The pre-equilibrium statistical model: Description of the nuclear equilibration process and parameterization of the model

Abstract

Abstract The model proposed by Griffin has been used to investigate the approach of a compound nucleus to statistical equilibrium. A set of master equations describing the equilibration process and utilizing Williams' transition-rate expressions are presented. These equations have been used to study the occupation probabilities and the instantaneous and time-integrated particle energy spectra as a function of the time elapsed from the initial target-projectile interaction. Comparisons of the results for a sample system formed with three excitons at excitation energies of 24 and 96 MeV are presented. The sensitivity of the results of the pre-equilibrium model to changes in the values of the model parameters used has been investigated. In addition, particle spectra resulting from closed-form and master-equation calculations are compared, as are the results obtained using several approximate sets of transition-rate expressions for closed-form calculations. The consequences of using different forms for the state density of the system have also been investigated. Finally, a fairly large number of published experimental particle energy spectra have been analyzed in terms of the pre-equilibrium model. Initial configurations consisting of three particles and holes for nucleon-induced reactions and five particles and holes for 4 He ion induced reactions were generally indicated by these analyses. Additionally, it is found that pre-equilibrium particle emission probably accounts for tens of percent of the total reaction cross section. Results of the data analysis are all generally consistent with other recent work on the pre-equilibrium statistical model.