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We recently introduced a wave-mechanical model for quasi-elastic neutronscattering (QENS) in proteins. We call the model ELM for "Energy LandscapeModel". We postulate that the spectrum of the scattered neutrons consists oflines of natural width shifted from the center by fluctuations. ELM is based ontwo facts: Neutrons are wave packets; proteins have low-lying substates thatform the free-energy landscape (FEL). Experiments suggest that the wave packetsare a few hundred micrometers long. The interaction between the neutron and aproton in the protein takes place during the transit of the wave packet. Thewave packet exerts the force $F(t) = dQ(t)/dt$ on the protein moiety, a part ofthe protein surrounding the struck proton. $Q(t)$ is the wave vector (momentum)transferred by the neutron wave packet to the proton during the transit. Theensuing energy is stored in the energy landscape and returned to the neutron asthe wave packet exits. Kinetic energy thus is changed into potential energy andback. The interaction energy is proportional to $Q$, not to $Q^2$. To developand check the ELM, we use published work on dehydrated proteins after reversingimproper normalizations. In such proteins only vibrations are active and theeffects caused by the neutron momentum can be studied undisturbed by externalfluctuations. ELM has predictive power. For example it quantitatively predictsthe observed inelastic incoherent fraction $S(Q, T)$ over a broad range oftemperature and momentum $Q$ with one coefficient if $S(0, T)$ is known.

A wave-mechanical model of incoherent neutron scattering II. Role of the momentum transfer