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- W3035774864 abstract "The Sayre equation can be derived as a special case of unitarity, and recently it was shown that the derivation applies to dynamical scattering and electron diffraction. Since both the triplet formula and the tangent formula can be derived from the Sayre equation, use of these direct methods to find the phases for electron diffraction amplitudes is fully justified. The most transparent form of the unitary equation is where  is the scattering amplitude operator, f is the final state, i the initial state, and n is a complete set of intermediate states; the sum over these states becomes an integral where the intermediate states form a continuum. If there is Friedel symmetry, the form of the Sayre equation derived from equation (1) is The prime on the sum means K ≠ 0. If Friedel symmetry is violated, Σ' | A(K) | 2 becomes This equation is a quantitative relationship which not only has an essentially unique solution for the phases, but which also constrains the magnitudes of the intensities." @default.
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- W3035774864 date "1995-08-13" @default.
- W3035774864 modified "2023-10-14" @default.
- W3035774864 title "Unitarity and the real world: applications of direct phasing to electron diffraction data" @default.
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- W3035774864 doi "https://doi.org/10.1017/s042482010013715x" @default.
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