Poincaré covariant particle dynamics. I. Intranuclear cascade model.

Abstract

To analyze the high energy heavy ion reactions performed at Lawrence Berkeley BEVALAC, Brookhaven AGS, and CERN SPS we present a dynamical model that is entirely Poincar\'e covariant. The description of strong interactions by Lorentz-scalar quasipotentials makes possible a relativistic extension of the cascade concept without losing its inherent simplicity. No field degrees of freedom appear explicitly, neither in elastic nucleon scattering nor in particle creation processes. Although various formalisms describe directly interacting relativistic particles with identical solutions for the two-particle case, they all suffer from different problems in many-particle systems. The basis of our approach is a Hamiltonian formulation for N pointlike nucleons, moving unconstrained in an 8N-dimensional phase space. One additional Lorentz scalar is introduced for an appropriate parametrization of all trajectories, defining also the connection to the proper times of the individual interacting nucleons. The creation of particles, for which Hamiltonian dynamics does not provide a generic mechanism, is incorporated phenomenologically as a ``perturbative'' process. We describe heavy ion collisions as a sequence of two-particle reactions without any additional fit to experimental data. Pion yield and mass spectra of the heavy fragments agree reasonably well with BEVALAC results. We do not compare to experimental high energy data because the employed mechanism of particle production is certainly improper in that regime. However, the numerical results give an impression on how the reaction evolves.