Effects of Virtual Nucleon Pairs to the Electromagnetic Structure of the Nucleon

Effects of virtual nucleon pairs to the electromagnetic structure of the nucleon are calculated covariantly in the charge independent pseudoscalar meson theory. A rigorous expression for the vertex operator is derived in §2, which is strongly reminiscent of the old-fashioned first- and second-order perturbation theory. Our method of approximation is to replace the complete set of eigenfunctions of the total Hamiltonian by some suitable functions, which are chosen in this paper so as to take into account the main contribution from the virtual nucleon pairs. These effects are proved, regardless of the magnitude of the coupling constant, to reveal itself only through the renormalization factors, which affect the relative magnitudes of the isotopic scalar and vector parts of the nucleon-current contributions and the meson-current contributions. Numerical results are almost the same with those obtained by cutting off the momentum integration at the nucleon mass in the second order perturbation calculation both for the ratio of the anomalous magnetic moments of the proton and the neutron and the mean-square radii of the charge distributions.