A set of coupled transport equations for the phase-space distribution functions of nucleons, deltas, and pions is solved with the test particle method to study pion production in relativistic heavy ion collisions. The experimentally observed concave shape of the pion spectra is well reproduced. The mechanism that causes the concave shape of the pion spectra is found to be due to the different contributions of the delta resonance produced during the early and the late stages of the heavy ion collision and due to the energy dependence of the pion and delta absorption cross sections. The dependence of the shape of the pion spectra on beam energy, target and projectile mass, and impact parameter is also studied. An approximate scaling function for the shape parameter of the pion spectra is found.

• Received 27 February 1991

DOI:https://doi.org/10.1103/PhysRevC.44.450