  Symbiotic stars are regarded as wide binary systems consisting of a hot white
dwarf and a mass losing giant. They exhibit unique spectral features at 6825
\AA\ and 7082 \AA, which are formed via Raman scattering of
\ion{O}{6}$\lambda\lambda$ 1032 and 1038 with atomic hydrogen. We adopt a Monte
Carlo technique to generate the same number of \ion{O}{6}$\lambda$1032 and
$\lambda$1038 line photons and compute the flux ratio $F(6825)/F(7082)$ of
these Raman scattered \ion{O}{6} features formed in neutral regions with a
simple geometric shape as a function of \ion{H}{1} column density $N_{HI}$. In
cylindrical and spherical neutral regions with the \ion{O}{6} source embedded
inside, the flux ratio $F(6825)/F(7082)$ shows an overall decrease from 3 to 1
as $N_{HI}$ increases in the range $10^{22-24}{\rm\ cm^{-2}}$. In the cases of
a slab geometry and other geometries with the \ion{O}{6} source outside the
\ion{H}{1} region, Rayleigh escape operates to lower the flux ratio
considerably. For moderate values of $N_{HI}\sim 10^{23}{\rm\ cm^{-2}}$ the
flux ratio behaves in a complicated way to exhibit a broad bump with a peak
value of 3.5 in the case of a sphere geometry. We find that the ratio of Raman
conversion efficiencies of \ion{O}{6}$\lambda\lambda$1032, 1038 ranges from 0.8
to 3.5. Our high resolution spectra of 'D' type HM~Sge and 'S' type AG~Dra
obtained with the {\it Canada-France-Hawaii-Telescope} show that the flux ratio
$F(6825)/F(7082)$ of AG~Dra is significantly smaller than that of HM~Sge,
implying that 'S' type symbiotics are characterized by higher $N_{HI}$ than 'D'
type symbiotics.
