Effective theories have applications in many areas of physics, from Newtonian mechanics through to condensed matter physics. In this thesis we discuss effective field theories in the context of constructing nucleon-nucleon interactions in a systematic and model-independent way. We start with the examination of the spin-singlet P-wave, by using distorted wave methods to remove the effects of long-range pion-exchange forces from the empirical 1P1 phase shift. The divergence appearing in this channel is renormalised using a counterterm that is provided by the relevant (Weinberg) power counting. This leaves an effective interaction strength that can be analysed, and from which one can extract an approximate scale for the underlying physics. We determine this scale to be close to the delta-resonance. We then turn to coupled (spin-triplet) waves, focussing predominantly on the 3S1-3D1 wave that contains the deuteron - an important system to understand in the context of nuclear forces. Starting with the 3S1-3D1 scattered waves, we again remove long-range pion-exchange forces from the empirical phase shifts, and extract an effective interaction matrix. The element that suffers from a divergence can be renormalised using counterterms provided by a renormalisation group analysis. Switching to negative energies we look for the deuteron boundstate, which is loosely bound and so pion physics plays an important role. Using the counterterms provided at positive energies, we extrapolate to the boundstate and treat this, two-pion-exchange and recoil one-pion-exchange as a combined perturbation to the system. We then use perturbation theory techniques to calculate the first-order correction to the energy and wave function, from which we calculate some deuteron observables.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:727879 |
| Date | January 2016 |
| Creators | Ipson, Katharine |
| Publisher | University of Manchester |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | https://www.research.manchester.ac.uk/portal/en/theses/effective-field-theory-of-nuclear-forces-and-the-deuteron(64fc49c5-34c5-431e-b8ce-238cb484635a).html |
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