Abstract: This book covers all aspects of the study of ground state electron density in condensed matter through Compton scattering of hard x-rays or gamma rays, i.e., photons with energies between 20 and 500 keV. This inelastic scattering process yields information about the momentum distribution of the electrons: it is complementary to x-ray diffraction studies of the position space electron density. After a brief historical introduction, the scattering cross-section is fully elaborated and the approximations within which the experiments can be interpreted are spelled out. All the experimental methods associated with the study of the electron’s momentum density distribution are described and the interpretative techniques are detailed, including the two methods of reconstructing the three-dimensional distribution from the measurement sets. Particular emphasis is placed on the use of synchrotron radiation as the radiation source, especially the use of circularly polarized synchrotron radiation to study the spin-dependent distribution in ferro-magnets. The book concludes with a comparison between Compton scattering methods and a number of allied techniques.

Keywords: condensed matter physics, electron density, ferromagnetism, scattering cross-sections, synchrotron radiation