Calculation of Gamow-Teller and two-neutrino double-$\beta$ decay properties for ${}^{130}\mathrm{Te}$ and ${}^{136}\mathrm{Xe}$ with a realistic nucleon-nucleon potential

We report on the calculation of Gamow-Teller and double-$\beta$ decay properties for nuclei around ${}^{132}\mathrm{Sn}$ within the framework of the realistic shell model. The effective shell-model Hamiltonian and Gamow-Teller transition operator are derived by way of many-body perturbation theory, without resorting to the empirical effective quenching factor for the Gamow-Teller operator. The results are then compared with the available experimental data, in order to establish the reliability of our approach. This is a mandatory step before we apply the same methodology, in forthcoming studies, to the calculation of the neutrinoless double-$\beta$ decay nuclear matrix elements for nuclei that are currently considered among the best candidates for the detection of this process.

Figure 1

One-body second-order diagrams included in the perturbative expansion of ${\chi }_0$. An asterisk indicates the bare operator $\mathrm{\Theta }$; a wavy line, the two-body potential $V_{\mathrm{low}k}$.

Figure 2

Experimental and calculated spectra of ${}^{130}\mathrm{Te}$ up to 2-MeV excitation energy (see text for details).

Figure 3

Same as Fig. 2, for ${}^{130}\mathrm{Xe}$.

Figure 4

Running sums of the ${}^{130}\mathrm{Te} B\left({\mathrm{GT}}^{-}\right)$ strengths as a function of the excitation energy $E_x$ up to 3000 keV (see text for details).

Figure 5

Running sums of the calculated $M_{2\nu }^{\mathrm{GT}}$ as a function of the excitation energy of the intermediate states. The blue area corresponds to the calculations with the bare GT operator; the black area, to those with ${\mathrm{GT}}_{\mathrm{eff}}$ (see text for details).

Figure 6

Change in proton occupancies between the ground states for ${}^{130}\mathrm{Te}\to {}^{130}\mathrm{Xe}$ decay (see text for details). The brown area corresponds to the occupation of the $0g_{7/2}$ orbital; the green area, occupation of the $1d$ orbitals; the red area, occupation of the $2s_{1/2}$ orbital; and the blue area, occupation of the $0h_{11/2}$ orbital.

Figure 7

Change in neutron vacancies between the ground states for ${}^{130}\mathrm{Te}\to {}^{130}\mathrm{Xe}$ decay (see text for details). Colored areas refer to the same orbitals as in Fig. 6.

Figure 8

Same as Fig. 2, for ${}^{136}\mathrm{Xe}$.

Figure 9

Same as Fig. 2, for ${}^{136}\mathrm{Ba}$.

Figure 10

Running sums of the ${}^{136}\mathrm{Xe} B\left({\mathrm{GT}}^{-}\right)$ strengths as a function of the excitation energy $E_x$ up to 4500 keV (see text for details).

Figure 11

Same as Fig. 5, for ${}^{136}\mathrm{Xe}\to {}^{136}\mathrm{Ba} 2\nu \beta \beta$ decay (see text for details).

Figure 12

Same as Fig. 6, for ${}^{136}\mathrm{Xe}\to {}^{136}\mathrm{Ba}$ decay (see text for details).

Figure 13

Same as Fig. 7, for ${}^{136}\mathrm{Xe}\to {}^{136}\mathrm{Ba}$ decay (see text for details).