Multiple scattering formalism

Most methods of band-structure calculation are based on the muffin-tin, atomic sphere approximation (ASA) or Wigner-Seitz construction for the electronic potential and 

To solve the single-site Dirac equation for a spin-dependent potential well, we start from the ansatz (Doniach and Sommers 1981 Feder et al. 1983 Strange et al. 1984), 

For the case where the magnetic ordering of the system is accounted for by a spherically symmetric potential with a spin-dependent part PB(r)ez a that is set up within the firamework of SDFT, the ansatz given in Equation (5.24) leads to the following set of radial differential equations, 

By requiring that the wave function Pv(r, E) in Equation (5.24) has a unique spin-angular character A in the limit r - 0, the index v may be identified with A. The corresponding single-site r-matrix is then obtained by introducing the auxiliary matrices a and b (Ebert and Gyorffy 1988 Faulkner 1977)  

Here p = /E( 1 + E/c2) is the momentum, the functions h (pr) are the relativistic Hankel functions of the first and second kind (Rose 1961) and [ ]r denotes the relativistic form of the Wronskian evaluated at r outside the potential well. Finally, the single-site r-matrix t(E) is obtained from the expression (Ebert and Gyorffy 1988)  

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Domany, E. Eutin-Wohlman, 0. and Mizrachi, L., "Multiple Scattering Formalism Application to Scattering by Two Spheres," J. Appl. Phys., 1984, pp. 132-136. 

Molecular modeling using multiple scattering formalism (75) provides XAFS observables (see also Sec. V.A). Therefore, one can simulate the XAFS from candidate structures and compare with experimental results to find which structure is correct. The theoretically derived (suggested) clay mineral structures can now be confirmed by experiments. 

Nonrelativistic multiple scattering formalism and the optical potential 232... 

A pedagogical discussion of nonrelativistic multiple scattering formalisms is presented, followed by a description of the approximation schemes used in numerical applications of the theory. Recent theoretical developments in the nonrelativistic approach, including medium corrections to the effective projectile-taiget nucleon interaction, off-shell contributions, and full integration ( full-folding ) of the nucleon-nucleus optical potential are discussed in detail. 

A reasonable way to estimate the size of the correlation correction to the relativistic tp potential is to make use of the semi-relativistic multiple scattering formalism [Ra 85] discussed in section 4.2. In analogy with the Watson theory, the leading correlation correction is quadratic in the relativistic NN invariant scattering operator and is proportional to two-body correlations in the target nucleus. 

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