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A method is suggested to produce, with the help of colliding laser photonswith bunches of relativistic ions having two energy levels, both intense beamsof monochromatic polarized X-ray fluorescence photons and significant number ofX-ray entangled photons, via double Doppler transformation. Nonlinearsusceptibility of the ions, the cross section and the rate of production ofsuch photons at RHIC are estimated. Such beams of X-ray photons can be detectedand applied to solve various problems, in a manner similar to the usage ofoptical photons.

X-Ray Entangled Photon Production in Collisions of Laser Beams with Relativistic Ions