On-the-fly doppler broadening for Monte Carlo codes

A methodology to allow on-the-fly Doppler broadening of neutron cross sections for use in Monte Carlo codes has been developed. The Monte Carlo code only needs to store 0K cross sections for each isotope and the method will broaden the 0K cross sections for any isotope in the library to any temperature in the range 77K-3200K. The methodology is based on a combination of Taylor series expansions and asymptotic series expansions. The type of series representation was determined by investigating the temperature dependence of U238 resonance cross sections in three regions: near the resonance peaks, mid-resonance, and the resonance wings. The coefficients for these series expansions were determined by a regression over the energy and temperature range of interest. Since the resonance parameters are a function of the neutron energy and target nuclide, the ψ and χ functions in the Adler-Adler multi-level resonance model can be represented by series expansions in temperature only, allowing the least number of terms to approximate the temperature dependent cross sections within a given accuracy. The comparison of the broadened cross sections using this methodology with the NJOY cross sections was excellent over the entire temperature range (77K-3200K) and energy range. A Monte Carlo code was implemented to apply the combined regression model and used to estimate the additional computing cost which was found to be less than <1%.