Quantifying uncertainties in neutron-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math> scattering with chiral nucleon-nucleon and three-nucleon forces

Abstract

Background: Modern ab initio theory combined with high-quality nucleon-nucleon (NN) and three-nucleon (3N) interactions from chiral effective field theory (EFT) can provide a predictive description of low-energy light-nuclei reactions relevant for astrophysics and fusion-energy applications. However, the high cost of computations has so far impeded a complete analysis of the uncertainty budget of such calculations.Purpose: Starting from NN potentials up to fifth order (${\mathrm{N}}^{4}\mathrm{LO}$) combined with leading-order 3N forces, we study how the order-by-order convergence of the chiral expansion and confidence intervals for the 3N contact and contact-plus-one-pion-exchange low-energy constants (${c}_{E}$ and ${c}_{D}$) contribute to the overall uncertainty budget of many-body calculations of neutron $^{4}\mathrm{He}$ ($n\ensuremath{-}\ensuremath{\alpha}$) elastic scattering.Methods: We compute structure and reaction observables for three-, four-, and five-nucleon systems within the ab initio frameworks of the no-core shell model and no-core shell model with continuum. Using a small set of design runs, we construct a Gaussian process model (GPM) that acts as a statistical emulator for the theory. With this, we gain insight into how uncertainties in the 3N low-energy constants propagate throughout the calculation and determine the Bayesian posterior distribution of these parameters with Markov-Chain Monte Carlo.Results: We find rapidly converging $n\ensuremath{-}\ensuremath{\alpha}$ phase shifts with respect to the chiral order. With the adopted leading-order 3N force, calculations based on the NN interaction at ${\mathrm{N}}^{4}\mathrm{LO}$ of Entem, Machleidt, and Nosyk [Phys. Rev. C 96, 024004 (2017)] are unable to reproduce the experimental phase shifts in the $3/{2}^{\ensuremath{-}}$ channel within the estimated chiral truncation errors. Closer agreement with empirical data is found when using an older parametrization of the NN interaction at order ${\mathrm{N}}^{3}\mathrm{LO}$ [Entem and Machledit, Phys. Rev. C 68, 041001(R) (2017)], and the position and width of the $P$-wave resonances can be used to reduce the uncertainty of the 3N low-energy constants.Conclusions: The present results point to a lack of spin-orbit strength when the newer parametrization of the chiral NN force up to fifth order is combined with the leading-order 3N force. The inclusion of higher-order 3N-force terms may be required to recover the missing strength. GPMs can act as fast and accurate emulators of ab initio many-body calculations of low-energy scattering and reactions of light nuclei, opening the way to a robust quantification of theoretical uncertainties grounded in the description of the underlying chiral Hamiltonian.