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Phase factors of Bloch functions in the localized approximation of the Koster - Slater theory


Published under licence by IOP Publishing Ltd
, , Citation R E Turner and D A Goodings 1965 Proc. Phys. Soc. 86 87



The theory of Koster and Slater for the electronic states around an impurity in a metal is formulated in terms of the Wannier functions of the host lattice. These functions are not uniquely defined, however, because they depend on how the arbitrary phase factors exp{(n, k)} associated with the Bloch functions are chosen. In this paper it is shown that the frequently used `localized approximation' of the Koster-Slater theory has the effect of fixing the relative phases of the Bloch functions, and consequently in this approximation the Wannier functions are uniquely defined. In the second part of the paper an approximation is described, valid in the region close to the impurity nucleus, which leads to expressions in terms of matrix elements of Bloch functions rather than Wannier functions. For two examples, the Knight shift at impurity atoms and the x-ray emission intensity, results are obtained which seem to be more acceptable physically than those previously derived.

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