Density patterns and energy-angle distributions from a simple cascade scheme for lastNe20+U238collisions

A simple but fully three-dimensional cascade approach, appropriate for considering heavy-ion collisions at a few hundred MeV per projectile nucleon, is applied to ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ + ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$. For impact parameters $b_{\mathrm{NeU}}$ of 0 and 5 fm the calculated results include densities $\rho (\overrightarrow{\mathrm{r}},t)$ of nucleon masses during the collision and energy-angle distributions $\frac{d^{2}n}{\mathrm{dEd}\Omega }$ of scattered nucleon masses emerging from the collision. All of the present calculations use idealized nucleon-nucleon interactions implying cross sections ${\sigma }_{\mathrm{NN}}$ that are purely elastic, isotropic, and independent of the initial $\mathrm{NN}$ state. Some of these calculations also introduce excluded-volume effects, such as those associated with a classical hard core in the $\mathrm{NN}$ interaction. The calculated density $\rho (\overrightarrow{\mathrm{r}},t)$ is quite sensitive to changes in the size of the excluded volume (we tried hard cores of radius 0, 0.5, and 0.9 fm). However, it is only in the case of zero excluded volume that $\rho (\overrightarrow{\mathrm{r}},t)$ shows much sensitivity to changes in ${\sigma }_{\mathrm{NN}}$ (we tried ${\sigma }_{\mathrm{NN}}=15.4, 25.4, \mathrm{and} 53.1$ mb). The distribution $\frac{d^{2}n}{\mathrm{dEd}\Omega }$ is rather insensitive to the excluded-volume feature but does depend sensitively on ${\sigma }_{\mathrm{NN}}$, on the impact parameter $b_{\mathrm{NeU}}$, and on the emitted-nucleon characteristics $E$ and $\Omega$. For one particular set of $\mathrm{NN}$ parameters—hard-core radius = 0.9 fm, ${\sigma }_{\mathrm{NN}}=25.4\mathrm{}$ mb—our cascade calculation reduces to a case in which each nucleon is modeled precisely as a classical frictionless billiard ball (a "hard sphere") of diameter equal to the hard-core radius. For this case our cascade results would be especially suitable for comparison with analogous fluid-dynamic results—these latter to be computed using the known equation of state of a hard-sphere gas.