  It is well known that in the presence of strong external electromagnetic
fields many processes forbidden in standard QED become possible. One example is
the one-photon annihilation process considered recently by the present authors
in the framework of a kinetic approach to the quasiparticle e-e+ gamma plasma
created from vacuum in the focal spot of two counter-propagating laser beams.
In these works the domain of large values of the adiabaticity parameter gamma
>> 1 (corresponding to multiphoton processes) was considered. In the present
work we estimate the intensity of the radiation stemming from photon
annihilation in the framework of the effective mass model where gamma < 1,
corresponding to large electric fields E < E_c=m^2/e and high laser field
frequencies (the domain characteristic for X-ray lasers of the next
generation). Under such limiting conditions the resulting effect is
sufficiently large to be accessible to experimental observation.
