Measurement of the Decay Rate of the Negative Ion of Positronium (${\mathrm{Ps}}^{-}$)

A new determination of the decay rate of the negative ion of positronium (${\mathrm{Ps}}^{-}$), using a beam-foil method and a stripping-based detection technique, is reported. The measured result of $\Gamma =2.089(15){\mathrm{ns}}^{-1}$ is a factor of 6 more precise than the previous experimental value of $\Gamma =2.09(9){\mathrm{ns}}^{-1}$, and is in excellent agreement with the theoretical value of $\Gamma =2.086(6){\mathrm{ns}}^{-1}$.

Figure 1

Schematic view of the setup used for measuring the decay rate of ${\mathrm{Ps}}^{-}$. Typical voltage settings are $U_e=-800\mathrm{V}$ and $U_a=+3.1\mathrm{kV}$.

Figure 2

Positron energy spectra resulting from the stripping of ${\mathrm{Ps}}^{-}$ ions which survived the acceleration by $U=3875\mathrm{V}$ across four different gap widths $d$. The dotted histograms represent the appropriately scaled background spectrum determined as discussed in the text. The broken vertical lines mark the integration interval used to evaluate the ${\mathrm{Ps}}^{-}$ rates.

Figure 3

Upper panel: rate of surviving ${\mathrm{Ps}}^{-}$ ions as a function of the gap width $d$, measured at an acceleration voltage of $U=3875\mathrm{V}$. The solid line represents the best fit by an exponential $\exp (-\mu d)$. Lower panel: residuals $\Delta R/R$ after subtraction of the fitted function from the data.

Figure 4

The uncorrected decay rate ${\Gamma }^{*}$ as a function of $1/\sqrt{U}$ (in order to show the results more clearly, the three data points at $U=3875\mathrm{V}$ and $U=3973\mathrm{V}$ are drawn at slightly shifted positions along the $1/\sqrt{U}$ axis). The best fit of the data by ${\Gamma }^{*}=\Gamma (1-\sqrt{T_0/U})$ under the constraint $T_0\ge 0\mathrm{eV}$ results in $T_0=0\mathrm{eV}$ and $\Gamma =2.089{\mathrm{ns}}^{-1}$ (solid line). To exemplify the sensitivity to the average initial longitudinal energy $T_0$ of the ${\mathrm{Ps}}^{-}$ ions, the slope expected for $T_0=13\mathrm{eV}$ [3] is shown by the broken line.