Positron Annihilation Experiments and the Band Structure of V3Si

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


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
$${\rm{\rho }}\left( {\underline {\rm{p}} } \right) = {\sum\limits_{\underline {\rm{k}} {\rm{,}}\ell } {\left| {\int {{{\rm{d}}^3}\underline {\rm{r}} \,\exp \left( { - {\rm{i}}\underline {\rm{p}} \cdot \underline {\rm{r}} } \right)} {{\rm{\psi }}_ + }\left( {\underline {\rm{r}} } \right){{\rm{\psi }}_{\underline {\rm{K}} {\rm{,}}\ell }}\left( {\underline {\rm{r}} } \right)} \right|} ^2}$$
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
$${\rm{N}}\left( {{{\rm{p}}_{\rm{z}}}} \right) = \smallint \smallint {\rm{\rho }}\left( {{{\rm{p}}_{\rm{x}}}{{\rm{p}}_{\rm{y}}}{{\rm{p}}_{\rm{z}}}} \right){\rm{d}}{{\rm{p}}_{\rm{x}}}{\rm{d}}{{\rm{p}}_{\rm{y}}}\,;\,{{\rm{p}}_{\rm{z}}}{\rm{ = mc\theta }}$$


Band Structure Fermi Surface Momentum Distribution Positron Annihilation Independent Particle Model 
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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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