Binding in light nuclei: Statistical NN uncertainties vs Computational accuracy

TL;DR

This paper investigates how statistical uncertainties in nucleon-nucleon interactions affect the calculated binding energies of light nuclei, using bootstrap methods and solving Faddeev and Yakubovsky equations, with implications for nuclear physics accuracy.

Contribution

It introduces a bootstrap-based analysis of statistical uncertainties in nucleon-nucleon interactions and their impact on light nuclei binding energies, providing a reliable error estimation method.

Findings

Approximately 30 bootstrap samples suffice for reliable error estimates.

Extrapolation along the Tjon-line predicts experimental alpha particle binding within uncertainties.

Statistical uncertainties significantly influence nuclear binding energy calculations.

Abstract

We analyse the impact of the statistical uncertainties of the the nucleon-nucleon interaction, based on the Granada-2013 np-pp database, on the binding energies of the triton and the alpha particle using a bootstrap method, by solving the Faddeev equations for $^3$H and the Yakubovsky equations for $^4$He respectively. We check that in practice about 30 samples prove enough for a reliable error estimate. An extrapolation of the well fulfilled Tjon-line correlation predicts the experimental binding of the alpha particle within uncertainties.