Hyperfine Structure of Positronium in Its Ground State

The energy difference between orthopositronium and parapositronium in the ground $n=1\mathrm{}$ state, which is called the hyperfine structure separation $\Delta \nu$, has been determined in an experiment similar to that of Deutsch, Brown, and Weinstein. The frequency difference between the $M=\pm 1$ and the $M=0\mathrm{}$ Zeeman levels of orthopositronium was measured in a static magnetic field of 8000 gauss at which it is about 2460 Mc/sec. A resonance curve was taken with fixed frequency by varying the magnetic field, and an observed fractional line width, $\frac{\Delta H_0}{H_{0r}}$, of about 4.5×${10}^{-3\mathrm{}}$ was obtained. The principal part of the line width (3.6×${10}^{-3\mathrm{}}$) is due to the annihilation lifetime of positronium; microwave power broadening and magnetic field inhomogeneity account for the remainder. No Doppler broadening is present despite the high velocity of the positronium atoms, because the mean free path of a positronium atom in the gas is small compared to the wavelength of the microwave radiation. The value of $\Delta \nu$ was computed from the observed values of the frequency and magnetic field at resonance by use of the Breit-Rabi formula to give the result: $\Delta \nu =(2.0333\mathrm{}\pm 0.0004)\times {10}^5$ Mc/sec. The error quoted is 5 times the statistical error and is believed to represent an upper limit to possible systematic errors. The value agrees with the values of Deutsch et al. of (2.0338±0.0004)×${10}^5$ Mc/sec and (2.0335±0.0005)×${10}^5$ Mc/sec, obtained with fields of 9500 and 9000 gauss, respectively, and hence confirms the use of the Breit-Rabi formula. The experimental values agree with the theoretical value for $\Delta \nu$ of 2.0337×${10}^5$ Mc/sec computed to order ${\alpha }^3$ ry by Karplus and Klein.