Abstract
The Bethe-Salpeter equation for the interaction of a spin-\textonehalf{} particle with a scalar particle via the exchange of a scalar particle is considered. For energies below the inelastic threshold, a modified Schwinger variational principle is used to compute the phase shifts. Compared to the analogous calculation for spinless particles, considerable structure is in evidence. Both the ${S}_{\frac{1}{2}}$ and the ${P}_{\frac{1}{2}}$ phase shift, if positive just above the elastic threshold, change sign in the physical region, while if they are negative just above the elastic threshold, they remain so.
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