Strong Coupling Meson Theory and Its Implications for the Spectrum and Structure of Nucleons

Abstract

We analyzed the pion-nucleon resonance states and the charge form factors of the proton and the neutron using the Pauli-Dancoff method of the strong coupling meson theory. The work by Pais and Serber on the Pauli-Dancoff representation has been cop1pleted by tracing the isomorphic variation domains of the new variables. It was shown by comparing with the Neumann theory of observation that one can correlate the collective motions of the meson cloud in ordinary and charge spaces with each other. We solve the Schrodinger equations for this correlation coefficient which determine the energy levels of excited states of the physical nucleon. Applying a coordinate transformation used by Coester in the collective model of a nucleus we showed that there exists a stable ground state. Its energy is much lower than the value obtained in the classical approximation. For the excited states with y=1, where the operator Yi is defined by Yi=L0i+T0i, we can easily solve the Schrodinger equation and get its eigenvalues and eigenfunctions. For the states with y>2 we show how we can use the semi-classical and non-adiabatic approximation method to solve the equation. We take the exponential function for the nucleon source for numerical evaluation. We fix the unrenormalized coupling constant fitting the energy value predicted by the theory with the experimental value for the first resonance state. With the coupling constant thus determin­ ed we showed that the energy levels of other excited states are much higher than experi­ mental values. Then we define the charge density operator and take its expectation value for the state characterizing the physical nucleon (l=t=1/2, y=O, a given spin direction and a given charge state). Taking the Fourier transform of this quantity we get the charge form factors. The mean square radii for the proton and the neutron take the reasonable values. The de­ pendence of the charge form factors on the momentum transfer explains the experiments quite well both for the proton and for the neutron. Finally we compare the strong coupling meson theory with the Chew-Low static theory and discuss unique outcomes of the strong coupling method.