Fine-Structure Measurement in the First Excited State of Positronium

The $2{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-2\mathrm{}{}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$ energy splitting of positronium has been observed by inducing rf transitions in a weak magnetic field (≃ 50 G) in the absence of a buffer gas and observing a resonant increase in the Lyman-$\alpha$ emission. We obtain 8628.4±2.8 MHz, which is within 2 standard deviations of the theoretical value computed to order $\alpha {}_{}{}^3{}_{}{}^{}R$ by Fulton and Martin.