Stark widths of Ar III spectral lines in the atmospheres of subdwarf B stars
Rafik Hamdi, Nabil Ben Nessib, Sylvie Sahal-Bréchot, Milan S. Dimitrijević
aa r X i v : . [ a s t r o - ph . S R ] N ov Stark widths of Ar III spectral lines in the atmospheres of subdwarf B stars
Rafik Hamdi ∗ Groupe de Recherche en Physique Atomique et Astrophysique, Facult´e des Sciences de Bizerte,Universit´e de Carthage, Tunisia.
Nabil Ben Nessib
Department of Physics and Astronomy, College of Science, King Saud University. PO Box 2455,Riyadh 11451, Saudi Arabia.
Sylvie Sahal-Br´echot
Laboratoire d’ ´Etude du Rayonnement et de la Mati`ere en Astrophysique, Observatoire de Paris, UMR CNRS 8112,UPMC, 5 Place Jules Janssen, 92195 Meudon Cedex, France.
Milan S. Dimitrijevi´c
Astronomical Observatory, Volgina 7, 11060 Belgrade, Serbia.Laboratoire d’ ´Etude du Rayonnement et de la Mati`ere en Astrophysique, Observatoire de Paris, UMR CNRS 8112,UPMC, 5 Place Jules Janssen, 92195 Meudon Cedex, France.
Abstract
Using semiclassical perturbation approach in impact approximation, we have calculated Stark widths for 32 spectrallines of doubly charged argon (Ar III). Oscillator strengths are calculated using Hartree-Fock method with relativisticcorrection (HFR) and an atomic model including 17 configurations. Energy levels are taken from NIST database.For perturbing levels for which the corresponding energy does not exist in NIST database, the calculated energies areused. Our widths are compared with the experimental results. The results presented here are of interest for modellingand investigation of stellar atmospheres since argon in different ionization stages is observed in many astrophysicalobjects. Finally, the importance of Stark broadening mechanism is studied in the atmospheric conditions of sdB stars.Electron impact Stark widths are compared to thermal Doppler widths as a function of temperature and optical depthof atmospheric layers.
Keywords: atomic data; atomic processes; line: profiles; stars: atmospheres
1. Introduction
Stark broadening parameters (width and shift) are ofinterest for the study of astrophysical and laboratory plasma.Stark Broadening parameters can be used in the determi-nation of temperature and density of laboratory plasma.For example, in Zhou et al. (2009), electron temperatureand density are determined simultaneously in a cold argonarc-plasma jet by using Stark broadening of two differentemission lines.Stark broadening is important for modelling and inves-tigation of stellar atmospheres of A and B stars (Popovi´c ∗ Corresponding author
Email addresses:
[email protected] (Rafik Hamdi), [email protected] (Nabil Ben Nessib), [email protected] (Sylvie Sahal-Br´echot), [email protected] (Milan S. Dimitrijevi´c ) Deanship of the Foundation Year, Department of Physics, UmmAl-Qura University, Makkah, Kingdom of Saudi Arabia. et al., 2001; Simi´c et al., 2005). Dimitrijevi´c et al. (2007)studied the Stark broadening on the line shapes of Cr IIspectral lines observed in stellar atmospheres of middlepart of the main sequence. They found that Stark broad-ening mechanism is very important and should be takeninto account, especially in the study of Cr abundance strat-ification.Besides main sequence stars, Stark broadening mecha-nism is important for white dwarfs. Hamdi et al. (2008)considered the broadening on Si VI lines in DO white dwarfspectra. They found that Stark broadening is dominantin broad regions of the considered DO atmospheres. Formuch cooler DB white dwarfs, Stark broadening is usuallythe dominant broadening mechanism (Dimitrijevi´c et al.,2011; Simi´c et al., 2009).Doubly charged Argon (Ar III) spectral lines are ob-served in many astrophysical plasmas. In Rodr´ıguez (1999),Ar III lines are used in the determination of abundance in
Preprint submitted to Advances in Space Research November 2, 2018 alactic H II regions. Blanchette et al. (2008), used ArIII λ Space Telescope Imaging Spectrograph on-board the
Hubble Space Telescope . Abundance of Ar IIIion was determined in the studied sdB stars.Stark widths measurement of Ar III spectral lines arereported in eight works: Plati˘sa et al. (1975); Baker &Burgess (1979); Konjevi´c & Pittman (1987); Puri´c et al.(1988); Kobilarov & Konjevi´c (1990); Djeniˇze et al. (1996);Bukvi´c et al. (2008); Djurovi´c et al. (2011). In Baker& Burgess (1979), Stark broadening parameters were de-termined in 870-890 ˚A wavelength interval. In all otherworks, Stark broadening parameters were determined in2140-3960 ˚A wavelength interval.In this work, we have calculated Stark widths for 32Ar III spectral lines. We have used semiclassical pertur-bation approach in impact approximation (Sahal-Br´echot,1969a,b). Energy levels are taken from NIST database(Ralchenko et al., 2011) and oscillator strengths are calcu-lated using Cowan code (Cowan, 1981). Our Stark widthsare compared with the experimental results of (Djurovi´cet al., 2011; Bukvi´c et al., 2008; Djeniˇze et al., 1996; Kobi-larov & Konjevi´c, 1990; Konjevi´c & Pittman, 1987; Plati˘saet al., 1975). Finally, the importance of collisions withelectrons in atmospheric conditions of subdwarf B (sdB)stars is studied. Electron impact Stark widths are com-pared with thermal Doppler width as a function of opticaldepth and as a function of the temperature of atmosphericlayers.
2. The impact semiclassical perturbation method
The impact semiclassical perturbation formalism is de-scribed in Sahal-Br´echot (1969a,b). The innovations tothis formalism are given in Sahal-Br´echot (1974, 1991);Fleurier et al. (1977); Dimitrijevi´c & Sahal-Br´echot (1996).For example in Sahal-Br´echot (1974) the expression of thequadrupole term for complex atoms was given. The profile F ( ω ) is Lorentzian for isolated lines: F ( ω ) = w/π ( ω − ω if − d ) + w (1)where ω if = E i − E f ~ i and f denote the initial and final states and E i and E f their corresponding energies.The total width at half maximum ( W = 2 w ) and shift( d ) (in angular frequency units) of an electron-impact broad-ened spectral line can be expressed as: W = N Z vf ( v ) dv X i ′ = i σ ii ′ ( v ) + X f ′ = f σ ff ′ ( v ) + σ el d = N Z vf ( v ) dv Z R D R πρdρ sin(2 ϕ p ) (2)where N is the electron density, f ( υ ) the Maxwellian veloc-ity distribution function for electrons, ρ denotes the impactparameter of the incoming electron, i ′ (resp. f ′ ) denotesthe perturbing levels of the initial state i (resp. final state f ). The inelastic cross section σ ii ′ ( υ ) (resp. σ ff ′ ( υ )) canbe expressed by an integral over the impact parameter ρ of the transition probability P ii ′ ( ρ, υ ) (resp. P ff ′ ( ρ, υ ) )as X i ′ = i σ ii ′ ( υ ) = 12 πR + Z R D R πρdρ X i ′ = i P ii ′ ( ρ, υ ) . (3)and the elastic contribution is given by σ el = 2 πR + Z R D R πρdρ sin δ + σ r ,δ = ( ϕ p + ϕ q ) . (4)The phase shifts ϕ p and ϕ q due respectively to the po-larization potential ( r − ) and to the quadrupolar poten-tial ( r − ), are given in Section 3 of Chapter 2 in Sahal-Br´echot (1969a) and R D is the Debye radius. All the cut-offs R , R and R are described in Section 1 of Chapter3 in Sahal-Br´echot (1969a). σ r is the contribution of theFeshbach resonances (Fleurier et al., 1977).The formulae for the ion-impact widths and shifts areanalogous to Eqs. (2)-(4), without the Feshbach reso-nances contribution to the width. For electrons, hyper-bolic paths due to the attractive Coulomb force are used,while for perturbing ions the hyperbolic paths are differentsince the force is repulsive.Semiclassical perturbation calculations need a relativelylarge set of oscillator strengths. In this work, oscillatorstrengths are calculated with the Hartree-Fock relativisticapproach using Cowan code (Cowan, 1981) and an atomicmodel including 17 configurations: 3s , 3s nl ( nl =4p,4f, 5p, 5f, 6p, 6f) (even parity) and 3s3p , 3s n ′ l ′ ( n ′ l ′ =3d, 4s, 4d, 5s, 5d, 5g, 6s, 6d, 6g) (odd parity).
3. Semiclassical perturbation Stark widths and com-parison with experiments
Djurovi´c et al. (2011) reported Stark width measure-ments of 19 Ar III spectral lines. The plasma source wasa low-pressure-pulsed arc. Electron densities of (3.5 - 9.0) × cm − were determined by two-wavelength inter-ferometry method and electron temperature of 16 000 -24 000 K was measured with the help of the Boltzmannplot technique. All spectral lines for which Djurovi´c et al.(2011) measured Stark parameters belong to the UV re-gion of 2630 - 3960 ˚A. Authors report that the errors ofthe measured widths vary from 15% to 50%. In Bukvi´c etal. (2008), Stark widths measurements of 12 Ar III spectrallines are reported. The plasma source was a mixture of Ar2 T(K) W ( ¯ ) S o2 - 4p P =3301.85 ¯ Figure 1: Electron impact Stark width (FWHM) for the 4 s S o2 -4 p P ( λ = 3301.85 ˚A) line as a function of electron temperatureat an electron density of 10 cm − . Solid line: Our Stark widthsobtained using semiclassical perturbation approach (Sahal-Br´echot,1969a,b).( ◮ ): experimental Stark width of Djurovi´c et al. (2011).( N ): experimental Stark width of Bukvi´c et al. (2008). ( (cid:4) ): experi-mental Stark width of Djeniˇze et al. (1996). ( (cid:3) and △ ): experimentalStark widths of Konjevi´c & Pittman (1987) given for temperatures21100 K and 26000 K respectively. ( (cid:7) and ♦ ): experimental Starkwidths of Plati˘sa et al. (1975) given for temperatures 21100 K and23080 K respectively. P o2 - 4p" D =3023.98 ¯ W ( ¯ ) T(K)
Figure 2: Same as in Fig. 1 but for the 4 s ′′ P o2 - 4 p ′′ D ( λ =3023.98 ˚A) transition. (72 %) and He (28 %) plasma created in the linear, lowpressure, arc discharge. The electron temperature belong-ing to the interval (26 000 - 30 000 K) was estimated usingBoltzmann plot technique. The electron density belongingto the interval (0.16 - 1.68) × cm − was determinedusing single laser interferometry technique at the wave-length 6328 ˚A of the He-Ne laser. According to Bukvi´c etal. (2008) the Stark widths were measured with 12 % error.Djeniˇze et al. (1996) reported Stark width measurementsof 13 Ar III spectral lines at an electron density of 3.5 × cm − and electron temperature of 38 000 K. Theplasma source was also an argon-helium mixture. Electrondensity was also measured using laser interferometry at6328 ˚A. Electron temperature was measured using Boltz-mann plot and ratios of Ar IV to Ar III lines and Ar III toAr II lines. The uncertainty of the results given by Djeniˇzeet al. (1996) vary from ±
14 % to ±
18 %. Kobilarov &Konjevi´c (1990) gives electron impact widths for six ArIII spectral lines. A low-pressure pulsed arc was used asplasma source. Electron-density was measured using Starkwidth of He II Pashen- α ±
15 %for the widths. Plati˘sa et al. (1975) reported Stark widthsof five Ar III spectral lines. Electron density was deter-mined using the same method as in Konjevi´c & Pittman(1987) and electron temperature were determined from theBotltzmann plot of relative intensities of eight Ar II lines.Plati˘sa et al. (1975) estimated that the error of the mea-sured widths is ±
30 %.In Table 1, we present our electron impact (W e ) and ionimpact (W i ) Stark widths (FWHM) with the experimen-tally determined Stark width (W m ) taken from Djurovi´cet al. (2011); Bukvi´c et al. (2008); Djeniˇze et al. (1996);Kobilarov & Konjevi´c (1990); Konjevi´c & Pittman (1987);Plati˘sa et al. (1975). Our Stark widths are calculated usingsemiclassical perturbation approach in impact approxima-tion (Sahal-Br´echot, 1969a,b). Energy levels needed forthis calculation are taken from NIST database (Ralchenkoet al., 2011) and oscillator strengths are calculated usingCowan code (Cowan, 1981) and the atomic model previ-ously described. For perturbing levels for which the corre-sponding energy do not exist in NIST database (Ralchenkoet al., 2011), we have used the energies that we have calcu-lated using Cowan code (Cowan, 1981). In NIST databasewe have found 125 energy levels and 497 classified elec-tric dipole transitions. Among these transitions, only 68are given with the corresponding oscillator strengths. Thisnumber of oscillator strengths is not sufficient to performa semiclassical perturbation calculation of 32 Stark widthswhich need a large number of oscillator strengths. So the3 T (K) W ( ¯ ) D o3 - 4p’ F =3336.17 ¯ Figure 3: Same as in Fig. 1 but for the 4 s ′ D o3 - 4 p ′ F ( λ = 3336.17˚A) transition. use of Cowan code for the calculation of oscillator strengthsis very interesting. In Hamdi et al. (2013) and Hamdi et al.(2011), we have used this method for Pb IV and we havedetermined Stark broadening parameters for 114 spectrallines. In our calculation, only electric dipole (E1) tran-sitions are taken into account. All wavelengths given inTable 1 are taken from NIST database (Ralchenko et al.,2011). For each value given in Table 1, the collision volume( V ) multiplied by perturber density ( N ) is much less thanone and the impact approximation is valid. In some cases,0.1 < N V ≤ N × V , equal to 0.20 has beenfound for 4p ′ D o3 - 4d ′ P transition for collisions withions. For each transition given in Table 1, our semiclassicalperturbation Stark width is W sc = W e +W i . Taking intoaccount the plasma composition for each experiment, wehave taken as ionic perturber singly ionized helium whenwe compared with Bukvi´c et al. (2008) and Djeniˇze etal. (1996), singly ionized argon when we compared withDjurovi´c et al. (2011) and singly ionized nitrogen when wecompared with Plati˘sa et al. (1975). In Kobilarov & Kon-jevi´c (1990); Konjevi´c & Pittman (1987), electron impactwidths were reported, for this reason broadening by colli-sion with ions is not given when we compare with thosetwo authors.The agreement of our Stark widths with Djurovi´c et al.(2011) values is 35% in average. All our values are greaterthan Djurovi´c et al. (2011) ones. The lower value of ratio W m W sc equal to 0.93 is found for the 3d ′ D o1 - 4p ′ D tran-sition. The largest differences between our values and ex-perimental Stark widths of Djurovi´c et al. (2011) are foundfor 4s ′ - 4p ′ transitions as for example for the 4s ′ D o2 - 4p ′ P transition for which the ratio W m W sc is equal to 0.67. Wenotice that this transition is classified by Djurovi´c et al. W ( ¯ ) D o3 - 4p’ D =3480.50 ¯ T (K)
Figure 4: Same as in Fig. 1 but for the 4 s ′ D o3 - 4 p ′ D ( λ =3480.50 ˚A) transition. (2011) as C (errors up to 50%). So, taken into account theaccuracy of the experimental results, the agreement withStark widths of Djurovi´c et al. (2011) is acceptable for alltransitions. Very good agreement is found with Bukvi´cet al. (2008) (8.6 % on average). The greatest difference(31%) between our Stark widths and Bukvi´c et al. (2008)ones is found for 4s ′′ P o2 - 4p ′′ D transition. For the3d ′′ P o1 - 4p ′′ P transition the ratio W m W sc is equal to 1.On average, our Stark widths agree with Djeniˇze et al.(1996) ones within 26%. Besides multiplets arising from4s, 4p, 4s ′ , 4p ′ , 3d ′′ , 4p ′′ parent energy levels, results forhigher multiplets arising from 5s, 4d ′ , 5s ′ are also given.An agreement better than 30% is found for these multi-plets except for 4p ′ D - 4d ′ P o2 transition, the differencebetween our calculated Stark width and the measured oneis 46%. The agreement between our electron impact Starkwidths and the values of Kobilarov & Konjevi´c (1990) iswithin 35%. In Kobilarov & Konjevi´c (1990), Stark widthsare given for two experimental conditions: T = 80 000K, Ne = 5.8 × cm − and T = 110 000 K, Ne = 1 × cm − . Our results agree better with the experi-mental Stark widths given for T = 80 000 K and Ne =5.8 × cm − . All our Stark widths are greater thanKobilarov & Konjevi´c (1990) ones. Our electron impactStark widths agree with Konjevi´c & Pittman (1987) oneswithin 40 %. All our results are greater than Konjevi´c &Pittman (1987) ones. The greatest difference (76%) be-tween our Stark widths and Konjevi´c & Pittman (1987)values is found for the 4 s ′ D o3 - 4 p ′ D ( λ = 3480.50 ˚A)transition. In Plati˘sa et al. (1975), measured Stark widthsare given for two experimental conditions: T = 21 100 K,Ne = 0.44 × cm − and T = 23 080 K, Ne = 0.80 × cm − . The agreement of our widths with the resultsof Plati˘sa et al. (1975) is not good specially for T = 23080 K and Ne = 0.80 × cm − . For some lines we4ound a factor greater than two between our Stark widthsand Plati˘sa et al. (1975) ones.In Fig. 1, we present our electron impact Stark width asa function of electron temperature for the interval (20 000- 120 000 K) along with experimental values of Djurovi´cet al. (2011); Bukvi´c et al. (2008); Djeniˇze et al. (1996);Kobilarov & Konjevi´c (1990); Konjevi´c & Pittman (1987)and Plati˘sa et al. (1975) for the transition 4 s S o2 - 4 p P ( λ = 3301.85 ˚A). All experimental values are normalized toan electron density of 10 cm − . This figure shows thatour results over estimate all the experimental values. Fig.2, Fig. 3 and Fig. 4, are the same as Fig. 1 but for thetransitions: 4 s ′′ P o2 - 4 p ′′ D ( λ = 3023.98 ˚A), 4 s ′ D o3 -4 p ′ F ( λ = 3336.17 ˚A) and 4 s ′ D o3 - 4 p ′ D ( λ = 3480.50˚A) respectively. Fig. 2 shows also that our theoreticalStark widths overestimate the experimental values. Wecan see also that our width at T = 30 000 K is very closeto Bukvi´c et al. (2008) value. In Fig. 3, we can see thatour electron impact Stark width underestimate the exper-imental value of Bukvi´c et al. (2008) and overestimate allothers results. The result of Djeniˇze et al. (1996) is theclosest to our value. Fig. 4 shows that our widths over-estimate the experimental values of Djeniˇze et al. (1996);Konjevi´c & Pittman (1987); Plati˘sa et al. (1975) and thatour width at T = 30 000 K is very close to Bukvi´c et al.(2008) one. Fig. 1, Fig. 3 and Fig. 4 show a large differ-ence between our widths and Plati˘sa et al. (1975) ones atT = 23080 K.Our results as a function of temperature and electrondensity will be published elsewhere and will be inserted inthe Stark-B database (Sahal-Br´echot et al., 2012), which isa part of Virtual Atomic and Molecular Data Center (Du-bernet et al., 2010). Besides the study and investigationof stellar atmospheres, this database is also devoted to thestudy of laboratory an fusion plasma. For example, ArIII ion spectral lines are observed by Graf et al. (2011) inthe spectrum of deuterium plasma in the Alcator C-ModTokamak. W ( ¯ ) T (K) 5.00 5.25 5.50 5.75 6.00W
Stark log gW
Doppler
Figure 5: Stark and Doppler widths for Ar III 4p P - 5s S o2 ( λ = 2170.22 ˚A) spectral line as a function of atmospheric layertemperature. Stark widths are shown for five values of model gravitylog g = 5-6, T eff = 22 000 K.
4. Stark broadening effect in sdB stars atmospheres
Subdwarf B (sdB) stars are low-mass core helium burn-ing stars with extremely thin hydrogen envelopes locatedon the extreme horizontal branch of the H-R diagram. ThesdB stars have a high effective temperature (20 000 K ≤ T eff ≤
40 000 K) and gravities (log g ≃ W D [˚A] = 7 . × − λ [˚A] s T[K]M Ar (5)where atomic weight of argon is M Ar = 39.948 au.The importance of Stark broadening mechanism for theAr III 4p P - 5s S o2 ( λ = 2170.22 ˚A) spectral line in at-mospheric conditions of sdB stars is studied. We use theatmospheric models of Jeffery et al. (2001) (http://star.arm.ac.uk/ csj/models/Grid.html) which are plane-parallel line-blanketed model atmospheres for hot stars in local ther-mal, radiative and hydrostatic equilibrium. The consid-ered atmospheres have the following composition: 0.0015 able 1: Our electron impact Stark widths (FWHM) (W e ) and ion impact Stark widths (W i ) calculated using SCP approach in impactapproximation (Sahal-Br´echot, 1969a,b) compared with experimental values of Djurovi´c et al. (2011); Bukvi´c et al. (2008); Djeniˇze et al.(1996) (W m ). Transitions, wavelengths, electron temperature (T) and electron density (N e ) are also given. Ref.: a: Djurovi´c et al. (2011); b:Bukvi´c et al. (2008); c: Djeniˇze et al. (1996); d: Kobilarov & Konjevi´c (1990); e: Konjevi´c & Pittman (1987); f: Plati˘sa et al. (1975). Transition Term λ (˚A) T (K) N e (10 cm − ) W m (pm) W e (pm) W i (pm) Ref.4s - 4p S o2 - P S o2 - P S o2 - P ′ - 4p ′ D o1 - P D o2 - P D o2 - P D o3 - P ′ - 4p ′ D o2 - D D o3 - D D o2 - D ′ - 4p ′ D o3 - F D o2 - F D o3 - F D o1 - F D o2 - F ′′ - 4p ′′ P o2 - P P o2 - P able 1: Continued.
Transition Term λ (˚A) T (K) N e (10 cm − ) W m (pm) W e (pm) W i (pm) Ref. P o1 - P P o1 - P ′′ - 4p ′′ P o2 - D P o2 - D P o1 - D ′ - 4p ′ D o1 - D D o2 - D ′′ - 4p ′′ P o2 - S ′′ - 4p ′′ P o2 - P P o1 - P P - S o2 P - S o2 P - S o2 ′ - 4d ′ D - P o2 ′′ - 5s ′ D - D o3 W ( ¯ ) optical depth (at 4000 ¯ ) 5.00 5.25 5.50 5.75 6.00W Stark log gW
Doppler
Figure 6: Stark and Doppler widths for Ar III 4p P - 5s S o2 ( λ =2170.22 ˚A) spectral line as a function of optical depth. Stark widthsare shown for five values of model gravity log g = 5-6, T eff = 22000 K. helium, 0.99741 hydrogen and 0.00047 carbon and nitro-gen.In Figs. 5 and 6, we show Stark and Doppler widthsfor Ar III 4p P - 5s S o2 ( λ = 2170.22 ˚A) spectral line asa function of atmospheric layer temperature and as a func-tion of the optical depth (at 4000 ˚A) respectively. Starkwidths are shown for five values of model gravity log g = 5-6, T eff = 22 000 K. As we can see in Fig. 5, forthe atmosphere with log g = 6, Stark broadening is thedominant broadening mechanism for the atmospheric lay-ers for which the temperature is higher than 43 000 K. Forthe atmosphere with log g = 5.75, Stark width is equalto Doppler width for the atmospheric layer with temper-ature T ≈
50 000 K. For the atmospheres with log g =5.50 and log g = 5.25, Stark width is higher than Dopplerone only for deep atmospheric layers. For the atmospherewith log g = 5, Stark width became comparable to Dopplerone for the deeper layer of the atmosphere (at T = 67638K, W Stark = 0.0565 ˚A and W
Doppler = 0.0639 ˚A). Oneshould take into account, however, that even when theDoppler width is larger than Stark width, due to differentbehaviour of Gaussian and Lorentzian distributions, Starkbroadening may be important in line wings.
5. Conclusions
In this work we have determined Stark widths for 32spectral lines of Ar III, our results are in relatively goodagreement with many experimental results. The betteragreement is found with Bukvi´c et al. (2008). The largestdisagreement is found with Plati˘sa et al. (1975). Compar-ison between theoretical and experimental results allowsto improve both theories and experiments. Our results7how that the use of the Cowan code (Cowan, 1981) forthe determination of oscillator strengths needed for SCPcalculation of Stark widths is very useful when no exper-imental data exist. Our study of the Stark broadening insdB stars shows the importance of this mechanism espe-cially for the atmospheres with high values of log g . Acknowledgment
This work has been supported by the Tunisian researchunit 05/UR/12-04. This work is also a part of the project176002 ”Influence of collisional processes on astrophysicalplasma line shapes” supported by the Ministry of Educa-tion, Science and Technological Development of Serbia. Apart of this work is presented in the 9 th SCSLSA.
References
Baker, E.A.M., & Burgess, D.D., Observations of high-density ef-fects on spectral line shapes in a dense (n e > cm − ) z-pinchdischarge , J. Phys. B: Atom. Molec. Phys., 12, 2097-2113, 1979.Blanchette, J.-P., Chayer, P., Wesemael, F. et al., FUSE determi-nation of abundances in long-period pulsating V1093 HER (PG1716+426) stars, ApJ, 678, 1329-1341, 2008.Bukvi´c, S., ˘Zigman, V., Sre´ckovi´c, A., & Djeniˇze, S., Line broadeningin the Ar III spectrum, J. Quant. Spectrosc. Radiat. Tranfer, 109,2869-2876, 2008.Cowan, R.D., The Theory of Atomic Structure and Spectra, Univer-sity of California Press, Berkeley, USA, 1981Dimitrijevi´c, M.S., & Sahal-Br´echot, S., Stark broadening of Li IIspectral lines, Physica Scripta, 54, 50, 1996.Dimitrijevi´c, M.S., Ryabchikova, T., Simi´c, Z., Popovi´c, L. ˇC &Daˇci´c, M., The influence of Stark broadening on Cr II spectralline shapes in stellar atmospheres, A&A, 469, 681-686, 2007.Dimitrijevi´c, M.S., Kovaˇcevi´c, A., Simi´c, Z. & Sahal-Br´echot, S.,Stark Broadening and White Dwarfs, Baltic Astronomy, 20, 495-502, 2011.Djeniˇze, S., Bukvi´c, S., Sre´ckovi´c, A., & Plati˘sa, M., Stark widthsof doubly ionized argon spectral lines, J. Phys. B: Atom. Molec.Phys., 29, 429-434, 1996.Djurovi´c, S., Mar, S., Pel´aez, J. & Aparicio, J.A., Stark broadeningof ultraviolet Ar III spectral lines, MNRAS, 414, 1389-1396, 2011.Dubernet, M.L., Boudon, V., Culhane, J.L., et al., Virtual atomicand molecular data center, J. Quant. Spectrosc. Radiat. Tranfer,111, 2151-2159, 2010.Fleurier, C., Sahal-Br´echot, S., & Chapelle, J., Stark profiles of someion lines of alkaline earth elements, J. Quant. Spectrosc. Radiat.Tranfer, 17, 595-604, 1977.Graf, A.T., May, M.J., & Beiersdorfer, P., A visible spectral surveyfrom the Alcator C-Mod tokamak, Can. J. Phys., 89, 615-626,2011.Hamdi, R., Ben Nessib, N., Milovanovi´c, N., Popovi´c, L. ˇC., Dimitri-jevi´c, M.S. & Sahal-Br´echot, S., Atomic data and electron-impactbroadening effect in DO white dwarf atmospheres: Si VI, MNRAS,387, 871-882, 2008.Hamdi, R., Ben Nessib, N., Dimitrijevi´c, M.S. & Sahal-Br´echot, S.,Ab initio determination of atomic structure and Stark broadeningparameters: Pb IV and recent results, Baltic Astronomy, 20, 552-557, 2011.Hamdi, R., Ben Nessib, N., Dimitrijevi´c, M.S. & Sahal-Br´echot, S.,Stark broadening of Pb IV spectral lines, MNRAS, 431, 1039-1047,2013.Jeffery, C.S., Woolf, V.M., & Pollacco, D.L., Time-resolved spectralanalysis of the pulsating helium star V652 Her, A&A, 376, 497-517, 2001. (http://star.arm.ac.uk/ csj/models/Grid.html) Kobilarov, R., & Konjevi´c, N., Plasma shift and broadening of anal-ogous transitions of Si II, Cl III, Ar IV, Cl II, and Ar III, Phys.Rev. A, 41, 6023-6031, 1990.Konjevi´c, N., & Pittman, T.L., Stark broadening of spectral linesof homologous, doubly-ionized inert gases , J. Quant. Spectrosc.Radiat. Tranfer, 37, 311-318, 1987.Konjevi´c, N., Plasma broadening and shifting of non-hydrogenicspectral lines: present status and applications, Physics Reports,316, 339-401, 1999.Ohl, R.G., Chayer, P., & Moos, H.W., Photospheric metals in thefar ultraviolet spectroscopic explorer spectrum of the subdwarf Bstar PG 0749+658, ApJ, 538, L95-L98, 2000.O’Toole, S.J., & Heber, U., Abundance studies of sdB stars usingUV echelle HST/STIS spectroscopy, A&A, 452, 579-590, 2006.Plati˘sa, M., Popovi´c, M., Dimitrijevi´c, M., & Konjevi´c, N., StarkBroadening of A III and A IV lines, Z. Naturforsch., 30, 212-215,1975.Popovi´c, L. ˇC, Simi´c, S., Milovanovi´c, N. & Dimitrijevi´c, M.S., Starkbroadening effect in stellar atmospheres: Nd II lines, ApJS, 135,109-114, 2001.Puri´c, J., Djeniˇze, S., Sre´ckovi´c, A., ´Cuk, M., Labat, J. & Plati˘sa,M., Stark broadening and regularities of ionized neon and argonspectral lines, Z. Phys. D - Atoms Molecules and Clusters, 8, 343-347, 1988.Ralchenko, Yu., Kramida, A.E., Reader, J., and NIST ASD Team(2011). NIST Atomic Spectra Database (ver. 4.1.0), [Online].Available: http://physics.nist.gov/asd [2012, April 5]. NationalInstitute of Standards and Technology, Gaithersburg, MD.Rodr´ıguez, M., The abundances of O, S, Cl, N, Ar, He and C inseven Galactic H II regions, A&A, 351, 1075-1086, 1999.Sahal-Br´echot, S., Impact theory of the broadening and shift of spec-tral lines due to electrons and ions in a plasma, A&A, 1, 91-123,1969.Sahal-Br´echot, S., Impact theory of the broadening and shift of spec-tral lines due to electrons and ions in a plasma (continued), A&A,2, 322-354, 1969.Sahal-Br´echot, S., Stark broadening of isolated lines in the impactapproximation, A&A, 35, 319-321, 1974.Sahal-Br´echot, S., Broadening of ionic isolated lines by interactionswith positively charged perturbers in the quasistatic limit, A&A,245, 322-330, 1991.Sahal-Br´echot, S., Dimitrijevi´c, M.S., & Moreau N., Virtual Lab-oratory Astrophysics: the STARK-B database for spectral linebroadening by collisions with charged particles and its link to theEuropean project VAMDC, J. Phys.: Conf. Ser., 397, 012019-012026, 2012Simi´c, Z., & Dimitrijevi´c, M.S., Stark broadening of Cd I spectrallines, A&A, 441, 391-393, 2005.Simi´c, Z., Dimitrijevi´c, M.S., & Kovaˇcevi´c, A., Stark broadening ofspectral lines in chemically peculiar stars: Te I lines and recentcalculations for trace elements, NewA, 53, 246-251, 2009.Zhou, Q., Cheng, C., & Meng, Y., Electron density and temperaturemeasurement by Stark broadening in a cold argon arc-plasma jetat atmospheric pressure, Plasma Sience and Technology, 11, 560-563, 2009.) z-pinchdischarge , J. Phys. B: Atom. Molec. Phys., 12, 2097-2113, 1979.Blanchette, J.-P., Chayer, P., Wesemael, F. et al., FUSE determi-nation of abundances in long-period pulsating V1093 HER (PG1716+426) stars, ApJ, 678, 1329-1341, 2008.Bukvi´c, S., ˘Zigman, V., Sre´ckovi´c, A., & Djeniˇze, S., Line broadeningin the Ar III spectrum, J. Quant. Spectrosc. Radiat. Tranfer, 109,2869-2876, 2008.Cowan, R.D., The Theory of Atomic Structure and Spectra, Univer-sity of California Press, Berkeley, USA, 1981Dimitrijevi´c, M.S., & Sahal-Br´echot, S., Stark broadening of Li IIspectral lines, Physica Scripta, 54, 50, 1996.Dimitrijevi´c, M.S., Ryabchikova, T., Simi´c, Z., Popovi´c, L. ˇC &Daˇci´c, M., The influence of Stark broadening on Cr II spectralline shapes in stellar atmospheres, A&A, 469, 681-686, 2007.Dimitrijevi´c, M.S., Kovaˇcevi´c, A., Simi´c, Z. & Sahal-Br´echot, S.,Stark Broadening and White Dwarfs, Baltic Astronomy, 20, 495-502, 2011.Djeniˇze, S., Bukvi´c, S., Sre´ckovi´c, A., & Plati˘sa, M., Stark widthsof doubly ionized argon spectral lines, J. Phys. B: Atom. Molec.Phys., 29, 429-434, 1996.Djurovi´c, S., Mar, S., Pel´aez, J. & Aparicio, J.A., Stark broadeningof ultraviolet Ar III spectral lines, MNRAS, 414, 1389-1396, 2011.Dubernet, M.L., Boudon, V., Culhane, J.L., et al., Virtual atomicand molecular data center, J. Quant. Spectrosc. Radiat. Tranfer,111, 2151-2159, 2010.Fleurier, C., Sahal-Br´echot, S., & Chapelle, J., Stark profiles of someion lines of alkaline earth elements, J. Quant. Spectrosc. Radiat.Tranfer, 17, 595-604, 1977.Graf, A.T., May, M.J., & Beiersdorfer, P., A visible spectral surveyfrom the Alcator C-Mod tokamak, Can. J. Phys., 89, 615-626,2011.Hamdi, R., Ben Nessib, N., Milovanovi´c, N., Popovi´c, L. ˇC., Dimitri-jevi´c, M.S. & Sahal-Br´echot, S., Atomic data and electron-impactbroadening effect in DO white dwarf atmospheres: Si VI, MNRAS,387, 871-882, 2008.Hamdi, R., Ben Nessib, N., Dimitrijevi´c, M.S. & Sahal-Br´echot, S.,Ab initio determination of atomic structure and Stark broadeningparameters: Pb IV and recent results, Baltic Astronomy, 20, 552-557, 2011.Hamdi, R., Ben Nessib, N., Dimitrijevi´c, M.S. & Sahal-Br´echot, S.,Stark broadening of Pb IV spectral lines, MNRAS, 431, 1039-1047,2013.Jeffery, C.S., Woolf, V.M., & Pollacco, D.L., Time-resolved spectralanalysis of the pulsating helium star V652 Her, A&A, 376, 497-517, 2001. (http://star.arm.ac.uk/ csj/models/Grid.html) Kobilarov, R., & Konjevi´c, N., Plasma shift and broadening of anal-ogous transitions of Si II, Cl III, Ar IV, Cl II, and Ar III, Phys.Rev. A, 41, 6023-6031, 1990.Konjevi´c, N., & Pittman, T.L., Stark broadening of spectral linesof homologous, doubly-ionized inert gases , J. Quant. Spectrosc.Radiat. Tranfer, 37, 311-318, 1987.Konjevi´c, N., Plasma broadening and shifting of non-hydrogenicspectral lines: present status and applications, Physics Reports,316, 339-401, 1999.Ohl, R.G., Chayer, P., & Moos, H.W., Photospheric metals in thefar ultraviolet spectroscopic explorer spectrum of the subdwarf Bstar PG 0749+658, ApJ, 538, L95-L98, 2000.O’Toole, S.J., & Heber, U., Abundance studies of sdB stars usingUV echelle HST/STIS spectroscopy, A&A, 452, 579-590, 2006.Plati˘sa, M., Popovi´c, M., Dimitrijevi´c, M., & Konjevi´c, N., StarkBroadening of A III and A IV lines, Z. Naturforsch., 30, 212-215,1975.Popovi´c, L. ˇC, Simi´c, S., Milovanovi´c, N. & Dimitrijevi´c, M.S., Starkbroadening effect in stellar atmospheres: Nd II lines, ApJS, 135,109-114, 2001.Puri´c, J., Djeniˇze, S., Sre´ckovi´c, A., ´Cuk, M., Labat, J. & Plati˘sa,M., Stark broadening and regularities of ionized neon and argonspectral lines, Z. Phys. D - Atoms Molecules and Clusters, 8, 343-347, 1988.Ralchenko, Yu., Kramida, A.E., Reader, J., and NIST ASD Team(2011). NIST Atomic Spectra Database (ver. 4.1.0), [Online].Available: http://physics.nist.gov/asd [2012, April 5]. NationalInstitute of Standards and Technology, Gaithersburg, MD.Rodr´ıguez, M., The abundances of O, S, Cl, N, Ar, He and C inseven Galactic H II regions, A&A, 351, 1075-1086, 1999.Sahal-Br´echot, S., Impact theory of the broadening and shift of spec-tral lines due to electrons and ions in a plasma, A&A, 1, 91-123,1969.Sahal-Br´echot, S., Impact theory of the broadening and shift of spec-tral lines due to electrons and ions in a plasma (continued), A&A,2, 322-354, 1969.Sahal-Br´echot, S., Stark broadening of isolated lines in the impactapproximation, A&A, 35, 319-321, 1974.Sahal-Br´echot, S., Broadening of ionic isolated lines by interactionswith positively charged perturbers in the quasistatic limit, A&A,245, 322-330, 1991.Sahal-Br´echot, S., Dimitrijevi´c, M.S., & Moreau N., Virtual Lab-oratory Astrophysics: the STARK-B database for spectral linebroadening by collisions with charged particles and its link to theEuropean project VAMDC, J. Phys.: Conf. Ser., 397, 012019-012026, 2012Simi´c, Z., & Dimitrijevi´c, M.S., Stark broadening of Cd I spectrallines, A&A, 441, 391-393, 2005.Simi´c, Z., Dimitrijevi´c, M.S., & Kovaˇcevi´c, A., Stark broadening ofspectral lines in chemically peculiar stars: Te I lines and recentcalculations for trace elements, NewA, 53, 246-251, 2009.Zhou, Q., Cheng, C., & Meng, Y., Electron density and temperaturemeasurement by Stark broadening in a cold argon arc-plasma jetat atmospheric pressure, Plasma Sience and Technology, 11, 560-563, 2009.