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Positron Annihilation Experiments and the Band Structure of V3Si

  • S. Berko
  • M. Weger
Part of the The IBM Research Symposia Series book series (IRSS)

Abstract

In the positron annihilation method1 the angular correlation between the two γ-rays emitted as a result of a two-photon positron-electron annihilation is measured. The angular correlation is directly connected to the momentum distribution of the annihilating electron-positron pair and depends mainly on the momenta of the electrons in the solid to be studied, since the positron thermalizes prior to annihilation. The probability of the annihilation γ-rays carrying away momentum p is given, in the independent particle model, by
$${\rm{\rho }}\left( {\underline {\rm{p}} } \right) = {\sum\limits_{\underline {\rm{k}} {\rm{,}}\ell } {\left| {\int {{{\rm{d}}^3}\underline {\rm{r}} \,\exp \left( { - {\rm{i}}\underline {\rm{p}} \cdot \underline {\rm{r}} } \right)} {{\rm{\psi }}_ + }\left( {\underline {\rm{r}} } \right){{\rm{\psi }}_{\underline {\rm{K}} {\rm{,}}\ell }}\left( {\underline {\rm{r}} } \right)} \right|} ^2}$$
(1)
where Ψ+ (r) is the ground state position wavefunction and Ψk, ℓ is the electron wavefunction with wave number k and band index ℓ; the summation is over all occupied states k,ℓ In the actual experiment, the angular distribution N(⦵) is obtained using long slits (fig. 1), so that only one component of the momentum is being measured
$${\rm{N}}\left( {{{\rm{p}}_{\rm{z}}}} \right) = \smallint \smallint {\rm{\rho }}\left( {{{\rm{p}}_{\rm{x}}}{{\rm{p}}_{\rm{y}}}{{\rm{p}}_{\rm{z}}}} \right){\rm{d}}{{\rm{p}}_{\rm{x}}}{\rm{d}}{{\rm{p}}_{\rm{y}}}\,;\,{{\rm{p}}_{\rm{z}}}{\rm{ = mc\theta }}$$
(2)

Keywords

Band Structure Fermi Surface Momentum Distribution Positron Annihilation Independent Particle Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Press, New York 1972

Authors and Affiliations

  • S. Berko
    • 1
  • M. Weger
    • 2
  1. 1.Brandeis UniversityWalthamUSA
  2. 2.The Hebrew UniversityJerusalemIsrael

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