Crossed-boson exchange contribution and Bethe-Salpeter equation
Abstract
The contribution to the binding energy of a two-body system due to the crossed two-boson exchange contribution is calculated, using the Bethe-Salpeter equation. This is done for distinguishable, scalar particles interacting via the exchange of scalar massive bosons. The sensitivity of the results to the off-shell behavior of the operator accounting for this contribution is discussed. Large corrections to the Bethe-Salpeter results in the ladder approximation are found. For neutral scalar bosons, the mass obtained for the 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 calculation involving charged bosons, which evidences a quite different pattern. Our results explain for some part those obtained by Nieuwenhuis and Tjon on a different basis. Some discrepancy appears with increasing coupling constants, suggesting the existence of sizeable contributions involving more than two-boson exchanges.
Keywords
Cite
@article{arxiv.nucl-th/9908007,
title = {Crossed-boson exchange contribution and Bethe-Salpeter equation},
author = {L. Theussl and B. Desplanques},
journal= {arXiv preprint arXiv:nucl-th/9908007},
year = {2009}
}
Comments
13 pages, 5 .eps figures, submitted to 'Few Body Systems'