Determination of the direct double-$\beta$-decay $Q$ value of ${}^{96}\mathrm{Zr}$ and atomic masses of ${}^{90-92,94,96}\mathrm{Zr}$ and ${}^{92,94-98,100}\mathrm{Mo}$

Experimental searches for neutrinoless double-$\beta$ decay offer one of the best opportunities to look for physics beyond the standard model. Detecting this decay would confirm the Majorana nature of the neutrino, and a measurement of its half-life can be used to determine the absolute neutrino mass scale. Important to both tasks is an accurate knowledge of the $Q$ value of the double-$\beta$ decay. The LEBIT Penning trap mass spectrometer was used for the first direct experimental determination of the ${}^{96}\mathrm{Zr}$ double-$\beta$ decay $Q$ value: $Q_{\beta \beta }=3355.85\left(15\right)$ keV. This value is nearly 7 keV larger than the 2012 Atomic Mass Evaluation [M. Wang et al., Chin. Phys. C 36, 1603 (2012)] value and one order of magnitude more precise. The 3-$\sigma$ shift is primarily due to a more accurate measurement of the ${}^{96}\mathrm{Zr}$ atomic mass: $m{(}^{96}\mathrm{Zr})=95.90827735\left(17\right)$ u. Using the new $Q$ value, the $2\nu \beta \beta$-decay matrix element, $|M_{2\nu }|$, is calculated. Improved determinations of the atomic masses of all other zirconium $\left({}^{90-92,94,96}\mathrm{Zr}\right)$ and molybdenum $\left({}^{92,94-98,100}\mathrm{Mo}\right)$ isotopes using both ${}^{12}{\mathrm{C}}_8$ and ${}^{87}\mathrm{Rb}$ as references are also reported.

Figure 1

Schematic of a subsection of the Low-Energy Beam and Ion Trap (LEBIT) Facility relevant to this article.

Figure 2

One of 88 ${}^{96}{\mathrm{Zr}}^{+}$ time-of-flight Ramsey cyclotron resonances used for the determination of ${\nu }_c\left({}^{96}{\mathrm{Zr}}^{+}\right)$/${\nu }_c({}^{96}{\mathrm{Mo}}^{+})$. This resonance contains about 1700 detected ${}^{96}{\mathrm{Zr}}^{+}$ ions. The solid line is the theoretical line shape [17] fitted to the data.

Figure 3

Data sets of cyclotron frequency ratios ${\nu }_c\left({}^{96}{\mathrm{Zr}}^{+}\right)$/${\nu }_c({}^{96}{\mathrm{Mo}}^{+})$ about the set's mean value. The statistical uncertainty in an individual cyclotron frequency ratio is represented by the error bars, and the $\pm 1-\sigma$ statistical uncertainty of the data set is shown as the shaded band.

Figure 4

Comparison of the mass excess values of the LEBIT measurements to AME2012 for ${}^{90-92,94,96}\mathrm{Zr}$ with ${}^{12}{C}_8^{+}$ (filled circles) and ${}^{87}{\mathrm{Rb}}^{+}$ (open circles) used as reference species. The AME2012 uncertainty for each isotope is shown as the horizontal lines around 0.

Figure 5

Comparison of the mass excess values of the LEBIT measurements to AME2012 for ${}^{92,94-98,100}\mathrm{Mo}$ with ${}^{12}{C}_8^{+}$ (filled circles) and ${}^{87}{\mathrm{Rb}}^{+}$ (open circles) used as reference species. The AME2012 uncertainty for each isotope is shown as the horizontal lines around 0. The JYFLTRAP ${}^{100}\mathrm{Mo}$ mass excess comparison is also shown.