Nuclear Binding Energies and NN uncertainties

TL;DR

This paper explores how NN-level experimental and systematic errors can estimate uncertainties in nuclear binding energy calculations, proposing simplified methods to gauge predictive accuracy across the periodic table.

Contribution

It introduces a straightforward approach to estimate theoretical uncertainties in nuclear binding energies using NN-level errors without solving the full many-body problem.

Findings

Estimated a priori error of 0.1-0.4 MeV per nucleon across nuclei A=2 to 208.

Found linear error growth with density in nuclear and neutron matter.

Suggested limiting computational efforts to achieve this accuracy.

Abstract

There is an increasing interest in quantifying the predictive power in nuclear structure calculations. We discuss how both experimental and systematic errors at the NN-level can be used to estimate the theoretical uncertainties by rather simple means and without solving the full nuclear many body problem. We emphasize the role of effective interactions defined by coarse graining the NN potential to length scales of the order of the minimal de Broglie wavelength probed between nucleons in nuclei. We find an a priori error of \DeltaB/A \sim 0.1 - 0.4MeV for the binding energy per particle throughout the periodic table for 2 \leq A \leq 208, and a linear growth of the error with density for nuclear matter \DeltaB/A \sim 3.75{\rho}n.m. and neutron matter \DeltaB/N \sim 3.5{\rho}n.. This suggests to limit the computational effort in solving the Nuclear Many Body Problem to such an accuracy.