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

TL;DR

This paper introduces a convolutional discrete Fourier transform method to accurately compute neutron cross sections in liquids, outperforming traditional techniques and aligning well with experimental data.

Contribution

A novel numerical Fourier transform method is proposed to replace physical approximations in neutron scattering calculations for liquids.

Findings

Higher dynamic range than conventional FFT

Close agreement with experimental cross section data

Effective in calculating neutron scattering in light water

Abstract

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 10eV. 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.