Ab initiocoupled-cluster approach to nuclear structure with modern nucleon-nucleon interactions
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Abstract
We perform coupled-cluster calculations for the doubly magic nuclei $^{4}\mathrm{He}$, $^{16}\mathrm{O}$, $^{40,48}\mathrm{Ca}$, for neutron-rich isotopes of oxygen and fluorine, and employ ``bare'' and secondary renormalized nucleon-nucleon interactions. For the nucleon-nucleon interaction from chiral effective field theory at order next-to-next-to-next-to leading order, we find that the coupled-cluster approximation including triples corrections binds nuclei within 0.4 MeV per nucleon compared to data. We employ interactions from a resolution-scale dependent similarity renormalization group transformations and assess the validity of power counting estimates in medium-mass nuclei. We find that the missing contributions from three-nucleon forces are consistent with these estimates. For the unitary correlator model potential, we find a slow convergence with respect to increasing the size of the model space. For the $G$-matrix approach, we find a weak dependence of ground-state energies on the starting energy combined with a rather slow convergence with respect to increasing model spaces. We also analyze the center-of-mass problem and present a practical and efficient solution.