Classical-equations-of-motion calculations of high-energy heavy-ion collisions

Abstract

Results are obtained with the classical-equations-of-motion approach which provides a complete microscopic, classical, description including finite-range interaction effects. Nonrelativistic classical-equations-of-motion calculations are made for equal mass projectile and target nuclei with $A_P=A_T=20\mathrm{}$ (Ne + Ne) at laboratory energies per projectile nucleon of $E_L=117, 400, \mathrm{and} 800$ MeV and at 400 MeV for $A_P=A_T=40\mathrm{}$ (Ca + Ca). A static two-body potential $V_{\mathrm{st}}$ is used which is fitted to ${\sigma }^{\mathrm{}\left(2\right)\mathrm{}}$, the ${sin}^2\theta$ weighted differential cross section. For $A_P=A_T=20\mathrm{}$ we also use a scattering equivalent momentum dependent potential $V_{\mathrm{tr}}$. $V_{\mathrm{st}}$ and $V_{\mathrm{tr}}$ give identical two-body scattering but are not equivalent for many-body scattering and are used to test for finite-range interaction effects in heavy-ion collisions. The evolution of central collisions is discussed. For these multiple scattering is large leading to high momentum components. Dissipation quite generally is larger at lower energies and is appreciable during the expansion phase of central collisions giving approximately thermalized distributions at the lower $E_L$. A peak at approximately the same momentum at all angles develops in the momentum distribution near the beginning of the expansion and changes roughly in step with the potential energy; for $A_P=A_T=20\mathrm{}$ at 800 MeV the peak persists to the final distributions. There are very appreciable differences in the densities, potential energies, and distributions between $V_{\mathrm{st}}$ and $V_{\mathrm{tr}}$ during the strong interaction stage. However, the final distributions are not significantly different even for $A_P=A_T=20\mathrm{}$ at 800 MeV. For $A_P=A_T=40\mathrm{}$ at 400 MeV a transverse peaking develops in the momentum distribution suggestive of collective effects. Noncentral collisions show typical nonequilibrium features and for larger impact parameters the final distributions show a strong single scattering component. This is true also of the impact parameter averaged distributions which are in fair agreement with experiment. A partial test of thermal models is made. Limitations and extensions of the classical-equations-of-motion approach are discussed. In particular we propose a new kinetic equation which includes finite-range interaction effects. Relativistic classical-equations-of-motion calculations to $O\left(\frac{v^2}{c^2}\right)$ are briefly discussed.