Reduction of separable Bethe-Salpeter equation kernels to quasipotential equations

Abstract

In view of relativistic three-body calculations we have investigated several quasipotential approximations to the Bethe-Salpeter equation assuming separable kernels with Yamaguchi-type form factors. In particular we have calculated $\ensuremath{\pi}\ensuremath{-}N$ and $N\ensuremath{-}N$ phase shifts with $l=0, 1$. As a result it is shown that the choice of a symmetric or unsymmetric reduction of the Bethe-Salpeter equation for $\ensuremath{\pi}N$ or $\mathrm{NN}$ scattering is less important in comparison to the choice of the analytic form of the pole. The quasiparticle equation proposed by Erkelenz and Holinde has turned out to be superior to other quasiparticle equations which have also been considered. As a consequence we present parameters for a separable potential to determine $\ensuremath{\pi}\ensuremath{-}N$ and $N\ensuremath{-}N$ phase shifts.NUCLEAR REACTIONS Separable Bethe-Salpeter kernels reduced to six different quasipotential equations; application to pion-nucleon and nucleon-nucleon phase shifts; $E=0\ensuremath{-}300$ MeV; $l=0, 1$.