The Charge Density and Magnetic Moments of the Nucleons

Abstract

Using pseudoscalar meson theory, the behavior of a single-nucleon system in an electric field is studied. From the electrostatic interaction, the interaction between neutrons and electrons is computed. From the spin-orbit interaction, the magnetic moments of neutron and proton are computed. The calculation is carried out relativistically, with nucleon and pseudoscalar meson fields both subjected to second quantization. The Hamiltonian of the nucleon-meson system is diagonalized to second order in the coupling parameters by two canonical transformations, and transitions induced by the electric field between single-nucleon states are investigated. For pseudoscalar coupling of 282 e.m. mesons, estimating the coupling constants for charge-symmetric theory from the observed singlet neutron-proton scattering length (using static nuclear forces), it is found that the volume integral of the neutron-electron interaction potential is about $\ensuremath{-}14 \mathrm{kev}\ifmmode\times\else\texttimes\fi{}(\frac{4\ensuremath{\pi}}{3}){(\frac{{e}^{2}}{\mathrm{m}{\mathrm{c}}^{2}})}^{3}$, and that ${\ensuremath{\mu}}_{P}$ and ${\ensuremath{\mu}}_{N}$ are about 1.7 and -5 nuclear magnetons respectively. Results are also given for pure charged theory. Pseudovector coupling is compared to pseudoscalar coupling, and is found to give the same magnetic moments, but a logarithmically divergent neutron-electron interaction. The influence of the contact interaction term is discussed.The results are compared with those of methods and with experimental values, and the neutron-electron interaction is computed approximately for several types of mesons with an improved non-relativistic method. Charge renormalization and the approximate distribution of the charge cloud around a neutron are discussed. The pseudoscalar meson contribution to the Lamb Shift of the $2S$ hydrogen level is estimated as +0.08 Mc.