Flux-across-surfaces theorem for a Dirac particle

We consider the asymptotic evolution of a relativistic spin-(1/2) particle, i.e., a particle whose wave function satisfies the Dirac equation with external static potential. We prove that the probability for the particle crossing a (detector) surface converges to the probability, that the direction of the momentum of the particle lies within the solid angle defined by the (detector) surface, as the distance of the surface goes to infinity. This generalizes earlier nonrelativistic results, known as flux across surfaces theorems, to the relativistic regime