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$0νββ$ and $2νββ$ nuclear matrix elements in the interacting boson model with isospin restoration

We introduce a method for isospin restoration in the calculation of nuclear matrix elements (NME) for $0νββ$ and $2νββ$ decay within the framework of interacting boson model (IBM-2). With this method, we calculate NME for all processes of interest in $0νβ^-β^-$, $2νβ^-β^-$, and in $0νβ^+β^+$, $0νβ^+ EC^+$, $R0νECEC$, $2νβ^+β^+$, $2νβ^+EC$, and $2νECEC$. With this method, the Fermi (F) matrix elements for $2νββ$ vanish, and those for $0νββ$ are considerably reduced.