2 Results and discussion

In order to examinate Stark broadening of Sc X, Sc XI, Ti XI and Ti XII spectral lines and to determine the corresponding broadening parameters (the full line width at half maximum - W and the line shift - d), the semiclassical perturbation formalism has been used, which, as well as the corresponding computer code (Sahal-Bréchot 1969a,b), have been updated and optimized several times (Sahal-Bréchot 1974; Fleurier et al. 1977; Dimitrijevic & Sahal-Bréchot 1984; Dimitrijevic et al. 1991; Dimitrijevic & Sahal-Bréchot 1996b). Also, we have published several times descriptions of the calculation procedure, with a discussion of updatings and validity criteria, as e.g. in Dimitrijevic & Sahal-Bréchot (1996c) and Dimitrijevic (1996). Atomic energy levels needed for calculations have been taken from Bashkin & Stoner (1978) for Sc X and Sc XI, and from Wiese & Musgrove (1989) for Ti XI and Ti XII. The oscillator strengths have been calculated within the Coulomb approximation (Bates & Damgaard 1949; and the tables of Oertel & Shomo 1968). For higher levels, the method of Van Regemorter et al. (1979) has been used.

Our results for electron-, proton-, and He III- impact line widths and shifts for 4 Sc X, 10 Sc XI, 4 Ti XI and 27 Ti XII multiplets are shown in Tables 1-4 (accessibles only in electronic form), for Sc X (Table 1) for temperatures from 200 000 K up to 5 000 000 K and perturber densities 10¹⁹ cm^-3-10²² cm^-3, for Sc XI (Table 2) for temperatures from 500 000 K up to 5 000 000 K and perturber densities 10¹⁸ cm^-3-10²² cm^-3, for Ti XI (Table 3) for temperatures from 500 000 K up to 5 000 000 K, and perturber densities 10¹⁸ cm^-3-10²² cm^-3, and for Ti XII (Table 4) for temperatures from 500 000 K up to 6 000 000 K, and perturber densities 10¹⁸ cm^-3-10²³ cm^-3.

Stark broadening data for densities lower than for tabulated data, are proportional to the perturber density. Moreover, we present in Tables 1-4 as well, a parameter c (Dimitrijevic & Sahal-Bréchot 1984), which gives an estimate for the maximum perturber density for which the line may be treated as isolated, when it is divided by the corresponding full width at half maximum. For each value given in Tables 1-4, the collision volume (V) multiplied by the perturber density (N) is much less than one and the impact approximation is valid (Sahal-Bréchot 1969a,b). Values for NV > 0.5 are not given and values for $0.1 < NV \le 0.5$ are denoted by an asterisk. When the impact approximation is not valid, the ion broadening contribution may be estimated by using the quasistatic approach (Sahal-Bréchot 1991 or Griem 1974). In the region between where neither of these two approximations is valid, a unified type theory should be used. For example in Barnard et al. (1974), a simple analytical formula for such a case is given. The accuracy of the results obtained decreases when broadening by ion interactions becomes important.

The present results are the first Stark broadening data concerning scandium X and XI as well as titanium XI and XII spectral lines. We hope that the presented data will be of interest for some problems in stellar and laboratory plasma research, modeling and diagnostic, as well as for consideration of plasmas in various devices in physics and technology, as e.g. subphotospheric layers, radiative transfer, investigation and modeling of fusion and laser-produced plasmas, and of soft X-ray lasers. Such results also have an interest for the checking and development of the Stark broadening theory for multicharged ion line shapes as e.g. for investigations of systematic trends along isoelectronic sequences.

Acknowledgements

This work is a part of the project "Astrometrical, Astrodynamical and Astrophysical Investigations", supported by Ministry of Science and Technology of Serbia.