We construct valence-space Hamiltonians for use in shell-model calculations, where the residual two-body interaction is based on symmetry principles and the low-momentum expansion from chiral effective field theory. In addition to the usual free-space contact interactions, we also include novel center-of-mass–dependent operators that arise due to the Galilean invariance breaking by in-medium effects. We fitted the low-energy constants to 441 ground- and excited-state energies in the $sd$ shell and obtained a root-mean-square derivation of 1.8 MeV at leading order and of 0.5 MeV at next-to-leading order, with natural low-energy constants in all cases. The developed chiral shell-model interactions enable order-by-order uncertainty estimates and show promising predictions for neutron-rich isotopes beyond the fitted data set.

• Received 23 April 2018

DOI:https://doi.org/10.1103/PhysRevC.98.044301