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Astron. Astrophys. 363, 1177-1185 (2000)

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5. Results and conclusions

The different [FORMULA]-values measured for every spectral line at the diverse instants of the plasma life have been divided by the corresponding [FORMULA] value and have been plotted against the measured temperature to check its influence in Stark broadening. No functional trend can clearly be distinguished from our data due to the small differences between them in comparison with the error band and the narrow range of temperatures found in our experiment. Therefore, the data have been plotted against [FORMULA] for each measured line. Very clear linear dependencies have been observed. The resulting width values at [FORMULA] m-3 have been determined from the linear fit ([FORMULA] from now on).

In relation to shifts, since the line centre is not available at null electron density, these have been obtained from a linear extrapolation of all line centres measured for each line as a linear function of [FORMULA]. The inverse linear dispersion at the given wavelength multiplied by the difference between any line centre and that obtained from the extrapolation yields the corresponding Stark shift, [FORMULA]. We have called [FORMULA] the shift evaluated from this linear fit at [FORMULA] m-3. As well as Stark widths, no clear functional trends of Stark shifts with temperature have been observed. One example of the plots performed for Stark parameter calibrations is shown in Fig. 6 for the SiIII 455.3 nm.

[FIGURE] Fig. 6. Stark width and shift calibrations for the SiIII 455.3 nm line. [FORMULA] is the linear correlation coefficient for the fit of the data.

The final results are listed in Table 1. As cited above, all data have been normalised at [FORMULA] m-3. Transition array and multiplet -with its identification number (Moore 1965) specified in parenthesis when available- are indicated in the first and second columns of the table, respectively. The corresponding wavelengths are presented in the third column. The multiplets have been ordered by increasing average wavelength and the spectral lines in a multiplet have been ordered by decreasing lower and upper quantum numbers. The measured [FORMULA] and [FORMULA] values are indicated in picometers in columns four and five, respectively. The Stark parameters obtained in this work (column six of the tables) are accompanied by their statistical error calculated as [FORMULA], where [FORMULA] and [FORMULA] are the statistical error of the coefficients in the linear fitting [FORMULA]. This way to compute the error usually overestimates its final level though it takes into account both the intrinsic quality of the fit and other errors which may be produced by a small but non-null [FORMULA] value. Data from previous experimental works (Puric et al. 1974; Platisa et al. 1977; Kusch & Schröder 1982; Djenize et al. 1992) are also listed in columns four and five. The plasma electron density and temperature conditions involved in each experiment are presented in Table 2. When the reviewers have evaluated the uncertainty for these data, it appears just next to the values in columns four and five of Table 1 as the usual qualified letter. In these columns we also give the Stark FWHM values obtained on the basis of various theoretical calculations. Label "th. G" in column six stands for the theoretical results calculated by Dimitrijevic & Konjevic (1980 , 1981) by the semi-classical formula of Griem (1974). Labels "th. SE" and "th. ASC" denote results obtained by Dimitrijevic & Konjevic (1980, 1981) and by Dimitrijevic (1983), on the basis of the semi-empirical calculations according to Griem (1974), and of the approximative semi-classical calculations, respectively. Finally, label "th. MSE" denotes results calculated on the basis of modified semi-empirical approach by Dimitrijevic & Konjevic (1980 , 1981 , 1987) and by Dimitrijevic (1983 , 1988). The temperature range for the theoretical values presented in the table is 10 000-30 000 K.


Table 1. Stark width and shifts for the SiIII lines measured in this work compared with results from previous experimental and theoretical works. Next to each measured value its statistical error as a percentage is indicated, or the qualified letter assigned by reviewers. All values are referred to [FORMULA] m-3 except those of Platisa et al. (1977) ([FORMULA] m-3).
a) A misprint or arithmetical error is likely in the value presented by the authors.


Table 2. Summary of electron density and temperature ranges concerning the experiments considered for comparisons with this work.

Stark linewidth data for multiplets (2), (4) and (5) are shown in Fig. 7. This work data have been represented with their error bars at the edges and at the middle point of the measured temperature interval. For the multiplet (2) - [FORMULA], 456.8 and 457.5 nm - the values measured in this work are higher than those from Puric et al. (1974) and Platisa et al. (1977), which are in a good agreement with SE model. Values from this work are, however, in a close agreement with ASC and MSE models, and this is also true for multiplets (4) - [FORMULA] nm - and (5) - [FORMULA], 379.6 and 379.1 nm -. Values calculated with both models are very similar from [FORMULA] K on, but the MSE model predicts a more pronounced decrease of Stark broadening with temperature. It is difficult to distinguish the model which fits better the experimental values, but multiplet (5) data from the present work and from Djenize et al. (1992) seem to indicate a better fit is produced by ASC model. Data from Kusch & Schröder (1982) also show a good agreement with this work and with ASC and MSE models in multiplet (4), although the data for multiplet (5) are approximately equidistant between these models and SE model. On the other hand, values predicted for the semi-classical G model are systematically higher than those measured in this work, although the differences decrease when the multiplet number increases (and also the upper level energy of the transition).

[FIGURE] Fig. 7. Stark FWHM at [FORMULA] m-3 versus temperature for the SiIII multiplets (2), (4) and (5) measured in this work ([FORMULA]). Results are compared with previous measurements: [FORMULA] (Puric et al. 1974), [FORMULA] (Platisa et al. 1977), [FORMULA] (Kusch & Schröder 1982) and [FORMULA] (Djenize et al. 1992), and with theoretical predictions: ______ G (Dimitrijevic & Konjevic 1980 , 1981), ______ ASC and ______ SE (Dimitrijevic and Konjevic 1980 , 1981; Dimitrijevic 1983) and - - - MSE (Dimitrijevic & Konjevic 1980 , 1981 , 1987; Dimitrijevic 1983 , 1988).

For multiplet (9) - [FORMULA], 482.0 and 482.9 nm -, which is among the most sensitive to the Stark effect, the measured FWHM in this work is about 400 pm at [FORMULA] m-3, whereas that measured by Djenize et al. (1992) is about 300 pm. To compare these data it is necessary to account for the temperature difference between both experiments (about 30 000 K). Such a discrepancy in the linewidth values is reasonable under the assumption of a decrease with T similar to that corresponding to multiplets (2), (4) and (5). For multiplet [FORMULA] - [FORMULA] and 746.3 nm -, the most sensitive to the Stark effect, there exists no previous experimental data with which to compare. Theoretical calculations for both multiplets have not been found in the literature.

In relation to the Stark shift, one previous work provides experimental values for only two lines. Puric et al. (1974) give for multiplet (2) a blue shift [FORMULA]-7 nm whereas in this work a red shift [FORMULA]-[FORMULA] nm has been measured. Shift calculations are not available in the literature.

As a final conclusion, Stark width and shifts of several interesting SiIII multiplets have been measured in this work. Although the temperature range is not wide enough to discriminate clearly between theories, results obtained are in good agreement with the approximative semi-classical calculations (ASC) of Dimitrijevic and Konjevic. This work offers probably the most extensive experimental compilation of SiIII Stark widths and shifts in the visible performed up to now.

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Online publication: December 5, 2000