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Effective Field Theory of Nuclear Forces and the Deuteron
[Thesis]. Manchester, UK: The University of Manchester; 2016.
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Abstract
Effective theories have applications in many areas of physics, from Newtonianmechanics through to condensed matter physics. In this thesis we discuss effectivefield theories in the context of constructing nucleon-nucleon interactions in asystematic and model-independent way.We start with the examination of the spin-singlet P-wave, by using distorted wavemethods to remove the effects of long-range pion-exchange forces from theempirical 1P1 phase shift. The divergence appearing in this channel is renormalisedusing a counterterm that is provided by the relevant (Weinberg) powercounting. This leaves an effective interaction strength that can be analysed, andfrom which one can extract an approximate scale for the underlying physics. Wedetermine this scale to be close to the delta-resonance.We then turn to coupled (spin-triplet) waves, focussing predominantly on the3S1 - 3D1 wave that contains the deuteron - an important system to understandin 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 divergencecan be renormalised using counterterms provided by a renormalisationgroup analysis. Switching to negative energies we look for the deuteron boundstate, which is loosely bound and so pion physics plays an important role. Usingthe counterterms provided at positive energies, we extrapolate to the boundstate and treat this, two-pion-exchange and recoil one-pion-exchange as a combinedperturbation to the system. We then use perturbation theory techniques tocalculate the first-order correction to the energy and wave function, from whichwe calculate some deuteron observables.
Layman's Abstract
Effective theories have applications in many areas of physics, from Newtonianmechanics through to condensed matter physics. In this thesis we discuss effectivefield theories in the context of constructing nucleon-nucleon interactions in asystematic and model-independent way.We start with the examination of the spin-singlet P-wave, by using distorted wavemethods to remove the effects of long-range pion-exchange forces from theempirical 1P1 phase shift. The divergence appearing in this channel is renormalisedusing a counterterm that is provided by the relevant (Weinberg) powercounting. This leaves an effective interaction strength that can be analysed, andfrom which one can extract an approximate scale for the underlying physics. Wedetermine this scale to be close to the delta-resonance.We then turn to coupled (spin-triplet) waves, focussing predominantly on the3S1 - 3D1 wave that contains the deuteron - an important system to understandin 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 divergencecan be renormalised using counterterms provided by a renormalisationgroup analysis. Switching to negative energies we look for the deuteron boundstate, which is loosely bound and so pion physics plays an important role. Usingthe counterterms provided at positive energies, we extrapolate to the boundstate and treat this, two-pion-exchange and recoil one-pion-exchange as a combinedperturbation to the system. We then use perturbation theory techniques tocalculate the first-order correction to the energy and wave function, from whichwe calculate some deuteron observables.