Bound-free transition form factors in hydrogen-like and multi-electron atoms

The bound-free transition form factor ( kappa mod exp(iq.r) mod nlm) is calculated directly in spherical coordinates for both hydrogenic and Slater-type orbitals. Using the exact Coulomb wave (r mod kappa ) associated with the field -Z/r, extremely concise analytical expressions are derived for the integral irrespective of either the triad nlm or of the quantisation axis. Results are given in terms of Appell hypergeometric polynomials F 1 of two variables.