Possible enhancement of laser gain condition in deformed DFB crystals emitting in the x-ray band.

X-ray Solid State lasers are very interesting because of the possible high-energy developable([1]) DFB x-ray laser emission has been demonstrated theoretically, even using the anomalous transmission angle([2+5]), but proved impossible([1,6]). We find that crystal deformation and relativistic excitation may interact, under proper conditions, originating Zeeman splitting of the states. In these conditions the crystal behavior is similar to a ring laser thus enabling coherent x-ray emission. We discuss the findings with a semi-empirical and rigorous description.