$^4$He energies and radii by the coupled-cluster method with many-body average potential

TL;DR

This paper introduces a reformulated coupled-cluster method using many-body average potentials, applied to helium-4, to clarify the structure of the theory and analyze correlations with modern nucleon-nucleon interactions.

Contribution

It presents a new framework for coupled-cluster calculations that simplifies the organization of many-body terms and applies it to $^4$He with realistic interactions.

Findings

Numerical results for $^4$He energies and radii with AV18 and CD-Bonn interactions.

Discussion of short-range and many-body correlations.

Framework potential for including three-nucleon forces.

Abstract

The reformulated coupled-cluster method (CCM), in which average many-body potentials are introduced, provides a useful framework to organize numerous terms appearing in CCM equations, which enables us to clarify the structure of the CCM theory and physical importance of various terms more easily. We explicitly apply this framework to $^4$He, retaining one-body and two-body correlations as the first illustrating attempt. Numerical results with using two modern nucleon-nucleon interactions (AV18 and CD-Bonn) and their low-momentum interactions are presented. The characters of short-range and many-body correlations are discussed. Although not considered explicitly, the expression of the ground-state energy in the presence of a three-nucleon force is given.