This paper measures how uncertain theorists are about a key nuclear quantity for searches of neutrinoless double‑beta decay in 76Ge. That decay, if seen, would show that lepton number is violated and that neutrinos are their own antiparticles. To turn an experimental half‑life into a property of the neutrino, researchers need the nuclear matrix element (NME). The authors adapt a statistical protocol to give a probability distribution for this NME and report a central value of 2.46 with a standard deviation of 0.25.

The team worked inside the interacting shell model, a microscopic approach that builds nuclear states from active nucleons moving in a few orbitals. They used the jj44 valence space, which treats 56Ni as an inert core and lets active nucleons occupy the 1p3/2, 1p1/2, 0f5/2 and 0g9/2 orbitals. Starting from three established effective Hamiltonians (JUN45, GCN2850, and JJ44b), they generated ensembles of perturbed interactions by varying the two‑body matrix elements uniformly by ±10%. For each starting interaction they sampled 200 perturbed Hamiltonians and computed a suite of low‑energy observables.

Those observables included the neutrinoless NME, the two‑neutrino NME, excitation energies of the first 2+, 4+ and 6+ states in both 76Ge and 76Se, electric quadrupole transition strengths B(E2), and Gamow–Teller strengths. For the Gamow–Teller transitions and the two‑neutrino NME they used a common phenomenological quenching factor q = 0.65. The neutrinoless NME was calculated without quenching, using the closure approximation to simplify intermediate states and modelling short‑range nucleon correlations with the Miller–Spencer Jastrow form. The authors did not include proton occupancies or neutron vacancies because reliable experimental benchmarks are not available for these nuclei.