  We consider an external potential, $-\lambda \phi$, due to one or more
nuclei. Following the Dirac picture such a potential polarizes the vacuum. The
polarization density as derived in physics literature, after a well known
renormalization procedure, depends decisively on the strength of $\lambda$. For
small $\lambda$, more precisely as long as the lowest eigenvalue,
$e_1(\lambda)$, of the corresponding Dirac operator stays in the gap of the
essential spectrum, the integral over the density vanishes. In other words the
vacuum stays neutral. But as soon as $e_1(\lambda)$ dives into the lower
continuum the vacuum gets spontaneously charged with charge $ 2e$. Global
charge conservation implies that two positrons were emitted out of the vacuum,
this is, a large enough external potential can produce electron-positron pairs.
  We give a rigorous proof of that phenomenon.
