Two-neutrino double-weak decays of $^{126}$Xe and $^{134}$Xe from different many-body methods
We calculate the nuclear matrix elements and corresponding half-lives for the two-neutrino double-electron capture of $^{126}$Xe and the two-neutrino double-beta decay of $^{134}$Xe. We use different many-body methods: the proton-neutron quasiparticle random-phase approximation, the nuclear shell model, the microscopic interacting boson model, and an effective field theory for heavy nuclei. For both nuclei, all our half-life predictions are generally consistent with each other when including theoretical uncertainties for each method. Interestingly, for all calculations the lower range of the predicted $^{134}$Xe half-life is shorter than $T^{2\nu}_{1/2} \approx 2\times10^{24}$\,y, which may be within the reach of next-generation experiments. For $^{126}$Xe, our results typically predict one order of magnitude longer half-lives than those for $^{134}$Xe.