  We perform rigorously the charge renormalization of the so-called reduced
Bogoliubov-Dirac-Fock (rBDF) model. This nonlinear theory, based on the Dirac
operator, describes atoms and molecules while taking into account vacuum
polarization effects. We consider the total physical density including both the
external density of a nucleus and the self-consistent polarization of the Dirac
sea, but no `real' electron. We show that it admits an asymptotic expansion to
any order in powers of the physical coupling constant $\alphaph$, provided that
the ultraviolet cut-off behaves as $\Lambda\sim e^{3\pi(1-Z_3)/2\alphaph}\gg1$.
The renormalization parameter $0
