The hot fermi gas model

Abstract

Ample production of fast particles has been observed in intermediate heavy ion reactions [1]. These particles have often been related to sources having velocities close to half that of the beam and temperatures ranging between a few and several tens MeV. For such temperatures neither the low temperature Fermi gas model nor the Boltzmann gas model are valid. A more correct treatment is necessary in order to understand the relationship between the incident energy per nucleon, the excitation energy of the source and its temperature. In this short paper we give simple closed expressions allowing to interpolate between the Fermi and the Boltzmann regimes.In the following we consider a gas of fermions (Nucleons) at a temperatureT trapped in a square potential well of depthU. We shall not deal with the dynamics of the expansion of the gas except through the calculation of the particle evaporation rate. Likewise we do not consider the implications of a possible liquid gas transition [2].We first approximate the variation of the chemical potential as a function of the temperature. Using that, we are able to compute and find approximations to the variations of the excitation energy with temperature and vice-versa. Finally we give expressions for the particle evaporation rate of a hot Fermi gas and compare them to the Weisskopf formula.