${}^{146}\mathrm{Nd},{}^{144}\mathrm{Sm}$, and other unexplored $2\beta$-decay isotopes

${}^{146}\mathrm{Nd}$ is one of only four (over a total of 35 existing) $2{\beta }^{-}$-decay isotope candidates whose half-lives currently lack experimental limits. The $\alpha$ activity of the ${}^{146}\mathrm{Sm}$ daughter nuclide allows placement of limits on the $2\beta$ decay using the ${}^{146}\mathrm{Nd}/{}^{142}\mathrm{Nd}$ abundance ratio $(T_{1/2}^{\beta \beta }\gtrsim 3\times {10}^9$ yr) or direct search for ${}^{146}\mathrm{Sm}$ with accelerator mass spectrometers $(T_{1/2}^{\beta \beta }\gtrsim 4.5\times {10}^{19}$ yr). With a similar approach, a modest $(\sim \text{Gyr})$ first limit on half-lives for the other unexplored $2\beta$ unstable isotopes and competitive limits (few $10{}^{13}\mathrm{yr})$ for ${}^{98}\mathrm{Mo}$ and ${}^{122}\mathrm{Sn}$ are also given. Finally, it is shown how the limit $T_{1/2}^{0\nu \epsilon {\beta }^{+}}\gtrsim {10}^{15}$ yr for the unexplored ${}^{144}\mathrm{Sm}0\nu \epsilon {\beta }^{+}$ decay may be obtained from the data of a GSO crystal scintillator.

Figure 1

Simplified schema of ${}^{146}\mathrm{Nd}\begin{array}{c}2{\beta }^{-}\\ ⟶\end{array}{}^{146}\mathrm{Sm}\begin{array}{c}\alpha \\ ⟶\end{array}{}^{142}\mathrm{Nd}$ decay chain [16, 37]. (The $Q$ values are given in keV.)