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We generalize the coupled-cluster (CC) approach with singles, doubles, andthe non-iterative treatment of triples termed $\Lambda$CCSD(T) to Hamiltonianscontaining three-body interactions. The resulting method and the underlying CCapproach with singles and doubles only (CCSD) are applied to the medium-massclosed-shell nuclei O16, O24, and Ca40. By comparing the results of CCSD and$\Lambda$CCSD(T) calculations with explicit treatment of three-nucleoninteractions to those obtained using an approximate treatment in which they areincluded effectively via the zero-, one-, and two-body components of theHamiltonian in normal-ordered form, we quantify the contributions of theresidual three-body interactions neglected in the approximate treatment. Wefind these residual normal-ordered three-body contributions negligible for the$\Lambda$CCSD(T) method, although they can become significant in thelower-level CCSD approach, particularly when the nucleon-nucleon interactionsare soft.

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