We present non-LTE calculations for an expanding red giant's atmosphere ionized from the outside by the radiation of a nearby hot radiation source. We show that the hydrogen emission lines emerge from a narrow transition zone where hydrogen changes from ionized to neutral. In this region the Balmer lines are optically thick, and their profiles crucially depend on the magnitude of optical thickness which in turn, depends on the velocity gradient within that region. Balmer decrements of the model calculations depend on the densities in the recombination zone of the radiatively ionized wind. We find a large variety of complex line profiles, that in some cases could be mistaken for accretion disk profiles. The profiles depend on the velocity law in the formation zone at sub-sonic velocities, but contrary to expectation, the profiles do not reflect the terminal velocity of the wind. The central part of our model profiles compare well with the observed profile of the eclipsing binary SY Mus at maximum light.