Elastic incoherent neutron scattering operating by varying instrumental energy resolution: Principle, simulations, and experiments of the resolution elastic neutron scattering (RENS)

The main aim of this paper is to present the scientific case of the resolution elastic neutron scattering (RENS) method that is based on the collection of elastic neutron scattering intensity as a function of the instrumental energy resolution and that is able to extract information on the system dynamical properties from an elastic signal. In this framework, it is shown that in the measured elastic scattering law, as a function of the instrumental energy resolution, an inflection point occurs when the instrumental energy resolution intersects the system relaxation time, and in an equivalent way, a transition in the temperature behavior of the measured elastic scattering law occurs when the characteristic system relaxation time crosses the instrumental energy resolution time. With regard to the latter, an operative protocol to determine the system characteristic time by different elastic incoherent neutron scattering (EINS) thermal scans at different instrumental energy resolutions is also proposed. The proposed method, hence, is not primarily addressed to collect the measured elastic scattering intensity with a great accuracy, but rather relies on determining an inflection point in the measured elastic scattering law versus instrumental energy resolution. The RENS method is tested both numerically and experimentally. As far as numerical simulations are concerned, a simple model system for which the temperature behavior of the relaxation time follows an Arrhenius law, while its scattering law follows a Gaussian behavior, is considered. It is shown that the system relaxation time used as an input for the simulations coincides with the one obtained by the RENS approach. Regarding the experimental findings, due to the fact that a neutron scattering spectrometer working following the RENS method has not been constructed yet, different EINS experiments with different instrumental energy resolutions were carried out on a complex model system, i.e., dry and D₂O hydrated lysozyme, in an extended temperature range. The resulting temperature behavior of the system relaxation time, obtained with RENS method, agrees very well with the one obtained in literature, for the same system, following the quasi-elastic neutron scattering (QENS) approach. The proposed scientific case puts into evidence the challenges of an RENS spectrometer working by varying the instrumental energy resolution; in particular, in comparison with QENS, the proposed RENS method requires a smaller amount of sample, which is an important point in dealing with biological and exotic systems; it is not affected by the use of model functions for fitting spectra as in QENS, but furnishes a direct access to relevant information.