It is well known that the distribution of electron momenta (electron density in momentum representation) of gases can be probed by Compton scattering of either photons (γ-rays or X-rays) or electrons. Recently it has been shown that Compton scattering of electrons is suited to the study of the electron momentum densities of solids on a microscopic scale. This technique, known as ECOSS, Electron Compton Scattering from Solids can be done in the electron microscope by electron energy loss spectrometry (EELS).
After a discussion of inherent approximations and the introduction of the reciprocal form factor a method is proposed in order to cope with the main difficulty, namely multiple scattering. Important applications of ECOSS are the study of anisotropy of momentum densities; correlation effects of conduction electrons in metals; and charge transfer in alloys
