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Up: Recombination coefficients for C lines

4 Results and discussion

The population structure of C + has been calculated for the electron temperatures in the range from 500 K to $20\,000$ K and for electron densities below 106 cm-3. Calculations for higher densities were also performed, including a full treatment of electron collisional processes between excited states, but this will be the subject of a subsequent paper. In the present work, we also use a full treatment of collisional processes but at the relatively low densities considered here, there is no significant difference between the full treatment and the more approximate treatment described by Storey ([1994]) and Kisielius et al. ([1998]).


   
Table 3: Effective recombination coefficients [10-14 cm3 s-1] for temperature range $T_{e} = 3500 - 20\,000$ K. Electron density Ne = 104 [cm-3]. Minimum recombination coefficient $\alpha _{min} = 3.0$
          Te [1000 K]
Transition $\lambda$[nm] Case 3.5 5.0 7.5 10.0 12.5 15.0 20.0
8h (2H$^{\rm o}$) - 6g (2G$^{\rm e}$) 1866.2 A 3.52+0 2.44+0 1.57+0 1.13+0 8.71-1 6.99-1 4.90-1
8h (2H$^{\rm o}$) - 5g (2G$^{\rm e}$) 931.4 A 3.19+0 2.22+0 1.43+0 1.03+0 7.90-1 6.34-1 4.44-1
7h (2H$^{\rm o}$) - 6g (2G$^{\rm e}$) 3068.8 A 8.18+0 5.58+0 3.52+0 2.51+0 1.91+0 1.52+0 1.05+0
7h (2H$^{\rm o}$) - 5g (2G$^{\rm e}$) 1157.9 A 7.82+0 5.33+0 3.37+0 2.39+0 1.82+0 1.45+0 1.01+0
7g (2G$^{\rm e}$) - 5f (2F$^{\rm o}$) 1144.4 A 4.23+0 3.05+0 2.06+0 1.53+0 1.21+0 9.97-1 7.80-1
7g (2G$^{\rm e}$) - 4f (2F$^{\rm o}$) 534.2 A 5.07+0 3.66+0 2.47+0 1.84+0 1.45+0 1.20+0 9.35-1
7f (2F$^{\rm o}$) - 3d (2D$^{\rm e}$) 237.5 A 3.28+0 2.50+0 1.81+0 1.42+0 1.17+0 1.02+0 9.61-1
        B 3.33+0 2.55+0 1.85+0 1.45+0 1.20+0 1.04+0 9.84-1
7d (2D$^{\rm e}$) - 3p (2P$^{\rm o}$) 179.6 A 3.82-1 3.16-1 2.49-1 2.08-1 1.81-1 1.64-1 1.55-1
        B 3.93+0 3.25+0 2.56+0 2.14+0 1.86+0 1.68+0 1.59+0
6h (2H$^{\rm o}$) - 5g (2G$^{\rm e}$) 1851.6 A 3.03+1 2.00+1 1.22+1 8.53+0 6.40+0 5.04+0 3.44+0
6g (2G$^{\rm e}$) - 5f (2F$^{\rm o}$) 1819.9 A 9.74+0 6.88+0 4.53+0 3.32+0 2.59+0 2.12+0 1.65+0
6g (2G$^{\rm e}$) - 4f (2F$^{\rm o}$) 646.2 A 1.26+1 8.88+0 5.85+0 4.29+0 3.35+0 2.74+0 2.13+0
6f (2F$^{\rm o}$) - 4d (2D$^{\rm e}$) 615.1 A 3.97+0 2.99+0 2.14+0 1.66+0 1.36+0 1.17+0 1.08+0
        B 4.03+0 3.05+0 2.18+0 1.69+0 1.39+0 1.20+0 1.11+0
6f (2F$^{\rm o}$) - 3d (2D$^{\rm e}$) 257.5 A 6.63+0 5.01+0 3.57+0 2.78+0 2.28+0 1.96+0 1.81+0
        B 6.74+0 5.09+0 3.64+0 2.83+0 2.32+0 2.01+0 1.86+0
6d (2D$^{\rm e}$) - 3p (2P$^{\rm o}$) 191.0 A 5.56-1 4.50-1 3.48-1 2.88-1 2.48-1 2.21-1 2.05-1
        B 6.41+0 5.18+0 4.01+0 3.32+0 2.85+0 2.55+0 2.37+0
5g (2G$^{\rm e}$) - 4f (2F$^{\rm o}$) 990.3 A 5.07+1 3.44+1 2.17+1 1.55+1 1.18+1 9.56+0 7.31+0
5f (2F$^{\rm o}$) - 4d (2D$^{\rm e}$) 923.0 A 9.16+0 6.76+0 4.70+0 3.58+0 2.90+0 2.47+0 2.21+0
        B 9.28+0 6.86+0 4.78+0 3.65+0 2.95+0 2.52+0 2.25+0
5f (2F$^{\rm o}$) - 3d (2D$^{\rm e}$) 299.3 A 1.76+1 1.30+1 9.02+0 6.88+0 5.56+0 4.74+0 4.23+0
        B 1.78+1 1.32+1 9.16+0 7.00+0 5.66+0 4.83+0 4.33+0
5d (2D$^{\rm e}$) - 3p (2P$^{\rm o}$) 213.8 A 9.07-1 7.24-1 5.54-1 4.54-1 3.88-1 3.46-1 3.18-1
        B 1.25+1 9.96+0 7.62+0 6.25+0 5.34+0 4.76+0 4.39+0
4f (2F$^{\rm o}$) - 3d (2D$^{\rm e}$) 426.7 A 8.06+1 5.65+1 3.72+1 2.73+1 2.14+1 1.79+1 1.51+1
        B 8.12+1 5.70+1 3.75+1 2.76+1 2.17+1 1.81+1 1.53+1
4f (2F$^{\rm o}$) - 2s2p2  (2D$^{\rm e}$) 106.4 A 5.22+0 3.66+0 2.40+0 1.76+0 1.39+0 1.16+0 9.76-1
        B 5.26+0 3.69+0 2.43+0 1.79+0 1.40+0 1.17+0 9.91-1
4d (2D$^{\rm e}$) - 4p (2P$^{\rm o}$) 1784.7 A 2.95-1 2.30-1 1.71-1 1.37-1 1.16-1 1.03-1 9.58-2
        B 6.52+0 5.09+0 3.79+0 3.05+0 2.57+0 2.28+0 2.13+0
4d (2D$^{\rm e}$) - 3p (2P$^{\rm o}$) 274.7 A 1.37+0 1.07+0 7.94-1 6.38-1 5.38-1 4.77-1 4.45-1
        B 3.03+1 2.37+1 1.76+1 1.42+1 1.19+1 1.06+1 9.90+0
4p (2P$^{\rm o}$) - 2s2p2  (2D$^{\rm e}$) 114.2 A 4.82+0 4.08+0 3.40+0 3.01+0 2.76+0 2.60+0 2.45+0
        B 1.25+1 1.03+1 8.24+0 7.02+0 6.24+0 5.74+0 5.45+0
3d (2D$^{\rm e}$) - 3p (2P$^{\rm o}$) 723.5 A 2.02+0 1.48+0 1.03+0 7.91-1 6.57-1 5.86-1 5.66-1
        B 1.42+2 1.04+2 7.25+1 5.59+1 4.65+1 4.15+1 4.00+1
3p (2P$^{\rm o}$) - 3s (2S$^{\rm e}$) 658.0 A 9.39+0 7.82+0 6.57+0 6.20+0 6.28+0 6.56+0 7.21+0
        B 7.19+1 5.50+1 4.04+1 3.29+1 2.88+1 2.67+1 2.67+1
3p (2P$^{\rm o}$) - 2s2p2  (2D$^{\rm e}$) 176.2 A 1.11+1 9.23+0 7.75+0 7.31+0 7.41+0 7.73+0 8.50+0
        B 8.48+1 6.48+1 4.77+1 3.88+1 3.39+1 3.15+1 3.14+1
3p (2P$^{\rm o}$) - 2s2p2  (2S$^{\rm e}$) 284.1 A 9.42+0 7.85+0 6.60+0 6.22+0 6.31+0 6.58+0 7.24+0
        B 7.21+1 5.52+1 4.06+1 3.30+1 2.89+1 2.68+1 2.68+1
3s$^{\prime}$ (2P$^{\rm o}$) - 2s2p2  (2S$^{\rm e}$) 123.2 A 2.56+0 2.13+0 1.77+0 1.62+0 1.55+0 1.51+0 1.50+0
        B 4.18+0 3.46+0 2.82+0 2.50+0 2.31+0 2.21+0 2.22+0
2s2p2  (2D$^{\rm e}$) - 2s22p  (2P$^{\rm o}$) 133.5 A 8.18+2 7.15+2 5.41+2 4.24+2 3.48+2 2.96+2 2.32+2
2s2p2  (2S$^{\rm e}$) - 2s22p  (2P$^{\rm o}$) 103.7 A 7.74+1 8.63+1 8.19+1 7.40+1 6.72+1 6.18+1 5.39+1
2p3  (2P$^{\rm o}$) - 2s2p2  (2D$^{\rm e}$) 106.6 A 4.06+0 3.40+0 2.75+0 2.39+0 2.18+0 2.06+0 2.05+0
        B 8.05+0 6.87+0 5.61+0 4.87+0 4.42+0 4.15+0 4.11+0
                       



   
Table 4: Effective recombination coefficients [10-14 cm3 s-1] for temperature range Te = 500 - 2500 K. Electron density Ne = 104 [cm-3]
          Te [1000 K]
Transition $\lambda$[nm] Case 0.50 0.75 1.00 1.25 1.50 2.00 2.50
8h (2H$^{\rm o}$) - 6g (2G$^{\rm e}$) 1866.2 A 2.07+1 1.45+1 1.12+1 9.22+0 7.83+0 6.02+0 4.88+0
8h (2H$^{\rm o}$) - 5g (2G$^{\rm e}$) 931.4 A 1.88+1 1.31+1 1.02+1 8.36+0 7.10+0 5.46+0 4.43+0
7h (2H$^{\rm o}$) - 6g (2G$^{\rm e}$) 3068.8 A 5.28+1 3.63+1 2.79+1 2.26+1 1.91+1 1.44+1 1.16+1
7h (2H$^{\rm o}$) - 5g (2G$^{\rm e}$) 1157.9 A 5.05+1 3.47+1 2.66+1 2.16+1 1.82+1 1.38+1 1.11+1
7g (2G$^{\rm e}$) - 5f (2F$^{\rm o}$) 1144.4 A 2.15+1 1.53+1 1.21+1 1.01+1 8.71+0 6.85+0 5.67+0
7g (2G$^{\rm e}$) - 4f (2F$^{\rm o}$) 534.2 A 2.58+1 1.84+1 1.46+1 1.21+1 1.04+1 8.22+0 6.80+0
7f (2F$^{\rm o}$) - 3d (2D$^{\rm e}$) 237.5 A 1.34+1 9.86+0 8.01+0 6.84+0 6.01+0 4.91+0 4.18+0
        B 1.36+1 1.00+1 8.12+0 6.93+0 6.10+0 4.98+0 4.25+0
7d (2D$^{\rm e}$) - 3p (2P$^{\rm o}$) 179.6 A 1.08+0 8.22-1 6.90-1 6.12-1 5.61-1 4.93-1 4.48-1
        B 1.12+1 8.47+0 7.11+0 6.31+0 5.78+0 5.08+0 4.61+0
6h (2H$^{\rm o}$) - 5g (2G$^{\rm e}$) 1851.6 A 2.31+2 1.54+2 1.16+2 9.21+1 7.63+1 5.63+1 4.42+1
6g (2G$^{\rm e}$) - 5f (2F$^{\rm o}$) 1819.9 A 5.46+1 3.83+1 2.99+1 2.47+1 2.10+1 1.63+1 1.33+1
6g (2G$^{\rm e}$) - 4f (2F$^{\rm o}$) 646.2 A 7.05+1 4.95+1 3.87+1 3.19+1 2.72+1 2.11+1 1.72+1
6f (2F$^{\rm o}$) - 4d (2D$^{\rm e}$) 615.1 A 1.70+1 1.25+1 1.01+1 8.53+0 7.46+0 6.04+0 5.12+0
        B 1.72+1 1.26+1 1.02+1 8.64+0 7.56+0 6.13+0 5.20+0
6f (2F$^{\rm o}$) - 3d (2D$^{\rm e}$) 257.5 A 2.85+1 2.08+1 1.68+1 1.43+1 1.25+1 1.01+1 8.56+0
        B 2.88+1 2.11+1 1.70+1 1.44+1 1.26+1 1.02+1 8.69+0
6d (2D$^{\rm e}$) - 3p (2P$^{\rm o}$) 191.0 A 1.84+0 1.40+0 1.16+0 1.01+0 9.06-1 7.67-1 6.76-1
        B 2.12+1 1.61+1 1.34+1 1.16+1 1.04+1 8.84+0 7.79+0
5g (2G$^{\rm e}$) - 4f (2F$^{\rm o}$) 990.3 A 3.46+2 2.35+2 1.79+2 1.44+2 1.21+2 9.05+1 7.21+1
5f (2F$^{\rm o}$) - 4d (2D$^{\rm e}$) 923.0 A 4.35+1 3.13+1 2.49+1 2.09+1 1.81+1 1.44+1 1.21+1
        B 4.39+1 3.16+1 2.52+1 2.11+1 1.83+1 1.46+1 1.22+1
5f (2F$^{\rm o}$) - 3d (2D$^{\rm e}$) 299.3 A 8.35+1 6.01+1 4.78+1 4.01+1 3.48+1 2.77+1 2.32+1
        B 8.42+1 6.06+1 4.83+1 4.06+1 3.52+1 2.80+1 2.35+1
5d (2D$^{\rm e}$) - 3p (2P$^{\rm o}$) 213.8 A 3.17+0 2.38+0 1.97+0 1.71+0 1.52+0 1.28+0 1.11+0
        B 4.35+1 3.27+1 2.70+1 2.34+1 2.09+1 1.75+1 1.53+1
4f (2F$^{\rm o}$) - 3d (2D$^{\rm e}$) 426.7 A 4.83+2 3.35+2 2.58+2 2.11+2 1.79+2 1.37+2 1.11+2
        B 4.85+2 3.36+2 2.60+2 2.12+2 1.80+2 1.38+2 1.12+2
4f (2F$^{\rm o}$) - 2s2p2  (2D$^{\rm e}$) 106.4 A 3.13+1 2.16+1 1.67+1 1.37+1 1.16+1 8.88+0 7.21+0
        B 3.14+1 2.17+1 1.68+1 1.37+1 1.16+1 8.94+0 7.25+0
4d (2D$^{\rm e}$) - 4p (2P$^{\rm o}$) 1784.7 A 1.13+0 8.40-1 6.85-1 5.88-1 5.20-1 4.29-1 3.70-1
        B 2.50+1 1.85+1 1.51+1 1.30+1 1.15+1 9.49+0 8.18+0
4d (2D$^{\rm e}$) - 3p (2P$^{\rm o}$) 274.7 A 5.26+0 3.90+0 3.18+0 2.73+0 2.42+0 1.99+0 1.72+0
        B 1.16+2 8.61+1 7.03+1 6.04+1 5.34+1 4.41+1 3.80+1
4p (2P$^{\rm o}$) - 2s2p2  (2D$^{\rm e}$) 114.2 A 1.44+1 1.10+1 9.20+0 8.10+0 7.33+0 6.32+0 5.66+0
        B 3.90+1 2.94+1 2.45+1 2.15+1 1.95+1 1.67+1 1.49+1
3d (2D$^{\rm e}$) - 3p (2P$^{\rm o}$) 723.5 A 1.03+1 7.30+0 5.74+0 4.77+0 4.11+0 3.24+0 2.69+0
        B 7.18+2 5.08+2 4.00+2 3.33+2 2.87+2 2.26+2 1.88+2
3p (2P$^{\rm o}$) - 3s (2S$^{\rm e}$) 658.0 A 3.02+1 2.29+1 1.90+1 1.66+1 1.49+1 1.27+1 1.12+1
        B 3.16+2 2.28+2 1.82+2 1.54+2 1.34+2 1.09+2 9.22+1
3p (2P$^{\rm o}$) - 2s2p2  (2D$^{\rm e}$) 176.2 A 3.57+1 2.70+1 2.24+1 1.96+1 1.76+1 1.50+1 1.32+1
        B 3.73+2 2.69+2 2.15+2 1.81+2 1.58+2 1.28+2 1.09+2
3p (2P$^{\rm o}$) - 2s2p2  (2S$^{\rm e}$) 284.1 A 3.04+1 2.30+1 1.91+1 1.67+1 1.50+1 1.27+1 1.13+1
        B 3.17+2 2.29+2 1.83+2 1.54+2 1.35+2 1.09+2 9.25+1
3s$^{\prime}$ (2P$^{\rm o}$) - 2s2p2  (2S$^{\rm e}$) 123.2 A 7.77+0 5.91+0 4.94+0 4.35+0 3.94+0 3.40+0 3.04+0
        B 1.25+1 9.50+0 7.97+0 7.04+0 6.39+0 5.54+0 4.96+0
2s2p2  (2D$^{\rm e}$) - 2s22p  (2P$^{\rm o}$) 133.5 A 1.99+2 2.02+2 2.94+2 4.22+2 5.46+2 7.22+2 8.06+2
2s2p2  (2S$^{\rm e}$) - 2s22p  (2P$^{\rm o}$) 103.7 A 4.15+1 3.16+1 2.76+1 2.79+1 3.16+1 4.45+1 5.84+1
2p3  (2P$^{\rm o}$) - 2s2p2  (2D$^{\rm e}$) 106.6 A 1.11+1 8.40+0 7.07+0 6.29+0 5.79+0 5.14+0 4.70+0
        B 1.91+1 1.46+1 1.24+1 1.13+1 1.06+1 9.72+0 9.09+0
                       



   
Table 5: Polynomial fitting for effective recombination coefficients at electron density Ne = 104 [cm-3]. Temperature range $T_{e} = 5000 - 20\,000$ K
Transition $\lambda$[nm] Case a b c d f %
                     
8h (2H$^{\rm o}$) - 6g (2G$^{\rm e}$) 1866.2 A 1.134 -0.878 -0.134 -0.033 -2.0410 0.00
8h (2H$^{\rm o}$) - 5g (2G$^{\rm e}$) 931.4 A 1.029 -0.878 -0.134 -0.033 -2.0409 0.00
7h (2H$^{\rm o}$) - 6g (2G$^{\rm e}$) 3068.8 A 2.506 -0.911 -0.113 -0.024 -2.1160 0.00
7h (2H$^{\rm o}$) - 5g (2G$^{\rm e}$) 1157.9 A 2.395 -0.911 -0.113 -0.024 -2.1160 0.00
7g (2G$^{\rm e}$) - 5f (2F$^{\rm o}$) 1144.4 A 1.530 -0.324 -0.188 -0.185 -1.3745 0.05
7g (2G$^{\rm e}$) - 4f (2F$^{\rm o}$) 534.2 A 1.836 -0.324 -0.188 -0.185 -1.3746 0.05
7f (2F$^{\rm o}$) - 3d (2D$^{\rm e}$) 237.5 A 1.422 0.037 -0.009 -0.251 -0.8371 0.39
        B 1.450 0.037 -0.007 -0.252 -0.8334 0.39
7d (2D$^{\rm e}$) - 3p (2P$^{\rm o}$) 179.6 A 0.208 -0.084 -0.048 -0.186 -0.7186 0.07
        B 2.143 -0.083 -0.048 -0.187 -0.7186 0.07
6h (2H$^{\rm o}$) - 5g (2G$^{\rm e}$) 1851.6 A 8.528 -0.948 -0.083 -0.015 -2.2204 0.00
6g (2G$^{\rm e}$) - 5f (2F$^{\rm o}$) 1819.9 A 3.320 -0.304 -0.174 -0.190 -1.4071 0.05
6g (2G$^{\rm e}$) - 4f (2F$^{\rm o}$) 646.2 A 4.290 -0.304 -0.174 -0.190 -1.4071 0.05
6f (2F$^{\rm o}$) - 4d (2D$^{\rm e}$) 615.1 A 1.661 0.023 -0.017 -0.243 -0.8835 0.34
        B 1.695 0.021 -0.016 -0.243 -0.8800 0.34
6f (2F$^{\rm o}$) - 3d (2D$^{\rm e}$) 257.5 A 2.778 0.023 -0.017 -0.243 -0.8835 0.34
        B 2.834 0.021 -0.016 -0.243 -0.8800 0.34
6d (2D$^{\rm e}$) - 3p (2P$^{\rm o}$) 191.0 A 0.288 -0.085 -0.059 -0.187 -0.7652 0.12
        B 3.315 -0.083 -0.058 -0.188 -0.7634 0.13
5g (2G$^{\rm e}$) - 4f (2F$^{\rm o}$) 990.3 A 15.451 -0.309 -0.154 -0.190 -1.5065 0.04
5f (2F$^{\rm o}$) - 4d (2D$^{\rm e}$) 923.0 A 3.585 -0.003 -0.028 -0.230 -0.9691 0.27
        B 3.649 -0.004 -0.028 -0.229 -0.9656 0.27
5f (2F$^{\rm o}$) - 3d (2D$^{\rm e}$) 299.3 A 6.878 -0.003 -0.028 -0.230 -0.9691 0.27
        B 7.001 -0.004 -0.028 -0.229 -0.9656 0.27
5d (2D$^{\rm e}$) - 3p (2P$^{\rm o}$) 213.8 A 0.454 -0.089 -0.058 -0.187 -0.7970 0.11
        B 6.247 -0.086 -0.056 -0.189 -0.7936 0.11
4f (2F$^{\rm o}$) - 3d (2D$^{\rm e}$) 426.7 A 27.273 -0.053 -0.039 -0.209 -1.1448 0.15
        B 27.586 -0.055 -0.039 -0.208 -1.1416 0.15
4f (2F$^{\rm o}$) - 2s2p2  (2D$^{\rm e}$) 106.4 A 1.765 -0.053 -0.039 -0.209 -1.1448 0.15
        B 1.785 -0.055 -0.039 -0.208 -1.1416 0.15
4d (2D$^{\rm e}$) - 4p (2P$^{\rm o}$) 1784.7 A 0.137 -0.067 -0.027 -0.211 -0.8425 0.09
        B 3.047 -0.066 -0.026 -0.212 -0.8391 0.09
4d (2D$^{\rm e}$) - 3p (2P$^{\rm o}$) 274.7 A 0.638 -0.067 -0.027 -0.211 -0.8424 0.09
        B 14.150 -0.066 -0.026 -0.212 -0.8391 0.09
4p (2P$^{\rm o}$) - 2s2p2  (2D$^{\rm e}$) 114.2 A 3.014 -0.643 -0.054 -0.092 -1.0502 0.01
        B 7.022 -0.231 -0.042 -0.144 -0.7814 0.03
3d (2D$^{\rm e}$) - 3p (2P$^{\rm o}$) 723.5 A 0.791 -0.508 0.036 -0.341 -1.3973 0.01
        B 55.869 -0.494 0.032 -0.336 -1.3773 0.01
3p (2P$^{\rm o}$) - 3s (2S$^{\rm e}$) 658.0 A 6.201 -0.304 0.412 0.215 -0.3676 0.13
        B 32.883 -0.752 0.140 -0.281 -1.4218 0.02
3p (2P$^{\rm o}$) - 2s2p2  (2D$^{\rm e}$) 176.2 A 7.312 -0.304 0.412 0.215 -0.3676 0.13
        B 38.774 -0.752 0.140 -0.281 -1.4218 0.02
3p (2P$^{\rm o}$) - 2s2p2  (2S$^{\rm e}$) 284.1 A 6.224 -0.304 0.412 0.215 -0.3676 0.13
        B 33.006 -0.752 0.140 -0.281 -1.4217 0.02
3s$^{\prime}$ (2P$^{\rm o}$) - 2s2p2  (2S$^{\rm e}$) 123.2 A 1.619 -0.982 0.196 -0.019 -1.2415 0.09
        B 2.495 -0.487 0.041 -0.105 -0.8786 0.20
2s2p2  (2D$^{\rm e}$) - 2s22p  (2P$^{\rm o}$) 133.5 A 423.926 -1.353 0.167 -0.047 -2.2304 0.02
2s2p2  (2S$^{\rm e}$) - 2s22p  (2P$^{\rm o}$) 103.7 A 73.955 -1.477 0.217 0.006 -1.8827 0.02
2p3  (2P$^{\rm o}$) - 2s2p2  (2D$^{\rm e}$) 106.6 A 2.387 -0.228 0.046 -0.107 -0.6876 0.09
        B 4.873 -0.163 0.022 -0.122 -0.6327 0.08
                     


In Table 3, we give the effective recombination coefficients $\alpha_{eff}(\lambda)$ for the strongest recombination lines of C II for the temperature range $3\,500 - 20\,000$ K. Only the lines with the $\alpha_{eff}(\lambda) \geq 3.0 \, 10^{-14}$ cm3s-1 and $\lambda > 91.2$ nm at one or more temperatures are presented. Table 3 is a specimen table showing only the strongest lines. More extensive tables showing weaker lines are available in electronic form from the CDS.

The effective recombination coefficient is defined such that the emissivity $\epsilon(\lambda)$, in a transition of wavelength $\lambda$ is

 \begin{displaymath} \epsilon(\lambda) = N_{e} N_+ \alpha_{eff}(\lambda) {{hc}\over{\lambda}} \; \; [\rm {ergs\, cm}^{-3}\ {\rm s}^{-1}]. \end{displaymath} (2)

We tabulate results for a single value of electron density Ne = 104 cm-3 because the recombination coefficients are not very sensitive to this parameter at low temperature.

The effective recombination coefficients $\alpha_{eff}(\lambda)$ for the lower temperatures $T_{e} = 500 - 2\,500$ K are presented in Table 4 for the same set of lines as given in Table 3. Once again the reader is referred to the electronic version of this paper at the CDS for more extensive tabulations.

Subsequently, the coefficients were fitted by a least-squares algorithm to the functional form

 
$\displaystyle \alpha_{eff}$ = $\displaystyle 10^{-14} \, a \,t^f$  
  $\textstyle \times$ $\displaystyle \left(1 + b \left(1-t\right) + c \left(1-t \right)^2 + d \left(1-t \right)^3 \right),$ (3)

where t = Te[K]/104, and a, b, c, d and f are constants.

We present the coefficients of the fits to the recombination coefficients in Table 5 for the same set of lines as given in Table 3. The fitting accuracy (the maximum error of fitting in percent) is also given. This gives an indication that fitting is very accurate for the temperature range ( $5000 - 20\,000$ K) considered here. Due to the more complex nature of recombination at lower temperatures caused by the interaction of dielectronic and radiative recombination, fits were not made for lower temperatures. Fit coefficients for a more extensive set of lines are available from the CDS.


 

 
Table 6: Comparison of state-specific recombination coefficients [10-13 cm3 s-1] with data from Nahar ([1995]) at electron density Ne = 104 [cm-3] and temperature $T_{e} = 10\,000$ K
State Nahar Present
       
2p3 2P$^{\rm o}$ 36.2 0.4
2s2p2 2D 10.8 21.0
2s23d 2D 4.2 3.7
2s22p 2P$^{\rm o}$ 4.1 36.6
2s24d 2D 2.6 2.7
2s24f 2F$^{\rm o}$ 1.7 1.7
2s25d 2D 1.6 1.7
2s25f 2F$^{\rm o}$ 1.6 1.6
2s23p 2P$^{\rm o}$ 1.2 3.9
2s24p 2P$^{\rm o}$ - 1.0
       


As part of a calculation of total electron-ion recombination coefficients for a range of atomic ions, Nahar ([1995]) reported state-specific recombination coefficients for some states of C +, derived from photoionization data calculated using similar methods to those used in the present work. The numbers given by Nahar are for direct recombination to each state, no cascade contributions are included. In Table 6 we compare the results of Nahar at $T_{e} = 1\,000$ K with the present work. For Rydberg states with $ l \geq 2$ we find good agreement with Nahar, with differences of $\leq 5$% for d-states and $\leq 1$% for f-states. For the 2s2p2 2D$\rm ^e$ state our recombination coefficient is about twice that found by Nahar. The recombination to this state is dominated by near-threshold resonances, whose position we have empirically adjusted downwards to agree with the experimental position, leading to a larger recombination coefficient, which is also in good agreement with that given by Nussbaumer & Storey (1983) for this state. The most significant difference between our work and that of Nahar is for the 2Po states. In the work of Nahar, the state with the largest direct recombination coefficient is given as 2p3 2Po, while we find this state to have a recombination coefficient two orders of magnitude smaller than that given by Nahar. We note, however that the value given by Nahar for this state is close to the value we find for the ground 2s22p 2Po state, and similarly for the 2s22p 2Po state of Nahar and our 2s23p 2Po state. The same pattern is also found for higher members of the 2Po series. We conclude that the order of the identification of the 2Po states given in Table 2 of Nahar is incorrect, although their contribution to the total recombination coefficient is not affected and broadly similar to that in the present work.


 

 
Table 7: Comparison of effective recombination coefficients [10-13 cm3 s-1] with data from Pèquignot et al. ([1991]) (PPB) at electron density Ne = 104 [cm-3] and temperature $T_{e} = 10\,000$ K
Transition $\lambda$[nm] Case Present PPB
           
5g (2G) - 4f (2F$^{\rm o}$) 990.3 A 1.545 1.621
4f (2F$^{\rm o}$) - 3d (2D) 426.7 A 2.727 2.795
3d (2D) - 3p (2P$^{\rm o}$) 723.5 A 0.079 0.065
      B 5.587 5.184
3p (2P$^{\rm o}$) - 3s (2S) 658.0 A 0.620 0.329
      B 3.288 1.444
3p (2P$^{\rm o}$) - 2s2p2 (2S) 284.1 A 0.622 0.606
      B 2.658 3.301
3p (2P$^{\rm o}$) - 2s2p2 (2D) 176.2 A 0.731 1.001
      B 3.877 4.391
2s2p2 (2D) - 2p (2P$^{\rm o}$) 133.5 A 42.39 3.450
           


In Table 7 we compare our effective recombination coefficients for some strong lines with the list given in Pèquignot et al. ([1991]) (PPB). There is reasonably good agreement for lines originating from the 5g, 4f and 3d states. At first sight the agreement is significantly worse for the lines originating from the 3p 2Po state. Most of the difference, however, arises from the branching ratios from the 3p 2Po state to lower states. In Case A, the total $\alpha_{eff}$ for this state is $1.973 \,\, 10^{-13} $ from our data and $1.936 \,\, 10^{-13}$ from PPB. In Case B the the corresponding values are $10.466 \,\, 10^{-13}$ and $8.493\, 10^{-13}$, a difference of 23%. In Case B, most of the recombination to the nd series passes through the 3p state rather than going directly to the ground 2p state. A possible cause of the difference in the Case B results is that the nd series is truncated at some relatively low principal quantum number in PPB, whereas in our calculation the infinite series of nd states is included.

The differences in the effective recombination coefficients for individual lines from the 3p 2Po can be explained by differences in the branching ratios, $\beta$, from the 3p 2Po state to lower states. In our calculation we have $\beta({3s~^2S}\rm ^e) = 0.314$, $\beta({2s2p^2~^2S\rm ^e}) = 0.315$ and $\beta({2s2p^2~^2D\rm ^e}) = 0.371$ while PPB give these parameters as 0.170, 0.313 and 0.517. We note that our values of $\beta$ are in reasonable agreement with data retrieved from the Opacity Project data base (Cunto et al. [1993]) which give 0.311, 0.311 and 0.378 respectively.

The difference in $\alpha_{eff}$ for the line 2s2p2 2D$\rm ^e$ -2s22p 2Po arises from dielectronic recombination being not included in PPB. Here our coefficient is in good agreement with the purely dielectronic coefficient $\alpha_{DR} = 45.36 \,\, 10^{-13}$ from Nussbaumer & Storey ([1983]).

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