Model-independent structure and resonant X-ray spectra of intermediate smectic phases

It is shown that the orientational structure of intermediate smectic phases can be determined using the symmetry properties of the general free energy with arbitrary orientational coupling between smectic layers, without addressing a particular model. The structure of three- and four-layer intermediate phases, obtained in this way, corresponds to experimental data. The same method enables one to predict the structure of intermediate phases with periodicity of five and six layers, which have not been observed experimentally so far. The resonant X-ray spectra of the five- and six-layer intermediate phases with predicted structure have also been calculated. These spectra are characterized by a number of features which enable one to distinguish five-layer and six-layer intermediate phases from phases with smaller periods.