Isotope abundance measurement of the half-life of the $\beta \beta$-decaying nucleus ${}^{96}\mathrm{Zr}$ from a 2.68 Gyr zircon sample

The decay half-life of the ${}^{96}\mathrm{Zr}$ isotope was measured by applying isotope geochemistry techniques to ancient (0.9 and 2.68 Gyr) ${\mathrm{ZrSiO}}_4$ (zircon) samples, with the objective to separate the single and double $\beta$-decay branches. The single $\beta$ decay provides one of the most direct tests for theoretical models describing neutrinoless $\beta \beta$ decays. Both the single and the double $\beta$-decay branches lead to the same final nucleus ${}^{96}\mathrm{Mo}$ and generate an isotopic anomaly over geological time scales. After a chemical separation, the Mo isotopic composition was measured by inductively coupled plasma mass spectrometry (ICPMS). The ${}^{96}\mathrm{Mo}$ isotopic anomaly was determined in two complete replicate analyses to be 107(40) and 88(20) ppm, which translates to a ${}^{96}\mathrm{Zr}$ half-life of $T_{1/2}=\left(2.{03}_{-0.31}^{+0.46}\right)\times {10}^{19}\mathrm{yr}$. With the $2\nu \beta \beta$ partial decay half-life of the ground-state to ground-state transition known from NEMO-3 to be $2.35\pm 0.21\times {10}^{19}$ yr and all other partial $\beta \beta$-decay half-lives expected to be many orders of magnitude longer, a lower limit for the single-$\beta$-decay half-life is set at $T_{1/2}^{\beta }\ge 6.2\times {10}^{19}$ yr.

Figure 1

Decay scheme of the $A=96$ triplet showing the energy position of ${}^{96}\mathrm{Zr}$ with respect to its neighbors ${}^{96}\mathrm{Nb}$ and ${}^{96}\mathrm{Mo}$ [4]. Indicated is the dominant single $\beta$-decay path from the ${}^{96}\mathrm{Zr}$ ground state to the $J^{\pi }=5^{+}$ state, and the ${}^{96}\mathrm{Nb}$ ground state decays dominantly to the $J^{\pi }=5^{+}$ excited state in ${}^{96}\mathrm{Mo}$.

Figure 2

Flow chart summarizing ion-exchange separation of Mo from Zr, Fe, and other elements. Removal of Fe is important as it results in an interference at $A=96$ from ${}^{56}\mathrm{Fe}{}^{40}\mathrm{Ar}^{+}$. Two successive separations using TEVA resin remove Zr by four to six orders of magnitude, followed by two successive separations using cation resin to remove Fe and Zr by an additional three to four orders of magnitude.

Figure 3

Shown in red circles are the isotopic excesses of the Mo element in the 2.68 Gyr old zircon sample. Stars indicate predicted excesses as a result of spontaneous fission of trace amounts of natural U in the zircon sample, while squares show the isotopic excesses measured in a 0.9 Gyr zircon sample. The $n\left({}^{97}\mathrm{Mo}\right)/\mathrm{n}({}^{95}\mathrm{Mo}$) ratio was fixed to correct mass-dependent fractionation.