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Abstract A direct method for structural interpretation of small-angle scattering data by monodisperse isotropic systems is presented. The spherical harmonics technique proposed by Stuhrmann [Acta Cryst. (1970), A26, 297-306] is used to choose the class of possible solutions. The method enables one to decompose scattering intensity into partial amplitudes corresponding to different multipole components of scattering density using the space and value density restrictions. If a particle possesses a rotational symmetry, its structure may be restored directly using the method; if not, additional information is required to get a set of possible solutions. The method is stable with respect to experimental errors. The efficiency of the procedure is shown in model examples. The application of the method to interpret the small-angle X-ray scattering curve of bacteriophage T7 produced a map of electron density with a resolution of about 12 Å.
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