5 Results from extended calculations

Using the above-mentioned atomic data, we have calculated the line intensity ratios R and G for C V, N VI, O VII, Ne IX, Mg XI, and Si XIII The wavelengths of these three (four) lines for each He-like ion treated in this paper are reported in Table 1.

All the relevant processes detailed in Sects. 3 and 4 between the seven levels are taken into account (full resolution): radiative de-excitation, collisional electronic excitation and de-excitation, radiative and dielectronic recombination, photo-excitation and induced emission (between ³S₁ and ³P levels).

We considered a broad range of densities ($n_{\rm e}$) and radiation temperatures ( $T_{\rm rad}$) calculated for photo-excitation between the ³S level and the ³P levels and a number of electron temperatures ($T_{\rm e}$). As well, we considered different values of the dilution factor of the radiation field (W) which could be used either for hot late-type stars or O, B stars.

We display the $G(T_{\rm e})$ line intensity ratios, from Tables 4 to 9, for the six ions, for five values of electron temperature ($T_{\rm e}$) including the temperature of maximum line formation for the He-like lines (cf. Mewe et al. 1985); and for two or more values of the radiation temperature ( $T_{\rm rad}$), and several values of $n_{\rm e}$. As one can note the ratio G is as expected to be sensitive to $T_{\rm e}$, while it is almost insensitive to the exact values of $n_{\rm e}$ and  $T_{\rm rad}$. The resonance line becomes sensitive at high density due to the depopulation of the 1s2s¹S₀ level to the 1s2p¹P₁ level (see Gabriel & Jordan 1972). Since the sum z+(x+y) is a constant or almost constant, the value of G is independent of the exact value of the dilution factor (W). Here the calculations were done for dilution factor W=1/2.

Finally, we display the $R(n_{\rm e})$ line intensity ratios for the six ions, in Tables 10 to 69, for the same values of electron temperature ($T_{\rm e}$) and much more values of radiation temperature ( $T_{\rm rad}$), and for three values of the dilution factor of the radiation field W=0.5, 0.1, 0.01.

Since as said previously in Sect. 4.3, the contribution of the blended dielectronic satellite lines depends on the spectral resolution, we give the values of R and G for Ne IX, Mg XI, and Si XIII, for four specific values of spectral resolutions (FWHM): RGS-1 at the first order (i.e. $\Delta \lambda=0.073$, 0.075 and 0.078 Å  for Ne IX, Mg XI and Si XIII respectively), LETGS (i.e. $\Delta \lambda=0.05$ Å), HETGS-MEG (i.e. $\Delta \lambda=0.023$ Å), and HETGS-HEG (i.e. $\Delta \lambda=0.012$ Å). In the cases where the differences (${<}1\%$) are negligible between two or more spectral resolutions, we display the results together (e.g. RGS and LETGS).