The surface current method in gray Dancoff factor calculation

The Dancoff correction is important in the calculation of the effective cross section of resonant isotopes in a heterogeneous system. Although the neutron current method is a simple and straightforward approach to estimate the Dancoff factor, its use is limited to the black Dancoff factor. In this paper, we expand the current method used to determine both the black and gray Dancoff factors. The method developed also relies on a neutron transport solver, where a fixed source on a fuel rod surface has an outward direction, a cosine distribution, and a constant shape. The detector is located on the surface of the rods to measure incoming and outgoing currents; therefore, there is no need to calculate the chord length, and the development, validation, and verification of the code can be omitted. The mathematical foundation of the suggested method is derived using the integral transport equation. The effects of the moderator and lattice configuration are followed by a sensitivity analysis of the Dancoff factor for several problems, including pressurized water reactor and cluster fuel assemblies. The maximum and average relative errors of the calculated results are approximately 0.3% and 0.05%, respectively.