Renormalization of the leading-order chiral nucleon-nucleon interaction and bulk properties of nuclear matter

TL;DR

This paper renormalizes the leading-order chiral nucleon-nucleon interaction using a modified Weinberg counting scheme, revealing a very strong tensor force that causes underbinding and slow convergence in nuclear matter calculations.

Contribution

It demonstrates that the renormalized LO chiral interaction exhibits an extraordinarily strong tensor force, impacting its suitability for many-body nuclear calculations.

Findings

The interaction shows saturation but underbinds nuclear matter.

The tensor force is unusually strong, causing large wound integral.

The interaction leads to slow convergence in many-body methods.

Abstract

We renormalize the two-nucleon interaction at leading order (LO) in chiral perturbation theory using the scheme proposed by Nogga, Timmermans, and van Kolck--also known as modified Weinberg counting. With this interaction, we calculate the energy per nucleon of symmetric nuclear matter in the Brueckner pair approximation and obtain a converged, cutoff-independent result that shows saturation, but also substantial underbinding. We find that the renormalized LO interaction is characterized by an extraordinarily strong tensor force (from one-pion exchange), which is the major cause for the lack of binding. The huge tensor force also leads to the unusually large wound integral of 40% in nuclear matter, which implies a very slow convergence of the hole-line or coupled-cluster expansion, rendering this interaction impractical for many-body calculations. In view of the unusual properties of the renormalized LO interaction and in view of the poor convergence of the nuclear many-body problem with this interaction, there is doubt if this interaction and its predictions can serve as a reasonable and efficient starting point that is improved by perturbative corrections.