Doctoral Dissertations
Date of Award
8-2024
Degree Type
Dissertation
Degree Name
Doctor of Philosophy
Major
Physics
Major Professor
Thomas Papenbrock
Committee Members
Thomas Papenbrock, Lucas Platter, Cristian Batista, Robert Hinde
Abstract
Chiral effective field theory is the state-of-the-art when it comes to describing low-energy nuclear phenomena in a systematically-improvable and model-independent fashion. It is grounded in quantum chromodynamics – the fundamental theory underlying nuclear interactions – and consists of pion and nucleon degrees of freedom. In this framework, nuclear interaction is mediated by pions at long distances (in comparison to length scales at which quarks and gluons can be resolved), while finite-range “contact” terms account for the physics at short-distances. Together, they are organized into a hierarchy based on the orders (in powers of small momenta over a large momentum scale) to which they contribute. The short-range contact terms involve unknown coefficients that must be renormalized using experimental data. In this dissertation, we use renormalization of short-range contacts to study one problem related to nuclear scattering and one related to nuclear binding.
The leading order interaction consists of one-pion exchange and a contact term. This interaction fails to capture the essential features of the scattering phase shifts in the ¹S₀ channel. The apparent breakdown scale at this order also comes out much smaller (330 MeV) than the expected 𝒪(1) GeV from the theory. We will show that the inclusion of additional long-range physics (in the form of two-pion exchange contributions) at the leading order solves the first problem and makes the second less severe. We will also demonstrate that the higher-order contact quadratic in momenta, which introduces an additional low energy constant, leads to systematic improvements in the description of phase shifts, as expected from effective expansions.
Next, we will shift our focus to renormalizing short-range contacts to reproduce the observed binding energies across a set of 18 medium-mass nuclei using the Hartree-Fock method. The interaction consists of two- and three-nucleon contributions up to next-to-next-to-leading order in chiral effective field theory, and we renormalize 11 short-range contacts. In the end, the root-mean-square deviation is 2.17 MeV across this set and 3.74 MeV when predicting binding energies across an expanded set of 107 nuclei. While these residuals are large compared to traditional mass models (going as low as 0.5 MeV), unlike those cases, our approach is grounded in chiral effective field theory and Hamiltonian methods, and paves the way forward for systematic mass predictions across the nuclear chart. Along the way, we will discuss the construction of fast Hartree-Fock emulators using the technique of eigenvector continuation, which reduces the associated computational burden.
Recommended Citation
Mishra, Chinmay, "Renormalization as a Tool for Nuclear Scattering & Binding. " PhD diss., University of Tennessee, 2024.
https://trace.tennessee.edu/utk_graddiss/10483