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.

Figures (2)

• Figure 1: Contributions to the ground-state energy of $^4$He as a function of the lattice spacing $a$. Energy $E_{\rm ref}$ of the reference state (blue diamonds connected by dotted line), CCSD energy $E_{\rm CCSD}$ (red squares connected by dashed-dotted line) and the exact energy $E_{\rm exact}$ (black circles connected by dashed lines).
• Figure 2: Same as Fig. \ref{['fig:4He']} but for $^3$He.