Analysis of the (n,f) Reaction in the Plutonium Isotopes

Abstract

This paper describes the modified Hauser-Feshbach formalism used to com- pute accurately fission cross sections for low-energy neutrons (from a few keV up to 5.5 MeV) in presence of intermediate structure in the second well. Application to the large plutonium isotope family (236 to 244) has been made with in particular reliable predic- tions of the cross sections of the short-lived nuclides. Special attention is paid to the choice of the model parameters entering in the calculations. The decay of a compound nucleus by fission is a complex multi-dimensional problem, whose de- scription still requires many model parameters. The elucidation and physical understanding of these parameters is an ongoing research process, and this paper reports our progress in the study of the fis- sion cross-sections for a long sequence of plutonium isotopes. Our ultimate goal is to replace many fitting parameters ubiquitous in current data evaluations with physically sound theory with fewer pa- rameters. If successful, such an approach would lead to reliable predictions of the fission cross-sections of nuclides for which measurements are unavailable or very poor, while at the same time deepen our understanding of the fission process. Here we present results obtained with a modern version of the AVXSF code (AVerage Cross Sec- tion of Fission), which treats in great detail the intermediate structure due to the presence of a sec- ond well on the fission path. The correct modeling of the class-II states properties and in particular, their coupling with the levels present in the first well as well as to the continuum, is crucial to infer meaningful barrier heights. Experimentally, those barrier heights can be inferred from an analysis of low-energy neutron-induced fission cross sections in the case of fertile nuclei, and transfer reactions leading to fission, e.g., ( t, p f ), in the case of fissile nuclei. The AVXSF code can treat both situations adequately in order to extract fission barrier heights. In the following, the theory and main equations implemented in the AVXSF code are introduced. Approximate formulae valid in specific situations are also discussed. A Monte Carlo option is used when analytic approximations fail and a full sampling of the level characteristics distributions is needed. We then present preliminary results on the neutron-induced fission cross sections obtained for a suite of plutonium isotopes, for which a consistent set of model input parameters was devel- oped. Our analysis encompasses neutron incident energies from a few keV up to 5.5 MeV, just below the onset of second-chance fission. The importance of fission barrier heights, nucleon pairing gaps and level densities is emphasized. This paper concludes on some examples of predicted cross sections with some reliability for the short-lived nuclides of the Pu series.