Global sensitivity analysis of bulk properties of an atomic nucleus

TL;DR

This paper introduces a fast, efficient method for global sensitivity analysis of nuclear properties, identifying key parameters influencing nuclear models and enabling advanced uncertainty quantification in nuclear physics.

Contribution

We develop a subspace-projected coupled-cluster method using eigenvector continuation, allowing rapid sensitivity analysis of nuclear properties across many parameter variations.

Findings

The method computes nuclear properties at over one million parameter sets in one hour.

Approximately 58% of the energy variance is due to a single contact-term.

The charge radius depends on multiple low-energy constants and their correlations.

Abstract

We perform a global sensitivity analysis of the binding energy and the charge radius of the nucleus $^{16}$O to identify the most influential low-energy constants in the next-to-next-to-leading order chiral Hamiltonian with two- and three-nucleon forces. For this purpose we develop a subspace-projected coupled-cluster method using eigenvector continuation [Frame D. et al., Phys. Rev. Lett. 121, 032501 (2018)]. With this method we compute the binding energy and charge radius of $^{16}$O at more than one million different values of the 16 low-energy constants in one hour on a standard laptop. For relatively small subspace projections, the root-mean-square error is about 1% compared to full space coupled-cluster results. We find that 58(1)% of the variance in the energy can be apportioned to a single contact-term in the $^3S_1$-wave, whereas the radius depends sensitively on several low-energy constants and their higher-order correlations. The results identify the most important parameters for describing nuclear saturation, and help prioritize efforts for uncertainty reduction of theoretical predictions. The achieved acceleration opens up for an array of computational statistics analyses of the underlying description of the strong nuclear interaction in nuclei across the Segr\'e chart.