Relation between the $2νββ$ and $0νββ$ nuclear matrix elements

A formal relation between the GT part of the nuclear matrix elements $M^0ν}_{GT}$ of $0νββ$ decay and the closure matrix elements $M^{2ν}_{cl}$ of $2νββ$ decay is established. This relation is based on the integral representation of these quantities in terms of their dependence on the distance $r$ between the two nucleons undergoing transformation. We also discuss the difficulties in determining the correct values of the closure $2νββ$ decay matrix elements.

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