3 Dielectronic recombination rate

Burgess (1965) pointed out the relevance of the dielectronic recombination (hereafter DR) process especially in the temperature region of maximum ion abundance. The collected dielectronic recombination rates are calculated in the zero electron density limit, which is a valid approximation for most of the astrophysical plasmas.

In the following, as in AR, we discuss the dielectronic recombination rates by isosequence and we explicitly declare when we have chosen different data from them.

All the available data were fitted, when needed, with the following formula:  

$$\alpha_{\mbox d}= {1\over T^{3/2}}\sum_{j=1}^{4}c_{j}\exp\left(-{E_{i} \over T}\right) \ \ \ [{\mbox{cm}}^{3}/\mbox{s}],$$ (7)

where T and E_i are given in eV and c_i in ${\mbox{cm}}^{3} ~{\mbox {s}}^{-1}$.The coefficients c_i and E_i are given in Table 1.

H-like - From C to Ni we used the data of Mattioli 1988(hereafter M) and Karim & Bhalla (1988)which for the same elements are in good agreement. For the elements not explicitly calculated we interpolated the DR rates along the isosequence. For Be IV and B V we used the data of Pindzola & Badnell (1992) that are a factor 2 less then those from previous calculations of Shore (1969) with the corrected values by Burgess & Tworkowski (1976). Moreover we divided by a factor 2 also the DR coefficients for HeII and Li III by Shore (1969).

He-like - We fitted with our formula the calculations of Chen (1986a) that are in very good agreement with Nielsen (1986) and Karim & Bhalla (1989). For C V we adopt Chen's (1988b) calculation in which the Coster-Kroning transitions are taken into account that are negligible for higher Z elements. For BeIII and B IV we adopted Pindzola & Badnell (1992).

Li-like - We adopt the DR calculations of Chen (1991). The total DR rate coefficient for the 11 lithium-like ions were calculated using the distorted wave technique and the multi-configuration Dirac-Fock method. The discrepancies with non-relativistic calculations of Roszman (1987) are more relevant for highly charged medium- and high-Z ions. For the other ions we have interpolated along the isosequence. For BeII and B III we have adopted the DR calculations of Pindzola & Badnell (1992).

Be-like - We adopt Badnell's (1987) calculations which for high Z agree well with Chen & Crasemann (1988). For O V and B II we use, respectively, the data of Badnell & Pindzola (1989) and Pindzola & Badnell (1992).

B-like - Recent calculations of Nahar (1995) and errata from Nahar (1996a), in the framework of a unified treatment of electron-ion recombination, show good agreement with low-T DR rates by Nussbaumer & Storey (1983), and high-T DR rates by Jacobs et al. (1979) for the ions from C to Al, and for Si and S. As for Fe, we use the data of AR. For most of the other ions calculations from SV, LM and M are available. For the other ions we used the Burgess (1965) general formula, corrected by Merts et al. (1976) (hereafter Burgess-Merts formula, BM), using the most recent data for oscillator strengths and energy transitions.

Iron is the most investigated element so that in the following we always adopt the criteria, except when more recent calculations are available, to normalize the DR calculation rates to the Fe calculations of AR. These criteria can be also justified by the fact that, as pointed out in LM (1991) and Hahn (1991), most of the coefficients show a regular trend along the same isosequence.

C-like - N-like - From Ar to Ni we followed the same procedure described for B-like ions. For the other elements, except for O III for which we used the data from Badnell & Pindzola (1989), we used the data of Jacobs et al. (1977a,b, 1979, 1980) and LM (1991).

O-like - F-like - From Ar to Ni we adopt the recent calculations of Dasgupta & Whitney (1990, 1994) that for F-like ions are in good agreement with Chen (1988a) calculations. For the other elements we used the calculations of SV.

Ne-like - We use the calculations of Chen (1986b), Romanik (1988)and for Na II the calculation of SV. For P VI and Cl VIII we adopted the data of LM(1991) multiplied by a factor 4 to take into to account the results of Romanik (1988) and Chen (1986b) for adjacient ions.

Na-like - Mg-like - As it has been indicated by Zhdanov (1982), Dube & LaGatutta (1987), Dube et al. (1985), at high temperature the inner shell transitions of the form $\rm 2s-3d$ become important, and this effect is more important for medium and high-Z elements. We follow the procedure of Mattioli (1988) that for Fe is in very good agreement with AR. For the other elements we adopt the calculations of Jacobs and LM taking into account the results obtained for Mg II and Si IV from LaGattuta & Hahn (1982, 1984). For S VI we adopt the data of Badnell (1991).

Al-like - to Co-like - For all these isosequences, except for Fe, detailed or recent calculations are not available so that we used data from SV, LM, M as well as the general BM formula. Up to the Mn-like isosequence we renormalize the results to the work of AR.

We mention that recently new calculations have been made on the recombination of Fe II (Nahar et al. 1997) and Fe IV (Nahar 1996b). In the case of Fe II the DR rate is a factor 2 above the AR curve whereas for Fe IV the Nahar results are an order of magnitude below the AR curve although Nahar claims a $10-30\%$ accuracy. We do not know the cause of the discrepancies but for consistency we prefer to use the AR results. In the last years Teng et al. (1994a-d, 1996) also applied fitting formula for several isoelectronic sequence i.e. H, He, Li, F and Ne. In general our results are within a 10% in agreement with those calculations essentially because we have fitted and/or interpolated the same data, but in some case their fitting formula yield divergences in the dielectronic rates.