Astron. Astrophys. 334, L26-L28 (1998)

2. Results

For the calculation we used the R-matrix method (Berrington et al. 1987 and Berrington et al. 1995) and covered the photon energy interval X= [1.2-3.2] (in K-edge energy units), where all channels are open. To describe the residual ion we used the SUPERSTRUCTURE code developed by Eissner et al. (1974). We chose the following two categories of configurations: i) K-shell closed: 1s² 2s², 1s² 2s2p, 1s² 2p² (¹ S) and 1s² 2s3s and ii) K-shell open: 1s2s² 2p, 1s2s2p², 1s2s² 3s, 1s2s² 3p, 1s2p³ (³ , ¹ ) and 1s2s2p3s. The latter case gives rise to 20 terms since neither the quintet nor the ³ , ³ , ¹ terms are required. The values of the scaling parameters occurring in the Thomas Fermi potential that we used to produce the 1s, 2s, 2p, 3s, and 3p orbitals are 1.3972, 1.2055, 1.1520, 2.4040 and 1.9149, respectively i.e. the values used for boron. A correlation configuration 1s² 2p3d was also introduced with = 9.5 to improve the description of the residual ion. We obtained fair agreement between the length and velocity forms of the 2s-2p weighted oscillator strength. The agreement between our calculated energies and the experimental ones was within 1% for the lowest terms and 2% for the 1s-hole terms for which data is available. Note that the 1s-hole terms are described by a few configurations using the nl orbitals of the K-shell closed configurations. For the ² symmetry (target ground state) 41 closed channels occur. For the ² S, ² P and ² D symmetries, representing the diffusion of the ejected electron by the residual ion, we have 23, 21 and 43 channels, respectively. From the R-matrix calculation, we obtained ionization energies which are in close agreement to the experimental ones (see Table 1 where experimental energies IP(exp) are taken from Moore,1966). These results have been obtained using the same set of scaling parameters for the series. In Fig. 1, we present the cross sections for the 1s photoionization versus energy in threshold units X: , where and are the photon and 1s ionization energies, respectively, in the case of CII. We see that the ratio of cross sections for the transitions 1s² 2s² 2p ² 1s2s² 2p ³ and 1s² 2s² 2p² 1s2s² 2p¹ is very close to statistical (3:1) for values of . In Figs. 2, 3 and 4 we display total and partial shake-up cross sections for ions of astrophysical interest: CII, NIII and OIV, respectively. Curve 5 represents the total shake-up cross section. Partial shake-up cross sections corresponding to the transitions 2s 3s (curve 4), 2p 3p (curve 2), 2s 2p (curve 3) and 2p 3s (curve 1), all relative to the 1s single photoionization cross section, are also displayed. This shows that the conjugate shake-up process corresponding to the 2p 3s transition is negligible and for this reason that curve is not drawn on Figs. 3 and 4. One sees that the importance of the shake-up processes (curves 5 on each figure) decreases with the increase of Z, ranging from about 15%, in the case of CII, to about 3.5% in the case of Ne. Comparing these values with 30% obtained in our previous calculation in the case of BI (Badnell et al. 1997) we have an image of the importance of these shake-up processes for the entire boron isoelectronic series (Table 1). Furthermore, one can see that the direct shake-up 2s 3s transition (curve 4) gives the dominant contribution, while the conjugate shake-up 2s 2p (curves 3) and direct shake-up 2p 3p (curves 2) transitions are broadly comparable. These features found in the case of boron are also present for all the other ions of the sequence.

Table 1. Relative shake-up cross sections and ionization potentials

Fig. 1. Single inner-shell photoionization cross sections (in Mb) versus for CII. and represent the photon and 1s ionization energies, respectively. With full lines are drawn () (1) and () (2) symmetries. With dashed line is drawn the () symmetry multiplied by a spin statistical weight of 3

Fig. 2. Shake-up cross sections, relative to the 1s photoionization cross section, versus X, for CII. Curve (5) represents the total relative shake-up cross section. The other curves represent the relative shake-up cross sections for the transitions: 2s 3s (curve 4), 2s 2p (curve 3), 2p 3p (curve 2) and 2p 3s (curve 1). The curve (1) was obtained by multiplying the actual values for the 2p 3s cross section by a factor of 10. Curve (3) refers to the excitations to terms of the 1s2s2 3p and 1s2p3 configurations

Fig. 3. Shake-up cross sections, relative to the 1s photoionization cross section, versus X, for NIII

Fig. 4. Shake-up cross sections, relative to the 1s photoionization cross section, versus X, for OIV

In Table 1 are displayed relative shake-up cross sections and ionization potentials for the first 6 members of the sequence. The first row has percentage values representing the magnitude of the total shake-up cross section relative to the K-shell single photoionization cross section for each ion. One observes a rapid decrease of importance of these shake-up processes as Z increases, but one also remarks that for the low-Z ions the effect of them is significant. This result suggests that the ionization equilibrium of multiply charged B, C, N, O, in a low-density soft-X ray photoionized plasma will be perturbed strongly by such processes (including shake-off). Consequently, for a detailed analysis of such plasmas one should take them into account. In the second row we give values of the dominant shake-up transitions relative to the single 1s photoionization cross section, while the third and forth rows contain the calculated (th) and experimental (exp) ionization potentials (in Ry). In the last row the K-edge potentials in eV are shown.

© European Southern Observatory (ESO) 1998

Online publication: May 12, 1998

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