180° Positron-Electron Scattering at 200 and 500 MeV

Abstract

To test the predictions of quantum electrodynamics, absolute and relative measurements of the positron-electron scattering cross section were made at 200 and at 500 MeV. Recoil electrons were detected with the spectrometer at 0° with respect to the incident-beam direction, and for the range of recoil momenta studied, the elastic-scattering cone was entirely contained in the angular acceptance of the spectrometer. This method permitted high precision and an experimental test of the radiative corrections. The absolute accuracy of the cross sections was 1%. The complete radiative corrections for this experiment are not yet available. However, for purposes of orientation, one may extrapolate existing calculations to the present situation. If one does this, the shape of the recoil spectrum near the incident positron momentum is consistent with the theory if the radiative corrections of the form $1+\epsilon$ are used (${\chi }^2$ probability of 0.5); the shape is in less good agreement if the correction has the form $e^{\delta }$ (${\chi }^2$ probability of 0.2). The most precise measurements made, where the corrections were about 15%, were in agreement with the theory. The accuracy has to be increased to decide between $e^{\delta }$ and $1+\delta$. If radiative corrections are assumed to be precisely known, the experiment determines $\frac{1}{K}$ to about 0.6 F, where a violation of quantum electrodynamics of the form $\sigma \to {\sigma }_0{(1-\frac{q^2}{K^2})}^2$ is assumed, and where $\sigma$ is the quantum-electrodynamical cross section and $q$ is the four-momentum transfer. A significant increase in sensitivity could be achieved by extending the experiment to available positron energies well above the relatively modest values used here.