Isovector and isoscalar spin-multipole giant resonances in the parent and daughter nuclei of double- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>β</mml:mi></mml:math> -decay triplets

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