Single-Quantum Annihilation of Positrons

Abstract

Total cross sections for the single-quantum annihilation of positrons in five elements have been measured. The monoenergetic positron beam was obtained by the use of a Siegbahn-Sl\atis intermediate-image spectrometer mounted with a ${\mathrm{Na}}^{22}$ source. Thin foils of $_{50}\mathrm{Sn}$, $_{73}\mathrm{Ta}$, $_{79}\mathrm{Au}$, $_{82}\mathrm{Pb}$, and $_{92}\mathrm{U}$ were used, successively, as targets mounted at the focal point of the spectrometer. The monoenergetic $\ensuremath{\gamma}$ photons due to the single-quantum annihilation was measured in coincidence with accompanying $K$ x rays from the target, using the NaI(Tl) scintillation detectors. The effect of the finite target thickness was evaluated carefully by measuring the energy distribution of incident positrons in the thin target. The exponent of $Z$ in the total cross section of this process for the incident positrons with 300-keV kinetic energy has been found to be 4.93\ifmmode\pm\else\textpm\fi{}0.31, in agreement with calculations by Johnson et al. The energy dependence of the total cross sections, measured for $_{82}\mathrm{Pb}$ and $_{92}\mathrm{U}$ in the positron energy range from 250 to 400 keV, has also been found to be in fairly good agreement with theoretical values calculated by other workers using the relativistic Coulomb wave functions for both the $K$-shell electron and the incident positron.