Double Beta Decay in pn-QRPA Model with Isospin and SU(4) Symmetry Constraints

The transition matrix elements for the 0 → 0 double beta decays are calculated for Ca, Ge, Se, Mo, Te and Te nuclei, using a δ-interaction. As a guide, to fix the particle-particle interaction strengths, we exploit the fact that the missing symmetries of the mean field approximation are restored in the random phase approximation by the residual interaction. Thus, the T = 1, S = 0 and T = 0, S = 1 coupling strengths have been estimated by invoking the partial restoration of the isospin and Wigner SU(4) symmetries, respectively. When this recipe is strictly applied, the calculation is consistent with the experimental limit for the 2ν lifetime of Ca and it also correctly reproduces the 2ν lifetime of Se. In this way, however, the two-neutrino matrix elements for the remaining nuclei are either underestimated (for Ge and Mo) or overestimated (for Te and Te) approximately by a factor of 3. With a comparatively small variation (< 10%) of the spin-triplet parameter, near the value suggested by the SU(4) symmetry, it is possible to reproduce the measured T 2ν 1/2 in all the cases. The upper limit for the effective neutrino mass, as obtained from the theoretical estimates of 0ν matrix elements, is < mν >∼= 1 eV. The dependence of the nuclear matrix elements on the size of the configuration space has been also analyzed. Fellow of the CONICET from Argentina Financial support from CNPq, Brazil is acknowledged