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

Derivation of phenomenological expressions for transition matrix elements for electron-phonon scattering