$0νββ$ 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 $≈$ 10%. We argue that this more consistent approach should be used from now on in the proton-neutron QRPA and in analogous methods.