Ab initio lattice study of neutron-alpha scattering with chiral forces at N3LO

TL;DR

This study performs the first ab initio lattice calculation of neutron-alpha scattering with chiral forces at N3LO, achieving good agreement with experimental phase shifts in some channels and identifying areas for further force refinement.

Contribution

It introduces a novel lattice effective field theory approach at N3LO for neutron-alpha scattering and analyzes discrepancies using a simplified toy model and advanced statistical methods.

Findings

Excellent agreement with empirical phase shifts in $^2S_{1/2}$ and $^2P_{3/2}$ channels.

Persistent discrepancies in the $^2P_{1/2}$ channel above 5 MeV.

Refinement of three-nucleon forces is needed for accurate $^2P_{1/2}$ channel description.

Abstract

We present the first ab initio lattice calculation of neutron-alpha ($n$-$\alpha$) scattering using nuclear lattice effective field theory (NLEFT) with chiral interactions at next-to-next-to-next-to-leading order (N3LO). Building on the high-fidelity chiral Hamiltonian introduced in Ref. [1], we compute scattering phase shifts in the $S$- and $P$-wave channels using the L\"uscher finite-volume method. Our results demonstrate excellent agreement with empirical $R$-matrix phase shifts in the $^2S_{1/2}$ and $^2P_{3/2}$ channels, while revealing persistent discrepancies in the $^2P_{1/2}$ channel for neutron energies above 5 MeV. To systematically investigate these discrepancies, we construct and analyze a simplified neutron-alpha toy model, demonstrating that these discrepancies are not due to the use of the L\"uscher finite-volume method. Additionally, we revisit our three-nucleon (3N) force fitting procedure, explicitly incorporating neutron-alpha scattering data through comprehensive Markov Chain Monte Carlo (MCMC) sampling. This analysis confirms the stability of nuclear binding-energy predictions and highlights the need for further refinements in the lattice N3LO three-nucleon forces to fully describe neutron-alpha scattering in the challenging ${}^2P_{1/2}$ channel.