Symbiotic binaries consist of a cool giant and a hot radiation source, which is ionizing a nebula. Recently two emission lines at lambda-6825 and lambda-7082, which are only observed in these systems, have been identified as Raman scattering of O VI lambda-1032 and lambda-1038 photons by neutral hydrogen. Strong O VI lines are produced in the compact H II region, probably near the ionizing component. The conversion into lambda-lambda-6825, 7082 photons will occur in the extended atmosphere of the cool giant. Because the scattering geometry in symbiotic stars rotates due to the binary motion, systematic changes in the intensity and polarization of the Raman scattered lines are expected. In this paper Monte Carlo simulations are presented in order to investigate the flux and polarization properties of the Raman scattered emission lines. Photon paths are calculated for an illuminated atmosphere with scatterings according to the Rayleigh phase matrix and for various scattering and absorption coefficients. Calculated flux and polarization phase curves for symbiotic binaries are given, and diagnostic possibilities of the Raman scattered emission lines explored. The results show that the lambda-lambda-6825, 7082 emission lines allow a determination of orbital parameters, such as period, inclination and orientation of the orbital plane. Additionally, information on the geometric structure of the nebular O VI region and on absorbing particles in the outer atmosphere of the red giant can be obtained.
