Multi-Group Covariance Data Generation from Continuous-Energy Monte Carlo Transport Calculations

The sensitivity and uncertainty (S/U) methodology in deterministic tools has been utilized for quantifying uncertainties of nuclear design parameters induced by those of nuclear data. The S/U analyses which are based on multi-group cross sections can be conducted by an simple error propagation formula with the sensitivities of nuclear design parameters to multi-group cross sections and the covariance of multi-group cross section. The multi-group covariance data required for S/U analysis have been produced by nuclear data processing codes such as ERRORJ or PUFF from the covariance data in evaluated nuclear data files. However in the existing nuclear data processing codes, an asymptotic neutron flux energy spectrum, not the exact one, has been applied to the multi-group covariance generation since the flux spectrum is unknown before the neutron transport calculation. It can cause an inconsistency between the sensitivity profiles and the covariance data of multi-group cross section especially in resolved resonance energy region, because the sensitivities we usually use are resonance self-shielded while the multi-group cross sections produced from an asymptotic flux spectrum are infinitely-diluted. In order to calculate the multi-group covariance estimation in the ongoing MC simulation, mathematical derivations for converting the double integration equation into a single one by utilizing sampling method have been introduced along with the procedure of multi-group covariance tally