Measurement of the positronium 13S1-23S1 interval by continuous-wave two-photon excitation

Using continuous-wave excitation to eliminate the problems inherent with pulsed laser measurements of nonlinear transitions, we have measured the 13S1-23S1 interval in positronium (Ps) to be 1 233 607 216.4±3.2 MHz. The quoted 2.6 ppb (parts per 109) uncertainty is primarily due to the determination of the Ps resonance relative to the Te2 reference line, with a 1.5 ppb contribution from a recent calibration of the Te2 line relative to the hydrogen 1S-2S transition. The uncertainty corresponds to 3.5×10-5 of the α2R∞ QED contribution to the 13S1-23S1 interval. Our measurement is sufficiently accurate to provide a test of the as yet uncalculated α4R∞ QED corrections