Precision measurement of the ${}^6$He half-life and the weak axial current in nuclei

Background: The $\beta$ decays of ${}^3$H and ${}^6$He can play an important role in testing nuclear wave-function calculations and fixing low-energy constants in effective-field theory approaches. However, there exists a large discrepancy between previous measurements of the ${}^6$He half-life.

Purpose: Our measurement aims at resolving this long-standing discrepancy in the ${}^6$He half-life and providing a reliable $ft$ value and Gamow-Teller matrix element for comparison with theoretical ab initio calculations.

Method: We measured the ${}^6$He half-life by counting the $\beta$-decay electrons with two scintillator detectors operating in coincidence.

Results: The measured ${}^6$He half-life is $806.89\pm 0.{11}_{\mathrm{stat}}{}_{-0.19}^{+0.23}{}_{\mathrm{syst}}$ ms corresponding to a relative precision of $3\times {10}^{-4}$. Calculating the statistical rate function we determined the $ft$ value to be $803.{04}_{-0.23}^{+0.26}$ s.

Conclusions: Our result resolves the previous discrepancy by providing a higher-precision result with careful analysis of potential systematic uncertainties. The result provides a reliable basis for future precision comparisons with ab initio calculations.

Figure 1

Compilation of the measured ${}^6$He half-lives given in Table . The dashed blue band shows the half-life adopted in Ref. [36] from the average of the two values found in Refs. [29, 33] and used in compilations ever since. The inset shows the five values with uncertainties below 1$\%$ [23, 29, 31, 32, 33] with the dashed red band depicting the value for the ${}^6$He half-life obtained in this paper.

Figure 2

Experimental setup with two thin scintillators placed in front of a measuring volume which can be closed off by a spring-loaded valve. The stainless steel insert was used to determine possible systematic effects due to diffusion of ${}^6$He into the walls of the measuring volume.

Figure 3

Schematic of the electronics setup.

Figure 4

Histogram for a full ${}^6$He counting cycle for the data with initial rates $<$40 kHz and the stainless steel insert out. The insert zooms into the transition point from beam on to beam off at which the valve in front of the measuring volume closes and the valve to the roughing pump opens.

Figure 5

${}^6$He decay curve for the data with 2-$\mu$s dead time, initial rates $<$40 kHz and the stainless steel insert out with the corresponding residuals. The ${\chi }^2$/DOF of the fit is 1578.2/1562.

Figure 6

${}^6$He half-life fit results for the different rate groups with the initial rates restrained to 32 kHz. Only statistical errors are given. The squares (circles) correspond to the stainless steel insert in (out) data. The dashed (solid) line shows the constant fit to the insert in (out) data with ${\chi }^2$/DOF of 1.6/4 (3.4/3). The results of the constant fits correspond to the averages given in Table .

Figure 7

Shifts in the fitted ${}^6$He half-life values as a function of changes in the dead time used in the dead-time correction. The data correspond to the averages of the different dead-time channels. The slope amounts to $-$0.00485 ms/ns.

Figure 8

Measured helium leak rates through the Viton O-ring of the valve sealing our measurement volume. The plot compiles three separate measurements. The line shows the prediction for the gas flow according to Eq. (46) of Ref. [44] for a diffusivity $D={10}^{-5}$ cm${}^2$/s and a steady-state flow $C_0=5.7\times {10}^{-8}$ mbar l/s.

Figure 9

${}^6$He half-life values as a function of delay in the starting point of the fits. The two solid lines correspond to the $\pm 1\sigma$ contours for the allowed variation (relative to the first data point) that one expects from the loss in statistics for this correlated data set.

Figure 10

Measured background rates during dedicated background runs (blue circles) and fitted background rates in half-life data taking runs (red squares).

Figure 11

Histogram of the time between two events as measured with a time-to-amplitude converter in the range 0–4 $\mu$s. We see a clear indication of spurious afterpulses at 0.75 $\mu$s.