Shell population and κ refinements with canonical and density-localized scattering factors in analytical form

Scattering factors for outer shells of the first- and second-row series of atoms have been obtained by expansions with Jacobi functions. Both canonical and density-localized shell form factors have been studied. For κ refinements, both first and second derivatives are computed by analytical methods. Density-localized shell distributions differ from canonical shell distributions within a small sphere (< 0.5 Å) about the nucleus. Shell population and κ refinements on uracil at the monopole level give virtually identical results with canonical and density-localized form factors.