Precise determination of the ${}^{113}\mathrm{Cd}$ fourth-forbidden non-unique $\beta$-decay $Q$ value

Using Penning trap mass spectrometry, we have performed a precise determination of the $Q$ value for the highly forbidden $\beta$ decay of ${}^{113}\mathrm{Cd}$. An independent measurement of the $Q$ value fixes the end-point energy in a fit to the ${}^{113}\mathrm{Cd}\beta$-decay spectrum. This provides a strong test of systematics for detectors that have observed this decay, such as those developed for $\beta \beta$-decay searches in cadmium and other isotopes. It will also aid in the theoretical description of the $\beta$-decay spectrum. The result, $Q_{\beta }=323.89\left(27\right)\mathrm{keV}$, agrees at the $1.3\sigma$ level with the value obtained from the 2012 Atomic Mass Evaluation [Chin. Phys. C 36, 1603 (2012)], but is a factor of almost four more precise. We also report improved values for the atomic masses of ${}^{113}\mathrm{Cd},{}^{113}\mathrm{In}$, and ${}^{112}\mathrm{Cd}$.

Figure 1

Nuclear level scheme for $\beta$-decay of ${}^{113}\mathrm{Cd}$.

Figure 2

Schematic diagram showing the subset of components of the LEBIT facility used in this work.

Figure 3

(a) A ${}^{113}\mathrm{Cd}^{+}$ time-of-flight resonance using a 1.5 s traditional quadrupole excitation scheme, and (b) a ${}^{113}\mathrm{In}^{+}$ time-of-flight resonance using a 1.5 s Ramsey quadrupole excitation scheme. The solid curves are fits of the theoretical traditional [38] and Ramsey [41] line shapes to the data.

Figure 4

Result for the ${}^{113}\mathrm{Cd}\beta$-decay $Q$ value obtained in this work (dotted line) with $\pm 1\sigma$ uncertainty (gray band). The result is compared to the value obtained from the AME2012 [28] and to measurements of the end-point of the ${}^{113}\mathrm{Cd}\beta$-decay spectrum using semiconductor detectors—Mit88 [22], Daw09 [27]; bolometers—Ale94 [23]; and scintillator detectors—Dan96 [24], Bel07 [26]. The error bars represent the statistical and any systematic uncertainties added in quadrature.

Figure 5

Comparison between the mass excesses of ${}^{113}\mathrm{In}$ and ${}^{113}\mathrm{Cd}$ measured in this work (open and closed circles) and the values listed in the AME2012 [28] (the zero line). The solid lines indicate the uncertainty in the AME2012 mass values. For each isotope two independent measurements were performed using either ${}^{115}\mathrm{In}$ or ${}^{112}\mathrm{Cd}$ as a reference. The error bars are the uncertainties in the measured masses obtained by adding the uncertainties in the measured ratio and reference mass in quadrature.