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

TL;DR

This paper applies principal component analysis to quantify uncertainties in an empirical shell-model interaction, identifying key parameter combinations affecting nuclear structure observables and enabling efficient error propagation.

Contribution

It introduces a cost-effective PCA-based method for uncertainty quantification in shell-model interactions, improving error analysis in nuclear theory.

Findings

Feynman-Hellmann approximation effectively replaces full Hessian calculations.

Principal components reveal dominant parameter sensitivities.

Uncertainty propagation to various nuclear observables demonstrated.

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 compare a cost-effective approximation, using the Feynman-Hellmann theorem, to the full Hessian and find it works well. Diagonalizing the Hessian yields the principal components of the interaction: 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-nucleus scattering matrix elements.