Enhancement of Annihilation Rate of Electron-Positron pairs in Periodic Fields

The enhancement of the partial annihilation rate of electron-positron pairs in crystals has been examined by assuming a two-band structure of electrons and using the lowest-order ladder graphs with static interaction. The intraband transitions of electrons due to the attractive force of positrons cause the enhancement of the rate over all the components of the momentum, while the interband transitions from the lower to the upper give a marked dehancement of HMC's (higher-momentum components) despite that the total annihilation rate remains still enhanced. Numerical computation has been made for several one-dimensional cases, and an asymmetry with respect to the zone face has been found even in the enhancement due to intraband transitions. An angular-correlation measurement has been made for silicon, and an evidence for the dehancement of HMC's has been found by comparing the date with the independent-particle theory of Stroud and Ehrenreich (Phys. Rev. 171 (1968) 399).