A Quantum theory of the scattering of soft x-ray from Compton effect caused electron standing wave in the materials

In the present investigation, low-energy x-rays ( 15 keV) scattered from powder, polymer, crystals and hydrogenous liquids (with preference for materials of low binding energy) at different scattering angles have been analysed. The scattered x-rays show unambiguous existence of a new modified line along with unmodified and Compton line. Since, the experimental observation of the inverse Doppler effect, i.e. increase of frequencies of reflecting waves from a receding boundary, has already been reported [Seddon and Bearpark (2003) Science, 302, 1537–1540]. Hence, it is quite logical to think that x-rays may also gain energy in contrast to Compton effect (where they lose energy) in material medium. Such type of new modified xray scattering (angle dependent) was observed. Expressions for photon of enhanced energy, hω3, initial momentum of plasmon q and the total scattering cross section σN of this new phenomenon have been derived. The σN is found out to be proportional to √ ∈ and is about 100 times less than the Compton cross section using high-energy x-ray photon (100’s of keV), usually used for Compton scattering studies. Both theoretically calculated and experimentally observed data match well with one another. The new modified line is to be clearly expected from materials of low atomic number with high dielectric constant using low-energy x-rays.