A Quantitative Comparison of the Counting Significance of van Hove Integral Spectroscopy and Quasielastic Neutron Scattering.

We have recently proposed a new method to access system dynamics via neutron scattering based on measuring the elastic scattered intensity: By varying the energy band-width that impinges on the sample (also known as instrumental energy resolution), the purely elastic-scattering from this variation is the running time-integral of the intermediate scattering function (I(t)) [Benedetto and Kearley, Sci. Rep. 9, 11284, 2019]. In this correspondence we denote our method "vHI", which stands for "van Hove Integral". The method is now widely accepted as "valid" and here we focus on the efficiency of the vHI method compared with the standard quasi-elastic neutron scattering (QENS) method. We use a numerical Monte-Carlo simulation of an instrument that is equally capable of measuring QENS and vHI under identical conditions. For an "experiment" in which the same number of neutrons enter the instrument, we present comparisons between QENS and vHI at three levels of data-reduction. Firstly, at the raw-data level vHI achieves 100 times more neutrons at the detector than QENS. Secondly, vHI has a factor of 2 less statistical error, which would translate to an overall gain of 4 for vHI in counting-time. Lastly, we compare the distortions caused in obtaining the final I(t) via time-Fourier transform (QENS) and polynomial time-derivative (vHI). Here, the statistical error is 10 times smaller for vHI. This last comparison is the most important result where the 10 times smaller residual for vHI gives a net gain in counting time of 100 better than QENS to obtain the same underlying dynamics of the system under study.