1 Introduction

Many non-LTE computations have been performed over more than thirty years in order to investigate radiative transfer effects and line formation in solar prominences. When one considers simple one-dimensional homogeneous and static models the first paper related to the helium spectrum in quiescent solar prominences which made satisfactory comparisons with observations is from Heasley et al. (1974, hereafter HMP). These authors removed several restrictive assumptions that were made before (see references in their paper). For example they used a multi-ion helium model atom with 20 energy levels and treated the radiative transfer problems in detail in the resonance lines and continua for the neutral and singly ionized helium. It was the first paper dealing with both hydrogen and helium spectra out of local thermodynamic equilibrium (NLTE). Their prominence models consisted of isobaric and isothermal slabs. Then a series of four papers with the same approach was published in the following years (Heasley & Mihalas 1976; Heasley & Milkey 1976, 1978, 1983. These authors used detailed atomic models for both hydrogen and helium. However their work suffered from some limitations such as the assumption of complete redistribution (CRD) in line formation, or the use of frequency-independent incident intensities for each line. They presented intensity ratios, integrated intensities and optical depths for several hydrogen and helium lines but no detailed emergent profile was shown.

Yakovkin et al. (1982) solved the integral diffusion equations for selected neutral helium levels with quantum number $n \leq 4$ under low-temperature plasma conditions and found that the excitation and ionization of helium are maximum near the boundaries. Other authors have considered different helium lines in different geometries in order to compare with specific observations. Morozhenko (1984) investigated the excitation of singlet helium levels in the frame of homogeneous and filamentary prominences. In a recent paper, Li et al. (2000) computed the He I $\lambda$5876 Å (D3) emission line profile using the two-cloud model and taking into account the multiplet. A work has been undertaken (Kucera et al. 1998; Andretta et al. 1999) in order to derive the neutral hydrogen column density and ionization state of helium from observations of hydrogen and helium continua.

In this paper we compute the essential parts of the neutral and ionized helium spectrum emitted by a model quiescent solar prominence. We use a plane-parallel slab standing vertically above the solar surface to represent the prominence. Computations allow departure from LTE for all atomic levels and the radiative transfer equations are solved for all lines and continua. Partial redistribution in frequency is included in the calculations of resonance lines. This represents a new step compared to the above-cited papers, towards a more physical approach. We obtain several radiative quantities related to the emergent spectrum. An important point is that we also get the emergent line profiles. This can be particularly useful for the interpretation of prominence spectra, especially when one observes optically thick lines such as the resonance lines of neutral (He I $\lambda\lambda$584 and 537 Å) or ionized helium (He II $\lambda$304 Å) from which the derivation of the plasma physical parameters is not straightforward.

We explain in detail the approch used for the computations in Sect. 2. Then computed models similar to those of Heasley and co-workers are presented in Sect. 3 in order to compare them with previous theoretical results of HMP and Heasley & Milkey (1978, hereafter HM3). The influence of the physical parameters of the models on the helium states mean populations and on the emerging spectrum is studied (Sect. 4) and some relations between helium line intensities and also the He I $\lambda$5876 Å (D3) versus H I $\lambda$4863 Å (H$\beta$) relation are considered in Sect. 5. In the conclusion, we indicate the future developments of this work.