4 Collision rates

The effective collision strength $\mit\Upsilon(T)$ was obtained from the calculated collision strengths as described in Hummer et al. (1993) and discussed in IP XI.

  

Figure 5: Thermally averaged collision strengths $\mit\Upsilon$ for excitation of the ground state fine-structure line in P  III, S  IV and Cl  V

The collisional de-excitation rate coeffficient q(T) is related to $\mit\Upsilon(T)$ by

$$q = {{8.63\ 10^{-6}\mit\Upsilon}\over{\omega T^{{{1}\over{2}}}}} \ \ \ {\rm cm}^3\ {\rm s}^{-1},$$ (1)

where $\omega$ is the statistical weight of the upper state and T is the electron temperature in K. Our values for $\mit\Upsilon(T)$ for the three ions are given in Table 5 and in Fig. 5.

 

Table 5: Effective collision strengths for excitation of the ²P$^{\rm o}$_1/2 - ²P$^{\rm o}$_3/2 fine-structure lines in P  III, S  IV and Cl  V

4.1 Comparison with earlier calculations.

The present results for S IV differ significantly from those of Johnson et al. (1986), that were also obtained from a close-coupling calculation. In order to understand the cause of the discrepancy we simulated their calculation by cutting off our CC expansion at six target terms. We found that as a result the resonances were all shifted to higher energies, particularly the broad and tall feature between .03 and .1 Ryd. Analysis of this feature shows that it is chiefly made up of resonances with configurations 3s3p²nl. Johnson et al. had included all parent terms to these resonances and correlation configurations in their calculation, but they omitted the channel coupling effects to higher terms. As a result the resonance positions were shifted and the overlap between the Maxwell velocity distribution function at low temperatures and the collision strength is very much smaller.

  

Figure 6: Thermally averaged collision strengths for excitation of the ground state fine-structure line in S IV. Full line: 21 term CC calculation, dotted line: 6 term CC calculation, triangles: results of Johnson et al. (1986)

Figure 6 shows a comparison of our present results including 21 target terms with the results obtained when the CC expansion is cut short at six terms and with the results of Johnson et al. (1986) who included the same six terms. Our six term results agree with those of Johnson et al., although they used different CI and target orbitals. It is clear that the migration of the resonances to higher energies effected by the omission of channel coupling effects causes the discrepancy.