  In this work, the transition matrix elements for inelastic electron--electron
scattering are investigated. The angular part is given by spherical harmonics.
For the weighted radial wave function overlap, analytic expressions are derived
in the Slater-type and the hydrogen-like orbital models. These expressions are
shown to be composed of a finite sum of polynomials and elementary
trigonometric functions. Hence, they are easy to use, require little
computation time, and are significantly more accurate than commonly used
approximations.
