Implementation in the reaction code system EMPIRE-2.19 of an advanced formalism for fission cross-section calculation

Full text: The implementation in the reaction code system EMPIRE-2.19 of an advanced formalism for fission cross-section calculation has been completed. The formalism is based on the optical model for fission and can be applied for nuclei exhibiting double- or triple-humped barrier starting from sub-barrier excitation energies. The optical model for fission, initially developed to describe the resonant structure of the fission cross section at sub-barrier excitation energies due to the vibrational states in the second well of a double-humped fission barrier, was extended to light actinides by including the relations for the transmission coefficients through a complex triple-humped fission barrier. The real part of the fission barrier is parameterised as a function of the nucleus deformation by five smoothly joined parabolas. The imaginary potential is introduced only in the deformation range corresponding to the second well because the tertiary well is supposed to be shallow enough to neglect the damping of class III vibrational states. The transition states are assumed to be rotational states built on vibrational or non-collective band-heads. As the excitation energy increases, the shell effect, which causes the splitting of the outer barrier, diminishes and the outer humps lump into a single one. Therefore, in the present formalism, triple-humped barriers are associated only to the discrete transition states; the contribution of continuum to the fission coefficients is calculated considering a double-humped barrier. The parameters of the second single barrier equivalent with the outer humps are being determined from the condition of equal transmission coefficients. The saddle-point transition states in continuum are described by level densities (BCS below the critical energy and a modified version of Fermi Gas above) accounting for collective enhancements specific to the nuclear shape asymmetry at each saddle point . The neutron cross sections of 232Th in the energy range 0.01-30 MeV for all relevant channels have been calculated with the EMPIRE 2.19 code. The direct interaction cross sections and the neutron transmission coefficients for the elastic channel were obtained within Coupled Channel method using ECIS03 code (as incorporated in Empire 2.19 code). The dispersive coupled channel optical model parameters of Soukhovitskii et al. were used for the neutron and proton channels. For the compound nucleus cross sections calculation the HRTW version of the statistical model with decay probabilities deduced in the optical model for fission was used. To improve the accuracy of the second and third chance fission evaluation, beside 232Th(n,f), the 232Th(γ,f) and 230Th(n,f) reactions have been simultaneously analysed. Consistent sets of parameters describing the double- and triple-humped fission barrier of the light actinides and very good agreement with the measured fission cross section have been achieved using the new treatment of the fission channel implemented in EMPIRE 2.19 code. The results confirm the attribution of the gross resonant structure in fission probability of these light actinides to the undamped vibrational states in the tertiary well. Sensitivity tests indicate a significant dependence of the fission barrier parameters on the optical model parameters and also on the pre-equilibrium models. (author)