Exactness of the normal-ordered two-body truncation of three-nucleon forces

Abstract

Reference-state-based many-body methods start from Hamiltonians that are normal ordered with respect to the reference state. In low-energy nuclear physics applications normal-ordered Hamiltonians consisting of two- and three-nucleon forces are usually truncated at the two-body rank with residual three-nucleon operators being discarded. Benchmark computations have shown that this truncation is accurate, but we lack an understanding about why it works. We show that the normal-ordered two-body truncation is exact for zero-range three-body forces when nuclei are computed using the coupled cluster with singles and doubles method. As the nuclear three-nucleon force is short ranged and a three-body contact is a leading term in effective field theories of quantum chromodynamics, our result provides an analytical basis for the popular normal-ordered two-body approximation.

6 pages, 2 figures, 1 table

References in corpus (21)

• Chiral effective field theory and nuclear forces
• Accurate nuclear radii and binding energies from a chiral interaction
• Structure and rotations of the Hoyle state
• Evolution of shell structure in neutron-rich calcium isotopes
• Ab initio predictions link the neutron skin of ${}^{208}$Pb to nuclear forces
• Coupled-cluster theory for three-body Hamiltonians
• Converged ab initio calculations of heavy nuclei
• Efficient calculation of chiral three-nucleon forces up to N3LO for ab initio studies
• Benchmark calculations for 3H, 4He, 16O and 40Ca with ab-initio coupled-cluster theory
• Chiral three-nucleon interaction and the carbon-14 dating beta decay
• In-medium similarity renormalization group with three-body operators
• Local nucleon-nucleon and three-nucleon interactions within chiral effective field theory
• What is ab initio in nuclear theory?
• Ab-initio computation of neutron-rich oxygen isotopes
• In medium T-matrix for nuclear matter with three-body forces - binding energy and single particle properties
• Impact of two-body currents on magnetic dipole moments of nuclei
• Normal ordering of three-nucleon interactions for ab initio calculations of heavy nuclei
• Multiscale physics of atomic nuclei from first principles
• Quantum Monte Carlo in Configuration Space with Three-Nucleon Forces
• How to renormalize coupled cluster theory
• Randomized Low-Rank Decompositions of Nuclear Three-Body Interactions

Cited by in corpus (3)

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