Velocity-Dependent Features of a Static Nucleon-Nucleon Potential

The consequences of assuming a pseudoscalar classical field with pseudoscalar coupling are considered in a static approximation. Virtual pair formation of nucleon-antinucleon pairs is not calculated but it is supposed that it gives rise to an attraction. The interaction is being studied mainly in order to see what features of commonly assumed static potentials may not apply. The quantitative features of the derived interaction are not expected to correspond to the physical one. The qualitative character of deviations from static potential behavior is believed, however, to have a bearing on the velocity-dependent features of the actual interaction. The work neglects some of the effects of the exclusion principle caused by the population of negative-energy states. Some of the qualitative nonstatic features are: (a) different magnitudes of the spin-orbit potential in even and odd states, (b) inadequacy of the usual procedure of the insertion of $\frac{e^2}{r}$ in the wave equation for the calculation of phase shifts in $p-p$ scattering; this inadequacy is connected with the fact that the standard form of the wave equation is obtained only after a transformation of a wave equation in which $\frac{e^2}{r}$ has a direct significance as a potential energy, (c) velocity (energy) dependence of core radii and of magnitude of effective potentials, (d) occurrence of quadratic term in the tensor interaction in the effective potential even though in an earlier stage of the calculation only linear terms are present.