4 Discussion

We shall not present here detailed comparisons with availaible experimental results, since these may be found in Stehlé (1994a) and (1996a) for individual lines, and in Stehlé & Jacquemot (1993), for the comparison between the Balmer series emissivity obtained with MMM profiles and the experimental results. The examples presented in these papers show that the line shape computation is accurate to better than 10$\%$. It differs from one line to another and from the line center to the line wings. The MMM approach slightly underestimates the ion dynamics effects in the line centres at low densities. Moreover, the description of short range interactions must be improved in the far wings or at large densities.

Spontaneous emission and fine structure effects are not included in the calculation. For a given electronic density and temperature, these effects are more important for the lowest lines of the series. The broadening effect of spontaneous decay can to a good approximation be introduced through a convolution with a Lorentz profile. Fine structure effects can also be qualitatively introduced through a convolution with the corresponding Dirac structure spectrum.

Broadening due to the interaction with neutral hydrogen atoms (or other atoms), leading to Van der Waals and resonance broadening are not included here, but could be by convolving the corresponding profile with the Stark profile.

To illustrate the new possibilities offered by the present extended tabulations, we calculated the emissivity of two different plasmas near the Balmer series limit, assuming that both are in Local Thermodynamical Equilibrium, and using the method described in Stehlé & Jacquemot (1993). These two cases are first, an hydrogen plasma with an electronic density equal to 10¹³ cm^-3 and a temperature of 10000 K (solar chromospheric plasma) and secondly 4.5 10¹⁴ cm^-3 and 44000 K (Figs. 2, 3).

The first case (Fig. 2) shows a large number of resolved lines. Each of them could provide information about the plasma conditions. The diagnostics will be more tightly constrained by using a part of the spectrum including several lines.

Figure 2: LTE emissivity of an hydrogen plasma at $N_{\rm e}$ = 1013 cm-3 and T = 10000 K

The same conclusions can be drawn in the second example (Tokamak case). The conditions have been chosen in order to reproduce the experimental line widths of the 2-8, 2-9, 2-10 and 2-11transitions (i.e. H8, H9, H10 and H11) given by Welch et al. (1995). After deconvoltion from experimental broadening, these authors obtain full half widths of 4.7, 5.9, 7.5 and 9.6 Å respectively. We were able to model 4.6, 5.8, 7.5 and 9.4 Å for parameters of 4.5 10¹⁴ cm^-3 and 44000 K. The spectrum (Fig. 3) corresponds qualitatively with the experimental ones. The H11 transition is partly merged with the H12 ones, which makes it more difficult to determine the half width. Our determination is only indicative, and ignores the fact that the experimental plasma is a plasma of deuterium instead of hydrogen. Thus Doppler broadening is smaller in the experiment (FWHM of the order of 0.3 Å for deuterium at 3900 Åfor 0.4 Å for hydrogen). Nethertheless it is interesting to note that our calculation gives a smaller electronic density than those obtained by these authors. This point has been underlined by Welch et al. (1997).

Figure 3: LTE emissivity of an hydrogen plasma at $N_{\rm e}$ = 4.5 1014 cm-3 and T = 44000 K

Acknowledgements

R.H. acknowledges the support of the European Network Human Capital and Mobility ERBCHRXTCT 930377. Most of the computations have been performed on the Cray C94 at IDRIS, France, whith the help of J. Chergui for the implementation of the codes. The authors are also grateful to the referee for his constructive comments.