Comment on "Elastic incoherent neutron scattering operating by varying instrumental energy resolution: Principle, simulations, and experiments of the resolution elastic neutron scattering (RENS)" [Rev. Sci. Instrum. 82, 105115 (2011)]

Experimental demonstration of the novel "van-Hove integral method (vHI)" for measuring diffusive dynamics by elastic neutron scattering

Quasi-elastic neutron scattering (QENS)-based on the seminal work of Nobel Laureate Brockhouse-has been one of the major methods for studying pico-second to nano-second diffusive dynamics over the past 70 years. This is regarded as an "inelastic" method for dynamics. In contrast, we recently proposed a new neutron-scattering method for dynamics, which uses the elastic line of the scattering to access system dynamics directly in the time domain (Benedetto and Kearley in Sci Rep 9:11284, 2019). This new method has been denoted "vHI" that stands for "van Hove Integral". The reason is that, under certain conditions, the measured elastic intensity corresponds to the running-time integral of the intermediate scattering function, [Formula: see text], up to a time that is inversely proportional to the energy band-width incident on the sample. As a result, [Formula: see text] is accessed from the time derivative of the measured vHI profile. vHI has been supported by numerical and Monte-Carlo simulations, but has been difficult to validate experimentally due to the lack of a suitable instrument. Here we show that vHI works in practice, which we achieved by using a simple modification to the standard QENS backscattering spectrometer methodology. Basically, we varied the neutron-energy band-widths incident at the sample via a step-wise variation of the frequency of the monochromator Doppler-drive. This provides a measurement of the vHI profile at the detectors. The same instrument and sample were also used in standard QENS mode for comparison. The intermediate scattering functions, [Formula: see text], obtained by the two methods-vHI and QENS-are strikingly similar providing a direct experimental validation of the vHI method. Perhaps surprisingly, the counting statistics of the two methods are comparable even though the instrument used was expressly designed for QENS. This shows that the methodology modification adopted here can be used in practice to access vHI profiles at many of the backscattering spectrometers worldwide. We also show that partial integrations of the measured QENS spectrum cannot provide the vHI profile, which clarifies a common misconception. At the same time, we show a novel approach which does access [Formula: see text] from QENS spectra.

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

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.

Elastic Scattering Spectroscopy (ESS): an Instrument-Concept for Dynamics of Complex (Bio-) Systems From Elastic Neutron Scattering

A new type of neutron-scattering spectroscopy is presented that is designed specifically to measure dynamics in bio-systems that are difficult to obtain in any other way. The temporal information is largely model-free and is analogous to relaxation processes measured with dielectric spectroscopy, but provides additional spacial and geometric aspects of the underlying dynamics. Numerical simulations of the basic instrument design show the neutron beam can be highly focussed, giving efficiency gains that enable the use of small samples. Although we concentrate on continuous neutron sources, the extension to pulsed neutron sources is proposed, both requiring minimal data-treatment and being broadly analogous with dielectric spectroscopy, they will open the study of dynamics to new areas of biophysics.

Scaling analysis of bio-molecular dynamics derived from elastic incoherent neutron scattering experiments

Numerous neutron scattering studies of bio-molecular dynamics employ a qualitative analysis of elastic scattering data and atomic mean square displacements. We provide a new quantitative approach showing that the intensity at zero energy exchange can be a rich source of information of bio-structural fluctuations on a pico- to nano-second time scale. Elastic intensity scans performed either as a function of the temperature (back-scattering) and∕or by varying the instrumental resolution (time of flight spectroscopy) yield the activation parameters of molecular motions and the approximate structural correlation function in the time domain. The two methods are unified by a scaling function, which depends on the ratio of correlation time and instrumental resolution time. The elastic scattering concept is illustrated with a dynamic characterization of alanine-dipeptide, protein hydration water, and water-coupled protein motions of lysozyme, per-deuterated c-phycocyanin (CPC) and hydrated myoglobin. The complete elastic scattering function versus temperature, momentum exchange, and instrumental resolution is analyzed instead of focusing on a single cross-over temperature of mean square displacements at the apparent onset temperature of an-harmonic motions. Our method predicts the protein dynamical transition (PDT) at Td from the collective (α) structural relaxation rates of the solvation shell as input. By contrast, the secondary (β) relaxation enhances the amplitude of fast local motions in the vicinity of the glass temperature Tg. The PDT is specified by step function in the elastic intensity leading from elastic to viscoelastic dynamic behavior at a transition temperature Td.