Direct, on-the-fly calculation of unresolved resonance region cross sections in Monte Carlo simulations

Abstract

The theory, implementation, and testing of a method for on-the-fly unresolved resonance region cross section calculations in continuous-energy Monte Carlo neutron transport codes are presented. With this method, each time that a cross section value is needed within the simulation, a realization of unresolved resonance parameters is generated about the desired energy and temperature-dependent single-level Breit-Wigner resonance cross sections are computed directly via use of the analytical ψ − χ Doppler integrals. Results indicate that, in room-temperature simulations of a system that is known to be highly sensitive to the effects of resonance structure in unresolved region cross sections, the on-the-fly treatment produces results that are in excellent agreement with those produced with the well-established probability table method. Additionally, similar agreement is observed between results obtained from the on-the-fly and probability table methods for another intermediate spectrum system at temperatures of 293.6 K and 2500 K. With relatively tight statistical uncertainties at the ∼ 10 pcm level, all on-the-fly and probability table keff eigenvalues agree to within 2σ. Also, we use the on-the-fly approach to show that accounting for the resonance structure of competitive reaction cross sections can have non-negligible effects for intermediate/fast spectrum systems. Biases of up to 90 pcm are observed. Finally, the consequences of the on-the-fly method with respect to simulation runtime and memory requirements are briefly discussed.