A semi-statistical model of high-energy collisions

Abstract

The emission of particles directly created in high-energy collisions is considered to be only partly governed by statistical laws as in Fermi's model. The motion of the created particles is to some degree related to the former motion of the incoming colliding particles. In first approximation this intermediate state is built up of two extremes: two Lorentz systems are introduced from which the particles are emitted isotropically and according to statistical laws. In the centre-of-momentum system (CMS) of the collision these two systems move in the directions of the incoming particles after collision. This approximation corresponds to the two-fireball model which we regard as a representative of a mathematical method of dealing with correlations. In further approximation phase space distributions are replaced by the thermodynamic Fermi or Bose distributions for relativistic particles. Both experimental data such as the nearly constant mean transverse momentum¯pt and phase space calculations with constant interaction volume show that the temperaturekT reaches an upper limit asymptotically at high energies; the asymptotic region begins at about 30 GeV. The comparison with experimental particle spectra from accelerators in the 10–30GeV region shows good agreement if one uses a smooth dependence ofkT on the collision energyE0 and, for each independent set of measurements, an individual choice of\(\bar \gamma _f \), the mean Lorentz factor of the “fireballs” in the CMS, and of ¯n, the mean number of created particles. The pt-distribution of pions and the dependence of¯pt on the particle mass can also be successfully described. At very high energies the model gives production ratios of the various kinds of particles which lie within the range of the experimental determinations. The dependence of\(\bar \gamma _f \) onE0 is concluded to be of the form\(\bar \gamma _f \propto E_0^{1/2} /\bar n(E_0 ) \approx 0.5E_0^{1/4} \), i.e. CMS anisotropy is related to multiplicity.