Measurements of the 23S1-23PJ (J=0,1,2) fine-structure splittings in positronium

Abstract

The $2^3$ ${\mathrm{S}}_1$→$2^3$ ${\mathrm{P}}_1$ and $2^3$ ${\mathrm{S}}_1$→$2^3$ ${\mathrm{P}}_0$ transition frequencies (${\nu }_1$ and ${\nu }_0$, respectively) in positronium have been measured for the first time and an improved measurement of the $2^3$ ${\mathrm{S}}_1$→$2^3$ ${\mathrm{P}}_2$ transition frequency (${\nu }_2$) has been made. The results ${\nu }_0$=18504.1±10.0±1.7 MHz, ${\nu }_1$=13001.3±3.9±0.9 MHz, and ${\nu }_2$=8619.6±2.7±0.9 MHz are in reasonable agreement with the predictions of quantum electrodynamics which are, to order ${\mathrm{\alpha }}^3$Ry, ${\nu }_0$(${\mathrm{\alpha }}^3$)=18496.1 MHz, ${\nu }_1$(${\mathrm{\alpha }}^3$)=13010.9 MHz, and ${\nu }_2$(${\mathrm{\alpha }}^3$)=8625.2 MHz. More precise measurements are planned to test the, as yet uncalculated, order ${\mathrm{\alpha }}^4$ Ry corrections.