Integration of free-free radiative-transition matrix elements

The calculation of radiative-transition matrix elements between continuum states of an electron moving in the finite-range spherical potential is concerned in this paper. We introduce a numerically safe and fast procedure which has been developed for this purpose. The numerical integration is employed within a certain finite region and the analytical integration outside. Both are performed by the computer program and the algorithm is presented here. Special care was given to the numerical stability so that the rapidly oscillating wave functions describing high-energy incident electrons (∝5 keV) may be integrated. The higher-order terms of the multipole expansion can be evaluated by this method, too. (orig.)