Precision measurement of the singlet positronium decay rate.

Abstract

This is a new measurement of the annihilation decay rate, $\lambda\sb{S}$, of parapositronium (p-Ps) as a test of quantum electrodynamics (QED). The measured value is $\lambda\sb{S}$ = (7991.5 $\pm$ 1.7) $\mu s\sp{-1}$. At 210 ppm accuracy this result is 6.5 times more accurate than the previous measurement and is the first measurement sensitive enough to test the relative order $\alpha\sp2ln\alpha$ term in the QED calculation of $\lambda\sb{S}$. This measurement, which is in agreement with theory, is particularly interesting in light of the 1500 ppm discrepancy between theory and experiment that still exists in the decay rate, $\lambda\sb{T}$, of orthopositronium (o-Ps). This measurement is made using $\beta$-decay positrons from a $\sp{68}$Ge-$\sp{68}$Ga source which form positronium in a variety of gas mixtures. The time interval between the emission of a positron and the detection of the annihilation $\gamma$-ray is measured with a time-to-digital converter. The distribution of the time intervals is collected as an annihilation lifetime spectrum. $\lambda\sb{S}$ is measured indirectly by using magnetic mixing. In a magnetic field the m = 0 ground states mix to produce a state, o-Ps$\sp\prime$, which has a faster decay rate, $\lambda\sbsp{T}{\prime}$. Hence, at any gas density, $\rho$, the histogram is fitted to two exponential components with decay rates, $\lambda\sb{T}(\rho)$ and $\lambda\sbsp{T}{\prime}(\rho)$. A quantity, $\Lambda(\rho)$, linear in the gas density and equal to $\lambda\sb{S}$ at zero density, is calculated from the two measured decay rates and the value of the magnetic field. It is found that $\Lambda(\rho)$ has a small slope due to spin exchange quenching in the gas. This slope is measured in a separate experiment and a correction is made for this. The quantity $\lambda\sb{S}$ is separately measured in N$\sb2$ and CO$\sb2$ (each mixed with various small percentages of isobutane) over a wide range of pressures and at two values of the magnetic field. The measured values of $\lambda\sb{S}$ are in agreement. The measurement in CO$\sb2$ is considered as a systematic test, hence the final value is obtained from the weighted average of the two, but the error assigned is that of the N$\sb2$-measurement. Various systematics are discussed and improvements are suggested.