Multi-group covariance matrices for the resolved resonace range of the hafnium isotopes

Abstract

The accuracy of the neutron properties of 174 Hf, 176 Hf, 177 Hf, 178 Hf, 179 Hf and 180 Hf have been investigated on the basis of experimental work carried out at the GELINA facility of the Institute for Reference Materials and Measurements. Six transmission data were interpreted with the REFIT code in term of resolved parameters. The propagation of the nuclear data uncertainties up to multi-group cross sections were performed with Monte Carlo techniques in association with conditional probabilities. Hafnium is a ductile metal which does not exist as a free element in nature. The hafnium isotopes 174 Hf, 176 Hf, 177 Hf, 178 Hf, 179 Hf and 180 Hf are found combined in zirconium compounds with a respective natural abundance of 0.16%, 5.26%, 18.60%, 27.28%, 13.62% and 35.08%. Owing to its mechanical and neutronic properties, it has been selected for a long time in reactor engineering to be used as neutron absorb- ing material holding in steel clad control rods to regulate the fission process. Some microscopic and integral data have shown the de- ficiencies of the existing data libraries to accurately describe the nuclear properties of the natural hafnium (1,2). In the epi- thermal energy range, the underestimation of the reactivity worth measured in the AZUR-Caramel experiment was in- terpreted as an overestimation of few percents (∼4%) of the natural hafnium capture cross section (3). Few years latter, this integral trend was partially confirmed by the Hf capture resonance integral deduced from time-of-flight data measured at the linac facility of the Renssealer Polytechnic Institute (RPI) (4). The reported value of 1959 ±2 barns is respectively 1.5%, 1.7% and 0.7% lower than the JEF-2.2 (1989 barns), JEFF-3.0 (1993 barns) and ENDF/B-VI.8 (1972 barns) recom- mended values. The resonance parameters extracted by Trbovitch were incorporated in the latest version of the Eu- ropean library JEFF-3.1. Unfortunately, this set of resonance parameters is not able to solve the larger part of the observed underestimation of the reactivity worth. In order to confirm the RPI results, new measurements of the capture and total cross sections were requested (5). The experimental campaign is in progress at the IRMM in the frame of the NUDAME program. This work is performed in collaboration with Serco Assurance. T. Ware started his Ph.D. thesis in 2006 in order to take an active part in this project. A parallel evaluation work is in progress at the CEA of Cadarache to obtain relevant isotopic variances and covari- ances for hafnium. For the thermal energy range, the analysis is based on the data recommended by Mughabaghab (6),