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$0νββ$ and $2νββ$ nuclear matrix elements, QRPA, and isospin symmetry restoration

Within QRPA we achieve partial restoration of the isospin symmetry and hence fulfillment of the requirement that the $2νββ$ Fermi matrix element $M^{2ν}_F$ 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 the isovector and isoscalar parts. The isovector parameter $g_{pp}^{T=1}$ need to be chosen to be essentially equal to the pairing constant $g_{pair}$, so no new parameter is needed. For the $0νββ$ decay the Fermi matrix element $M^{0ν}_F$ is substantially reduced, while the full matrix element $M^{0ν}$ is reduced by $\approx$ 10%. We argue that this more consistent approach should be used from now on in the proton-neutron QRPA and in analogous methods.