Angular Distribution of Single-Quantum Annihilation Radiation

Abstract

Angular distributions of radiation accompanying single-quantum annihilation of positrons by $K$-shell electrons are calculated. These angular distributions differ from the corresponding Born-approximation calculations, both in magnitude and in shape. For transversely polarized positrons the radiation exhibits an azimuthal asymmetry. The asymmetry, togetherwith the spin-independent part of the differential cross section, is presented for various elements ranging from $Z=47\mathrm{}$ to $Z=92\mathrm{}$. Because of the relatively large magnitude of the asymmetry for high-$Z$ targets, it is suggested that detection of the radiation caused by positrons, transversely polarized by an electrostatic analyzer, could provide an alternative means for measuring the longitudinal polarization of positrons emitted in nuclear $\beta$-decay. Total cross sections obtained by numerically integrating the angular distributions agree precisely with a previous total-cross-section calculation and serve as a measure of the accuracy of the present results.