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.

PJ Salen, Fysikgården 2
Opponent: Apl. Prof. Dr. Pierre Capel, Institute of Nuclear Physics, Johannes Gutenberg-Universität Mainz


Sean Miller

Chalmers, Physics, Subatomic, High Energy and Plasma Physics

Wave-packet continuum discretisation for nucleon-nucleon scattering predictions

Journal of Physics G: Nuclear and Particle Physics,; Vol. 49(2022)

Journal article

Posterior predictive distributions of neutron-deuteron cross sections

Physical Review C,; Vol. 107(2023)

Journal article

Our understanding of the universe is anchored in reproducing experimental data with theoretical models using statistics. It is through this practice that we have learned that the strong nuclear force, acting between nucleons, is essential for the existence of atomic nuclei. However, our models of this force have not yet simultaneously reproduced all nuclear experimental data, from two-nucleon collisions to massive neutron stars. This is a challenge that, to be overcome, demands tremendous statistical studies of our models, which poses a dire need for computing power and efficient algorithms to reproduce data by simulation.

This thesis presents the steps I have taken to efficiently simulate the collisions of three nucleons. The difficulties of performing such simulations have left a lot of data untapped for the statistical study of our models. An outcome of my work is the development of an open-source code, named Tic-tac, for simulating three-nucleon collisions at the efficiency required by statistical studies.

Strong interactions for precision nuclear physics (PrecisionNuclei)

European Commission (EC) (EC/H2020/758027), 2018-02-01 -- 2023-01-31.

Subject Categories

Subatomic Physics


Basic sciences


C3SE (Chalmers Centre for Computational Science and Engineering)



Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 5187



PJ Salen, Fysikgården 2

Opponent: Apl. Prof. Dr. Pierre Capel, Institute of Nuclear Physics, Johannes Gutenberg-Universität Mainz

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