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Three-nucleon force and continuum play important roles in reproducing theproperties of atomic nuclei around driplines. Therefore it is valuable to buildup a theoretical framework where both effects can be taken into account tosolve the nuclear Schr\"odinger equation. To this end, in this letter, we haveexpressed the chiral three-nucleon force within the continuum Berggrenrepresentation, so that bound, resonant and continuum states can be treated onan equal footing in the complex-momentum space. To reduce the model dimensionand computational cost, the three-nucleon force is truncated at thenormal-ordered two-body level and limited in the $sd$-shell model space, withthe residual three-body term being neglected. We choose neutron-rich oxygenisotopes as the test ground because they have been well studied experimentally,with the neutron dripline determined. The calculations have been carried outwithin the Gamow shell model. The quality of our results in reproducing theproperties of oxygen isotopes around the neutron dripline shows the relevanceof the interplay between three-nucleon force and the coupling to continuumstates. We also analyze the role played by the chiral three-nucleon force, bydissecting the contributions of the $2\pi$ exchange, $1\pi$ exchange andcontact terms.

Chiral three-nucleon force and continuum for dripline nuclei and beyond