0νββand2νββnuclear matrix elements, quasiparticle random-phase approximation, and isospin symmetry restoration
Within the quasiparticle random-phase approximation (QRPA) we achieve partial restoration of the isospin symmetry and hence fulfillment of the requirement that the $2\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ Fermi matrix element ${M}_{F}^{2\ensuremath{\nu}}$ vanishes, as it should, unlike in the previous version of the method. This is accomplished by separating the renormalization parameter ${g}_{pp}$ of the particle-particle proton-neutron interaction into isovector and isoscalar parts. The isovector parameter ${g}_{pp}^{T=1}$ needs to be chosen to be essentially equal to the pairing constant ${g}_{\mathrm{pair}}$, so no new parameter is needed. For the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay the Fermi matrix element ${M}_{F}^{0\ensuremath{\nu}}$ is substantially reduced, while the full matrix element ${M}^{0\ensuremath{\nu}}$ is reduced by $\ensuremath{\approx}$10$%$. We argue that this more consistent approach should be used from now on in the proton-neutron QRPA and in analogous methods.