Transition probability functions for inelastic electron--electron   scattering
  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. 
Stefan L\"offler, Peter Schattschneider
cond-mat.mtrl-sci physics.chem-ph