Density Functional Theory and Phase Shifts

This thesis describes how phase shifts of the nucleon-nucleon system may be utilized to determine the nuclear Density Functional (DF). The nucleonnucleon interaction, hereafter denoted by N-N interaction, is input to quantum many-body calculations. However, this approach complicates the determination of physical quantities such as the calculation of spectroscopic information and of energy levels. A major advantage in employing the approach via Density Functional Theory (DFT) to this system is that the N-N problem can be considered to be a non-interacting, single-particle system.

In order to use DFT one must know the density functional, and this is typically the most difficult aspect of this approach. Usually the DF is parameterized in terms of the density and density gradients, and these parameters are then fit-to-data. In this thesis we consider how the density functional can be related to the phase shifts of the harmonically-trapped twobody system.

Research focusing on a specific density functional within the Local Density Approximation (LDA) was found to produce fair results in reproducing the general N-N interaction ground-state energy. In this methodology, the phase shift formula was approximated to first-order via the effective range expansion, which simplified the problem. This provided a fair description of the ground-state energy for the two-body system, with roughly two-percent error between the theoretical model and the exact energies.