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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.
To combine results from the three starting interactions and the ensembles, the authors used Bayesian Model Averaging. In plain terms, this means they treated the spread of computed values as a probability distribution and weighted the different calculations against available spectroscopic data. The outcome is a constrained distribution for the 76Ge neutrinoless NME with mean 2.46 and standard deviation 0.25. The authors present this as a quantification of the intrinsic theoretical spread within the interacting shell model in the chosen valence space.
Beyond the central number, the study includes a correlation analysis among the computed observables. Those correlations help check internal consistency of the calculations and reveal structural dependencies. The authors argue that such patterns can guide future efforts to improve effective interactions and reduce uncertainty in key observables used by experiments.
There are important caveats. The estimate quantifies uncertainty inside one theoretical framework (the interacting shell model) and inside one valence space (jj44). Choices made in the calculation matter: the ±10% perturbation window, the fixed single‑particle energies, the use or omission of quenching, the closure approximation, and the specific short‑range correlation model all affect results. The authors also limited sampling to 200 perturbed Hamiltonians per interaction for practical reasons. These factors mean the 2.46 ± 0.25 result should be read as the spread expected under the authors’ stated assumptions, not as a final or method‑independent uncertainty for the NME.