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

$^{146}$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 $^{146}$Sm daughter nuclide allows placement of limits on the 2$\beta$ decay using the $^{146}$Nd/$^{142}$Nd abundance ratio ($T^{\beta\beta}_{1/2} \gsim 3 \times 10^9$ yr) or direct search for $^{146}$Sm with accelerator mass spectrometers ($T^{\beta\beta}_{1/2} \gsim 4.5 \times 10^{19}$ yr). With a similar approach, a modest ($\sim$ Gyr) first limit on half-lives for the other unexplored $2\beta$ unstable isotopes and competitive limits (few $10^{13}$yr) for $^{98}$Mo and $^{122}$Sn are also given. Finally, it is shown how the limit $T^{0\nu\epsilon\beta^+}_{1/2} \gsim 10^{15}$ yr for the unexplored $^{144}$Sm $0\nu\epsilon \beta^+$ decay may be obtained from the data of a GSO crystal scintillator.