Precise $\beta$ branching-ratio measurement for the $0^{+}\to 0^{+}$ superallowed decay of ${}^{34}\mathrm{Ar}$

We have measured the branching ratio for the superallowed $0^{+}\to$ $0^{+}\beta$ transition from ${}^{34}\mathrm{Ar}$ to be 0.9448(8), and determined its $ft$ value to be 3058.1(28) s, a result with $\pm 0.09$% precision, which is a factor of 3 improvement over the previous result based on current world data. The $ft$-value ratio for the mirror pair of superallowed transitions ${}^{34}\mathrm{Ar}$ $\to {}^{34}\mathrm{Cl}$ and ${}^{34}\mathrm{Cl}$ $\to {}^{34}\mathrm{S}$ becomes the most precise yet measured and, in a sensitive test of the method used to calculate the isospin-symmetry-breaking correction, ${\delta }_C$, it agrees well with the ratio as calculated with Woods-Saxon radial wave functions. This confirms the method used in the most recent survey of superallowed decays to extract $V_{\text{ud}}$, the up-down quark-mixing element of the Cabibbo-Kobayashi-Maskawa matrix. In addition, our branching-ratio results for the four observed Gamow-Teller branches to $1^{+}$ states in ${}^{34}\mathrm{Cl}$ are shown to agree well with shell-model calculations based on the same effective interactions that were used in the determination of ${\delta }_C$.

Figure 1

(a) The deposited energy vs position as obtained with the PSSD in the MARS focal plane. The spectrometer had already been optimized for ${}^{34}\mathrm{Ar}$ production and the extraction slits (vertical dotted lines) had been set. All the impurity-isotope labels are placed where the peaks of the respective activities had been seen with the slits wide open. (b) The projection of total counts between the slits. From this and subsequent spectra recorded during our measurement, we established that the contribution of ${}^{32}\mathrm{Cl}$ and ${}^{31}\mathrm{S}$ to the extracted ${}^{34}\mathrm{Ar}$ beam was 0.10(5)% and 0.43(14)%, respectively.

Figure 2

Implantation profiles of ${}^{34}\mathrm{Ar}$ (solid line) and the two contaminant activities ${}^{31}\mathrm{S}$ and ${}^{32}\mathrm{Cl}$ (dashed lines). The beam enters from the left. The shaded region shows the actual thickness of the Mylar collection tape. Our collected sample contains only those ions that are stopped in the tape.

Figure 3

Beta-decay scheme of ${}^{34}\mathrm{Ar}$, showing the five observed $\beta$-delayed $\gamma$-ray transitions in ${}^{34}\mathrm{Cl}$. Each energy level is labeled with its ($J^{\pi },T$) as well as its energy, expressed in keV, relative to the ${}^{34}\mathrm{Cl}$ ground state. Basic content is from the most recent evaluation [8]; however, the branching percentages and the presence of a $\gamma$-ray transition between the 666- and 146-keV levels come from this measurement.

Figure 4

(a) Spectrum of measured time differences between the arrival of a $\gamma$ ray and that of a $\beta$ particle for all identified coincidence events. Note that the $\beta$ signal was electronically delayed so that the prompt-coincidence peak appears near the center of the spectrum. (b) Measured time-difference spectrum for events corresponding only to the 666-keV $\gamma$ ray.

Figure 5

Spectrum of $\gamma$ rays observed in prompt coincidence with positrons from the decay of ${}^{34}\mathrm{Ar}$. The principal peaks are labeled with their energy in bold type and, where present, their corresponding single- and double-escape peaks are denoted by “SE” and “DE” subscripts, respectively. The small peak labeled “$511+171$” is due to the sum of two annihilation photons, one of which has backscattered into the detector.

Figure 6

The measured energy deposition (dots with error bars) in the $\beta$ detector for the decay of ${}^{34}\mathrm{Ar}$ to the 666-keV state in ${}^{34}\mathrm{Cl}$ is compared with the EGSnrc-simulated spectrum (solid line). The dashed vertical line at 50 keV indicates our electronic threshold. The difference between the simulated and measured spectra below 50 keV indicates the events lost because of the threshold.

Figure 7

Typical arrival-time spectrum of the collected ${}^{34}\mathrm{Ar}$ ions measured over the course of one run. The initial drop in intensity is generated by the decrease in local density of the hydrogen in the target cell as the primary beam heats the gas around its path. A fan located inside the gas target mitigates the effect and ensures a rapid transition to stable conditions.

Figure 8

Partial level scheme of ${}^{34}\mathrm{Cl}$, showing the excited states populated by the $\beta$ decay of ${}^{34}\mathrm{Ar}$ and the $\gamma$ transitions that occur or may occur following the $\beta$ decay. The four transitions shown with solid lines are the strongest ones; they correspond to the $\gamma$-ray peaks identified in Fig. 5. The weak 519-keV transition, shown dashed, is masked by the tail of the 511-keV peak in the spectrum in Fig. 5 but its strength has been determined. All five of these transitions appear in the decay scheme in Fig. 3. The dotted lines indicate possible weaker transitions, for which we set only upper limits.

Figure 9

Portion of the summed $\beta$-coincident $\gamma$-ray spectrum of Fig. 5, which focuses on the 511-keV annihilation peak and the weak 519-keV peak from the transition between the 666- and 146-keV states in ${}^{34}\mathrm{Cl}$. The inset focuses further onto the 519-keV peak. The histogram represents the data, while the smooth curve is the function we used to fit the 511-keV peak shape.

Figure 10

Mirror-pair $f{t}^a$/$f{t}^b$ values for $A=26$, 34, 38, and 42, where the “$a$” and “$b$” superscripts denote decays of the $T_Z=-1$ and $T_Z=0$ parents, respectively. The black and grey bands connect calculated results that utilize Woods-Saxon (WS) and Hartree-Fock (HF) radial wave functions, respectively. The measured results for $A=26$, 34, and 38 appear as open circles with error bars.