Measurement of the $\beta -\nu$ Correlation using Magneto-optically Trapped ${}^{21}\mathrm{N}\mathrm{a}$

The beta-neutrino correlation coefficient, , in is inferred from detecting the and low-energy recoil daughter nucleus. is produced at the 88-Inch Cyclotron at Lawrence Berkeley National Laboratory and 800 000 atoms are maintained in a magneto-optical trap. From the measured time of flight of recoil ions in the presence of a drift electric field, we find . There may be a dependence on the trapped atom population. This and other systematic uncertainties are discussed.

Figure 1

${\beta }^{+}$ decay of ${}^{21}\mathrm{N}\mathrm{a}$ with $ft$ values for each branch.

Figure 2

Detector and electrode geometry. The scintillator for the $\Delta E$ and $E$ components of the $\beta$ detector are shown in solid black.

Figure 3

Monte Carlo simulation of the time of flight spectra for ${}^{21}\mathrm{N}\mathrm{e}^{1+}(3/2^{+})$ given $a_{\beta \nu }=1$ and $a_{\beta \nu }=0$. There are ${10}^7$ events in each spectrum.

Figure 4

Recoil ${}^{21}\mathrm{N}\mathrm{e}$ spectra fit with the Monte Carlo simulation. Residuals are shown for ten bins for clarity and divided by the statistical uncertainty per bin.

Figure 5

The $\beta$ energy spectrum for ${}^{21}\mathrm{N}\mathrm{e}^{1+}$ with a $\beta$ detector threshold at 50 keV (dashed line). Accidental and proton beam induced coincidences have been subtracted. The $\approx 1\%$ excess of counts below 300 keV is due to Compton scattering of 511 keV $\gamma$ rays.

Figure 6

$a_{\beta \nu }$ at different trap populations. The dotted line is the fit to the ${}^{21}\mathrm{N}\mathrm{e}^{1+}$ data that depends linearly on the trap population and the dashed line is for the population-independent fit. The ${}^{21}\mathrm{N}\mathrm{e}^{2+}$ data have been slightly offset horizontally for clarity. Error bars shown are statistical only, before readjustment by $\sqrt{{\chi }_r^2}$ (see text).