ON INTEGRATING THE TECHNIQUES OF DIRECT-METHODS WITH ANOMALOUS-DISPERSION .4. A SIMPLIFIED PERTURBATION TREATMENT FOR SAS PHASING

Results from probabilistic theory for the single-wavelength anomalous- scattering (SAS) Friedel pair, two-phase structure invariants, psi(H) = phi(H) + phi(-H), are used to show that the SAS three-phase structur e invariants, psi(HK) = phi(H) + phi(K) + phi(-H-K), tend to positive values that are easily estimated. Appropriate averages of the estimate s provide SAS perturbation corrections in the form of positive origin shifts for the probability distribution of psi(HK) values and for the tangent formula. The theoretical probabilistic results are verified by empirical statistical analyses of model-calculated phases and experim entally measured structure-factor magnitudes for a small-molecule and a protein crystal structure.