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

TL;DR

This paper demonstrates that the normal-ordered two-body truncation of three-nucleon forces is exact for zero-range forces in coupled cluster calculations, providing an analytical basis for its widespread use in nuclear physics.

Contribution

It proves the exactness of the normal-ordered two-body approximation for zero-range three-body forces in coupled cluster methods, clarifying its theoretical foundation.

Findings

Normal-ordered two-body truncation is exact for zero-range three-body forces.

The result explains the accuracy of the approximation in low-energy nuclear physics.

Provides an analytical basis for the normal-ordered two-body approximation.

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.