Ab initio Rayleigh-Schr\"odinger perturbation calculation including three-body force

TL;DR

This paper develops a third-order Rayleigh-Schrödinger perturbation theory including three-body forces for nuclear Hamiltonians, demonstrating its accuracy and computational efficiency compared to non-perturbative methods across various nuclei.

Contribution

The paper introduces RSPT3 for Hamiltonians with three-body interactions, showing it effectively captures three-body effects with reduced computational cost.

Findings

RSPT3 accurately predicts binding energies and radii.

Normal-ordered two-body approximation effectively captures main three-body effects.

RSPT3 agrees well with coupled cluster and in-medium similarity renormalization group methods.

Abstract

We first derive the Rayleigh-Schr\"odinger many-body perturbation theory up to third order (RSPT3) for Hamiltonians with three-body interaction. The structure of closed-shell nuclei in a wide mass range from 4He to 48Ca has been investigated by the RSPT3 with explicit NN+3N Hamiltonian. The RSPT3 calculations are performed within Hartree-Fock bases. The perturbative contribution of antisymmetrized Goldstone diagrams (diagrammatic expansion for RSPT) with normal-ordered interaction has been analyzed. We demonstrate that the normal-ordered two-body level (NO2B) approximation which neglects the residual three-body term can catch the main effect of full three-body force in RSPT calculation. We also present rigorous benchmarks for RSPT3 with non-perturbative coupled cluster and in-medium similarity renormalization group using the same chiral NNLOsat NO2B interaction. The three methods are in good agreement with each other for binding energies and radii. However, the RSPT3 provides an alternative that is computationally inexpensive but comparable in accuracy to state-of-the-art non-perturbative many-body methods.