We present a fully local nucleon-nucleon potential in chiral effective field theory (χEFT) retaining pions, nucleons and Δ-isobars as explicit degrees of freedom, and use it in hypersperical-harmonics and quantum Monte Carlo calculations of ground and excited states of 3H, 3He, 4He, 6He, and 6Li nuclei. The calculation of the potential is carried out by including one- and two-pion-exchange contributions up to next-to-next-to-leading order (N2LO) and contact interactions up to next-to-next-to-next-to-leading order (N3LO). The low-energy constants multiplying these contact interactions are fitted to the 2013 Granada database in two different ranges of laboratory energies, either 0--125 MeV or 0--200 MeV, and to the deuteron binding energy and nn singlet scattering length. Fits to these data are performed for three models characterized by long- and short-range cutoffs, RL and RS respectively, ranging from (RL,RS)=(1.2,0.8) fm down to (0.8,0.6) fm. The long-range (short-range) cutoff regularizes the one- and two-pion exchange (contact) part of the potential.
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