Precise measurement of<i>n</i>=2 positronium fine-structure intervals

The n=2 fine-structure transitions in positronium have been measured by observation of increased Lyman-\ensuremath{\alpha} radiation at microwave induced resonances. We used an accelerator based slow positron beam to produce positronium in the ${2}^{3}$${\mathit{S}}_{1}$ excited state inside a waveguide. Our results are ${\ensuremath{\nu}}_{0}$=18 499.65\ifmmode\pm\else\textpm\fi{}1.20\ifmmode\pm\else\textpm\fi{}4.00 MHz, ${\ensuremath{\nu}}_{1}$=13 012.42\ifmmode\pm\else\textpm\fi{}0.67\ifmmode\pm\else\textpm\fi{}1.54 MHz, and ${\ensuremath{\nu}}_{2}$=8 624.38\ifmmode\pm\else\textpm\fi{}0.54\ifmmode\pm\else\textpm\fi{}1.40 MHz for the ${2}^{3}$${\mathit{S}}_{1}$\ensuremath{\rightarrow}k${2}^{3}$${\mathit{P}}_{0,1,2}$ transition frequencies, respectively. The first error is statistical and the second is systematic. This is in agreement with recent bound state QED calculations.