2 Results and discussion

For the determination of Stark broadening parameters (the full line width at half maximum - W and the line shift - d) of neutral calcium, the semiclassical perturbation formalism has been used. This formalism, 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 1996). The calculation procedure, with the discussion of updatings and validity criteria, has been briefly reviewed in Dimitrijevic (1996, 1997). Atomic energy levels needed for calculations have been taken from Sugar & Corliss (1979). 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.

All results are for temperatures from 2500 up to 50000 K. In Table 1 (accessible only in electronic form), electron-, proton-, and He II-impact broadening parameters for 189 Ca I multiplets for perturber density of 10¹¹ cm^-3 are shown. Data for electron-, proton-, and He II-impact broadening parameters for Ca I for perturber densities of 10¹² cm ^-3 - 10¹⁹ cm^-3 are shown in Table 2 (accessible only in electronic form). Table 3 (accessible only in electronic form) shows Mg II-, Si II-, and Fe II-impact broadening parameters for 189 Ca I multiplets, for perturber density of 10¹¹ cm^-3.

Stark broadening data for densities lower than for tabulated data, are proportional to the perturber density. Moreover, we present in Tables 1-3 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. The validity of the impact approximation has been estimated for data shown in Tables 1-3, by checking if the collision volume (V) multiplied by the perturber density (N) is much less than one (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.

There are two experimental studies reporting results of measurements of neutral calcium line Stark broadening parameters (Kusch & Pritschow 1970; Hühn & Kusch 1973). Kusch & Pritschow (1970) have investigated experimentaly Stark widths and shifts of four neutral calcium lines from plasma produced in a pulsed capillary discharge, and reported results for an electron density of 10¹⁸ cm^-3. Only for one line (the 5188.8 Å line from the 4p¹P$^\circ -5$d¹D multiplet) exist a sufficiently complete set of atomic data needed for an adequate application of our approach. For this line, however, the impact approximation condition is not satisfied for the reported electron density. Hühn & Kusch (1973) published experimental Stark widths for the 4318.6 Å and 4425.4 Å lines from the 4s4p³P$^\circ -4$p^{2 3}P and 4s4p³P $^\circ -4$s4d³D multiplets, from plasma produced in a high pressure arc. Only the 4425.4 Å line may be compared with our results. For an electron density of 10¹⁷cm^-3 and the temperature 10000 K, Hühn & Kusch (1973) obtain for the full width at half maximum the value of 0.29 Å, while our result is 1.26 Å. The semiclassical result of Griem (1974) is 1.51 Å. As one can see, the agreement between the experimental result and both theories is very poor. The differences between the calculation methods used by us and those of Griem (1974), have been discussed in detail in Dimitrijevic & Sahal-Bréchot (1996). The reasons for such large difference between experiment and theory have been discussed in detail in Konjevic & Roberts (1976), and the principal point of their remarks

on the experiment is the lack of an independent measurement of electron density.

It is surprising that in spite of the importance of neutral calcium lines, there are not more experimental data. Reliable experimental data for Stark broadening of Ca I lines will be important for the check of theory, as well as for abundance determinations and other problems in astrophysics and plasma physics.

Acknowledgements

This work has been supported by the Ministry of Science and Technology of Serbia through the project "Astrometrical, Astrodynamical and Astrophysical Researches''.