Pion-exchange contributions to the nuclear charge,current, and Hamiltonian operators

Using a Foldy-Wouthuysen reduction procedure and the time-dependent perturbation theory, we have calculated the one-pion-exchange contribution to the nuclear charge and current densities to order $\text{(}\text{v}\text{c}\text{)}{}^2$. At the same time a renormalization scheme defines the pion-exchange potential including nonstatic and three-body correction terms of order $\text{(}\text{v}\text{c}\text{)}{}^2$. The requirements of relativity are investigated, and it is found that the retardation effect in the potential and charge density plays a critical role. The covariance conditions for the potential, charge, and current densities are shown to be satisfied to the order we have calculated. Finally, the deuteron case is discussed in detail. Throughout the calculation the role of the equivalence theorem is stressed.