$0\nu\beta\beta$-decay of ${}^{48}$Ca in the shell model

We discuss neutrinoless double beta ($0\nu\beta\beta$) decay of ${}^{48}$Ca and test the closure approximation, a widely used approach for $0\nu\beta\beta$ nuclear matrix element calculations. In the shell model framework we calculate $0\nu\beta\beta$ nuclear matrix element of ${}^{48}$Ca using both closure approximations and the nonclosure approach, and we estimate the uncertainties associated with the closure approximation. We also demonstrate that the nonclosure approach can be used to calculate $0\nu\beta\beta$ decay rates of heavy nuclei, such ${}^{72}$Ge or ${}^{82}$Se, thus avoiding unmanageable computational costs.