Nondiagonal momentum density of Si by coherent inelastic X-ray scattering

When the coherent superimposition of two (nearly) plane waves is used as the initial photon state of an inelastic X-ray scattering experiment on solids (coherent Compton scattering), information can be obtained about the projection of nondiagonal elements of the one-particle density matrix in momentum space on the scattering vector q, provided the requirements of the impulse approximation are fulfilled. The double differential scattering cross section for this new scattering phenomenon is derived and then subjected to impulse approximation. It is further demonstrated that the standing wave pattern, which on passing the Bragg reflection range is sweeping the atomic sites, yields an appropriate approach to the desired initial photon state for coherent Compton scattering. Experimental coherent Compton spectra from 111 and 220 Bragg reflections are used to extract the corresponding projections of nondiagonal elements of the density matrix. Possible experimental improvements are discussed.