We present a study of the modeling of prominence slabs. Our models consider a collection of threads in energy balance with the surrounding corona and submitted to illumination from the underlying chromospheric layers. The models are isobaric, but temperature variations within the slab occur as a result of the energy balance constraint. We compute the non-LTE radiative transfer for a hydrogen model atom with five bound levels. The ionization is treated consistently with non-LTE radiative transfer and ambipolar diffusion (AD). The AD also affects the energy balance because of the transport of hydrogen ionization energy. We compute the emitted Lyman and Balmer spectra of our models and compare them with the observations. We find that the consideration of ambipolar diffusion increases the emission in Lyβ (and higher members of the Lyman series) as compared with the other lines. This contrasts with isothermal models that yield Lyβ emission that is too low. However, the AD models give excessive Lyβ emission, viz., too small a Lyα/Lyβ ratio compared with observations. We also compute models that include a cold core in which mechanical energy is dissipated. These models increase the Hα/Lyα ratio to values similar to the observed values for a moderate number of threads along the line of sight. However, these models still give too low a Lyα/Lyβ ratio. We conclude that the prominence observations in Lyβ show intensities that are not compatible with a steady state, field-aligned interface between the cold prominence and the hot coronal material. Also, the observations are not consistent with an isothermal slab isolated from the corona. Consequently, we suggest that at the prominence-corona interface, there is a substantial angle between the temperature gradient and the field, although this angle is significantly smaller than 90°.
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