3. Wavelengths and oscillator strengths

The wavelengths in air, , and the oscillator strengths, f, for the nd-n'f, nf-n'g, ng-n'h, nh-n'i (n = 3-6, n' = 4-30) transitions in C II, the nf-n'g, ng-n'h, nh-n'i, ni-n'k (n = 4-7, n' = 5-30) transitions in C III and the nd-n'f, nf-n'g, ng-n'h, nh-n'i, ni-n'k (n= 5-10, n' = 6-30) transitions in C IV are presented in Tables 6, 7 and 8 respectively in the 400-1100 nm spectral region. The wavelengths were deduced from the l 3 (C II), l 4 (C III) and l 3 (C IV) term energies reported in Tables 3 (click here)-5 (click here) and from the experimental energy levels published by Bashkin & Stoner (1975) and Tunklev et al. (1997) for smaller values of the l-quantum number. From the estimated mean uncertainty affecting the term energies obtained in the present work (see Sect. 2.3), the predicted wavelengths in Tables 6-8 should be accurate to within a few 0.01 nm.

For the calculation of oscillator strengths, we used the relativistic Hartree-Fock (HFR) method with the help of the codes written by Cowan (1981). These computations were performed using the following sets of configurations:

C II: 1s²2s²nd (n = 3-6) + 1s²2s²ng (n = 5-30) + 1s²2s²ni (n = 7-30) + 1s²2s2p² + 1s²2s2p3p + 1s²2s2p4p + 1s²2s2p4f (even parity) and 1s²2s²nf (n = 4-30) + 1s²2s²nh (n = 6-30) + 1s²2s2p3d + 1s²2s2p4d (odd parity);

C III: 1s²2snf (n = 4-7) + 1s²2snh (n = 6-30) + 1s²2snk (n = 8-30) + 1s²2p3d + 1s²2p4d (odd parity) and 1s²2sng (n = 5-30) + 1s²2sni (n = 7-30) + 1s²2p4f (even parity);

C IV: 1s²nd (n = 3-10) + 1s²ng (n = 5-30) + 1s²ni (n = 7-30) (even parity) and 1s²nf (n = 4-30) + 1s²nh (n = 6-30) + 1s²nk (n = 8-30) (odd parity).

Scaling factors (0.90) were introduced for the Slater integrals while the ab initio spin-orbit parameters, calculated by the Blume-Watson method, were retained. Moreover, the average energies were adjusted using the experimental energy levels (Bashkin & Stoner 1975; Tunklev et al. 1997) and predicted values reported in Tables 3-5. Comparison with previously published oscillator strengths is possible only for transitions involving relatively small n-values. As an example, within the framework of the Opacity Project (OP), f-values for nl-n'l' transitions (n, n' 10, l, l' 4) were calculated by Fernley et al. (1997) and Tully et al. (1990) in the cases of C II and C III respectively and compiled in the TOPBASE atomic database (Cunto et al. 1993) at the CDS (http://cdsweb.u-strasbg.fr/OP.html). These OP oscillator strengths are compared in Fig. 1 (click here) with the results obtained in the present work. In general, the agreement between both sets of oscillator strengths is within a few percent if we except the 5f-7g, 6f-8g, 6f-9g, 6f-10g singlet and 5f-8g triplet transitions of C III for which the discrepancies reach 25%. An exception occurs also for the C III 5f ¹Fg ¹G line for which the f-value obtained in the present work is one order of magnitude smaller than the OP result. However, for this particular transition, our calculated line strength is affected by strong destructive interference effects (cancellation effects) indicating that the corresponding f-value may be expected to show a large error.

  
Figure 1: Comparison between the oscillator strengths (log gf) obtained in the present work and the Opacity Project results compiled in the TOPBASE atomic database (Cunto et al. 1993) for the nd-n'f, nf-n'g (n = 3-5, n' = 4-10) transitions of C II () and the nf-n'g (n = 4-7, n' = 5-10) transitions of C III ()