Partial restoration of spin-isospin SU(4) symmetry and the one-quasiparticle random-phase approximation method in double-β decay

Abstract

The one-quasiparticle random-phase approximation (one-QRPA) method is used to describe simultaneously both double-β-decay 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 ββ2ν decay, producing the 2ν moments in ⁴⁸Ca, ⁷⁶Ge, ⁸²Se, ⁹⁶Zr, ¹⁰⁰Mo, ^128,130Te, and ¹⁵⁰Nd, that are of the same order of magnitude as the experimental ones; however, the agreement with ββ2ν data is only modest. To include contributions coming from induced nuclear weak currents, we extend the ββ0ν-decay formalism employed previously in C. Barbero et al., Nucl. Phys. A 628, 170 (1998), which is based on the Fourier-Bessel expansion. The numerical results for the ββ0ν moments in the above mentioned nuclei are similar to those obtained in other theoretical studies although smaller on average by ∼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 also 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 this restoration, since the ββ0ν moments are not experimentally measurable. The recipe proposed here is based on physically robust arguments. The numerical uncertainties in the ββ moments, related to (i) their strong dependence on the residual interaction in the particle-particle 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, generated by the residual interaction, is crucial in the description of the ββ decays, regardless of the nuclear model used.