Convolutional discrete Fourier transform method for calculating thermal neutron cross section in liquids

Being exact at both short-and long-time limits, the Gaussian approximation is widely used to calculate neutron incoherent inelastic scattering functions in liquids. However, to overcome a few numerical difficulties, extra physical approximations are often employed to ease the evaluation. In this work, a new numerical method, called convolutional discrete Fourier transform, is proposed to perform Fourier transform of exp[- f (t)]. We have applied this method to compute the differential cross sections of light water up to 10 eV. The obtained results, thoroughly benchmarked against experimental data, showed a much higher dynamic range than conventional fast Fourier transform. The calculated integral cross sections agree closely with the light water data in the state-of-the-art nuclear data library. It is in evidence that this numerical method can be used in the place of the extra physical approximations.(c) 2022 Elsevier Inc. All rights reserved.

Automated summary

The Gaussian approximation is often used to calculate neutron incoherent inelastic scattering functions in liquids due to its accuracy in both short and long time limits. However, additional physical approximations are commonly employed to overcome numerical difficulties in the evaluation process. In this study, a new numerical method called convolutional discrete Fourier transform is proposed to perform Fourier transform of exp[- f (t)]. The results obtained from applying this method to computing the differential cross sections of light water up to 10 eV showed a higher dynamic range compared to conventional fast Fourier transform. The calculated integral cross sections closely matched the data in the state-of-the-art nuclear data library for light water. The numerical method proposed in this study can be a replacement for the extra physical approximations used.