Precision measurement of the decay rate of the negative positronium ion Ps${}^{-}$

The negative positronium ion Ps${}^{-}$ is a bound system consisting of two electrons and a positron. Its three constituents are pointlike leptonic particles of equal mass, which are subject only to the electroweak and gravitational force. Hence, Ps${}^{-}$ is an ideal object in which to study the quantum mechanics of a three-body system. The ground state of Ps${}^{-}$ is stable against dissociation but unstable against annihilation into photons. We report here on a precise measurement of the Ps${}^{-}$ ground-state decay rate $\Gamma$, which was carried out at the high-intensity NEutron induced POsitron source MUniCh (NEPOMUC) at the research reactor FRM II in Garching. A value of $\Gamma =2.0875\left(50\right){\mathrm{ns}}^{-1}$ was obtained, which is three times more precise than previous experiments and in agreement with most recent theoretical predictions. The achieved experimental precision is at the level of the leading corrections in the theoretical predictions.

Figure 1

Artist's view of the Ps${}^{-}$ ion. The two electrons (green) are in a singlet state with their spins aligned antiparallel, while the spin orientation of the positron (red) is random. Averaged distances between the constituents are taken from [11].

Figure 2

Schematic view of the experimental setup. From left to right: The positron postacceleration stage, the Ps${}^{-}$ production foil together with the Ps${}^{-}$ acceleration gap, which are mounted on a high-precision piezoelectric translation stage, the field-free decay gap, and the Ps${}^{-}$ stripping device. The positron detection unit attached to the stripping stage is shown separately in Fig. 3. The setup is immersed in a coaxial magnetic field of $\approx$60 Gauss, which is produced by several Helmholtz coils surrounding the vacuum chamber (not shown). Bottom part: The electric potential along the symmetry axis of the setup.

Figure 3

Schematic view of the positron detection stage. Positrons, leaving the stripping unit with a kinetic energy of $\approx$40 keV, are deflected by ${15}^{\circ }$ using a dipole magnet and detected in a Si-surface barrier detector.

Figure 4

(a) Observed rate of Ps${}^{-}$ ions surviving a decay gap of 4.1 mm (statistical errors are of the size of the dots), and (b) Ps${}^{-}$ decay rates $\Gamma$, measured for different positron energies $E_{e^{+}}$. The measurements were performed using the Heidelberg method where the Ps${}^{-}$ ions are accelerated over the decay gap. The Ps${}^{-}$ acceleration voltage $U_{{\mathrm{Ps}}^{-}}=U_{\mathrm{Acc}}-U_{\mathrm{Prod}}$ was kept fixed at 3900 V. The solid (green) line is the expected decay rate; the dashed lines are to guide the eye.

Figure 5

Energy spectra observed with the Si detector at decay gap widths of $d=3.1$ mm and $d=38$ mm, corresponding to 0.4 and 4.7 decay lengths, respectively. The energies of the positrons are shifted slightly below 40 keV due to the energy loss in the mylar foil mounted in front of the Si detector. The $d=38$ mm spectrum was normalized to the one measured at $d=3.1$ mm at energies above 55 keV.

Figure 6

Positron spectra observed at seven decay-gap widths after summing over all measurement cycles (black dots). The solid (red) line represents the background spectrum derived from the measurement at $d=38$ mm as discussed in the main text.

Figure 7

Background-corrected positron spectra.

Figure 8

Top: Decay curve for Ps${}^{-}$ at an acceleration voltage of $2498$V. The statistical error bars of the individual Ps${}^{-}$ count rates are smaller than the symbols. The solid line represents the best fit by an exponential decay law. Bottom: Residuals observed with respect to the best fit.

Figure 9

Contour plot of confidence levels in the space spanned by the two fitting parameters $N_0$ and $\mu$ from the ${\chi }^2$ fitting of the decay curve by $N\left(d\right)=N_0\text{exp}(-\mu d)$.

Figure 10

Calculated Ps${}^{-}$ decay rate according to [5] in comparison to the measured value from the present work. The (red) dots are reflecting the running sum over the lowest terms in the expansion of $\Gamma$ in terms of the fine-structure constant $\alpha$.