Isovector spin-multipole strength distributions in double-$\beta$-decay triplets

In this work the energetics and strength distributions of isovector spin-dipole and spin-quadrupole transitions from the ground states of the 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 (${}^{136}\mathrm{Xe}, {}^{136}\mathrm{Ba}$), of double-$\beta$-decay initial and final nuclei, to the $J^{\pi }=0^{-},1^{-},2^{-},1^{+},2^{+}$, and $3^{+}$ excited states of the intermediate odd-odd nuclei ${}^{76}\mathrm{As}, {}^{82}\mathrm{Br}, {}^{96}\mathrm{Nb}, {}^{100}\mathrm{Tc}, {}^{116}\mathrm{In}, {}^{128,130}\mathrm{I}$, and ${}^{136}\mathrm{Cs}$ are investigated. The calculations are performed using a proton-neutron quasiparticle random-phase approximation (pnQRPA) theory framework with the Bonn-A two-body interaction in no-core single-particle valence spaces.

Figure 1

Strength distributions for $A=76$. (a) $L=1, {\beta }^{-}$, (b) $L=1, {\beta }^{+}$, (c) $L=2, {\beta }^{-}$, (d) $L=2, {\beta }^{+}$. The solid line denotes the sum of the dashed, dotted, and dash-dotted individual contributions. Energies are measured relative to the ground state of the odd-odd final nucleus. The strengths are given in units of ${\mathrm{fm}}^2$ for $J^{\pi }=0^{-},1^{-},2^{-}$ and in ${\mathrm{fm}}^4$ for $J^{\pi }=1^{+},2^{+},3^{+}$.

Figure 2

The same as in Fig. 1 for $A=82$.

Figure 3

The same as in Fig. 1 for $A=96$.

Figure 4

The same as in Fig. 1 for $A=100$.

Figure 5

The same as in Fig. 1 for $A=116$.

Figure 6

The same as in Fig. 1 for $A=128$.

Figure 7

The same as in Fig. 1 for $A=130$.

Figure 8

The same as in Fig. 1 for $A=136$.