Dynamics of electron density in a medium revealed by Mössbauer time-domain interferometry

Nuclear resonant scattering of synchrotron radiation allows the detection of energy transfers in the sample in the order of $\Delta E/E\approx {10}^{-13}.$ This extreme energy resolution is used in Mössbauer time domain interferometry to provide an inelastic scattering method similar or even superior to high resolution inelastic neutron scattering. The interferometer consists of two nuclear targets as interferometer arms, and a nonresonant sample placed in between, and detects slow dynamics of the electron density in a time range of nuclear response, typically from 10 ns to 200–500 ns. It has access to scattering vectors from 0.1 Å to beyond 10 Å. The general theory of the interferometer is provided and it is evaluated how the Van Hove correlation function presenting the electron density fluctuations of the sample in space and time can be measured. Exemplarily, it is shown how the temporal behavior of diffusion can be studied with diffusivities in the range from ${10}^{-16}$ to ${10}^{-13}{\mathrm{m}}^2/\mathrm{s}.$