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arXiv · 1710.00254

Partial restoration of spin-isospin SU(4) Symmetry and the One-QRPA method in Double Beta Decay

V. dos S. Ferreira·F. Krmpotić·C. A. Barbero·A. R. Samana
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Abstract

The one-QRPA method is used to describe simultaneously both double decay beta modes, giving special attention to the partial restoration of spin-isospin SU(4) symmetry. To implement this restoration and to fix the model parameters, we resort to the energetics of Gamow-Teller resonances and to the minima of the single $β^+$-decay strengths. This makes the theory predictive regarding the $ββ_{2ν}$-decay, producing the $2ν$ moments in $^{48}$Ca, $^{76}$Ge, $^{82}$Se, $^{96}$Zr, $^{100}$Mo, $^{128,130}$Te, and $^{150}$Nd, that are of the same order of magnitude as the experimental ones; however, the agreement with $ββ_{2ν}$ data is only modest. To include contributions coming from induced nuclear weak currents, we extend the $ββ_{0ν}$-decay formalism employed previously in C. Barbero et. al, Nuc. Phys. A628, 170 (1998). The numerical results for the $ββ_{0ν}$ moments in the above mentioned nuclei are similar to those obtained in other theoretical studies although smaller on averag by $\sim 40\%$. We attribute this difference basically to the one-QRPA-method, employed here for the first time, instead of the currently used two-QRPA-method. The difference is partially due to the way of carrying out the restoration of the spin-isospin symmetry. It is hard to say which is the best way to make the restoration, since the $ββ_{0ν}$ moments are not experimentally measurable. The numerical uncertainties in the $ββ$ moments, related with i) their strong dependence on the residual interaction in the p-p channel when evaluated within the QRPA, and ii) lack of proper knowledge of single-particle energies, have been quantified. It is concluded that the partial restoration of the SU (4) symmetry is crucial in the description of the $ββ$-decays, regardless of the nuclear model used.

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V. dos S. Ferreira, F. Krmpotić, C. A. Barbero, A. R. Samana. 2017-09-30. Partial restoration of spin-isospin SU(4) Symmetry and the One-QRPA method in Double Beta Decay. https://doi.org/10.1103/physrevc.96.044322

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