Infrared extrapolations for atomic nuclei

TL;DR

This paper investigates systematic errors in nuclear binding energy calculations caused by harmonic oscillator model-space truncations, introduces an infrared scaling variable for controlled extrapolations, and demonstrates improved accuracy in ground-state energy predictions.

Contribution

It identifies the infrared scaling variable relevant for nuclear calculations and shows how to perform controlled extrapolations to reduce systematic errors.

Findings

Infrared component of error is well-understood for controlled extrapolations.

Using large oscillator frequencies suppresses ultraviolet corrections.

Tens of MeV infrared extrapolations yield accurate ground-state energies.

Abstract

Harmonic oscillator model-space truncations introduce systematic errors to the calculation of binding energies and other observables. We identify the relevant infrared scaling variable and give values for this nucleus-dependent quantity. We consider isotopes of oxygen computed with the coupled-cluster method from chiral nucleon-nucleon interactions at next-to-next-to-leading order and show that the infrared component of the error is sufficiently understood to permit controlled extrapolations. By employing oscillator spaces with relatively large frequencies, well above the energy minimum, the ultraviolet corrections can be suppressed while infrared extrapolations over tens of MeVs are accurate for ground-state energies. However, robust uncertainty quantification for extrapolated quantities that fully accounts for systematic errors is not yet developed.