Propagation of Uncertainties of the Nucleon-Nucleon Potential to the Neutron-Deuteron Elastic Scattering Cross Section

R Skibiński,J Golak,H Witała,K Topolnicki,Yu Volkotrub

doi:10.1142/s2010194518600510

Abstract

Faddeev formalism is used to study the propagation of theoretical uncertainties from the two-nucleon force to three-nucleon scattering observables. Predictions are obtained with the One-Pion-Exchange Gaussian interaction, for which correlations between its parameters are known. Within the Monte Carlo approach we are able to estimate uncertainties of three-nucleon observables arising from the imprecise knowledge of the One-Pion-Exchange Gaussian potential parameters. We found that the uncertainties of this type are small for three-nucleon elastic scattering cross section at investigated here energies up to the nucleon laboratory energy of 200 MeV. They remain smaller than the dominant theoretical uncertainty arising from using various models of nucleon-nucleon interactions. We also compare the above-mentioned results with other types of theoretical uncertainties, that is with the ones stemming from order truncation errors and regulator dependencies, present in calculations based on the chiral interaction.

Highlights

A careful analysis of modern precise nuclear data requires the state-ofthe-art theoretical approaches and estimations of uncertainties of theoretical results
Using in ab-initio calculations nuclear interactions based on different physical assumptions, the uncertainties of potential parameters and, in the case of the chiral forces, the truncation errors related to neglecting the higher orders of chiral expansions as well as the dependence on regulator functions belong to the most important sources of theoretical uncertainties in the few-nucleon sector
Knowing the multivariate normal distribution of the OPE-Gaussian potential parameters defined by their expectation values and covariances, it is possible to apply the Monte Carlo statistical approach to estimate related uncertainties for 3N observables

Summary

Introduction

A careful analysis of modern precise nuclear data requires the state-ofthe-art theoretical approaches and estimations of uncertainties of theoretical results. Using in ab-initio calculations nuclear interactions based on different physical assumptions, the uncertainties of potential parameters and, in the case of the chiral forces, the truncation errors related to neglecting the higher orders of chiral expansions as well as the dependence on regulator functions belong to the most important sources of theoretical uncertainties in the few-nucleon sector.

Results

Conclusion