Neutrinoless double-β decay of 48Ca in the shell model: Closure versus nonclosure approximation

Neutrinoless double-beta decay (0 nu beta beta) is a unique process that could reveal physics beyond the Standard Model. Essential ingredients in the analysis of 0 nu beta beta rates are the associated nuclear matrix elements. Most of the approaches used to calculate these matrix elements rely on the closure approximation. Here we analyze the light neutrino-exchange matrix elements of Ca-48 0 nu beta beta decay and test the closure approximation in a shell-model approach. We calculate the 0 nu beta beta nuclear matrix elements for Ca-48 using both the closure approximation and a nonclosure approach, and we estimate the uncertainties associated with the closure approximation. We demonstrate that the nonclosure approach has excellent convergence properties which allow us to avoid unmanageable computational cost. Combining the nonclosure and closure approaches we propose a new method of calculation for 0 nu beta beta decay rates which can be applied to the 0 nu beta beta decay rates of heavy nuclei, such as Ge-76 or Se-82.