$\beta\beta$-decay nuclear matrix elements and half-life predictions in the interacting boson model with isospin restoration*

Recently, we have introduced a method for isospin restoration in the calculation of nuclear matrix elements (NME) for $0\nu\beta\beta$ and $2\nu\beta\beta$ decay within the framework of IBM-2 [1]. With this method, we calculate NME for all processes of interest in $0\nu\beta^-\beta^-$, $2\nu\beta^-\beta^-$, and in $0\nu\beta^+\beta^+$, $0\nu\beta^+ EC^+$, $0\nu ECEC$, $2\nu\beta^+\beta^+$, $2\nu\beta^+EC$, and $2\nu ECEC$. With isospin restoration, we find that the Fermi (F) matrix elements for $2\nu\beta\beta$ vanish, as expected, and those for $0\nu\beta\beta$ are considerably reduced. By combining these matrix elements with recently calculated phase-space factors [2-4] we are able to make our most accurate half-life predictions for all discussed processes.\\[4pt] [1] J.\ Barea, J. Kotila and F.\ Iachello, In preparation.\\[0pt] [2] J. Kotila and F.\ Iachello, Phys. Rev. C \textbf{85}, 034316 (2012).\\[0pt] [3] J. Kotila and F.\ Iachello, Phys. Rev. C \textbf{87}, 024313 (2013).\\[0pt] [4] J. Kotila, J. Barea, and F.\ Iachello, Phys. Rev. C \textbf{89}, 064319 (2014).