Stark broadening of Ca IV spectral lines of astrophysical interest

Transcription

1 doi: /mnras/stu1855 Stark broadening of Ca IV spectral lines of astrophysical interest A. Alonso-Medina and C. Colón Dpto. Física Aplicada. E.T.S.I.D. Industrial, Universidad Politécnica de Madrid, Ronda de Valencia 3, Madrid, Spain Accepted 2014 September 5. Received 2014 September 3; in original form 2014 July 28 ABSTRACT Ca IV emission lines are under the preview of Solar Ultraviolet Measurements of Emitted Radiation device aboard the Solar and Heliospheric Observatory. Also, lines of the Ca IV in planetary nebulae NGC 7027 were detected with the Short Wavelength Spectrometer on board the Infrared Space Observatory. These facts justify an attempt to provide new spectroscopic parameters of Ca IV. There are no theoretical or experimental Stark broadening data for Ca IV. Using the Griem semi-empirical approach and the COWAN code, we report in this paper calculated values of the Stark broadening parameters for 467 lines of Ca IV. They were calculated using a set of wavefunctions obtained by using Hartree Fock relativistic calculations. These lines arising from 3s 2 3p 4 ns(n = 4, 5), 3s 2 3p 4 4p, 3s 2 3p 4 nd(n = 3, 4) configurations. Stark widths and shifts are presented for an electron density of cm 3 and temperatures T = , and K. As these data cannot be compared to others in the literature, we present an analysis of the different regularities of the values presented in this work. Key words: atomic data atomic processes. 1 INTRODUCTION Stark broadening parameters data of spectral lines are needed for the modelling of a stellar plasma. Stark broadening mechanism plays an important role in analysis and modelling of B-type and A-type stellar atmospheres. Calcium is an important element in astrophysics. The calcium abundance is an indicator of the stellar object history. So as example, Ca II lines were detected in the atmospheres of white dwarfs (WDs) at high temperatures (above K) Zuckerman et al. (2003), and were used to estimate the calcium abundance. Since 1966 various authors talked about the presence of strong emission lines of Ca IV in the solar spectra. Thus, Gabriel, Fawcett & Jordan (1966) and Fawcett & Gabriel (1966) identified nine ultraviolet lines corresponding to transitions of Ca IV. Later, Feuchtgruber et al. (1997) observed the presence of Ca IV infrared lines in the planetary nebula NGC Also, in the planetary nebula NGC 2707 Feuchtgruber, Lutz & Beintema (2001) observed the Ca V lines in addition to lines of Ca VII on the planetary nebula NGC Calcium in higher ionization stage (Ca X) was observed in photosphere of the hot WD KPD by Werner, Rauch & Kruk(2008). Rauch et al. (2007) introduced Ca V lines in his atmospheric model. The aim of this work is to provide calculations of Stark broadening parameters of Ca IV, helping to fill the gap for Stark broadening data of different species of calcium. This goal was partially addressed with our calculations of Stark broadening parameters of Ca III, Alonso-Medina & Colón (2013). cristobal.colon@upm.es Analysis of regularities and systematic trends of Stark broadening parameters has always generated a great interest in atomic physics in order to make possible the interpolation of new data. Also is possible checking the consistency of a set of data in absence of experimental data to compare the theoretical results. In this work, we present an analysis of the regularities of Stark broadening parameters within multiplets, and the systematic trends of the parameters versus the temperature. Three times ionized calcium, Ca IV, belongs to the chlorine I sequence. The previous works, published in the literature, about the atomic parameters of the Ca IV are scarce. The earliest works were those of Bowen (1928), Ekefors (1931), Ram (1933), Weissberg & Kruger (1935), Kruger & Phillips (1937) and Tsien (1939). In 1961, Varsavsky present some calculated atomic parameters of Å and resonance lines of Ca IV. In 1966, Gabriel et al. and Fawcett & Gabriel identified new lines of Ca IV spectrum. New spectral lines of Ca IV were identified by Svensson & Ekberg (1968) and Smitt, Svensson & Outred (1976). Theoretical energy levels and transition probabilities of chlorine sequence were presented by Huang et al. (1983). The first compilation of energy levels of Ca IV, based on the previous cited works, were made by Moore (1958), Sugar & Corliss (1985) and Kelly (1987). Later, an exhaustive work about the energy levels of Ca IV was made by Ekberg et al. (1990). In the bibliography, experimental values about transition probabilities are not found. Calculus about oscillator strengths for the chlorine isoelectronic sequence was made by Ganas (1981), Verner, Verner & Ferland (1996), Wilson, Hibbert & Bell (2000), Biémont & Träbert (2000), Sing & Mohan (2001), Berrington, Pelan & Waldock (2001), Froese Fischer, Tachiev & Irimia (2006) and C 2014 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society

2 1568 A. Alonso-Medina and C. Colón Table 1. Calculated transition probabilities A ij for two resonance lines of Ca IV. Wavelength Transition Transition probabilities A ij (10 8 s 1 ) λ (Å) Upper level Lower level This a b c d e (i) (j) work s3p 62 S 1/2 3s 2 3p 52 P 3/ s3p 62 S 1/2 3s 2 3p 52 P 1/ a Verner et al. (1996). b Wilson et al. (2000). c Biémont & Träbert (2000). d Berrington et al. (2001) from gf values. e Froese Fischer et al. (2006). Table 2. Ca IV 3s 2 3p 5 3s3p 6,3s 2 3p 4 3d 3s 2 3p 4 4p and 3s 2 3p 4 4s 3s 2 3p 4 4p line-widths (FWHM), ω (pm), and shifts, d (pm), normalized to Ne = cm 3. We present values only for 11 lines. The remaining up to 60 lines are present online. No Wavelength Transition levels T d ω (pm) λ (Å) a Configuration Term J J (10 4 K) (pm) s 2 3p 4 ( 3 P) 4p 3s 2 3p 4 ( 3 P) 5s 4 P 4 P 3/2 5/ s 2 3p 4 ( 3 P) 4p 3s 2 3p 4 ( 3 P) 5s 4 P 4 P 5/2 5/ s 2 3p 4 ( 3 P) 4p 3s 2 3p 4 ( 3 P) 5s 4 D 4 P 7/2 5/ s 2 3p 4 ( 3 P) 4p 3s 2 3p 4 ( 3 P) 5s 2 D 2 P 3/2 1/ s 2 3p 4 ( 3 P) 4p 3s 2 3p 4 ( 3 P) 5s 4 P 2 P 1/2 3/ s 2 3p 4 ( 3 P) 4p 3s 2 3p 4 ( 3 P) 5s 4 D 2 P 3/2 3/ s 2 3p 4 ( 3 P) 4p 3s 2 3p 4 ( 3 P) 5s 4 D 2 P 5/2 3/ s 2 3p 4 ( 1 D) 4p 3s 2 3p 4 ( 1 D) 5s 2 D 2 D 3/2 3/ s 2 3p 4 ( 1 D) 4p 3s 2 3p 4 ( 1 D) 5s 2 P 2 D 1/2 3/ s 2 3p 4 ( 1 D) 4p 3s 2 3p 4 ( 1 D) 5s 2 F 2 D 7/2 5/ s 2 3p 4 ( 1 D) 4p 3s 2 3p 4 ( 1 D) 5s 2 D 2 D 3/2 5/ Note. A positive shift is red. a Ekberg et al. (1990). Träbert (2014). In addition, no experimental or theoretical values about Ca IV Stark parameters can be found in the literature. In this work, we present semi-empirical approximate values of the Stark broadening parameters for 467 spectral lines of Ca IV arising from 3s 2 3p 4 ns(n = 4, 5), 3s 2 3p 4 4p and 3s 2 3p 4 nd(n = 3,4) configurations. The results have been obtained by using the Griem (1968) semi-classical calculations. Stark widths and shifts are calculated for an electron density of cm 3 and temperatures T = K, and presented in the tables for T = , and K. As these data cannot be compared to others in the literature, we present an analysis of the different regularities of the values presented in this work.

3 Stark broadening of Ca IV 1569 Table 3. Ca IV 3s 2 3p 5 3s 2 3p 4 ns (4, 5) and 3s 2 3p 4 4p 3s 2 3p 4 5s line-widths (FWHM), ω (pm), and shifts, d (pm), normalized to Ne = cm 3. We present values only for 25 lines. The remaining up to 206 lines are present online. No Wavelength Transition levels T ω d λ (Å) a Configuration Term J J (10 4 K) (pm) (pm) s 2 3p 5 3s3p 6 2 P 2 S 1/2 1/ s 2 3p 5 3s3p 6 2 P 2 S 3/2 1/ s 2 3p 4 ( 1 D)4s 3s 2 3p 4 ( 3 P)4p 4 P 4 P 5/2 5/ s 2 3p 4 ( 3 P)3d 3s 2 3p 4 ( 3 P)4p 4 D 4 D 1/2 1/ s 2 3p 4 ( 3 P)3d 3s 2 3p 4 ( 3 P)4p 4 D 4 D 3/2 1/ s 2 3p 4 ( 3 P)3d 3s 2 3p 4 ( 3 P)4p 4 D 4 D 1/2 3/ s 2 3p 4 ( 3 P)3d 3s 2 3p 4 ( 3 P)4p 4 D 4 D 3/2 3/ s 2 3p 4 ( 3 P)3d 3s 2 3p 4 ( 3 P)4p 4 D 4 D 5/2 3/ s 2 3p 4 ( 3 P)4s 3s 2 3p 4 ( 3 P)4p 4 P 4 D 3/2 3/ s 2 3p 4 ( 3 P)3d 3s 2 3p 4 ( 3 P)4p 4 D 4 D 3/2 5/ s 2 3p 4 ( 3 P)3d 3s 2 3p 4 ( 3 P)4p 4 D 4 D 5/2 5/ s 2 3p 4 ( 3 P)3d 3s 2 3p 4 ( 3 P)4p 4 D 4 D 7/2 5/ s 2 3p 4 ( 3 P)4s 3s 2 3p 4 ( 3 P)4p 4 P 4 D 3/2 5/ s 2 3p 4 ( 3 P)4s 3s 2 3p 4 ( 3 P)4p 4 P 4 D 5/2 5/ s 2 3p 4 ( 3 P)3d 3s 2 3p 4 ( 3 P)4p 2 P 4 D 3/2 5/ s 2 3p 4 ( 3 P)3d 3s 2 3p 4 ( 3 P)4p 4 D 4 D 5/2 7/ s 2 3p 4 ( 3 P)3d 3s 2 3p 4 ( 3 P)4p 4 D 4 D 7/2 7/ s 2 3p 4 ( 1 S)4s 3s 2 3p 4 ( 3 P)4p 4 P 4 D 5/2 7/ s 2 3p 4 ( 1 D)3d 3s 2 3p 4 ( 3 P)4p 2 P 2 P 3/2 3/ s 2 3p 4 ( 3 P)4s 3s 2 3p 4 ( 3 P)4p 2 P 2 D 1/2 3/

4 1570 A. Alonso-Medina and C. Colón Table 3 Continued No Wavelength Transition levels T ω d λ (Å) a Configuration Term J J (10 4 K) (pm) (pm) s 2 3p 4 ( 3 P)4s 3s 2 3p 4 ( 3 P)4p.2 P 2 D 3/2 5/ s 2 3p 4 ( 3 P)3d 3s 2 3p 4 ( 1 D)4p 2 D 2 F 3/2 5/ s 2 3p 4 ( 3 P)4s 3s 2 3p 4 ( 1 D)4p 2 D 2 F 5/2 7/ s 2 3p 4 ( 1 D)4s 3s 2 3p 4 ( 1 D)4p 2 D 2 D 3/2 3/ s 2 3p 4 ( 1 D)4s 3s 2 3p 4 ( 1 D)4p 2 D 2 D 5/2 5/ Note. A positive shift is red. a Ekberg et al. (1990). In this paper, we describe in Section 2 the theoretical calculations and in Section 3 the results and discussion, including the regularity of the Stark broadening parameters. 2 THEORETICAL CALCULATIONS Our calculation procedure is the same as presented by the authors in previous works, as example: Alonso-Medina & Herrán (1996), Colón & Alonso-Medina (2002), Colón et al. (2006), Alonso- Medina & Colón (2011, 2013) andcolón, Moreno-Díaz & Alonso- Medina (2013). In this way, the Stark line width and Stark line shifts were calculated from the Griem semi-empirical formulas. In 1968, Griem suggested a simple semi-empirical impact approximation, based on Baranger s original formulation (Baranger 1958) andtheuse of an effective Gaunt factor, proposed by Seaton (1962) andvan Regemorter (1962). In this way, we use the followings semiempirical formulas ( π ) ( ) [ 3/2 1/2 EH ω se 8 N e i r i ( ) 2 E g se 3 ma 0 kt E i i + ( ) E f r f 2 g se (1) E f f f ( π ) 3/2 d 8 N e 3 ma 0 g sh ( E E i i i ( ) [ 1/2 EH ( ) Ei i i r i 2 kt E i i i ) ( ) ( ) f E f f E E f f r f 2 g sh f E f f (2) In these formulas, ω se and d are the Stark line width and shifts respectively in angular frequency units, E H is the hydrogen ionization energy, N e is the free electron perturber density, T the electron temperature, E = (3/2)kT the mean energy of the perturbing electron and g se and g sh are the effective Gaunt, calculated by the expression suggested by Niemann et al. (2003), which produces a good fit to the calculations presented by Van Regemorter (1962). These factors are slowly varying functions of x i i = E/ E i i,where E i i is the energy difference between a perturbing level i and the perturbed level i. The indices i and f denote the initial (upper) and final (lower) levels of the transitions, respectively. ω se is the half-width at half-maximum of the Lorentz profile in frequency units. ω se is proportional to the full width at half-maximum (FWHM) line ω in wavelength units, through the expression ω = ω se λ 2 /(πc). The atomic matrix elements were obtained using relativistic Hartree Fock relativistic calculations (HFR) and configuration interaction in an intermediate coupling (IC) scheme. The COWAN code (Cowan 1981) was selected for this calculation. The basis set used in this work consists of five configurations of even parity, namely, 3s 1 3p 6,3s 2 3p 4 ns (4, 5) and 3s 2 3p 4 nd (3, 4) and three configurations of odd parity, namely, 3s 2 3p 5,3s 2 3p 4 and 3p 6 4p. For the IC calculations, we used the standard method of least-squares fitting of experimental energy levels programs of Cowan s programs. The experimental levels used in our procedure were the presented by Ekberg et al. (1990). To not use in the fit an excessive number of parameters, we have excluded, following the Cowan suggestions, some parameters. We take for all the F k, G k and R k integrals not adjusted in the fitting procedure the HFR ab initio values scaled down by a factor of 0.85 (as suggested by Cowan). For the spin orbit integrals ζ nl characterized by small numerical values and not adjusted in the fitting procedures we used the HFR ab initio values without scaling. Our results are close from those published by Ekberg et al. (1990) and therefore we do not present here details. The wave functions obtained in this description have been used in this work to obtain the matrix elements. As we have indicated above, there are no experimental values of transition probabilities with which to compare our results. Then the only possibility is to compare with other theoretical works. This type of comparison has a certain kind of problem. In the comparison, discrepancies can be present that are in many cases due to the theoretical approach of each author. The HFR method and the Cowan code (in his first calculations, ab initio calculations) are optimized for the calculation of energy levels. It sometimes happens that by forcing a fit to the energy levels, that produces wavelengths very close to the experimental, there are

5 Stark broadening of Ca IV 1571 Table 4. Ca IV 3s 2 3p 5 3s 2 3p 4 3d, 3s 2 3p 5 3s 2 3p 4 4d and 3s 2 3p 4 4p 3s 2 3p 4 4d line-widths (FWHM), ω (pm), and shifts, d (pm), normalized to Ne = cm 3. We present values only for 14 lines. The remaining up to 201 lines are present online. No Wavelength Transition levels T ω d h λ (Å) a Configuration Term J J (10 4 K) (pm) (pm) s 2 3p 4 ( 3 P) 4p 3s 2 3p 4 ( 3 P) 4d 4 P 4 D 3/2 5/ s 2 3p 4 ( 3 P) 4p 3s 2 3p 4 ( 3 P) 4d 4 P 4 D 5/2 5/ s 2 3p 4 ( 3 P) 4p 3s 2 3p 4 ( 3 P) 4d 4 P 4 D 5/2 7/ s 2 3p 4 ( 3 P) 4p 3s 2 3p 4 ( 3 P) 4d 4 D 4 D 7/2 7/ s 2 3p 4 ( 3 P) 4p 3s 2 3p 4 ( 3 P) 4d 4 S 4 P 3/2 3/ s 2 3p 4 ( 3 P) 4p 3s 2 3p 4 ( 3 P) 4d 4 S 4 P 3/2 5/ s 2 3p 4 ( 3 P) 4p 3s 2 3p 4 ( 3 P) 4d 4 D 4 F 5/2 5/ s 2 3p 4 ( 3 P) 4p 3s 2 3p 4 ( 3 P) 4d.4 D 4 F 7/2 9/ s 2 3p 4 ( 3 P) 4p 3s 2 3p 4 ( 3 P) 4d.2 D 2 F 5/2 7/ s 2 3p 4 ( 1 D) 4p 3s 2 3p 4 ( 1 D) 4d 2 F 2 G 5/2 7/ s 2 3p 4 ( 1 D) 4p 3s 2 3p 4 ( 1 D) 4d 2 F 2 G 7/2 9/ s 2 3p 4 ( 1 D) 4p 3s 2 3p 4 ( 1 D) 4d 2 F 2 F 7/2 7/ s 2 3p 4 ( 1 D) 4p 3s 2 3p 4 ( 1 D) 4d 2 D 2 F 5/2 7/ s 2 3p 4 ( 1 D) 4p 3s 2 3p 4 ( 1 D) 4d 2 D 2 D 3/2 5/ Note. A positive shift is red. a Ekberg et al. (1990) important changes in the transition probabilities with respect to the previously calculated ab initio, especially in those lines that being very weak are very sensitive to small changes in the composition of the level. In Table1, we contrast our estimates with values obtained by other authors for the resonance lines and Å, respectively 3s 2 3p 52 P 3/2 3s3p 62 S 1/2 and 3s 2 3p 52 P 1/2 3s3p 62 S 1/2. We have chosen these lines for their astrophysical interest and for being the most studied. Moreover, the description on the base LS levels involved is very similar to the description obtained ab initio, before the fitting process, and allows a comparison with the results of other authors, although our approaches have been different. 3 RESULTS AND DISCUSSION Our results for the Stark line-width (FWHM) and line shift at an electron density of cm 3 and several temperatures T = , and K are displayed in Tables 2, 3 and 4. The complete tables are presented online and text included only those corresponding to the most intense spectral lines referenced by Ekberg. The first column of these tables shows an arbitrary number, which coincides with the one presented in online tables. In the second column, we present the corresponding wavelengths, in Å (Ekberg et al. 1990) for each studied transition. The third column indicates the configuration of the energy levels. In column 4, we displayed

6 1572 A. Alonso-Medina and C. Colón Figure 1. Partial Grotrian diagram of the Ca IV corresponding to the transitions 3s 2 3p 4 ( 3 P) 3d 4 D 3s 2 3p 4 ( 3 P) 4p 4 D that shows the Stark broadening of spectral lines involved (data in brackets next to the wavelength). Figure 2. Calculated Stark widths FWHM (ω (pm), ) and shifts (d (pm), ) versus temperature for some Ca IV lines at an electron density of cm 3.

7 Stark broadening of Ca IV 1573 the temperatures. Stark broadening line-widths (in pm) and Stark broadening line-shift (in pm) are showed in the two last columns. In the literature, there are no experimental values. Also, we have not found values calculated by other authors. So we cannot compare our values with no other result. We present the Stark broadening for all intense lines identified by Ekberg et al. (1990). We have also included, online, the broadening of the ultraviolet resonance transitions arising from the 3s 2 3p 4 5s configuration levels that had high theoretical transition probabilities. Stark broadenings of tenths of picometre were found for these last lines. The most important feature of these results is that about half of the lines calculated in this work show Stark broadenings of tenths of Å. Deserve special attention, the spectral lines , , and Å which have high experimental intensities and high theoretical Stark broadening. Another feature of our results is that there are broadening parameters for lines corresponding to the same multiplet, which are relatively different values. This behaviour can be seen in Fig. 1. In this figure, we present a partial Grotrian diagram of the Ca IV corresponding to the transitions 3s 2 3p 4 ( 3 P) 3d 4 D 3s 2 3p 4 ( 3 P) 4p 4 D. We observe that lines arising from the same level have a similar broadening. However for lines arising from different levels, the values found are different. Situations like this have been observed in different elements and different atomic species and are most common with growing the complexity of the atomic system studied. Recently, Pélaez et al. (2009) found similar irregularities of Stark parameters of Xe II spectral lines. This behaviour is explained in some cases by the fact that the levels of the 3s2 3p4 3d configuration are mixed with levels of 3s2 3p4 4s configuration and in other cases because the spectral lines with different levels from different angular momentum, J, have large differences in the number of levels that interact in broadening processes. In order to compare the dependence of the Stark parameters on the electron temperature, in Fig. 2 we display the calculated Stark widths FWHM (ω(å)) and Stark line shifts (d(å)) versus temperature for , , and Ca IV lines. As expected, the trends found coincide with the theoretically anticipate. These lines have been chosen for the reason previously noted (high experimental intensity and high Stark broadening). Also, these lines arising from levels that present differences in energy of the order of cm 1 and are in a relatively short wavelength range ( 400 Å). Therefore appear that these lines could be used in the diagnosis of plasmas. In conclusion, by using the cowan code we have obtained the matrix elements necessary to calculate the Stark broadening parameter of Ca IV spectral lines. Clear trends in the Stark widths are seen in our results. There are several ways to perform these calculations. We prefer the semi-empirical method of Griem. Our experience is that the semiclassical method Sahal Brechot gives results similar to ours and that both methods give good results within the margins of experimental error, when calculations can be compared with measured values, Simić et al. (2008), Simić(2009) and Alonso-Medina &Colón (2011). ACKNOWLEDGEMENTS This work has been supported by the Spanish DGI project MAT REFERENCES Alonso-Medina A., Herrán C., 1996, Phys. Scr., 54, 332 Alonso-Medina A., Colón C., 2011, MNRAS, 414, 713 Alonso-Medina A., Colón C., 2013, MNRAS, 431, 2703 Baranger M., 1958, Phys. Rev., 112, 855 Biémont E., Träbert E., 2000, J. Phys. B: At. Mol. Opt. Phys., 33, 2939 Berrington K. A., Pelan J. 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8 1574 A. Alonso-Medina and C. Colón Table 3. Ca IV 3s 2 3p 5 3s 2 3p 4 ns (4, 5) and 3s 2 3p 4 4p 3s 2 3p 4 5s line-widths (FWHM), ω (pm), and shifts,d(pm), normalized to Ne = cm 3. Table 4. Ca IV 3s 2 3p 5 3s 2 3p 4 3d, 3s 2 3p 5 3s 2 3p 4 4d and 3s 2 3p 4 4p 3s 2 3p 4 4d line-widths (FWHM), ω (pm), and shifts, d (pm), normalized to Ne = cm 3 ( oxfordjournals.org/lookup/suppl/doi: /mnras/ stu1855/-/dc1). Please note: Oxford University Press is not responsible for the content or functionality of any supplementary materials supplied by the authors. Any queries (other than missing material) should be directed to the corresponding author for the paper. This paper has been typeset from a Microsoft Word file prepared by the author.