Theoretical uncertainties of the elastic nucleon-deuteron scattering observables

TL;DR

This paper evaluates the theoretical uncertainties in nucleon-deuteron elastic scattering observables up to 200 MeV, highlighting the dominance of model uncertainties over parameter uncertainties and validating the One-Pion-Exchange Gaussian potential.

Contribution

It provides a detailed analysis of various theoretical uncertainties, especially from nuclear interaction models, in nucleon-deuteron scattering predictions using the OPE Gaussian potential.

Findings

Parameter uncertainties are generally small, up to a few percent at 200 MeV.

Model uncertainties dominate over parameter uncertainties in predictions.

The OPE Gaussian model accurately describes scattering data and compares well with other potentials.

Abstract

Theoretical uncertainties of various types are discussed for the nucleon-deuteron elastic scattering observables at the incoming nucleon laboratory energies up to 200 MeV. We are especially interested in the statistical errors arising from uncertainties of parameters of a nucleon-nucleon interaction. The obtained uncertainties of the differential cross section and numerous scattering observables are in general small, grow with the reaction energy and amount up to a few percent at 200 MeV. We compare these uncertainties with the other types of theoretical errors like truncation errors, numerical uncertainties and uncertainties arising from using the various models of nuclear interaction. We find the latter ones to be dominant source of uncertainties of modern predictions for the three-nucleon scattering observables. To perform above mentioned studies we use the One-Pion-Exchange Gaussian potential derived by the Granada group, for which the covariance matrix of its parameters is known, and solve the Faddeev equation for the nucleon-deuteron elastic scattering. Thus beside studying theoretical uncertainties we also show a description of the nucleon-deuteron elastic scattering data by the One-Pion-Exchange Gaussian model and compare it with results obtained with other nucleon-nucleon potentials, including chiral N$^4$LO forces from the Bochum-Bonn and Moscow(Idaho)-Salamanca groups. In this way we confirm the usefulness and high quality of the One-Pion-Exchange Gaussian force.