Asymptotic Approximation for Bethe-Salpeter Equation and its Applications to Deuteron

Abstract

Bethe-Salpeter equation is solved for bound state composed of two fermions mediated by pion exchange force of the pseudovector coupling. Expanding the amplitude by gamma matrices the one-dimensional integral equation is derived. It reproduces the binding energy of deuteron. The relation with the quadrupole moment is also discussed in the framework of the asymptotic approximation.