Extension of coupled-cluster theory with a noniterative treatment of connected triply excited clusters to three-body Hamiltonians

We generalize the coupled-cluster (CC) approach with singles, doubles, and the noniterative treatment of triples termed Lambda CCSD(T) to Hamiltonians containing three-body interactions. The resulting method and the underlying CC approach with singles and doubles only (CCSD) are applied to the medium-mass closed-shell nuclei O-16, O-24, and Ca-40. By comparing the results of CCSD and Lambda CCSD(T) calculations with explicit treatment of three-nucleon interactions to those obtained using an approximate treatment in which they are included effectively via the zero-, one-, and two-body components of the Hamiltonian in normal-ordered form, we quantify the contributions of the residual three-body interactions neglected in the approximate treatment. We find these residual normal-ordered three-body contributions negligible for the Lambda CCSD(T) method, although they can become significant in the lower-level CCSD approach, particularly when the nucleon-nucleon interactions are soft.