A wave-mechanical model of incoherent quasielastic scattering in complex systems

Quasielastic incoherent neutron scattering (QENS) is an important tool for the exploration of the dynamics of complex systems such as biomolecules, liquids, and glasses. The dynamics is reflected in the energy spectra of the scattered neutrons. Conventionally these spectra are decomposed into a narrow elastic line and a broad quasielastic band. The band is interpreted as being caused by Doppler broadening due to spatial motion of the target molecules. We propose a quantum-mechanical model in which there is no separate elastic line. The quasielastic band is composed of sharp lines with twice the natural line width, shifted from the center by a random walk of the protein in the free-energy landscape of the target molecule. The walk is driven by vibrations and by external fluctuations. We first explore the model with the Mössbauer effect. In the subsequent application to QENS we treat the incoming neutron as a de Broglie wave packet. While the wave packet passes the protons in the protein and the hydration shell it exchanges energy with the protein during the passage time of about 100 ns. The energy exchange broadens the ensemble spectrum. Because the exchange involves the free-energy landscape of the protein, the QENS not only provides insight into the protein dynamics, but it may also illuminate the free-energy landscape of the protein-solvent system.