Positron annihilation and Compton scattering are important probes of the Fermi surface. Relying on conservation of energy and momentum, being bulk sensitive and not limited by short electronic mean-free-paths, they can provide unique information in circumstances when other methods fail. Using a variety of examples, their contribution to knowledge about the electronic structure of a wide range of materials is demonstrated.
Dugdale, S. Probing the Fermi Surface by Positron Annihilation and Compton Scattering: Электронная структура и Ферми поверхность. Fiz. Nizk. Temp.2014, 40, 426-438.