The efficiency of most popular approach to generating short wavelength radiation involving particle beams. FEL, is limited by the Thomson scattering cross section. If one were to use a beam of particles have a resonant scattering cross section for some frequency, a greatly enhanced gain might be expected. A natural candidate is a hydrogenic positive ion, having Z 2, with a single bound electron. The fact that the ion is charged allows the beam to be accelerated to relativistic energies gamma 1, therefore one can exploit the properties of relativistic kinematics which dictate that the back scattered radiation will have its wavelength shortened by a factor 2 gamma sq.
This article is from 'Osa Proceedings of the Topical Meeting (5th) on Short-Wave Length Coherent Radiation: Generation and Applications Held in Monterey, California on 8-10 April 1991. Volume 11,' AD-A252 973, p82-86.