Zeeman Effect in Positronium Annihilation at Low Temperatures.

Abstract

The annihilation of positronium is discussed as a means of obtaining a precise measurement of the Compton wavelength of the electron. In particular the spectral line shape of the annihilation radiation is calculated for positronium thermalized in helium gas cooled to the region of its critical point with an applied magnetic field sufficient to yield a three photon to two photon branching ratio of unity for theS0 component. Under such conditions the rapid thermalization of the positronium and the long half-life of two photon decay out of the predominantly triplet state make possible the production of rather narrow spectral distributions. An exact solution of the Zeeman effect in positronium is included. This study suggests that a wavelength determination beyond the one part per million level is attainable within the range of present technology.