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arXiv · 2508.01507

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

Maxwell Rothman·Ben Johnson-Toth·Francesca Bonaiti·Gaute Hagen·Matthias Heinz·Thomas Papenbrock
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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.

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Maxwell Rothman, Ben Johnson-Toth, Francesca Bonaiti, Gaute Hagen, Matthias Heinz, Thomas Papenbrock. 2025-11-05. Exactness of the normal-ordered two-body truncation of three-nucleon forces. https://doi.org/10.1103/psnh-gc5k

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