Temperatures in heavy-ion collisions from pion multiplicities

Abstract

A thermodynamically consistent treatment of the nuclear interaction is employed to study the dependence of pion production on the nuclear equation of state in heavy-ion collisions. Massive baryon resonances, heavy mesons and the Bose condensation of pions are incorporated into a macrocanonical relativistic quantum-statistical treatment of the highly excited system. The measured pion multiplicities, which vary over eight orders of magnitude in the bombarding energy range from 30 MeV/nucleon to 4 GeV/nucleon, are reproduced within a simple one-dimensional fluiddynamical model if it is assumed that nuclear matter is rather incompressible. The pion yields are in this model directly related to the compression energy, which amounts to one-half of the total center-of-mass energy at all BEVALAC energies. The maximum compression derived is uncertain by about 10% and 30% at E lab = 0.4 and 1.8 GeV/ nucleon, respectively. The temperatures of the system in the moment of the chemical freeze-out of the pion/delta degree of freedom are determined from the measured pion yields and range from 10 MeV to 100 MeV. An extrapolation to CERN/BNL energies, i.e. E lab > 10 GeV/ nucleon, yields T = 150–200 MeV. A strong energy dependence of the cross sections and the slopes of hard γ's is predicted by this model. The calculated photon yields are in surprising agreement with the data on γ- production at intermediate energies.