The role of momentum transfer during incoherent neutron scattering is explained by the energy landscape model

Abstract

We recently introduced a model of incoherent quasielastic neutron scattering (QENS) that treats the neutrons as wave packets of finite length and the protein as a random walker in the free energy landscape. We call the model ELM for “energy landscape model.” In ELM, the interaction of the wave packet with a proton in a protein provides the dynamic information. During the scattering event, the momentum Q(t) is transferred by the wave packet to the struck proton and its moiety, exerting the force F(t)=dQ(t)/dt. The resultant energy E⋆ is stored elastically and returned to the neutron as it exits. The energy is given by E⋆=kB(T0+χQ), where T0 is the ambient temperature and χ (≈ 91 K Å) is a new elastobaric coefficient. Experiments yield the scattering intensity (dynamic structure factor) S(Q;T) as a function of Q and T. To test our model, we use published data on proteins where only thermal vibrations are active. ELM competes with the currently accepted theory, here called the spatial motion model (SMM), which explains S(Q,T) by motions in real space. ELM is superior to SMM: It can explain the experimental angular and temperature dependence, whereas SMM cannot do so.