  In the literature on electron-phonon scatterings very often a
phenomenological expression for the transition matrix element is used which was
derived in the textbooks of Ashcroft/Mermin and of Czycholl. There are various
steps in the derivation of this expression. In the textbooks in part different
arguments have been used in these steps, but the final result is the same. In
the present paper again slightly different arguments are used which motivate
the procedure in a more intuitive way. Furthermore, we generalize the
phenomenological expression to describe the dependence of the matrix elements
on the spin state of the initial and final electron state.
