Bose-Enhancement and Pauli-Blocking Effects in Transport Models

The ability of semi-classical transport models to correctly simulate Pauli blocking and Bose enhancement is discussed. In the context of simple quantum mechanical systems, it is shown that using (1 ± f) enhancements is inadequate to describe systems far from equilibrium. The relaxation of (1 + f) descriptions toward equilibrium is studied both in the context of simple models, including a hot pion gas confined to a box. We give simple estimates for the characteristic number of collisions for a system to relax toward equilibrium. Semi-classical simulations form the backbone of the phenomenology for high-energy and intermediate-energy heavy-ion physics. The semi-classical nature of such descriptions is justified if Compton wave lengths are smaller than the size of the reaction volume, and if phase space filling factors, f , are much less than unity. The first condition is generally fulfilled whenever incident beam energies exceed ≈ 40 · A MeV. The second condition is violated for lower energy collisions by nucleons, as excitation energies are less than the Fermi energy until beam energies exceed ≈ 100 ·A MeV. For relativistic heavy-ion collisions, E/A > 10 GeV, phase-space-filling factors for pions also approach unity. For these two regimes, quantum statistics must be incorporated into simulations.