We compute nuclear matrix elements of neutrinoless double-$\beta$ decay mediated by light Majorana-neutrino exchange in the $A=6$ system. The goal is to benchmark two many-body approaches, the no-core shell model and the multireference in-medium similarity renormalization group (SRG). We use a SRG-evolved next-to-next-to-next-to-leading chiral order two-body potential for the nuclear interaction, and make the approximation that the isospin is conserved. We compare the results of the two approaches as a function of the cutoff on the many-body basis space. Although differences are seen in the predicted nuclear radii, the ground-state energies and neutrinoless double-$\beta$ decay matrix elements produced by the two approaches show significant agreement. We discuss the implications for calculations in heavier nuclei.

• Received 24 September 2019
• Revised 7 May 2020
• Accepted 2 June 2020

DOI:https://doi.org/10.1103/PhysRevC.102.014302