Recursive calculation of closed-form scattering factors for atomic orbitals

Recurrence relations are derived for calculating closed-form expressions for the Fourier-Bessel transform of electronic charge densities represented by Gaussian- and Slater-type atomic orbitals. The derivation is based on hypergeometric and Legendre-function representations of the transform and the use of their recurrence properties. The scattering-factor calculations are discussed in detail. A table of closed-form expressions for Gaussian-type orbitals, not hitherto available, has been calculated using the new method and is available on request.