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 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.

arXiv comment30 pages, 11 figures, 2 tables

References in corpus (25)

• The Shell Model as Unified View of Nuclear Structure
• A History of Dark Matter
• WIMP dark matter candidates and searches - current status and future prospects
• Error Estimates of Theoretical Models: a Guide
• Model-independent WIMP Scattering Responses and Event Rates: A Mathematica Package for Experimental Analysis
• First Results from the DarkSide-50 Dark Matter Experiment at Laboratori Nazionali del Gran Sasso
• Non-Empirical Interactions for the Nuclear Shell Model: An Update
• Ab initio coupled-cluster approach to nuclear structure with modern nucleon-nucleon interactions
• Quantifying Correlated Truncation Errors in Effective Field Theory
• Uncertainty analysis and order-by-order optimization of chiral nuclear interactions
• Eigenvector continuation with subspace learning
• Uncertainty Quantification for Nuclear Density Functional Theory and Information Content of New Measurements
• Global sensitivity analysis of bulk properties of an atomic nucleus
• A recipe for EFT uncertainty quantification in nuclear physics
• Factorization in large-scale many-body calculations
• Exploring Bayesian parameter estimation for chiral effective field theory using nucleon-nucleon phase shifts
• Quantified Gamow Shell Model interaction for $psd$-shell nuclei
• BIGSTICK: A flexible configuration-interaction shell-model code (updated)
• Uncertainty Quantification for Optical Model Parameters
• Error analysis of nuclear forces and effective interactions
• Triton binding energy with realistic precision
• Uncertainty quantification in nuclear shell model
• Statistical error propagation in ab initio no-core full configuration calculations of light nuclei
• Is the unusual near-threshold potential behavior in elastic scattering of weakly bound nuclei a precision error?
• Sensitivity analysis of random two-body interactions

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