  We consider vacuum polarization effects in the one-photon annihilation
channel within a kinetic description of the e+ e- plasma produced from the
vacuum in the focal spot of counter-propagating laser beams. This entails
essential changes in the structure of the photon kinetic equation. We
investigate the domain of large adiabaticity parameters gamma >> 1 where the
photon radiation turns out to be very small. A more thorough examination of the
domain gamma < 1 needs separate investigation. However, an exploratory study
has shown that the one-photon annihilation channel can lead for some domains of
laser field parameters (e.g., for the XFEL) to contributions accessible for
observation.
