Implementation of local chiral interactions in the hyperspherical harmonics formalism

TL;DR

This paper implements local chiral nuclear interactions within the hyperspherical harmonics method to accurately compute properties of light nuclei, benchmarking against Monte Carlo results and analyzing uncertainties.

Contribution

It introduces a novel implementation of local chiral interactions in the hyperspherical harmonics formalism, including three-body forces at NNLO, enabling detailed nuclear property calculations.

Findings

Benchmarking shows good agreement with Monte Carlo calculations.

Order-by-order truncation errors are confirmed.

Uncertainty analysis of charge radii using muonic atom data.

Abstract

With the goal of using chiral interactions at various orders to explore properties of the few-body nuclear systems, we write the recently developed local chiral interactions as spherical irreducible tensors and implement them in the hyperspherical harmonics expansion method. We devote particular attention to three-body forces at next-to-next-to leading order, which play an important role in reproducing experimental data. We check our implementation by benchmarking the ground-state properties of $^3$H, $^3$He and $^4$He against the available Monte Carlo calculations. We then confirm their order-by-order truncation error estimates and further investigate uncertainties in the charge radii obtained by using the precise muonic atom data for single-nucleon radii. Having local chiral Hamiltonians at various orders implemented in our hyperspherical harmonics suites of codes opens up the possibility to test such interactions on other light-nuclei properties, such as electromagnetic reactions.