Extending the reach of uncertainty quantification in nuclear theory
Doktorsavhandling, 2023

The theory of the strong interaction—quantum chromodynamics (QCD)—is unsuited to practical calculations of nuclear observables and approximate models for nuclear interaction potentials are required. In contrast to phenomenological models, chiral effective field theories (χEFTs) of QCD grant a handle on the theoretical uncertainty arising from the truncation of the chiral expansion. Uncertainties in χEFT are preferably quantified using Bayesian inference, but quantifying reliable posterior predictive distributions for nuclear observables presents several challenges. First, χEFT is parametrized by unknown low-energy constants (LECs) whose values must be inferred from low-energy data of nuclear structure and reaction observables. There are 31 LECs at fourth order in Weinberg power counting, leading to a high-dimensional inference problem which I approach by developing an advanced sampling protocol using Hamiltonian Monte Carlo (HMC). This allows me to quantify LEC posteriors up to and including fourth chiral order. Second, the χEFT truncation error is correlated across independent variables such as scattering energies and angles; I model correlations using a Gaussian process. Third, the computational cost of computing few- and many-nucleon observables typically precludes their direct use in Bayesian parameter estimation as each observable must be computed in excess of 100,000 times during HMC sampling. The one exception is nucleon-nucleon scattering observables, but even these incur a substantial computational cost in the present applications. I sidestep such issues using eigenvector-continuation emulators, which accurately mimic exact calculations while dramatically reducing the computational cost. Equipped with Bayesian posteriors for the LECs, and a model for the truncation error, I explore the predictive ability of χEFT, presenting the results as the probability distributions they always were.

PJ-salen, Kemigården 1
Opponent: Associate Professor Heiko Hergert, Michigan State University


Isak Svensson

Chalmers, Fysik, Subatomär, högenergi- och plasmafysik

Svensson, I. Ekström, A. Forssén, C. Inference of the low-energy constants in delta-full chiral effective field theory including a correlated truncation error.

An atomic nucleus consists of neutrons and protons, the so-called nucleons. The strong nuclear interaction, which binds nucleons to nuclei, is unfortunately hard to describe theoretically and we are uncertain about many of its detailed properties. Theoretical predictions of nuclear properties are therefore always inaccurate to some degree. To make matters worse, nuclei generally comprise many nucleons and we must solve a computationally demanding many-body problem to make the predictions in the first place. Due to these challenges, predictions of nuclear observables with quantified theoretical uncertainties is a relatively new, and very active, field of research.

In this thesis I push the boundaries of what is currently possible in this regard. The strong nuclear interaction is described in terms of an effective field theory with a relatively large number of parameters, whose values we must infer by matching model predictions to empirical data. I use advanced sampling techniques to quantify probability distributions for these parameters, which I then use to make probabilistic predictions of observables, primarily for collisions between two nucleons. I construct models of the theoretical error in the quantum mechanical calculations and investigate effects on predictions. With the aim of including a wider variety of empirical data in the analysis I use modern emulation techniques, which sacrifice a little accuracy in return for a major computational speedup when computing observables.

Strong interactions for precision nuclear physics (PrecisionNuclei)

Europeiska kommissionen (EU) (EC/H2020/758027), 2018-02-01 -- 2023-01-31.


Subatomär fysik


Grundläggande vetenskaper



Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 5289



PJ-salen, Kemigården 1

Opponent: Associate Professor Heiko Hergert, Michigan State University

Mer information

Senast uppdaterat