Implementation of local chiral interactions in the hyperspherical harmonics formalism

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.

Comments: 21 pages, 5 figures, 4 tables