Frequency multiplier in X-ray region has not been reported. This paper proposes to design the x-ray frequency multiplier, which is based on recent discovery of anti- Compton effect of X-rays from polyethylene terepthalate and low density polyethylene. Electronic system of most of the polymeric atom get excited and some electrons recoil when it is irradiated with x-ray in Compton process. When recoil electron transfers its energy partly or fully to incident x-ray photon it produces anti-Compton effect. At high scattering angle about 160°, the wavelength of anti-Compton scattered radiation decreases by 0.047A<sup></sup>0 and there is enhancement of frequency. Fixing another polymer crystal at the calculated position of anti-Compton line, the wavelength of re-scattered radiation at 160° can further be decreased by 0.047A<sup>0</sup> or thereby enhancing the frequency. This principle of repeated scattering can be used to multiply the X-ray frequency. In general, x-ray absorption depends approximately on Z. while maximum possible diffracting power is proportional to only Z<sup>2</sup>, where Z is the atomic number. Thus the crystals of polymer are expected to form better monocromator for designing XFM. The production of high energetic and low intense x-ray by XFM may be used in radiotherapy.
A nature loves symmetry it is quite logical to think that, X-rays may also exhibit the reverse of Compton effect. Such new modified scattering from low-density polyethylene (LDPE) and polyethylene terepthalate has been observed. The Compton scattered ejected electrons collide with other incident photons before reaching the continuum state transferring a part or whole of its kinetic energy to the photons; thereby producing photons of shorter wavelength called anti-Compton effect. In Quantum theory, external fields (if it changes rapidly) can cause transition from a state of positive energy to negative energy. The lifetime of the excited state is inversely proportional to square of the average atomic number. Hence solid polymers are the ideal system to observe anti-Compton scattering, since binding energy is less. Initial state wave function (psi) <SUB>i</SUB> was calculated by LDPE by extended Huckel-LCAO-MO theory. Final state wave function (psi) <SUB>f</SUB> was formulated and differential cross section was expressed in terms of the profile function J(z) using impulse approximation (IA). This scattering cross section was compared with quantum electrodynamics scattering cross section i.e. Klein-Nishina scattering cross section to solve J(z). The anti-Compton wavelength shift was calculated using relativistic corrections in the IA, hence the valence electron contribution terms z = -P<SUB>o</SUB>cos(phi) , where (phi) is the angle between the electrons initial momentum and the x-ray vector. The anti-Compton profile for the LDPE was obtained from z ~ J(z) graph. The volume plasmon excitation energy was experimentally found out to be 12 eV.