Dynamics from elastic neutron-scattering via direct measurement of the running time-integral of the van Hove distribution function

Abstract

We present a new neutron-scattering approach to access the van Hove distribution function directly in the time domain, I(t), which reflects the system dynamics. Currently, I(t) is essentially determined from neutron energy-exchange. Our method consists of the straightforward measurement of the running time-integral of I(t), by computing the portion of scattered neutrons corresponding to species at rest within a time t , (conceptually elastic scattering). Previous attempts failed to recognise this connection. Starting from a theoretical standpoint, a practical realisation is assessed via numerical methods and an instrument simulation.

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

“…The longest observation time, corresponding to the inverse of the best energy resolution (narrowest HWHM), is max{t obs } = 1.66/min{dE 1 } = 55 ps, and the shortest observation time, corresponding to the inverse of the broadest energy resolution (largest HWHM), is min{t obs } = 1.66/ max{dE 1 }=0.5 ps. The 1.66 factor for the proper conversion from HWHM to observation time has been explained in our previous work 32 (as well as the "0.6579 meV ps" factor for the proper conversion from energy to time). Also, in the vHI mode, N is the number of neutrons for each "configuration" of the primary spectrometer.…”

“…www.nature.com/scientificreports www.nature.com/scientificreports/ In fact, it is also possible to further increase the count-gain of vHI by adjusting the energy-width of the secondary spectrometer, dE 2 . It turns out that the vHI approximation holds for secondary spectrometer energy-widths up to four times smaller than the energy-width of the primary spectrometer 32 . This "secondary resolution count-gain" has been computed with our MC code by adjusting the energy-width of the secondary spectrometer to be four times smaller than that of the primary.…”

“…We take a pedagogic approach here by basing the in silico instrument on existing backscattering QENS spectrometers as illustrated in Fig. 1, which could also used for vHI 22,32 . The in silico instrument changes between the QENS and vHI modes by simply altering the way in which the primary monochromator is scanned.…”

“…However, since here we are interested in assessing precision rather than accuracy, we do not correct by the energy resolution, something that will anyway decrease the statistical significance of QENS-extracted I(t). The procedure to access the I(t) from the measured vHI profile is to obtain a polynomial time-derivative: basically, mapping the measured data in the power of time and then plot its derivative 32 . In this case there is no need of any energy-resolution correction.…”

“…An alternative approach that has been proposed a number of times is to measure the "elastic" scattering to get some (overall) measure of the system dynamics [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31] . We recently showed a new method based on elastic scattering, our method being unique in that it accesses I(t) directly 32 . The basic principle is straightforward.…”