Reconstruction of isospin and spin-isospin symmetries and double beta decay

Abstract

It is shown that the nondynamical violation of the isospin and Wigner SU(4) symmetries, induced by the Hartree-Fock-BCS approximation, can be circumvented by using the quasiparticle random-phase approximation. The suppression mechanism for the \ensuremath{\beta}\ensuremath{\beta}-decay transition rates, proposed by Vogel and Zirnbauer, is found to be closely related to the restoration of SU(4) symmetry. It is suggested that the extreme sensitivity of the \ensuremath{\beta}\ensuremath{\beta}-decay amplitude on the proton-neutron coupling is a consequence of the explicit violation of the SU(4) symmetry and therefore an artifact of the model. A prescription is given for fixing this interaction strength within the quasiparticle random-phase approximation itself, which in this way acquires predicting power on both single and double \ensuremath{\beta}-decay lifetimes.