  We prove that the initial value problem for the Dirac equation
  $
  \left ( -i\gamma^\mu \partial_\mu + m \right) \psi
  = \left(\frac{e^{- |x|}}{|x|} \ast ( \overline \psi \psi)\right) \psi \quad
\text{in } \ \R^{1+3} $
  is globally well-posed and the solution scatters to free waves asymptotically
as $t \rightarrow \pm \infty$, if we start with initial data that is small in
$H^s$ for $s>0$. This is an almost critical well-posedness result in the sense
that $L^2$ is the critical space for the equation. The main ingredients in the
proof are Strichartz estimates, space-time bilinear null-form estimates for
free waves in $L^2$, and an application of the $U^p$ and $V^p$-function spaces.
