Relativistic nuclear fluid dynamics

By use of finite-difference methods we solve in three spatial dimensions the classical relativistic equations of motion for the collision of two heavy nuclei. These equations express the conservation of nucleon number, momentum, and energy, for a specified nuclear equation of state. For ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$+${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ at laboratory bombarding energies per nucleon of 250 MeV and 2.1 GeV, we calculate the time evolution of the matter distribution for several impact parameters. Nearly central collisions deform and compress the system enormously, whereas in peripheral collisions the projectile is fragmented into a portion that proceeds roughly straight ahead at its original velocity and other portion that deposits its energy in the target. For a given impact parameter we construct from the velocity vectors at some large time the energy and angular distributions for the expanding matter. An integration of these results over impact parameter then gives us the double differential cross section $\frac{d^2\sigma }{d\mathrm{Ed}\Omega }$. For the 250-MeV case we compare calculated and experimental results in the form of proton energy spectra for four laboratory angles ranging from 30° to 120°. The calculations reproduce correctly the experimental slopes at each angle, as well as the overall decrease in the experimental cross section when going from forward to backward angles. However, at 30° the calculated values are only one-half the experimental ones, whereas at 120° they are twice as large. These comparisons, together with comparisons of calculations done by other workers, suggest that heavy nuclei are partially transparent to each other during collisions at high energy, but that the process is not solely a superposition of individual nucleon-nucleon collisions. Instead, coherent collective-field effects play some role.