Umklapp Annihilation of Positronium in Crystals

Abstract

Previous experiments with positron annihilation in single crystals of quartz have revealed an interesting series of narrow peaks on the momentum distribution of the annihilation photons. Our experiments repeat these observations and also confirm that no very long lifetime exists. We outline a simple theoretical model based upon the necessity of treating the positronium electron and the remaining electrons in the crystal as indistinguishable. The model yields results compatible with both momentum and lifetime data.