Estimate of crossed-boson-exchange contributions to the binding energy   of two-body systems
  Binding energies calculated from using the Bethe-Salpeter equation in the simplest ladder approximation significantly differ from those obtained in the non-relativistic standard instantaneous approximation. While they should a priori be better, they turn out to be further away from an exact calculation in the case of scalar neutral particles or from experiment in the case of the Coulomb interaction. Part of the discrepancy is due to the omission in the interaction kernel of contributions corresponding to crossed-boson-exchange diagrams. The role of these contributions is examined numerically, using a simple approximation. The sensitivity to both the coupling constant and the mass of the exchanged boson is considered. 
G. Le Gorrec, B. Desplanques