Precise measurement ofn=2 positronium fine-structure intervals

The n=2 fine-structure transitions in positronium have been measured by observation of increased Lyman-α 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 ${\nu }_0$=18 499.65±1.20±4.00 MHz, ${\nu }_1$=13 012.42±0.67±1.54 MHz, and ${\nu }_2$=8 624.38±0.54±1.40 MHz for the $2^3$ ${\mathit{S}}_1$→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.