Uncertainty quantification of an empirical shell-model interaction using principal component analysis

Abstract

Recent investigations have emphasized the importance of uncertainty quantification (UQ) to describe errors in nuclear theory. We carry out UQ for configuration-interaction shell model calculations in the 1s-0d valence space, investigating the sensitivity of observables to perturbations in the 66 parameters (matrix elements) of a high-quality empirical interaction. The large parameter space makes computing the corresponding Hessian numerically costly, so we construct a cost-effective approximation using the Feynman-Hellmann theorem. Diagonalizing the approximated Hessian yields the principal components: linear combinations of parameters ordered by sensitivity. This approximately decoupled distribution of parameters facilitates theoretical error propagation onto structure observables: electromagnetic transitions, Gamow-Teller decays, and dark-matter interaction matrix elements.

Toward the discovery of matter creation with neutrinoless double-beta decay

“…8 indicate that no parameter variation was explored. These kinds of uncertainties have been recently evaluated more systematically in the shell model for energy levels (Yoshida et al, 2018a) and electroweak matrix elements in light nuclei (Fox and Johnson, 2019), and in heavier systems with EDF theory (Neufcourt et al, 2019).…”