  We derive a mean-field model that is based on a two-component Pauli-like
equation and incorporates quantum, spin, and relativistic effects up to second
order in $1/c$. Using a Lagrangian approach, we obtain the self-consistent
charge and current densities that act as sources in the Maxwell equations. A
physical interpretation is provided for the second-order corrections to the
sources. The Maxwell equations are also expanded to the same order. The
resulting self-consistent model constitutes a suitable semi-relativistic
approximation to the full Dirac-Maxwell equations.
