Bloch sums description

Finally - and equally important - Jens contribution to the formal treatment of GOS based on the polarization propagator method and Bethe sum rules has been shown to provide a correct quantum description of the excitation spectra and momentum transfer in the study of the stopping cross section within the Bethe-Bloch theory. Of particular interest is the correct description of the mean excitation energy within the polarization propagator for atomic and molecular compounds. This motivated the study of the GOS in the RPA approximation and in the presence of a static electromagnetic field to ensure the validity of the sum rules. 

To base considerations on states with localized extra electrons or holes, the Wannier-type transformation is introduced, yielding localized states within each unit cell. The number of these states equals the number of bands included in the Wannier transformation. In the case of elemental semiconductors such as diamond or siUcon these are one-electron states localized at the middle of the nearest atoms bonds so that n=l,2,3,4 (see Chap. 3 for the discussion of the connection between Bloch and Wannier states). A local description arises through the decomposition of the bkn into a sum of local operators marked with a cell index R (translation vector of the direct lattice) ... 

Within the electronic band structure description of a solid, the absorption as represented by e"((o) is the sum of all possible transitions between occupied and empty electronic states of the same k-vector within the reduced energy band scheme (vertical or direct transitions). Note that k in this context represents the wave vector of the electron in the crystal, the electron being described by a Bloch wave. Let the final and initial states be separated by the... 

---