Precision Redetermination of the Fine-Structure Interval of the Ground State of Positronium and a Direct Measurement of the Decay Rate of Parapositronium

Abstract

A precision redetermination of the fine-structure interval of the ground state of positronium, $\Delta v$, has been made in an experiment similar to earlier experiments. 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 about 7900 G. The dependence of $\Delta \nu$ on gas pressure (argon) was observed for the first time. The result for $\Delta \nu$ is $\Delta {\nu }_{\exp }=(2.034\mathrm{} 03\pm 0.00012)\times {10}^5$ Mc/sec, where the error quoted is one standard deviation and represents an improvement in accuracy by a factor of 4 compared to earlier work. This value is in reasonable agreement with the theoretical value of $\Delta {\nu }_{\mathrm{theor}}=2.034\mathrm{}27\times {10}^5$ Mc/sec, but a calculation of the ${\alpha }^4-\mathrm{R}\mathrm{y}$ term in the theory is needed. The result for the fractional fine-structure pressure shift is $\left(\frac{1}{\Delta \nu }\right){\left(\frac{\partial \Delta \nu }{\partial P}\right)}_{300{}_{}{}^{\circ }{}_{}{}^{}\mathrm{K}}=\frac{(-0.93\mathrm{}\pm 0.18)\times {10}^{-7\mathrm{}}}{\mathrm{Torr}}$ of Ar, in which a one-standard-deviation statistical error is quoted. This value has the same sign but is 20 times larger than the fractional hfs pressure shift for hydrogen in argon. The experiment also yields the first direct measurement of the parapositronium annihilation rate ${\lambda }_{p\mathrm{expt}}=0.799\mathrm{}\pm 0.011\times {10}^{10}$ ${\sec }^{-1\mathrm{}}$, where a one-standard-deviation error is given. This value is in excellent agreement with the theoretical value of ${\lambda }_{p\mathrm{theor}}=0.798\mathrm{}\times {10}^{10}$ ${\sec }^{-1\mathrm{}}$.