  We have identified a mechanism of collective nuclear de-excitation in a
Bose-Einstein condensate of $^{135}$Cs atoms in their isomeric states,
$^{135m}$Cs, suitable for the generation of coherent gamma photons. The process
described here does not correspond to single-pass amplification, which cannot
occur in atomic systems due to the large shift between absorption and emission
lines, nor does it require the large densities associated to standard Dicke
super-radiance. It thus overcome the limitations that have been hindering the
generation of coherent gamma rays in many systems. Therefore, we propose an
approach for generation of coherent gamma rays, which relies on a combination
of well established techniques of nuclear and atomic physics, and can be
realized with currently available technology.
