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The physical nucleon in static source meson theory

Annals of Physics
Publication Date
DOI: 10.1016/0003-4916(59)90015-6


Abstract A wave function for the physical nucleon in static source meson theory has been constructed by the method of moments. The wave function includes contributions from states containing as many as five mesons, and is shown to be a good approximation to the ground state of the Hamiltonian. Because of the restrictive nature of the static model, the probability that the meson cloud have a particular angular momentum or isotopic spin turns out to be almost independent of the dynamics of the system. Since the matrix elements of the nucleon spin and isotopic spin operators can be expressed in terms of these probabilities, such matrix elements are determined essentially by the kinematics of the meson cloud. This fact renders unreliable any predictions of the static model which depend on matrix elements of the nucleon operators. The consistent failure of the static model to explain satisfactorily the scalar part of the magnetic moment may be ascribed to this cause. The quantities which depend on meson operators are more closely related to the dynamics of the system. The vector part of the magnetic moment is in agreement with experiment, and the electron-neutron interaction turns out much too large; these results differ little from those obtained by the Chew—Low one-meson approximation. However, the contributions of the many meson states are not negligible, and the mean number of mesons is found to be closer to two than to one. Evaluation of the charge renormalization enables us to test the scattering amplitudes predicted by the static model against the sum rules of Cini and Fubini. It is found that, for the conventional value of renormalized coupling constant, the sum rules are strongly violated. This result, together with the substantial many meson component of the wave function, casts doubt on the validity of the one-meson approximation in the static model.

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