Multiple scattering theory Green functions

To improve the latter a number of 0 N) methods have been recently proposed but practically all of them exploit Hamiltonian formalism. However, in Refs. 4,5 the locally self-consistent multiple scattering (LSMS) method based on the real space multiple scattering theory has been outlined, and in Ref. 6 its central idea in the form of the local interaction zone (LIZ) was incorporated into the Green s function technique, leading to the locally self-consistent Green s function method (LSGF). 

All ab initio applications of multiple scattering theory in dilute substitutional alloys rely on the one-to-one correspondence configuration. This holds both for the calculation of transition probabilities [7], represented by Eq. (7), and the electronic structure [8], represented by the Green s function equation [9]... 

These formulas must be summed over a spin index to give the corresponding total densities. In multiple scattering theory, the Green function as given by Eq. (7.37) is subdivided into terms valid in separate atomic cells. The elements with r = r are single sums over the cells. Hence the density of states of given spin in a particular cell r/y is... 

Butler, W.H., Zhang, X.-G. and Gonis, A. (1992). The Green function cellular method and its relation to multiple scattering theory, Mat. Res. Symp. Proc. 253, 205-210. 

The absorption cross section for core transitions can be solved in real space using the Green s function approach in the frame of multiple scattering theory In this approach the limited mean free path of the photoelectron determines the finite size of the cluster of atoms around the central absorbing atom to be considered in the calculations. An important feature of the solution of the absorption cross section in real space is that physical processes determining the unoccupied density of states of condensed matter appear explicitly. Moreover, the spectra of systems without long range order can also be solved. 

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