Delta isobars and nuclear saturation

Abstract

We construct a nuclear interaction in chiral effective field theory with explicit inclusion of the $\Delta$-isobar $\Delta(1232)$ degree of freedom at all orders up to next-to-next-to-leading order (NNLO). We use pion-nucleon ($\pi N$) low-energy constants (LECs) from a Roy-Steiner analysis of $\pi N$ scattering data, optimize the LECs in the contact potentials up to NNLO to reproduce low-energy nucleon-nucleon scattering phase shifts, and constrain the three-nucleon interaction at NNLO to reproduce the binding energy and point-proton radius of $^{4}$He. For heavier nuclei we use the coupled-cluster method to compute binding energies, radii, and neutron skins. We find that radii and binding energies are much improved for interactions with explicit inclusion of $\Delta(1232)$, while $\Delta$-less interactions produce nuclei that are not bound with respect to breakup into $\alpha$ particles. The saturation of nuclear matter is significantly improved, and its symmetry energy is consistent with empirical estimates.