Multiple scattering theory (MST) is the mathematical formalism that is used to describe the propagation of a wave through a collection of scatterers. Examples are acoustical waves traveling through porous media, light scattering from water droplets in a cloud, or x-rays scattering from a crystal. A more recent application is to the propagation of quantum matter waves like electrons or neutrons through a solid.
As pointed out by Jan Korringa,[1] the origin of this theory can be traced back to an 1892 paper by Lord Rayleigh. An important mathematical formulation of the theory was made by Paul Peter Ewald.[2] Korringa and Ewald acknowledged the influence on their work of the 1903 doctoral dissertation of Nikolai Kasterin, portions of which were published in German in the Proceedings of the Royal Academy of Sciences in Amsterdam under the sponsorship of Heike Kamerlingh Onnes.[3] The MST formalism is widely used for electronic structure calculations as well as diffraction theory, and is the subject of many books.[4][5]
The multiple-scattering approach is the best way to derive one-electron Green's functions. These functions differ from the Green's functions used to treat the many-body problem, but they are the best starting point for calculations of the electronic structure of condensed matter systems that cannot be treated with band theory.
The terms "multiple scattering" and "multiple scattering theory" are often used in other contexts. For examples, Molière's theory of the scattering of fast charged particles in matter,[6] or Glauber multiple scattering theory[7] for high-energy particle multiple-scattering off nucleons in a nucleus are also denominated that way.
- ^ J. Korringa (1994). "Early history of Multiple Scattering Theory for ordered systems". Physics Reports. 238 (6): 341–360. Bibcode:1994PhR...238..341K. doi:10.1016/0370-1573(94)90122-8.
- ^ P. P. Ewald (1916). "On the foundation of crystal optics". Annalen der Physik. 354 (1): 1–38. Bibcode:1916AnP...354....1E. doi:10.1002/andp.19163540102.
- ^ N. Kasterin (1898). "Concerning the dispersion of acoustic waves in a non-homogeneous medium". Royal Academy of Sciences in Amsterdam. Minutes of the regular meetings of the mathematics and physics division of 26 February: 460–480.
- ^ Antonios Gonis; William H. Butler (2000). Multiple Scattering in Solids. Springer. ISBN 978-0387988535.
- ^ J.S. Faulkner; G.M. Stocks; Y. Wang (2018). Multiple Scattering Theory: Electronic Structure of Solids. IOP Publishing Ltd. ISBN 978-0-7503-1490-9.
- ^ A. A. Bednyakov (2014). "On the Molière theory of multiple scattering of charged particles (1947–1948) and its critique in subsequent years". Physics of Particles and Nuclei. 45 (5): 991–999. Bibcode:2014PPN....45..991B. doi:10.1134/s1063779614050037. S2CID 122407525.
- ^ Glauber, R.J. (1959). "High energy collision theory" (PDF). Brittin WE, Dunham LG, eds. Lectures in Theoretical Physics, Volume I. Wiley-Interscience.
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