Angular distributions in a unified model of pre-equilibrium and equilibrium neutron emission

An alternative mathematical formulation is presented for the generalized master equation of the exciton model, introduced by Mantzouranis et al. to describe pre-equilibrium effects in angular distributions of emitted particles in nuclear reactions. The exciton model proposed in this paper includes internal transitions with Δn=2, 0, -2, and describes both the pre-equilibrium and the equilibrium stages of the reaction process. A simple, but exact formula is given to calculate mean lifetimes of exciton states and their Legendre coefficients, from which double differential cross sections can be easily calculated. The mathematical improvements of the generalized exciton model greatly facilitate a systematical comparison with experimental data. In this paper the neutron inelastic scattering data for 34 elements measured by Hermsdorf et al. at 14.6 MeV were used for such intercomparison. The results show underestimation of angular distributions at backward angles. However, a good overall fit of all angular distributions is obtained by adjustment of only two global parameters. It is concluded that further study with regard to the physics of the model is required. Some local variations in the angular distribution coefficients as a function of the mass number might be ascribed to level-density effects. Although it appeared that the presently adopted formulas and parameters in exciton model calculations are not adequate to give detailed predictions of the energy and angular distributions, meaningful improvements were obtained by variation of final-state parameters. Finally, some attention was devoted to the unification of the exciton and Hauser-Feshbach models. By introducing a proper definition of ''equilibrium'' emission it is shown that consistent results are obtained for neutron emission spectra calculated with the two models