Relation between the $2\nu \beta \beta$ and $0\nu \beta \beta$ nuclear matrix elements

A formal relation between the GT part of the nuclear matrix elements M^0\nu}_{GT} of $0\nu \beta \beta$ decay and the closure matrix elements $M_{cl}^{2\nu }$ of $2\nu \beta \beta$ 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 $2\nu \beta \beta$ decay matrix elements.