Thomas-Reiche-Kuhn Sum Rule for Electron Transitions in Solids

A well-known sum rule obtained for electron transitions between the atomic states by Thomas, Reiche and Kuhn (TRK) is examined for the case of transitions between delocalized electron states in cubic lattices. A characteristic point of the original TRK sum rule for the atomic states was its lack of dependence on the initial state of transitions. This situation holds also for the free-electron states in a metal but is changed in the case of electrons influenced by the presence of the field of the crystal core. Corrections to the original TRK result can be represented as a function of the quantum parameter labelling the initial electron state. Other moments of the spectral distribution function than those leading to the TRK sum rule have been calculated. A comparison of the relations found between different spectral moments for solids with similar relations obtained by Traini for the spectral moments of the atomic states has been done.