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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.

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<p> A repulsive meson-meson interaction was suggested many years ago (1951 by Schiff) as a possible mechanism for nuclear saturation, but very little has been done since then. This is mainly because the meson field equation becomes nonlinear due to the meson-meson interaction. We realized that the nonlinear field equation is analytically solvable, within classical and adiabatic approximations, if the space is reduced to a one-dimensional one. Within the above context we investigate the effect of the meson-meson interaction on nuclear forces. The approximations which Schiff used are critically examined. A variational method for determining the meson field, which Schiff suggested but did not fully investigate, is found to be a very efficient approximation. Finally, quantum corrections are briefly examined.</p> / Thesis / Master of Science (MSc)

<p> We study the Coulomb effect on the proton-proton low-energy scattering parameters when all other effects are represented by a separable potential.</p> <p> For this purpose, we present a formulation for the scattering of two particles via a separable potential. We treat the same problem when any potential, particularly a Coulomb potential or a separable potential, is added to the separable potential. The properties of scattering from a separable potential plus a (local or non-local) potential lead us to the possibility of obtaining a one term separable potential equivalent to a two term separable potential, and a model for the nuclear potential as a sum of a separable potential and a non-separable potential.</p> <p> We determine, to the first order in Me^2/β where β^-1 is the range of the separable potential, the parameters for Yamaguchi's and Naqvi's separable potentials from proton-proton scattering data. We use these parameters to calculate the low-energy proton-proton scattering parameters when the Coulomb interaction is removed. Our results show that the shape dependence of these parameters are somewhat larger than obtained by Heller et al in their investigation on local potentials. Implications of our results concerning the charge symmetry and charge independence of the nuclear forces are discussed.</p> / Thesis / Master of Science (MSc)

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