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

TL;DR

This paper extends coupled-cluster theory to include three-body interactions explicitly and assesses the importance of residual three-body terms in nuclear calculations, finding them negligible at the $ ext{Λ}$CCSD(T) level.

Contribution

The paper introduces a non-iterative coupled-cluster method for three-body Hamiltonians and evaluates the significance of residual three-body interactions in nuclear systems.

Findings

Residual three-body contributions are negligible at the $ ext{Λ}$CCSD(T) level.

Explicit three-body treatment improves accuracy over approximate methods.

Residual effects are more significant in lower-level CCSD calculations.

Abstract

We generalize the coupled-cluster (CC) approach with singles, doubles, and the non-iterative 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 O16, O24, and Ca40. 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.