Relativistic Terms in the Interaction between Nucleons in Pseudoscalar and Vector Meson Theory

The second-order interaction between nucleons in the pseudoscalar and vector meson theory is calculated, all terms being taken into account. It is shown that in both cases the exact expression for the interaction caused by virtual exchange of mesons involves contact interaction terms which cancel the well-known direct coupling terms of the Hamiltonian. The remaining interaction is essentially different from the expressions given by usual derivations. Its singularity for small separations $r$ of the nucleons, usually obtained to be in $r^{-3\mathrm{}}$ for pseudoscalar and vector fields, is reduced for the former and not for the latter, so that no singularity can be removed by a mixture of the mentioned fields. For pseudoscalar mesons, all interaction terms are proportional to some power of the nucleon velocity, whereas for vector mesons there is a non-vanishing static approximation in $r^{-1\mathrm{}}$. It seems impossible from the present treatment to draw precise and reliable conclusions about the deuteron.