Nonperturbative renormalization of the neutrinoless double-β operator in p-shell nuclei

We use Lee-Suzuki mappings and related techniques to construct effective two-body p-shell interactions and neutrinoless double-beta operators that exactly reproduce the results of large no-core-shell-model calculations of (fictitious) double-beta decay in nuclei with mass number A = 6. We then apply the effective operators to the (also fictitious) decay of nuclei with A = 7, 8, and 10, again comparing with no-core calculations in much larger spaces. The results with the effective two-body operators are generally good. In some cases, however, they differ non-negligibly from the full no-core results, suggesting that three-body corrections to the decay operator in heavier nuclei may be important. An application of our procedure and related ideas to f p-shell nuclei such as Ge-76 should be feasible within coupled-cluster theory.