Studying x-ray atomic scattering form factor for K-shell and total atom for three and four electron systems

The partitioning technique has been used to analyze the three and four electron systems into three-pairs electronic wave functions for Li-like ions (Li, Be⁺, B⁺⁺) and six-pairs electronic wave functions for Be-like ions (Li^-, Be, B⁺) by using Hartree-Fock wave functions of Clementi and Rotti.In this work the atomic scattering factor f(s) for K-shell and total atom for three and four electron systems are studied. The physical importance of this factor appears in its relation with the several important atomic properties such as, the coherent scattering intensity, the total scattering intensity, the incoherent scattering function, the coherent scattering cross section, the total incoherent cross section, the nuclear magnetic shielding constant, the differential cross section of electrons scattering from atom and the geometrical structure factor. Also the one particle radial density distribution function D(r) has been studied, where the atomic scattering factor f(s) is the Fourier transform of the electron density ρ(r₁) and . The accuracy of results was checked by determining the total energy. All results are calculated in atomic units.