Analytical results for Coulomb integrals with hydrogenic and Slater-type orbitals

Atomic form factors containing the product of the Coulomb wavefunction (r mod k) with either the hydrogenic or Slater-type orbital (r mod nlm), are calculated in a closed form, for an arbitrary triple nlm. By choosing the quantisation axis for mod nlm> along the vector k, it is shown that the present integrals can be reduced to a linear combination of easily calculable hypergeometric polynomials of two and three variables. Results are particularly useful for second-order theories of charge exchange, notably CDW and CIS approximations.