  We consider the Hartree-Fock approximation of Quantum Electrodynamics, with
the exchange term neglected. We prove that the probability of static
electron-positron pair creation for the Dirac vacuum polarized by an external
field of strength $Z$ behaves as $1-\exp(-\kappa Z^{2/3})$ for $Z$ large
enough. Our method involves two steps. First we estimate the vacuum expectation
of general quasi-free states in terms of their total number of particles, which
can be of general interest. Then we study the asymptotics of the Hartree-Fock
energy when $Z\to+\infty$ which gives the expected bounds.
