Crossed-boson-exchange contribution and Bethe-Salpeter equation

The contribution to the binding energy of a two-body system due to the cros sed two-boson exchange contribution is calculated, using the Bethe-Salpeter equation. This is done for distinguishable, scalar particles interacting v ia the exchange of scalar massive bosons. The sensitivity of the results to the off-shell behaviour of the operator accounting for this contribution i s discussed. Large corrections to the Bethe-Salpeter results in the ladder approximation are found. For neutral scalar bosons, the mass obtained for t he two-body system is close to what has been calculated with various forms of the instantaneous approximation, including the standard non-relativistic approach. The specific character of this result is demonstrated by a calcu lation involving charged bosons, which evidences a quite different pattern. Our results explain for some part those obtained by Nieuwenhuis and Tjon o n a different basis. Some differencies appear with increasing coupling cons tants, suggesting the existence of sizeable contributions involving more th an exchanges.