QENS scattering functions

For H in metals the measured QENS intensity, after the necessary ra v data corrections (background subtraction, detector efficiency, etc.) is proportional to the incoherent scattering function S , (Q, co) which can be written as the two-fold Fourier transform (in space and time) of the single-particle, space-time van Hove correlation function, Gg(r,t),... 

For data fitting, it is easier to work with the scattering function than with the double-differential cross-section since there are no experimental parameters. During a normal QENS experiment, one measures in Q-o) space motions, which occur in real space and in time. The scattering fimctions are the four-dimensional Fourier transforms of the van Hove correlation function G(r,t) [10]. 

Quasi-elastic neutron scattering (QENS) is related to stochastic particle motions. Because the displacements are random, the diffusive motion of particles in liquids caimot be quantized, and the energies are continuously distributed. Unlike the case of cooperative motions like phonons in solids or molecular vibrational excitations, in the dynamic scattering function S(Q,(o), there are no 5-functions at finite momentum and energy transfers. Instead, the dynamic scattering function is centered at zero-energy transfer with a characteristic quasielastic line width proportional to the diffusivity of the particles. 

As mentioned above, incoherent neutron scattering methods—elastic (ENS), QENS, and inelastic (INS)—offer many advantages when studying hydrogen atom dynamics in a protein and its hydration water. The RCM is one good example [21]. In the INS case E 0), the intermediate scattering function (ISF) for a hydrogen atom harmonically bound to a molecule is... 

Quasielastic neutron scattering (QENS) is a rather indirect method with many limitations. It makes use of the small ( quasielastic ) energy shift that neutrons experience in any scattering by a moving particle, say by the diffusive translations of protons on a molecule. Mathematically, the normalized scattered neutron intensity as a function of kinetic neutron energy E (or frequency (o=2nElh) is related to the time Fourier transform of the dynamic pair-distribution function G(r, i) of the sample material [6, 32]. Hence in Pick s approxima-... 

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