Atomic scattering factors for the lithium- and beryllium-isoelectronic sequences from accurate analytic Hartree-Fock wave functions*

Abstract

The most widely used atomic scattering factors are based on numerical self-consistent field (SCF) wave functions, some of which are of low accuracy. Atomic scattering factors obtained from recent analytic Hartree-Fock wave functions of higher accuracy than the older numerical SCF functions are reported here for the lithium- and beryllium-isoelectronic sequences. In both sequences, the calculations are made for the nuclear charges 3 ≤ Z ≤ 10. These results represent previously unreported SCF factors for the two sequences except for Li, Be and C +2 . The present factors for Li, Be and C +2 are found to be in excellent agreement with the corresponding factors determined from recent, accurate numerical Hartree-Fock solutions. The use of such analytic functions permits high-precision evaluation of the form factors for arbitrary values of λ −1 sin θ , an operation which is less readily performed using the conventional numerical solutions. In addition, the influence of increasing nuclear charge on various approximate wave functions is examined by comparing the SCF factors for these isoelectronic sequences with the factors derived from other types of wave functions. In this connection, the relative reliability of the SCF factors is discussed. Finally, an explanation is given for the observation that for a given atomic or ionic species of the sequences, the various scattering curves obtained from different approximate wave functions tend to cross in such a manner so that the areas beneath them are approximately equal.