New x-ray scattering from polymers and its quantum profile analysis applied to materials characterization

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) _i was calculated by LDPE by extended Huckel-LCAO-MO theory. Final state wave function (psi) _f 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_ocos(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.