Non-empirical pairing functional from low-momentum two- and three-body interactions

We present systematic calculations of pairing gaps in semi-magic nuclei across the nuclear chart using the Energy Density Functional method. A non-empirical pairing functional is derived at lowest order in the low-momentum, vacuum two-nucleon interaction, including the Coulomb force, and chiral three-nucleon interaction. The particle-hole part of the functional is built to reproduce the Hartree-Fock level density obtained with the same interaction. Energies of odd nuclei are calculated self-consistently in the equal-filling approximation, which allows a direct comparison to odd-even mass difference data. We assess the relative contributions of two-body and three-body direct terms, blocking, and missing higher-order terms of the perturbative expansion to pairing in finite nuclei.