Numerical investigations of the Dirac equation and bound state quantum electrodynamics in atoms : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Physics at Massey University, Albany, New Zealand

Simple item page
dc.confidentialEmbargo : Noen_US
dc.contributor.advisorSchwerdtfeger, Peter
dc.contributor.authorPiibeleht, Morten
dc.date.accessioned2022-06-28T01:36:26Z
dc.date.accessioned2022-10-25T22:39:09Z
dc.date.available2022-06-28T01:36:26Z
dc.date.available2022-10-25T22:39:09Z
dc.date.issued2022
dc.description.abstractThis thesis addresses, from a computational perspective, several open questions in relativistic atomic structure theory, which is the theoretical description of atoms based on the Dirac equation and quantum electrodynamics (QED). The first part of this thesis investigates several fundamental problems of the Dirac equation with the help of a novel numerical solver based on the one-dimensional finite element (FEM) basis set. Significant effort is made to validate and benchmark the solver, which is reliably able to converge to accurate results at numerical floating-point precision, including when nuclear potentials derived from nuclear models with finite spacial extent (as opposed to a point nucleus) are used. The solver is then applied to the Dirac equation in the challenging high nuclear charge regime where the Dirac equation exhibits several mathematical difficulties. In particular, the problem of the 1s bound state diving into the sea of negative energy continuum states is studied and the diving resonance state is numerically traced and analysed. As a type of workaround, a modified version of the Dirac equation where the negative energy plane-wave states are projected out of the Hilbert space is also solved and studied in the high nuclear charge regime. The second part of the thesis involves expanding the QED self-energy treatment in the atomic structure software GRASP. The configuration interaction (CI) portion of the code is significantly refactored to allow for the implementation of new additional effective operators that provide a more modern multi-electron treatment of QED self-energy effects. The implementation is tested by evaluating the QED and other post-Dirac-Coulomb corrections for the ground states of the beryllium-like isoelectronic sequence, which was also discovered to exhibit an interesting ground state configuration transition at high nuclear charge.en_US
dc.identifier.urihttp://hdl.handle.net/10179/17634
dc.publisherMassey Universityen_US
dc.rightsThe Authoren_US
dc.subjectAtomic structureen
dc.subjectMathematical modelsen
dc.subjectDirac equationen
dc.subjectQuantum electrodynamicsen
dc.subjectBound states (Quantum mechanics)en
dc.subject.anzsrc510201 Atomic and molecular physicsen
dc.titleNumerical investigations of the Dirac equation and bound state quantum electrodynamics in atoms : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Physics at Massey University, Albany, New Zealanden_US
dc.typeThesisen_US
massey.contributor.authorPiibeleht, Mortenen_US
thesis.degree.disciplinePhysicsen_US
thesis.degree.grantorMassey Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophy (PhD)en_US
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
PiibelehtPhDThesis.pdf
Size:
6.82 MB
Format:
Adobe Portable Document Format
Description:
Download
Collections
Theses and Dissertations