  Without developing a correct theory, the rate of the production of entangled
photon pairs in the X-ray region by high energy electrons is estimated for
experimental parameters used in a few experiments on X-ray parametric down
conversion. Taking into account the need for X-ray entangled X-ray photons, it
is proposed to begin the experimental study of such mechanism of nonlinear
X-ray optics before the launch of the X-ray free electron lasers.
