1 Introduction

This is the third in a series of papers dealing with the theoretical recombination spectra of once ionized abundant elements, with the previous two papers dealing with O II (Storey [1994]) and Ne II (Kisielius et al. [1998]). In this paper, as in the earlier papers, we calculate theoretical recombination line intensities making use of high quality bound-bound and bound-free radiative data calculated using the techniques developed for the Opacity Project (OP) (Seaton [1987]; Berrington et al. [1987]). This entails the use of the R-matrix method to solve the Schrödinger equation in the close-coupling approximation of electron-ion collision theory. The radiative data deposited in the OP database (Cunto et al. [1993]) for photoionization of C ⁺, however, is tabulated at too coarse a mesh for recombination work, so an improved calculation of these data is described in this paper (Sect. 2). In this approach, autoionizing states appear as resonances in the photoionization cross-sections and effects such as the mean free electron energy being comparable to the resonance widths and non-zero background cross-sections between resonances are correctly treated. The omission of these effects can significantly affect the recombination coefficients at low temperature (Nussbaumer & Storey [1983]). We also discuss the problem of radiative damping of resonances (Kisielius et al. [1998]).

The case of C II differs from the ions previously discussed in that there is extensive, although not complete, experimental information (Moore [1970]) about the positions of autoionizing states lying close to the C ⁺ ionization threshold, which are responsible for the process of low-temperature dielectronic recombination (Storey [1981], [1982]). These experimental data enable us to empirically correct the calculated positions of these states, which appear as resonances in the calculated photoionization cross-sections (Sect. 2.4).

The calculation described here deals only with the doublet states of C ⁺. There are also quartet states converging on the 2s2p (³P^o) state of C ²⁺, but these can only be populated by direct recombination from the C ²⁺ 2s2p (³P^o) state or by dielectronic recombination through quartet autoionizing states. At nebular temperatures ( $T \leq 20\,000$ K), there will not be significant population in the C ²⁺ 2s2p (³P^o) state so direct recombination to the quartets will be insignificant. The quartet autoionizing states can only autoionize through weak spin-orbit (and other weak relativistic) interactions with doublet autoionizing states, since there is no quartet continuum available. Such interactions are weak among the states just above the ionization threshold, so we do not expect the quartet states to have any significant effect on the intensities of the doublet lines treated here. Recombination lines from quartet states are nonetheless observed, even at nebular temperatures. For a treatment of dielectronic recombination through the doublet and quartet states see Badnell ([1988]).

The term structure of C ⁺ also differs from that of O ⁺ and Ne ⁺ in that due to the zero spin and orbital angular momentum of the C ^{2+ 1}S state, each valence orbital only gives rise to one atomic term usually with negligible fine-structure. As a result, there are fewer recombination lines and they are of much greater intensity than in O II and Ne II. It is therefore possible to detect recombination lines of C II from higher principal quantum numbers than for the other two ions, and this opens up the possibility of testing the theory for a greater range of ionic states (Liu et al. [2000]). Our tabulated results are consequently also more extensive. We also extend the calculations to lower temperatures ($\geq 500$ K) following the observation of the 1335 Å and 4267 Å lines from an old nova remnant (Ferland et al. [1984]).

Recombination lines of C II are also seen in the spectra of the stellar winds of Wolf-Rayet central stars of planetary nebulae (DeMarco et al. [1998]) where particle densities are much higher than in PN. In a further paper, we will present a theoretical treatment of the C II recombination spectrum at high density, where collisional processes become important.