  A periodically bent Si crystal is shown to efficiently serve for producing
highly monochromatic radiation in a gamma-ray energy spectral range. A
short-period small-amplitude bending yields narrow undulator-type spectral
peaks in radiation from multi-GeV electrons and positrons channeling through
the crystal. Benchmark theoretical results on the undulator are obtained by
simulations of the channeling with a full atomistic approach to the
projectile-crystal interactions over the macroscopic propagation distances. The
simulations are facilitated by employing the MBN Explorer package for molecular
dynamics calculations on the meso- bio- and nano-scales. The radiation from the
ultra-relativistic channeling projectiles is computed within the
quasi-classical formalism. The effects due to the quantum recoil are shown to
be significantly prominent in the gamma-ray undulator radiation.
