With the advent of the present and future spatial X-ray missions, it becomes crucial to model correctly the line spectrum of X-ray emitting media such as the photoionized plasma observed in the central regions of Active Galactic Nuclei (AGN), or in X-ray binaries. We have built a photoionization code, Titan, solving the transfer of a thousand lines and of the continuum with the "Accelerated Lambda Iteration" method, which is one of the most efficient and at the same time the most reliable for line transfer. In all other photoionization codes the line intensities are computed with the so-called "escape probability formalism", used in its simplest approximation. In a previous paper (Dumont et at. 2003), it was shown that this approximation leads to a wrong estimation of the emitted X-ray line intensities, especially in the soft X-ray range. The errors can exceed one order of magnitude in the case of thick media (Thomson thickness of the order of unity). In the present paper, we show that it also happens, but for different reasons, in the case of moderately thin media (Thomson thickness of 0.001 to 0.1), characteristic of the Warm Absorber in Seyfert 1 or of the X-ray emitting medium in Seyfert 2. Typically, the errors on the line fluxes and line ratios are of the order of 30% for a column density of 10(20) cm(-2), and a factor five for a column density of 10(23) cm(-2), in conditions giving rise to the spectra observed in these objects. We explain why this problem is less acute in cooler media, like the Broad Line Region of AGN. We show some examples of X-ray spectra appropriate for Seyfert 2 and for the Warm Absorber of Seyfert 1. We conclude that though it is quite important to introduce numerous accurate X-ray data in photoionization codes, it should be accompanied by more elaborate methods than escape probability approximations to solve the line transfer.
