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.

13 pages, 8 figures

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• Chiral effective field theory and nuclear forces
• Improved nuclear matter calculations from chiral low-momentum interactions
• Accurate nuclear radii and binding energies from a chiral interaction
• Improved chiral nucleon-nucleon potential up to next-to-next-to-next-to-leading order
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• Delta-excitations and the three-nucleon force
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• Weinberg eigenvalues for chiral nucleon-nucleon interactions
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