Investigations on the point-wise neutron cross-section temperature interpolation methods

This paper is on the problem of temperature interpolation for Doppler-broadened neutron cross sections. Unlike most of the existing studies where the problem was treated as a pure numerical interpolation problem, in this study, the problem is investigated from the physics nature of temperature dependence of neutron cross sections. It is pointed out that if one could find a set of “perfect” interpolate coefficients, which can reproduce the Maxwell–Boltzmann distribution at the target temperature from the known ones at a set of reference temperatures, then regardless of the cross section type and/or shape, the Doppler-broadened cross section would be exactly reproduced as well by use of the same set of interpolation coefficients. Based on this rule, a new Maxwellian kernel interpolation (MKI) scheme is developed, in which the interpolation coefficients are determined by finding the best representation of Maxwellian distribution at the target temperature. Results for challenging U238 cross section temperature interpolation problems demonstrate that the performance of the proposed scheme is fully comparable with that of the “Log–Log” scheme, which so far has been reported to have the supreme accuracy. It is also revealed that these interpolation schemes capable of re-building the Maxwellian distribution with better accuracy are generally able to obtain a better accuracy for neutron cross section.

► This paper reports our research on Doppler-broadened XS interpolation.
► We found that the method is approximately equivalent to interpolating the kernel of Maxwellian distribution.
► Based on the above fact, the new Maxwellian kernel interpolation scheme is developed.
► Test applications demonstrate that the new scheme has satisfactory accuracy.
► Other interpolation methods are evaluated from the viewpoint of MKI.