T operators and their matrix elements for a general periodic potential

A new approach for the treatment of the T operator is provided which cures the difficulties of the multiple-scattering approach to the general (non-muffin-tin) periodic potential problem. Solely from potential periodicity, i.e., without discriminating between muffin-tin and non-muffin-tin cases, the T operators are shown to admit a direct integral decomposition in terms of the reduced T operators. This feature is further exploited by introducing Bloch periodic scattering states which finally results in a closed (compact) expression for the on-shell matrix elements. In the L representation, their functional form is related to that derived within multiple-scattering theory for the muffin-tin case but irrespective of whether the potential is muffin tin or not, the structure dependence cannot be separated from that of the potential (as known in the multiple-scattering approach for the muffin-tin case). However, this separation can be restored by introducing various approximations which partially break the Bloch periodicity. Hence, the separation between structure and potential, even in the muffin-tin case, is shown to be an approximate result.