3 Results and discussion

Effective collision strengths obtained for all the transitions among 3s, 3p, 3d, 4s, 4p, 4d and 4f states are given in Tables 3-7 for Al III, Si IV, S VI, Ar VIII and Ca X, respectively. The temperature range considered is around the temperature (T$_{\rm max}$) of maximum fractional abundance in ionization equilibrium of the respective species. According to the calculation by Arnaud & Rothenflug (1985), Log T$_{\rm max}$ for Al III, Si IV, S VI, Ar VIII and Ca X are, respectively, 4.6, 4.8, 5.3, 5.6 and 5.8.

For Al III, Si IV and S VI, Dufton & Kingston (1987) reported their rate coefficients for the transitions among 3s, 3p, 3d, 4s and 4p. They took account of only 5-states (3s, 3p, 3d, 4s and 4p) in their calculation. In principle, the present 11-state calculation should be much better than theirs, especially for the n = 3-4 transition. Figure 1 shows a typical example (the 3s-4p) of the comparison between their result and the present one. There is a discrepancy of up to a factor of two. Mitroy & Norcross (1989) also obtained the rate coefficient for Al III. They used five atomic states and four pseudostates ($\overline{\mbox {4d}}$, $\overline{\mbox{4f}}$, $\overline{\mbox{5s}}$ and $\overline{\mbox{5p}}$)in the close-coupling approximation. Their results are much smaller than those of present calculation for the 3s-4p transition, whereas for the n = 3-3 transitions the agreement between the two calculations is good within 10%. It is seen that the effect of including n=5 states in the present calculation is important. Keenan et al. (1996) determined the rate coefficients for Na-like ions, based on the interpolation of results in the R-matrix calculations available for some particular Na-like species. When compared with the present calculation, their data in some cases show a large disagreement. Figure 2 shows one example. The procedure taken by Keenan et al. (1996) implicitly assumes a scaling of the effective collision strengths along the isoelectronic sequence.

  

Figure 1: Effective collision strengths of the 3s-4p excitation for Al III, Si IV and S VI as a function of temperature (in K). Al III: -- present, $\bigcirc$ Dufton & Kingston (1987), $\bigtriangleup$ Mitroy & Norcross (1989), Si IV: - - - present, $\bullet$ Dufton & Kingston (1987), S VI: - - - - present, $\circledcirc$ Dufton & Kingston (1987)

  

Figure 2: Effective collision strengths of the 3s-4s excitation for Ar VIII and Ca X as a function of temperature (in K). Ar VIII: --- present, - $\cdot$ - Keenan et al. (1996), Ca X: - - - present, - $\cdot$ $\cdot$ - Keenan et al. (1996)

  

Figure 3: Cross section for the 3s-3p excitation of Si IV as a function of electron energy (in Ryd). The excitation energy of this transition is 0.6524 Ryd. --- present, $\bigcirc$ the experiment of Wåhlin et al. (1991)

  

Table 3: Effective collision strengths for Al III

  

Table 4: Effective collision strengths for Si IV

  

Table 5: Effective collision strengths for S VI

  

Table 6: Effective collision strengths for Ar VIII

  

Table 7: Effective collision strengths for Ca X

There is no experimental determination of the rate coefficients for the Na-like ions considered here. Experimental data are available, however, for the excitation cross sections of Si IV (Wåhlin et al. 1991) and Ar VIII (Guo et al. 1993). In Fig. 3, we compare the present cross section for the 3s-3p excitation of Si IV with the corresponding experimental values. No adjustment has been done of the absolute magnitude in both the cross section data. In this sense, the agreement is quite good. For Ar VIII, a similar agreement is obtained between the present calculation and the experiment (see Paper I, where a comparison of the cross section for Ar VIII with several other calculations has also been made). Since no experimental data are available to test the resonance structure in the cross sections for the present ions, it is difficult to critically assess the accuracy of the present rate coefficients. From other R-matrix calculations for other ions, however, the values given in Tables 3-7 should be reliable for practical applications.

Acknowledgements

The R-matrix code used here has been kindly provided to the present authors by Dr. K.A. Berrington under the UK-Japan collaboration program on the theory of atomic collision. The present work was supported by a Grant-in-Aid for Scientific Research on Priority Area "Atomic Physics of Multicharged Ions'' from the Ministry of Education, Science and Culture of Japan.