Approximating the Three-Nucleon Continuum

Doctoral thesis, 2022

Three-nucleon forces (3NFs) are necessary to accurately describe the properties of atomic nuclei. These forces arise naturally together with two-nucleon forces (2NFs) when constructing nuclear interactions using chiral effective field theories (χEFTs) of quantum chromodynamics. Unlike phenomenological nuclear interaction models, χEFT promises a handle on the theoretical uncertainty in our description of the nuclear interaction. Recently, methods from Bayesian statistics have emerged to quantify this theoretical truncation error in physical predictions based on chiral interactions. Alongside quantifying the truncation error, the low-energy constants (LECs) of the chiral interactions must be inferred using selected experimental data. In this regard, the abundant sets of experimentally measured nucleon-nucleon (NN) and nucleon-deuteron (Nd) scattering cross sections serve as natural starting points to condition such inferences on. Unfortunately, the high computational cost incurred when solving the Faddeev equations for Nd scattering has thus far hampered Bayesian parameter estimation of LECs from such data. In this thesis, I present the results from a two-part systematic investigation of the wave-packet continuum discretisation (WPCD) method for reliably approximating two- and three-nucleon (NNN) scattering states with an aim towards a quantitative Bayesian analysis in the NNN continuum. In the first part, I explore the possibilities of using graphics processing units to utilise the inherent parallelism of the WPCD method, focusing on solving the Lippmann-Schwinger equation. In the second part, I use the WPCD method to solve the Faddeev equations for Nd scattering and analyse the reliability of the approximations of the WPCD method. This allows me to quantify the posterior predictive distributions for a range of low-energy neutron-deuteron cross sections conditioned on NN scattering data and NN interactions up to fourth order in χEFT.