Classical microscopic calculations of high-energy collisions of heavy ions

Nonrelativistic classical microscopic (equations of motion) calculations have been made for collisions between nuclei mostly with 50 nucleons each and for relative velocities of $0.5c$ and $0.8c$ (nonrelativistic laboratory energies of 117 and 300 MeV/nucleon, respectively). The trajectories of all the nucleons are calculated with two-body forces between all pairs of nucleons. The potentials are sums of attractive and repulsive Yukawa potentials of reasonable ranges and are adjusted to give reasonable binding and kinetic energies and to fit the $\mathrm{NN}$ cross section ${\sigma }_{\nu }$ appropriate for the viscosity and thus for shock phenomena; ${\sigma }_{\nu }$ strongly emphasizes transverse momentum transfers. Ensemble averages are taken over (10) initial distributions and care is taken to monitor—the relativelv minor—effects of evaporation of the individual noninteracting nuclei. Central collisions corresponding to small impact parameters $b$ (less than about a nuclear radius $R$) are "explosive" and seem fairly well equilibrated at maximum compression and subsequently. There is some similarity to development of shocks. After an initial penetration of about a mean free path, there is rapid dissipation of the collisional translational energy with associated large internal energies and large compressions (to somewhat less than twice normal density), followed finally by an explosive expansion; the angular distributions are roughly isotropic for quite small $b$ but show some transverse peaking for very small $b$. For small $b(\lesssim 0.5R)$ and for $v=0.5c$, but not for $0.8c$, we find large fused residues with $A\approx 60$. Transparency and nonequilibrium effects develop rapidly with increasing $b$ and are somewhat more important for $v=0.8c$ than for $0.5c$. For $b\gtrsim R$ (noncentral collisions) the nuclei retain much and for $b\gtrsim 1.5R$ most of their initial identity, suffering relatively little immediate mass loss with, however, quite appreciable loss of collisional translational energy for $b\approx R$.