Soft X-ray transition matrix elements: The role of approximation of the valence states

The coordinate, momentum and potential forms of the interband transitions matrix elements are equivalent when the initial and the final states are exactly known. For the soft X-ray transitions we assume exact core states, and approximate valence states. Then the three different forms of the matrix elements are no longer equivalent and are related by new, more general expressions. From these the qualitative conclusions regarding the appropriate form of the approximated valence states are derived. It turns out, that the orthogonalization of the approximate valence wave function to the core states is very important for the correct behaviour of the photon energy dependence of the soft X-ray emission. These results are illustrated by simple numerical examples.