  We investigate the phenomenon of the diffraction of charged particles by thin
material targets using the method of the de Broglie-Bohm quantum trajectories.
The particle wave function can be modeled as a sum of two terms
$\psi=\psi_{ingoing}+\psi_{outgoing}$. A thin separator exists between the
domains of prevalence of the ingoing and outgoing wavefunction terms. The
structure of the quantum-mechanical currents in the neighborhood of the
separator implies the formation of an array of \emph{quantum vortices}. The
flow structure around each vortex displays a characteristic pattern called
`nodal point - X point complex'. The X point gives rise to stable and unstable
manifolds. We find the scaling laws characterizing a nodal point-X point
complex by a local perturbation theory around the nodal point. We then analyze
the dynamical role of vortices in the emergence of the diffraction pattern. In
particular, we demonstrate the abrupt deflections, along the direction of the
unstable manifold, of the quantum trajectories approaching an X-point along its
stable manifold. Theoretical results are compared to numerical simulations of
quantum trajectories. We finally calculate the {\it times of flight} of
particles following quantum trajectories from the source to detectors placed at
various scattering angles $\theta$, and thereby propose an experimental test of
the de Broglie - Bohm formalism.
