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We recently proposed a new method to calculate the standard nuclear matrixelements for neutrinoless double-$\beta$ decay ($0\nu\beta\beta$) of${}^{48}$Ca going beyond the closure approximation. Here we extend thisanalysis to the important case of ${}^{82}$Se, which was chosen as the baseisotope for the upcoming SuperNEMO experiment. We demonstrate that using amixed method that considers information from closure and non-closureapproaches, one can get excellent convergence properties for the nuclear matrixelements, which allows one to avoid unmanageable computational costs. We showthat in contrast with the closure approximation the mixed approach has a veryweak dependence on the average closure energy. The matrix elements for theheavy neutrino-exchange mechanism that could contribute to the $0\nu\beta\beta$decay of ${}^{82}$Se are also presented.

Neutrinoless double-$\beta$ decay of ${}^{82}$Se in the shell model: beyond closure approximation