We describe a non-LTE photoionization code to calculate the wind structure
and emergent spectrum of a red giant wind illuminated by the hot component of a
symbiotic binary system. We consider spherically symmetric winds with several
different velocity and temperature laws and derive predicted line fluxes as a
function of the red giant mass loss rate, \mdot. Our models generally match
observations of the symbiotic stars EG And and AG Peg for \mdot about 10^{-8}
\msunyr to 10^{-7} \msunyr. The optically thick cross- section of the red giant
wind as viewed from the hot component is a crucial parameter in these models.
Winds with cross-sections of 2--3 red giant radii reproduce the observed
fluxes, because the wind density is then high, about 10^9 cm^{-3}. Our models
favor winds with acceleration regions that either lie far from the red giant
photosphere or extend for 2--3 red giant radii.Comment: 51 pages, LaTeX including three tables, requires 15 Encapsulated
Postscript figures, to appear in Ap