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

2025/08/02 by Rothman, Maxwell, Johnson-Toth, Ben, Bonaiti, Francesca +3 · 5 citations
#FOS: Physical sciences #Nuclear Theory (nucl-th)

paper · doi:10.48550/arxiv.2508.01507

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.

Citations

• Nuclear effective field theory: Status and perspectives
• The In-Medium Similarity Renormalization Group: A novel ab initio method for nuclei
• Accurate nuclear radii and binding energies from a chiral interaction
• Theodore Dru Alison Cockerell
• Isotopic Chains Around Oxygen from Evolved Chiral Two- and Three-Nucleon Interactions
• Evolution of Shell Structure in Neutron-Rich Calcium Isotopes
• Continuum Effects and Three-Nucleon Forces in Neutron-Rich Oxygen Isotopes
• Medium-Mass Nuclei with Normal-Ordered Chiral N N + 3 N Interactions
• Chiral effective field theory and nuclear forces
• Lattice simulations for few- and many-body systems
• Few-nucleon forces and systems in chiral effective field theory
• Modern theory of nuclear forces
• Modern theory of nuclear forces
• Self-consistent Green's function method for nuclei and nuclear matter

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• NuLattice: Ab initio computations of atomic nuclei on lattices
• Structure of the doubly magic nuclei ²⁰⁸Pb and ²⁶⁶Pb from ab initio computations

Related

• Medium-Mass Nuclei with Normal-Ordered Chiral N N + 3 N Interactions
• Ab initio Rayleigh-Schrödinger perturbation calculation including three-body force
• Correlations in light nuclei and their relation to fine tuning and uncertainty quantifications of many body forces in low-energy nuclear physics
• Modern theory of nuclear forces
• Nuclear symmetry energy and the role of three-body forces