Effects of Electron Correlation in X-Ray and Electron Diffraction. II. Influence of Nuclear Charge in Two-Electron Systems

The electron—electron and electron—nuclear radial distribution functions P(r12) and D(r) have been calculated for ground states of heliumlike systems (Z=2 to 8). Computations were based on the correlated and uncorrelated wavefunctions published by Roothaan et al. Elastic and inelastic scattering factors for calculating the intensities I([open phi]) of x rays scattered by two-electron systems were determined from the distribution functions. The correction functions ΔP(r12) and ΔI([open phi]) representing the differences between correlated and uncorrelated results were found to follow a simple dependency on atomic number. It was observed that universal functions could be established which closely approximated each of the functions D(r)/Z*, P(r12)/Z*, I([open phi]), ΔP(r12), and Z*ΔI([open phi]) for all of the systems studied if the functions were expressed in terms of the reduced variables r′=Z*r and [open phi]′=2 arcsin[Z*−1 sin([open phi]/2)]. The appropriate Z* was very nearly the Slater effective nuclear charge. The experimental determination of P(rij) from x-ray scattering and the magnitude of correlation effects to be expected are briefly discussed.