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

Phys. Rev. C 22, 1025 – Published 1 September 1980
A. R. Bodmer, C. N. Panos, and A. D. MacKellar


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 AP=AT=20 (Ne + Ne) at laboratory energies per projectile nucleon of EL=117, 400, and 800 MeV and at 400 MeV for AP=AT=40 (Ca + Ca). A static two-body potential Vst is used which is fitted to σ(2), the sin2θ weighted differential cross section. For AP=AT=20 we also use a scattering equivalent momentum dependent potential Vtr. Vst and Vtr 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 EL. 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 AP=AT=20 at 800 MeV the peak persists to the final distributions. There are very appreciable differences in the densities, potential energies, and distributions between Vst and Vtr during the strong interaction stage. However, the final distributions are not significantly different even for AP=AT=20 at 800 MeV. For AP=AT=40 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(v2c2) are briefly discussed.

NUCLEAR REACTIONS Heavy ion (Ne + Ne, Ca + Ca); laboratory energy /n=117, 400, 800 MeV; classical microscopic many-body calculations.


  • Received 5 October 1979
  • Published in the issue dated September 1980

© 1980 The American Physical Society

Authors & Affiliations

A. R. Bodmer and C. N. Panos*

  • Argonne National Laboratory, Argonne, Illinois 60439 and University of Illinois at Chicago Circle, Chicago, Illinois 60680

A. D. MacKellar

  • University of Kentucky, Lexington, Kentucky 40506

  • *Present address: Physics Dept., University of Ioannina, Ioannina, Greece.

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