Measurement of the Longitudinal Polarization of Positrons Emitted by Sodium-22

Abstract

Measurement of the preponderance of $1{}_{}{}^3{}_{}{}^{}S_{1,0}^{}{}_{}{}^{}$ states of positronium over $1{}_{}{}^1{}_{}{}^{}S_{0,0}^{}{}_{}{}^{}$ states formed in a gas at moderately high field $H$ (10 to 15 kilogauss), yields directly the preponderance of positron spins opposed to H over those parallel, just prior to capture, the magnitude and sign of the Paschen-Back effect may be inferred from the field value and the known triplet-singlet energy separation at zero field. By using suitable gases, the two-photon annihilation events from $1{}_{}{}^3{}_{}{}^{}S_{1,0}^{}{}_{}{}^{}$ are differentiated from those from $1{}_{}{}^1{}_{}{}^{}S_{0,0}^{}{}_{}{}^{}$ by requiring strict angular correlation at 180°; positronium atoms in the latter state, being only about ${10}^{-10\mathrm{}}$ sec old at annihilation, have retained enough of the kinetic energy at formation to yield a broad angular correlation, while the former states, being on the average 30 times older at annihilation, yield a narrow component. The relative efficiency for counting the triplet/singlet states can in practice be made ∼1.5, in the presence of all other two-quantum annihilation events. Positrons emitted into the hemisphere about $+z$, plus those scattered by the source material or source-backing into that hemisphere, are found to be polarized along $+z$ by an amount 0.15. Taking, for those positrons ultimately slowed and counted, that ${〈\frac{v}{c}〉}_{\mathrm{effective}}$ at emission is 0.75, it is implied that their longitudinal polarization at emission is at least $0.4〈\frac{v}{c}〉$, this lower limit to apply if there be no back-scattering, no depolarization during the slowing process, and no de-alignment on the part of the positronium. The sodium-22 positrons are unmistakably right-handed. The sought-for connection between failure of parity conservation and polarization of betas from an unpolarized source is thus experimentally established.