THOMAS-REICHE-KUHN SUM-RULE FOR ELECTRON TRANSITIONS IN SOLIDS

A well-known sum rule obtained for electron transitions between the at omic 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 sta tes was its lack of dependence on the initial state of transitions. Th is 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 fi eld of the crystal core. Corrections to the original TRK result can be represented as a function of the quantum parameter labelling the init ial electron state. Other moments of the spectral distribution functio n than those leading to the TRK sum rule have been calculated. A compa rison of the relations found between different spectral moments for so lids with similar relations obtained by Traini for the spectral moment s of the atomic states has been done.