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Title: Self-consistent Green's function studies of modern Hamiltonians in finite and infinite systems
Author: McIlroy, Christopher
Awarding Body: University of Surrey
Current Institution: University of Surrey
Date of Award: 2019
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This dissertation presents an ab initio investigation of modern nuclear Hamiltonians predicted by chiral effective field theory (ChEFT) and lattice quantum chromodynamics (LQCD), in both infinite and finite matter using self-consistent Green's function (SCGF). The third order algebraic diagrammatic construction [ADC(3)] originally devised for quantum chemistry, was used to approximate the self-energy in both systems. This is the first application of ADC(3) to infinite matter. These calculations implemented both two- and three-nucleon ChEFT interactions to compute the equation of state of pure neutron matter and symmetric nuclear matter, whilst also obtaining the spectral function. The procedure was benchmarked using the NNLOsat interaction against a previous SCGF calculation based on the T-matrix approach. The benchmark showed good convergence with respect to the model space but it yielded an apparent lack in the binding energy of ~30% at the saturation density of symmetric nuclear matter when compared to the SCGF T-matrix results and the available literature. After the benchmark a preliminary investigation in to modern N²⁻⁴LO nucleon-nucleon interactions extended to include the N²LO three-nucleon interaction was conducted. These results were reviewed with in the current perceived limitations of the SCGF formalism developed here. In this study, increasing the regulator cut off or the order of the chiral expansion for the nucleon-nucleon interaction decreased the observed binding energy whilst also lowering the saturation density. The calculation of finite nuclei used a potential derived from LQCD by the HAL QCD collaboration at an unphysical pion mass, MPS=469 MeV/c². The short-range repulsion of this interaction requires one to include a resummation of ladder diagrams from the excluded model space. The effectiveness of the ladder resummation from outside the computational model space is considered by the infrared convergence of the total binding energies. The introduction of these missing ladder diagrams leads to a complete diagonalisation of short-range degrees of freedom independently of the choice of model space. The binding energy of Helium-4 was calculated to be -4.80 MeV. The heavier doubly magic nuclei, Oxygen-16 and Calcium-40, had binding energies of -17.9 MeV and -74.4 MeV respectively. This means whilst Calcium-40 is observed to be bound with respect to Alpha break up, Oxygen-16 is expected to be unstable.
Supervisor: Barbieri, Carlo ; Stevenson, Paul Sponsor: Science and Technology Facilities Council (STFC)
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral