  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.
