Multiple scattering theory derivation

T = -iOyK the time reversal operator [11], For the non-relativistic case Durham [12] derived an expression for within the framework of multiple scattering theory. To... 

We have provided a pedagogical derivation of the traditional, nonrelativistic form of multiple scattering theory based on the optical potential formalism. We have also discussed in detail each of the important advances made over the past ten years in the numerical application of the NR formalism. These include the full-folding calculation of the first-order optical potential, off-shell NN t-matrix contributions, relativistic kinematics and Lorentz boost of the NN t-matrix, electromagnetic effects, medium corrections arising from Pauli blocking and binding potentials in intermediate states, nucleon... 

Most recently, Freed (84) has developed a generalized theory in terms of a multiple scattering representation of scattering of fluid waves by the polymer molecules and derived the precise result ... 

In this section we will succinctly review the derivations of the Watson and KMT multiple scattering optical model formalisms and briefly discuss a few of the recent extensions of these theories which are relevant here. 

Expressions for these coefficients can be derived from the theory of optical potentials, which has been developed for nuclear [14], atomic [64] and molecular collisions [65], In a simple approximation, we let a) = 7, lk, a)w k) and find for the multiple-scattering coefficients the coupled... 

In the last decade order N electronic structure calculations [1, 2] made possible the study of large supercells containiug from 100 to 1000 atoms. Namely Faulkner, Wang and Stocks [2,3] have shown that simple linear laws, the so called qV relations, link the local charge excesses and the local Madelung potentials in metallic alloys. These qV linear laws have been obtained from the numerical analysis of data produced by Locally Self-consistent Multiple Scattering (LSMS) [1] calculations, while their formal derivation within the density functional theory has not yet been obtained. As a matter of fact, the above laws can be considered to hold at least within the approximations underlying I/SMS calculations, i.e. the l/ocal Density and the muffin-tin approximations. 

Extension of Fano s formalism to the general case of multiple discrete states embedded in multiple continua was first conducted by Mies [54]. Like Fano, Mies assumed a prediagonalized basis. By imposing the asymptotic condition for the continuum state from the scattering theory, Mies derived the complete solution to the total continuum problem and gave formulas for energies and widths of resonances. 

In the final version of the Paris potential, also known as the parametrized Paris potential [14], each component (there is a total of 14 components, 7 for each isospin) is parametrized in terms of 12 local Yukawa functions of multiples of the pion mass. This introduces a very large number of parameters, namely 14 x 12 = 168. Not all 168 parameters are free. The various components of the potential are required to vanish at r = 0 (implying 22 constraints [14]). One parameter in each component is the nNN coupling constant, which may be taken from other sources (e.g., nN scattering). The 2n-exchange contribution is derived from dispersion theory. The range of this... 

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