Symbiotic stars are binary systems comprising a hot component which
ionizes material shed by a cool, low-gravity companion. The resulting
`composite' spectra contain sharp nebular lines superimposed on a
red-star spectrum, which usually includes molecular absorption bands.
Two of the optical emission lines - 
Å and
Å - have been identified as resulting from inelastic
Raman scattering of OVI 
Å photons off
neutral hydrogen in the cool stellar wind (Schmid 1989). These lines
are highly polarized ( Schmid & Schild 1990, 1994) because of the
asymmetric nature of the scattering geometry, and
intermediate-dispersion spectropolarimetry shows that the
Å emission lines display a range of
complex intensity and polarization characteristics which demonstrate
that the scattering must take place in an extended, expanding cool-star
wind (e.g., Harries & Howarth 1996b, hereafter Paper I).
While many mass-loss tracers, such as CO or dust, represent minority
species by mass, the 
6825, 7082 Å lines result from
scattering off neutral hydrogen - a major component of the wind. The
polarization profiles of the Raman lines
encode both velocity and spatial information; it is the aim of this work
to develop models which aid in the interpretation of spectropolarimetric
observations, with the long-term goals of constraining both mass-loss
rates and velocity laws for red-giant winds, for a variety of subtypes,
and of obtaining binary orbital parameters for the systems.
The first attempt to model the polarization properties of symbiotic
systems was carried out by Schmid (1992), who adopted a geometry of
rotational symmetry about the binary axis, with a photon source
illuminating a geometrically thin red-giant photosphere. The free
parameters of the model were the binary separation and the absorption
cross-sections for OVI photons and Raman-scattered photons.
Schmid found that his model is able to reproduce observed 
line-intensity ratios, and that the predicted
line polarizations obtained are comparable with observations.
The major simplification of Schmid's work was the assumption of a `billiard ball' geometry for the red-giant component. Subsequent observations (e.g., Paper I) have demonstrated that the polarization profiles are highly structured; the presence of this structure shows that it is essential to take account of the extension of the red-giant atmosphere, and of the velocity gradients within it, to model the data properly. The code described in the following sections treats the polarized radiative transfer by following multiple Rayleigh and Raman scatterings in a spherically symmetric wind and stellar photosphere.