Abstract
When radiation is Compton-scattered the emerging beam is Doppler broadened because of the motion of the target electrons. An analysis of this broadened lineshape the Crompton profile, provides detailed information about the electron momentum distribution in the scatter. The technique is particularly sensitive to the behaviour of the slower moving outer electrons involved in bonding in condensed matter and can be used to test their quantum-mechanical description. The review begins with a brief survey of the historical development of the subject to within a decade of the present. The behaviour of quantum systems from a momentum viewpoint, is explained and the conditions under which the scattering experiment can be interpreted directly in terms of electron momentum density are discussed. The experimental techniques with gamma -rays, X-rays and electron beams are compared. Finally, recent results on insulators and conductors are surveyed and the extent to which they challenge conventional assumptions of band theory is critically reviewed.
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