Isovector and isoscalar spin-multipole giant resonances in the parent and daughter nuclei of double- β -decay triplets

Abstract

The strength distributions, including giant resonances, of isovector and isoscalar spin-multipole transitions in the commonly studied double-$\ensuremath{\beta}$-decay triplets are computed in the framework of the quasiparticle random-phase approximation (QRPA) using the Bonn-$A$ two-body interaction in no-core single-particle valence spaces. The studied nuclei include the double-$\ensuremath{\beta}$ parent and daughter pairs ($^{76}\mathrm{Ge}$, $^{76}\mathrm{Se}$), ($^{82}\mathrm{Se}$, $^{82}\mathrm{Kr}$), ($^{96}\mathrm{Zr}$, $^{96}\mathrm{Mo}$), ($^{100}\mathrm{Mo}$, $^{100}\mathrm{Ru}$), ($^{116}\mathrm{Cd}$, $^{116}\mathrm{Sn}$), ($^{128}\mathrm{Te}$, $^{128}\mathrm{Xe}$), ($^{130}\mathrm{Te}$, $^{130}\mathrm{Xe}$), and ($^{136}\mathrm{Xe}$, $^{136}\mathrm{Ba}$). The studied transitions proceed from the ground states to the ${J}^{\ensuremath{\pi}}={0}^{\ensuremath{-}},{1}^{\ensuremath{-}},{2}^{\ensuremath{-}}$ (spin-dipole transitions) and ${J}^{\ensuremath{\pi}}={1}^{+},{2}^{+},{3}^{+}$ (spin-quadrupole transitions) excited states in these nuclei. Comparison of the present results with potential future data may, indirectly, shed light on the reliability of QRPA-based nuclear-structure frameworks in description of the wave functions of nuclear states relevant for the two-neutrino and neutrinoless double $\ensuremath{\beta}$ decays in the studied triplets.