Transition from out-of-plane to in-plane emission in Au + Au collisions

We have measured the proton elliptic flow excitation function for the Au+Au system spanning the beam energy range (2-8)A GeV. The excitation function shows a transition from negative to positive elliptic flow at a beam energy, Etr {approx} 4A GeV. Detailed comparisons with calculations from a relativistic Boltzmann equation are presented. The comparisons suggest a softening of the nuclear equation of state from a stiff form (K {approx} 380 MeV) at low beam energies (Ebeam < 2A GeV) to a softer form (K {approx} 210 MeV) at higher energies ( Ebeam < 4A GeV) where the calculated baryon density rho {approx} 4 rho 0.