Relativistic Effects for the Deuteron

It is seen from Tables I, II, and III than an appreciable spin-spin dependence of the neutron-proton interaction can be expected to arise as a result of using Eqs. (1) and (9). This spin dependence is of the wrong sign to account for the empirically known difference in energies of the singlet and triplet states of the deuteron. Its presence suggests that the spatial dependence of spin dependent forces is not wholly the same as that of the other forces. The possibility of finding a simple equation in which the empirical spin dependence will be a natural consequence is still open. It is shown that the relativistic correction to the kinetic energy is only a small part of the corrections called for by invariance. The relativistic refinements made so far in the combined theory of ${\mathrm{H}}^2$ and ${\mathrm{H}}^3$ are shown to be questionable from this point of view, as well as on account of the possible presence of terms in relative momenta which are not determined by requirements of invariance alone.