Precision half-life measurement of ${}^{29}\mathrm{P}$

A new precision half-life measurement of ${}^{29}\mathrm{P}$ was conducted using the TwinSol $\beta$-counting station at the University of Notre Dame Nuclear Science Laboratory. The resulting value of $t_{1/2}^{\mathrm{new}}=4.1055\left(44\right)\mathrm{s}$ is the most precise ${}^{29}\mathrm{P}$ half-life measurement to date. Utilizing this measurement and reevaluating the world data leads to a new world average of $t_{1/2}^{\mathrm{world}}=4.1031\left(58\right)\mathrm{s}$, which improves the Birge ratio from 3.11 to 1.45 and is 2.3 times more precise than the previous world value. The new Cabibbo-Kobayashi-Maskawa matrix element $V_{\mathrm{ud}}$ for ${}^{29}\mathrm{P}$ shifts closer into agreement with the superallowed pure Fermi value. The uncertainty in the mixed transition value of $V_{\mathrm{ud}}$, however, is still dominated by the Fermi to Gamow-Teller mixing ratio $\rho$. Using the new world half-life and assuming the validity of the standard model, a new predicted value for $\rho$ and its associated correlation parameters have been evaluated in order to guide future determination of $\rho$.

Figure 1

Dead time per event results for the ${}^{29}\mathrm{P}$ half-life measurement via the clock subtraction method (top panel) and the source pulser method (bottom panel). The average of the clock method data is given by the dashed blue lines. The weighted average of the source pulser method data is given by the solid red lines.

Figure 2

Top: Summed $\beta$-decay curve of the 31 standard runs of 160 s and the residuals divided by the square root of the number of counts in each bin with strong indication of a contaminant. The red line over the residuals represents the five-point moving average. Bottom: Same as above with the inclusion of an ${}^{26m}\mathrm{Al}$ contaminant in the fit function.

Figure 3

Summed $\beta$-decay curve for the three 650-s long runs combined with the residuals divided by the square root of the number of counts in each bin. The red line over the residuals represents the five-point moving average. The top panel shows the fit results assuming ${}^{26m}\mathrm{Al}$ as the only contaminant, whereas the bottom panel shows the fit result with ${}^{26m}\mathrm{Al}$ and a second contaminant, which, in this case, is assumed to be ${}^{15}\mathrm{O}$.

Figure 4

Fitted half-lives for the long runs with leading bins removed and the fit performed on the remaining bins with the top panel showing the results for a fit with ${}^{26m}\mathrm{Al}$ as the only contamination and the bottom showing the results with an additional floating contaminant. Up to 15 half-lives were removed for each, and the red lines indicate the uncertainty on the summed fit without any bin removal.

Figure 5

Half-lives of ${}^{29}\mathrm{P}$ vs the initial activity (top panel), the background activity (middle panel), and background activity added to the activity of the second contaminant (bottom panel) for each run. The color notates the discriminator voltage, and the shape notates the photomultiplier tube voltage. The final half-life result from the fitting of all the runs together 4.1055(44) s is given by solid red lines.

Figure 6

Half-lives of ${}^{29}\mathrm{P}$ when a summed fit is performed on all runs of identical settings according to photomultiplier voltage, threshold voltage, and irradiation time. The weighted average for each partition is given by the solid lines. The Birge ratio for each setting is given at the top of each partition.

Figure 7

${}^{29}\mathrm{P}$ half-lives [32, 33, 34] considered in the evaluation of the new world value. The triangle points colored red were removed from our evaluation. The scaled uncertainty on the overall ${}^{29}\mathrm{P}$ half-life of 4.1031(58) s is represented by the red band.

Figure 8

The relative uncertainties for quantities needed to calculate $\mathcal{F}{t}^{\mathrm{mirror}}$.

Figure 9

Measurements of $V_{\mathrm{ud}}$ from the mirror $\beta$ decays. The current values are given in blue circles, whereas the previous ${}^{29}\mathrm{P}{V}_{\mathrm{ud}}$ value is notated by the green diamond. The blue lines give the weighted average of the five $V_{\mathrm{ud}}$ values, whereas the $V_{\mathrm{ud}}$ value for the more precise superallowed $\beta$ decays [23] are represented by the red band.