  Using a Monte Carlo technique, we investigate the center shifts that are
expected to occur for the broad H$\alpha$ wings and the He II $\lambda$ 6545
feature as a function of the neutral hydrogen column density in symbiotic
stars.These two features are proposed to be formed via Raman scattering of UV
continuum around Ly$\beta$ and He II $\lambda$ 1025 emission line by neutral
hydrogen. The branching ratio of Raman scattering to Rayleigh scattering for UV
radiation around Ly$\beta$ is a non-linearly increasing function of the
wavelength, which results in enhanced Raman optical fluxes redward of the
H$\alpha$ line center as $N_{HI}$ increases. However, we find that the amount
of wing center shift is quite small about $20{\rm km s^{-1}}$ as $N_{HI}$
increases from $10^{20}{\rm cm^{-2}}$ to $10^{21}{\rm cm^{-2}}$. Assuming that
He II $\lambda$~1025 emission is characterized by a Gaussian profile, the Raman
scattered He II 6545 feature exhibits near Gaussian profiles with the peak
shifted redward for $N_{HI}<10^{22}{\rm cm^{-2}}$. The redward center shift
amounts to $1{\rm \AA}$ for $N_{HI}\sim 10^{20}{\rm cm^{-2}}$ and decreases as
$N_{HI}$ increases up to $N_{HI}\sim 10^{22}{\rm cm^{-2}}$, above which no
center shift is observed. The redward peak shift is due to the fact that the
incident emission profile is symmetric with respect to He II $\lambda$~1025
line center whereas the Raman conversion rate is increasing towards the line
center of Ly$\beta$. We emphasize that the determination of $N_{HI}$ by
locating the exact peak position of the He II 6545 feature will lift the
degeneracy to allow a more accurate estimate of the covering factor of the
neutral region, providing strong constraints on the mass loss process occurring
in symbiotic stars.
