Quasi-Elastic Neutron Scattering (QENS)

In a typical neutron scattering experiment, the most important ingredients are:

• The incoming neutrons, with wave vector k = k̂ 2π/ λ, with the unit vector k̂ pointing in the direction of k and the wavelength λ;
• The sample, i.e. the scatterer;
• The scattered neutrons, with new wave vector k'. In principle, k' differs from k in both the magnitude | k' | and direction. The angle formed by these two vectors is defined as 2θ.

In QENS, the incoming neutrons have a kinetic energy of the order of 25 meV (thermal neutrons) or lower (cold neutrons), and the amount of energy transferred during a scattering event ranges from less than 1 μeV to ca. 100 μeV. Thus, although the incoming neutron can lose or gain energy from the interaction with the sample (inelastic scattering), the amount of such energy transfer ΔE = ℏω is sufficiently small to make the so-called elastic approximation. Consequently, the magnitude of the scattering vector q, defined as difference between outgoing and incoming wave vector, can be safely approximated to

A QENS measurement consists thus in counting the number of neutrons scattered as a function of the energy transfer ℏω and scattering vector q (i.e. recording a series of spectra, see Examples). Such spectra can then be related to the diffusion constant D of the particles within the sample by fitting them with the Lorentzian function

Figure 1: Schematic representation of a neutron scattering experiment. Inset: Scattering geometry. Figure from [1].

Mainly, three types of spectrometers can be used for QENS:

• Time-of-Flight spectrometers, in which the energy transfer of neutrons interacting with the sample are calculated from their time of arrival to the detectors;
• Backscattering spectrometers, in which only those neutrons, which after interacting with the sample have a very well defined energy (typically ca. 2 meV) are scattered back from the so-called analyzers to the detectors. Figure 2 is a schematic representation of the backscattering spectrometer IN10 at the Institut Laue-Langevin (ILL);
• Spin-Echo spectrometers, which measure small changes in neutron velocities very precisely by analyzing how their spins precess - while passing through a magnetic field - before and after interaction with the sample.

Recent QENS experiments have been performed on aqueous (D₂O) solutions of a model protein, bovine serum albumin (BSA), on the backscattering spectrometer BASIS, at the Oak Ridge National Laboratory (ORNL). The aim of such experiments is to investigate self-dynamics of proteins in solution, as a function of protein concentration, salt (YCl₃) concentration and temperature.
Figure 3 shows one of the measured spectra. The total spectrum (red circles) is a superposition of several contributions, such as global protein diffusion L_γ and protein internal motions L_Γ.