Non-Adiabatic Treatment of the Relativistic Two-Body Problem

The method of Tamm and Dancoff, for the non-adiabatic treatment of the relativistic interaction of two nucleons, is generalized in order to include nucleon pair creation and higher order effects in the exchange of mesons. This generalized form of the Tamm-Dancoff method is shown to give results which are equivalent to those obtained from the relativistic equation of Bethe and Salpeter. A detailed study is made of two limiting cases: (a) no pair of nucleons is created in the intermediate states, but an arbitrary number of mesons can be present at the same time; (b) the maximum number of mesons present at a given time is one, but the number of pairs is unrestricted.The two methods are applied to the calculation of the lowest order correction to the scalar meson interaction of two nucleons. It is shown that the exact correction, which is of the second order in the nucleon velocities, can only be obtained through the inclusion of the fourth- and sixth-order interaction processes involving, in the corresponding Feynman diagrams, the crossing of the meson lines.