Oscillator strengths in the silicon sequence: Relativistic Quantum Defect Orbital and Multiconfigurational Dirac-Fock calculations

SUPPLEMENT SERIES Astron. Astrophys. Suppl. Ser. 124, 397-404 (1997) Oscillator strengths in the silicon sequence: Relativistic Quantum Defect Orbital and Multiconfigurational Dirac-Fock calculations E. Charro, I. Martı́n, and C. Lavı́n Departamento de Quı́mica-Fı́sica, Facultad de Ciencias, Universidad de Valladolid, E-47005 Valladolid, Spain Received June 11; accepted November 22, 1996 Abstract. Oscillator strengths for 3s2 3p2 → 3s2 3p1 3d1 and 3s2 3p2 → 3s2 3p1 4s1 transitions in the silicon sequence (KVI - XeXLI) have been calculated using the Relativistic Quantum Defect Orbital (RQDO) method, with and without explicit inclusion of core-valence correlation, and the multiconfigurational Dirac-Fock (MCDF) approach. Our f -values, which are of interest in astrophysics and fusion plasma research, are compared with other theoretical results in the cases for which these are available. Key words: atomic data — atomic processes 1. Introduction Excitation energies and oscillator strengths in highly stripped ions are needed for estimating the energy loss through impurity ions in fusion plasmas and for diagnostics and modelling of the plasmas. Precision spectroscopy both in astrophysical and in beam-foil measurements also demands accurate theoretical values. Furthermore, the systematic trends in atomic structure with respect to the nuclear charge Z can best be studied along an isoelectronic sequence. Some of the strong lines appearing in laboratory plasmas or in astrophysical sources belong to the n = 3 → n0 = 3 transition arrays of the silicon sequence. Their role in solar identifications is very important; for example, FeXIII is well represented in the solar spectrum, photographed under quiet solar conditions (Behring et al. 1976) or in solar flares (Dere 1978). Highly ionized members of the silicon isoelectronic sequence have recently been investigated. A comprehensive study of the spectra of Si-like ions between CuXVI and MoXXIX has been reported by Sugar et al. (1990). Send offprint requests to: E. Charro This work has since then been extended to KrXXIII and MoXXIX by Jupén et al. (1991), and to GeXIX, SeXXI, SrXXV, YXXVI and ZrXXVII by Ekberg et al. (1992). Several investigations of energies and oscillator strengths for Si-like ions have also appeared in the literature. For the neutral atom SiI and the first ions of its sequence there are some experimental and theoretical studies (Ho & Henry 1987; Ryan et al. 1989; Becker et al. 1980; O’Brien & Lawler 1991; Livingston et al. 1981; Mendoza & Zeippen 1988; Nahar & Pradhan 1993). Opacity calculations by Nahar & Pradhan (1993) are the most recent theoretical study of SiI, SIII, ArV and Ca VII. For instance, Biémont (1986a, 1986b), Bromage (1980), and Bromage et al. (1978), have applied the relativistic Hartree-Fock (HXR) code of Cowan (1981) to some ions. Their work is semiempirical in the sense that the Slater integrals were adjusted to optimize the agreement with experimental level energies. Using the multiconfiguration Dirac-Fock (MCDF) program of Desclaux (1975), Huang (1985) has performed fully relativistic ab initio calculations for Si-like ions in the range Z = 15 − 106. Among the standard methods suitable for predicting oscillator strengths for transitions in highly ionized and in heavy atoms, the multiconfiguration Dirac-Fock approach seems to be one of the most reliable ones (Dyall et al. 1989). However, this approach becomes too time- consuming if the number of transitions to be determined is very large. According to Curtis (1987), the spectroscopic classification of the relevant lines exceeds the general capability of ab initio methods, and sometimes requires the application of semiempirical methods. Recently, Laughlin (1992) pointed out, after comparing lifetimes obtained with a numerical Coulomb approximation and a model potential with accurate experimental measurements for some alkali-like systems, that high accuracy may be achieved with relatively simple computational procedures, as long as they are appropriate to the problem. The structure of Si-like ions is quite interesting from the atomic physics point of view. There are four electrons outside the closed 2p6 shell and the number of configurations within the n = 3 complex is 12. The ground level is 3s2 3p2 3 P0 , and there are two low-lying metastable levels, 3s2 3p2 1 D2 and 1 S0 . In these work we report oscillator strengths for the singlet-singlet transitions: 3s2 3p2 1 D2 − 3s2 3p1 3d1 1 D2 , 3s2 3p2 1 D2 − 3s2 3p1 3d1 1 F3 , 3s2 3p2 1 D2 − 3s2 3p1 4s1 1 P1 , as well as for the fine structure lines of the multiplet 3s2 3p2 3 P − 3s2 3p1 4s1 3 P in silicon-like ions ranging from KVI up to XeXLI. Systematic trends are analised by plotting our f -values versus the reciprocal of the atomic number, Z. The calculations have been done with two different approaches, the semiempirical Relativistic Quantum Defect Orbital (RQDO) method (Simons 1974; Martı́n & Simons 1976; Lavı́n et al. 1992; Karwowski & Martı́n 1991; Martı́n et al. 1993), where in some cases the importance of the polarization of the core by the active electron has been stressed, and the MCDF formalism using the code by Dyall et al. (1989), in the cases where there is not any other MCDF result reported in the literature. This is the most complex electronic structure to which the RQDO method has so far been applied. In this respect, our calculations will serve as a test on the capability of such a simple formalism for providing good estimates of oscillator strengths in complex systems. A further incentive for this study has been the lack of experimental data for oscillator strenghts in these transitions, as well as the fact that only a calculation has been reported, to our knowledge, for the highly ionized atoms of the sequence (Huang 1985). 2. Computational procedures 2.1. Relativistic quantum defect orbital method The Quantum Defect Orbital (QDO) (Simons 1974; Martı́n & Simons 1976; Lavı́n et al. 1992) formalism and its relativistic (RQDO) (Karwowski & Martı́n 1991; Martı́n et al. 1993) version have been described in detail. We shall, thus, only mention here some aspects of the theory that are relevant to the present calculations. The relativistic quantum defect orbitals are determined by solving analytically a quasirelativistic secondorder Dirac-like equation with a model Hamiltonian that contains the quantum defect (Karwowski & Martı́n 1991). This model Hamiltonian allows for an effective variation of the screening effects with the radial distance and as a consequence, the radial solutions behave at least approximately correctly in the core region of space, and display a correct behaviour at large radial distances. These can be expected to be, in most cases, the most relevant regions that contribute to the transition integral. The relativistic quantum defect orbitals lead to closed-form analytical expresions for the transition integrals. This allows us to calculate transition probabi (...truncated)