3 Results and discussion

Effective collision strengths are calculated for transitions from the ground 1s^{2 1}S₀ state to all fine-structure levels of the excited states of 1s2$\ell$ ($\ell=0,1$) and 1s3$\ell$ ($\ell=0,1,2$)configurations. They are obtained for a temperature range $T_{\rm e}=(1 \ 10^6 - 1 \ 10^8)$ K. This is the range of the largest fractional abundance of SXV, if they are in ionization equilibrium (Arnaud & Rothenflug [1985]). The resulting effective collision strengths are analytically fitted to the form  

$${\mit\Upsilon}(i \rightarrow f) = \sum_{j=1}^5 a_j(\log(T_{\rm e}/{\mbox {K}}))^{j-1}\,.$$ (7)

The fitting coefficients a_j are presented in Table 2. Equation (7) with these coefficients reproduces the present effective collision strengths within 2%. It should be noted here that fitting is valid only in the temperature range $6.0\leq\log(T_{\rm e}/{\mbox {K}})~\leq 8.0$.

  

Table 2: The coefficients a_j for representing effective collision strengths in the Eq. (7)

 

Figure 1: Effective collision strengths of the $\rm 1s^2~^1S_0-1s2p^3P_0$ excitation for SXV as a function of temperature (in K). $\protect\rule[1pt]{15pt}{1pt}$ present, - - - - Keenan et al. ([1987]), $\bigcirc$ Zhang & Sampson ([1987])

 

Figure 2: Effective collision strengths of the $\rm 1s^2~^1S_0-1s2p^3P_1$ excitation for SXV as a function of temperature (in K). $\protect\rule[1pt]{15pt}{1pt}$ present, - - - - Keenan et al. ([1987]), $\bigcirc$ Zhang & Sampson ([1987])

 

Figure 3: Effective collision strengths of the $\rm 1s^2~^1S_0-1s2p^3P_2$excitation for SXV as a function of temperature (in K). $\protect\protect\rule[1pt]{15pt}{1pt}$ present, - - - - Keenan et al. ([1987]), $\protect\bigcirc$ Zhang & Sampson ([1987]), $\protect\times$ Norrington et al. ([1998])

 

Figure 4: Effective collision strengths of the $\rm 1s^2~^1S_0 - 1s3p ^3P_0$ excitation for SXV as a function of temperature (in K). $\protect\rule[1pt]{15pt}{1pt}$present, - - - - Keenan et al. ([1987])

 

Figure 5: Effective collision strengths of the $\rm 1s^2~^1S_0 - 1s3p ^3P_1$ excitation for SXV as a function of temperature (in K). $\protect\rule[1pt]{15pt}{1pt}$ present, - - - - Keenan et al. ([1987])

 

Figure 6: Effective collision strengths of the $\rm 1s^2~^1S_0 - 1s3p ^3P_2$ excitation for SXV as a function of temperature (in K). $\protect\rule[1pt]{15pt}{1pt}$ present, - - - - Keenan et al. ([1987])

As mentioned in the Introduction two groups (Zhang & Sampson [1987]; Keenan et al. [1987]) reported effective collision strengths for SXV. A comparison is made between the present result and the previous data. Figures 1 - 6 show the comparison for the excitation of the levels 1s2p ³P$_{\!J}$ and 1s3p ³P$_{\!J}$ with J=0,1,2. For other transitions the comparison is essentially the same as shown in the previous paper (Nakazaki et al. [1993]) and not repeated here. From the figures, it is found that the values of Zhang & Sampson ([1987]) are in good agreement with the present ones. Zhang & Sampson ([1987]), however, reported their result only for the excitation to n=2 levels. The result of Keenan et al. ([1987]) agrees with that of the present calculation for all the transitions but the excitations to 1s3s ¹S₀ and 1s3p ³P_J (J=0,1,2) levels. The difference in the latter transitions may be ascribed to an inadequate number of states included in the R-matrix calculation which they used for their interpolation. All the R-matrix calculations include 11 lowest LS states, while the present calculation takes into account 19 LS states. Note that Keenan et al. ([1987]) reported no result for the excitation of the levels of 1s3d configuration.

In Fig. 3, we show a typical comparison between the present results and those of Dirac R-matrix calculation by Norrington et al. ([1998]). Figure 3 shows that the present result agrees very well with the fully-relativistic calculation except in the region of low temperature. Comparisons for other transitions (not shown here) have the same conclusion. This confirms the validity of the present method of the calculation of fine-structure transitions. In the region of low temperature, a small difference is seen between the two results. This may be ascribed to the difference in the resonance structure in the two sets of collision strength. Norrington et al. ([1998]) took account of only the states up to n=3. The present calculation includes the states with n=4. As for the resonance structure, therefore, the present calculation should be more accurate.

In conclusion the present paper presents the rate coefficients for excitation from the ground 1s^{2 1}S₀ state to all the fine-structure levels of 1s2$\ell$ ($\ell=0,1$) and 1s3$\ell$ ($\ell=0,1,2$) configurations of SXV. In this sense the present calculation gives the most comprehensive data on the rate coefficients for the electron impact excitation of SXV. The result may be of significance in application, e.g. to high temperature plasma in astronomy or laboratory.