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UBC Theses and Dissertations

A new hamiltonian for systems of nucleons and pions Hsieh, William Wei


This thesis presents new interaction potentials for studying systems of nucleons and pions at intermediate energies. Using a quantum field theory approach, the fundamental dynamical variables are taken to be the Fermion and Boson creation operators, F⁺ and B⁺. First, considering systems with only nucleons, a 2-body nucleon interaction potential is introduced, from which the familiar pair of coupled differential equations for the deuteron is derived. Next, turning to systems of nucleons and pions, focusing primarily on the reaction p+p → π⁺+d , we introduce unconventional, penta-linear interaction potentials of the form "F⁺F⁺FFB⁺ + adjoint". With these unconventional potentials, we can identify F⁺10> and B⁺10> with physical nucleons and physical pions— quite unlike the conventional situation with the Chew Hamiltonian, where F⁺10> cannot be identified with a physical nucleon. The differential scattering cross section for pp → π⁺d ( (with polarized incident protons) is then derived in terms of our potentials. Finally, we include a simple perturbation study of the deuteron state using our potentials.

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