We present solutions of the BCS gap equation in the channels ${}^{1}S_0$ and ${}^{3}P_2–{}^{3}F_2$ 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 (${\mathrm{N}}^3\mathrm{LO}$) as well as local and semilocal chiral NN interactions up to ${\mathrm{N}}^2\mathrm{LO}$ and ${\mathrm{N}}^4\mathrm{LO}$, respectively. In particular, we investigate for the first time the impact of subleading 3N forces at ${\mathrm{N}}^3\mathrm{LO}$ 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 quasilinear 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.

• Received 18 October 2016

DOI:https://doi.org/10.1103/PhysRevC.95.024302