Precise measurement of branching ratios in the $\beta$ decay of ${}^{38}\mathrm{Ca}$

We present the full description of a measurement of the branching ratios for the $\beta$ decay of ${}^{38}\mathrm{Ca}$. This decay includes five allowed $0^{+}\to 1^{+}$ branches and a superallowed $0^{+}\to 0^{+}$ one. With our new result for the latter, we determine its $ft$ value to be $3062.3\pm 6.8$ s, a result whose precision (0.2%) is comparable to the precision of the 13 well-known $0^{+}\to 0^{+}$ transitions used up until now for the determination of $V_{\text{ud}}$, the up-down quark-mixing element of the Cabibbo-Kobayashi-Maskawa matrix. The ${}^{38}\mathrm{Ca}$ superallowed transition thus becomes the first addition to this set of transitions in nearly a decade and the first for which a precise mirror comparison is possible, thus enabling an improved test of the isospin-symmetry-breaking corrections required for the extraction of $V_{\text{ud}}$.

Figure 1

The deposited energy versus position as obtained with the PSSD in the MARS focal plane. The spectrometer had already been optimized for ${}^{38}\mathrm{Ca}$ production. Vertical lines show the position of the extraction slits in MARS during these measurements; note that the slits were set asymmetrically to minimize the contribution from impurities.

Figure 2

$\beta$-decay scheme of ${}^{38}\mathrm{Ca}$ showing the four strongest $\beta$ branches and the most intense subsequent $\gamma$-ray transitions in ${}^{38}\mathrm{K}$. For each level, its ($J^{\pi }$, T) is given as well as its energy, expressed in keV, relative to the ${}^{38}\mathrm{K}$ ground state [5]. Branching percentages come from this measurement. As discussed later in Sec. 3f, there are other weak $\gamma$ rays present, which complicate this scheme somewhat. Note that there is also a very weak (0.03%) $\gamma$-ray branch from the 130-keV isomer to the ground state [6].

Figure 3

(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 1567-keV $\gamma$ ray.

Figure 4

Spectrum of $\gamma$ rays observed in prompt coincidence with positrons from the decay of ${}^{38}\mathrm{Ca}$. The small peak labeled “$511+171$” is the sum of two annihilation photons, one of which has backscattered into the detector. The “$511+1567$” peak is the result of coincidence summing between a 1567-keV $\gamma$ ray and annihilation radiation from the positron decay that preceded it.

Figure 5

The measured energy deposition (solid circles, gray) in the $\beta$-detector for the decay of ${}^{38}\mathrm{Ca}$ is compared with the egsnrc-simulated spectrum (solid line, black). The dashed vertical line at 120 keV indicates our threshold.

Figure 6

Typical time profile of the collected ${}^{38}\mathrm{Ca}$ beam 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 7

Portions of the summed $\beta$-coincident $\gamma$-ray spectrum, in which we have singled out many of the weak peaks listed in Table 4. Those peaks identified with unbracketed energies have measured intensities; those with bracketed energies are only assigned a limit. The unlabeled strong peak in panels (a) and (b) of the figure is at 1567 keV. The unlabeled one in panel (c) is at 3211 keV; the one in panel (d) is at 3848 keV.

Figure 8

Partial level scheme of ${}^{38}\mathrm{K}$, showing the excited states populated by the $\beta$ decay of ${}^{38}\mathrm{Ca}$ 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 have already appeared in Fig. 2 and correspond with the $\gamma$-ray peaks identified in Fig. 4. The dashed lines identify additional weak observed transitions, and the dotted lines indicate even weaker transitions, for which we set only upper limits. Note that the 130-keV state is a 924-ms isomer; it has a very weak $\gamma$-ray branch to the ground state, which is not shown.