Pairing in neutron matter: New uncertainty estimates and three-body forces

TL;DR

This paper investigates neutron matter pairing gaps using chiral EFT interactions, introduces uncertainty estimates from different chiral orders, and compares methods for solving the BCS gap equation.

Contribution

It provides the first analysis of subleading three-nucleon forces at N$^3$LO on pairing gaps and compares convergence of different numerical methods for the gap equation.

Findings

Subleading 3N forces at N$^3$LO significantly affect pairing gaps.

Uncertainty estimates are derived from variations across chiral orders.

The modified Broyden method shows robust convergence for solving the gap equation.

Abstract

We present solutions of the BCS gap equation in the channels ${}^1S_0$ and ${}^3P_2-{}^3F_2$ in neutron matter based on nuclear interactions derived within chiral effective field theory (EFT). Our studies are based on a representative set of nonlocal nucleon-nucleon (NN) plus three-nucleon (3N) interactions up to next-to-next-to-next-to-leading order (N$^3$LO) as well as local and semilocal chiral NN interactions up to N$^2$LO and N$^4$LO, respectively. In particular, we investigate for the first time the impact of subleading 3N forces at N$^3$LO on pairing gaps and also derive uncertainty estimates by taking into account results for pairing gaps at different orders in the chiral expansion. Finally, we discuss different methods for obtaining self-consistent solutions of the gap equation. Besides the widely-used quasi-linear method by Khodel et al. we demonstrate that the modified Broyden method is well applicable and exhibits a robust convergence behavior. In contrast to Khodel's method it is based on a direct iteration of the gap equation without imposing an auxiliary potential and is straightforward to implement.