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\begin{document} 

   \title{STARK WIDTHS OF Sc IV SPECTRAL LINES WITHIN 4s-4p TRANSITION ARRAY}
   
   \author{MILAN S. DIMITRIJEVI\'C
          \inst{1,2}\fnmsep\thanks{Corresponding author: {mdimitrijevic@aob.rs}}
                   }

   \institute{Astronomical Observatory, Volgina 7, 11060 Belgrade,
Serbia
         \and
   LERMA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universities, UPMC Univ. Paris 06,
 5 Place Jules Janssen, 92195 Meudon Cedex, France}
 
  \abstract{Stark full widths at half maximum of six 4s - 4p  Sc IV spectral lines, broadened by collisions with 
  electrons, have been calculated for electron density of 10$^{17}$ cm$^{-3}$ 
  by using the modified semiempirical method. The results are provided for temperatures
from 10 000 K to 160 000 K. They are used also to discuss the similarities of Sc IV spectral lines within 
multiplet, supermultiplet and transition array. Obtained results will be included in the STARK-B 
database which is also a part of Virtual atomic and molecular data center (VAMDC).}

   \keywords{Stark broadening,
   	atomic data,
   	atomic processes,
   	line profiles.}

   \maketitle
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%________________________________________________________________

\section*{INTRODUCTION}

Broadening of spectral lines by fluctuating electric microfield
produced by charged particles moving near an emitter/absorber,
known as Stark broadening, is important for many topics in physics and 
astronomy. Data on Stark broadening are needed for laboratory plasmas 
diagnostic and investigation \citep{Ko99, To06, Pe09}, laser produced 
plasma analysis, modelling and diagnostics \citep{Go99, So00, Ri70, Se01}  
and inertial fusion plasma \citep{Ga83, Ke90, Gr92}. Stark broadening 
data are also useful in technology, as for example for laser welding and piercing 
of various metals \citep{Ho05, Di14}, design, investigation and 
improvement of effectivity of various light sources based on plasma  
\citep{Se01, Wi97}, and the design and developing of lasers \citep{Cs04, Di14}. 
In many astrophysical plasmas Stark broadening of spectral lines 
is very important or at least non negligible and should be taken 
into account \citep{Be97, Po01b, Di03, Di14}. 

 Stark broadening data are particularly important for stellar plasma research, and for analysis
 and synthesis of stellar spectra  \citep{Be97, Di14}. In atmospheres of white dwarfs, pre white dwarf 
 stars, and post AGB (Asymptotic Giant Branch) stars  this is  usually the main broadening mechanism 
\citep{Ta03,Mi04,Si06,Dufour11}. It can not be neglected and in some atmospheric layers of A and late 
B stars \citep{Si05a, Si05b, Simic09}. As an example, \citet{Po01b} have shown that, for A-type star 
atmospheres, the inclusion of Stark broadening can change the equivalent widths by 10-45\%. Consequently,
for determination of abundances, the importance of Stark broadening of analysed spectral lines
should be checked. 

For some astrophysical problems, like modelling of stellar atmospheres, radiative transfer or derivation
of accurate atmospheric parameters, we need a very large number of various atomic data, including Stark broadening
\citep{Dufour11}. We note as well that \citet{Rauch07} emphasized the crucial importance of an accurate 
and as much as possible complete Stark broadening data set for large number of atoms and ions, ``for sophisticated 
analysis of stellar spectra by means of NLTE model atmospheres''.

The development of satellite-born astronomy, enabling to obtain stellar spectra with earlier not possible resolution,
as well as development of computers enabling very sophisticated NLTE synthesis and modelling of stellar spectra,
made that earlier astrophysically insignificant data on trace elements now are important. Scandium is present 
and observed in stellar spectra \citep{Ad00, Ad01, Ka17} so that its Stark broadening parameters are needed. However, 
there is no at all experimental data for Stark broadening of scandium lines. For Sc IV there is no neither
theoretical data. Results of Stark broadening parameter calculations exist only for Sc II \citep{Po96, Po97}, Sc III
\citep{Di92}, Sc X \citep{El11, Di98a, Di98b} and Sc XI \citep{Di98a, Di98b}.

In order to provide the Stark broadening data, needed first of all for stellar astrophysics, for Sc IV spectral lines,
which are absent completely in the literature, Stark Full Widths at Half intensity
Maximum (FWHM) $W$ for six transitions have been calculated here, by using the modified semiempirical method 
(MSE, \cite{Di80, Di86, Di01}) for collisions of Sc IV ions with electrons. The obtained results will be used 
for the discussion of similarities of Stark widths within a supermultiplet. Also, the obtained results will
be implemented in the STARK-B database \citep{starkb, Sah15},  a repository for spectral line broadening
and shifts due to collisions with charged particles, and also a node of Virtual Atomic and Molecular Data Center
- VAMDC \citep{vamdc, Rixon11, Dub16}.  

%__________________________________________________________________

\section*{THE MODIFIED SEMIEMPIRICAL METHOD}


Within the frame of the modified semiempirical (MSE) approach \citep{Di80, Di86, Po01b}
the electron impact full width at half intensity maximum (FHWM) of an isolated non 
hydrogenic ion line is given  as

$$W_{MSE}=N{8\pi\over 3}{\hbar^2\over m^2}\bigl({2m\over{\pi
kT}}\bigr)^{1/2}{\pi\over\sqrt{3}}{{\lambda}^2\over 2{\pi}c}\cdot
\{\sum_{\ell_i\pm1}\sum_{A_{i'}J_{i'}}\vec{\Re}^2\times$$

$$\times[n_i\ell_iA_iJ_i,n_i(\ell_i\pm
1)A_{i'}J_{i'}]\widetilde{g}(x_{\ell_i,\ell_i\pm 1})+$$

$$+\sum_{\ell_f\pm1}\sum_{A_{f'}J_{f'}}\vec{\Re}^2[n_f\ell_fA_fJ_f,n_f(\ell_f\pm
1)A_{f'}J_{f'}]\widetilde{g}(x_{\ell_f,\ell_f\pm 1})
+$$

$$+\bigr(\sum_{{i'}}\vec{\Re}_{i{i'}}^2\bigl)_{\Delta n\ne
0}g(x_{n_i,n_i+1})+\bigr(\sum_{{f'}}\vec{\Re}_{f{f'}}^2\bigl)_{\Delta n\ne
0}g(x_{n_f,n_f+1})\},\eqno(1) $$

\noindent where the initial level is  denoted as $i$ and the final one as
 $f$. The square of the matrix
element $\{\vec{\Re}^2[n_k\ell_kA_kJ_k,(\ell_k\pm
1)A_{k'}J_{k'}], \ \ \ k=i, f\}$  is given by the expression

$$\vec{\Re}^2[n_k\ell_kA_kJ_k,n_k(\ell_k\pm
1)A_k'J_k']=$$

$$={\ell_>\over{2J_k+1}}Q[\ell_k
A_k,(\ell_k\pm 1)A_k']Q(J_k,J_k')[R^{n_k^*(\ell_{k}\pm
1)}_{n_k^*\ell_k}]^2.\eqno(2).$$ 

\noindent Here, $\ell_>={\rm max}(\ell_k,\ell_{k}\pm 1)$
and
$$\bigl(\sum_{k'}\vec{\Re}^2_{kk'}\bigr)_{\Delta n\neq 0}=
({3n_k^*\over{2Z}})^2{1\over 9}(n{^*_k}^2+3\ell_k^2+3\ell_k+11)\eqno(3)$$

In Eq. (1)

$$x_{\ell_k,\ell_{k'}}={E\over{\Delta E_{\ell_k,\ell_{k'}}}},\hskip0.3cm k=i, f$$

\noindent $E={3\over{2}}kT$ is the electron kinetic energy and $\Delta
E_{\ell_k,\ell_{k'}}=|E_{\ell_k}-E_{\ell_{k'}}|$ is the energy difference between
levels $\ell_k$ and $\ell_k\pm$1 ($k=i, f$),

$$x_{n_k,n_k+1}\approx
{E\over{\Delta E_{n_k,n_k+1}}},$$

\noindent where for $\Delta n\neq 0$, the energy difference between energy levels with
$n_k$ \hskip1mm and \hskip1mm $n_k$+1, $\Delta E_{n_k,n_k+1}$ is approximated  as 

$$\Delta E_{n_k,n_k+1} = 2Z^2E_H/n^{*3}_k, \eqno(4)$$

\noindent $n^*_k=[E_HZ^2/(E_{ion}-E_ k)]^{1/2}$ is the effective principal quantum
number, $Z$ is the residual ionic charge (charge ``seen'' by optical electron; for example $Z$=1 for neutrals) and
$E_{ion}$ is the appropriate spectral series limit. $N$ and $T$ are electron density and temperature,
respectively and $Q(\ell A,\ell'A')$,  $Q(J,J') $  multiplet and
line factors. The value of $A$ depends
on the adopted coupling scheme (see e.g. \citet{So79}). For the $LS$ 
coupling scheme, which is applied in this work, $A=L$, for the $jK$, 
$A=K$ and for the $jj$ approximation $A=j$. With $g(x)$ \citep{Griem68, Griem74} and $\widetilde{g}(x)$ \citep{Di80} 
are denoted the corresponding Gaunt factors.
The needed radial integrals $[R^{n_k^*\ell_{k}\pm 1}_{n_{k}^*\ell_{k}}]$ 
have been calculated here within the Coulomb approximation by using the method of \citet{b10} and the tables of
\citet{Oer68}. We note that if for the higher principal quantum numbers there is no the corresponding data in \citet{Oer68}, 
the radial integrals may be calculated with the help of the article of  \citet{Van79}. 


   
\begin{table*}
\caption{This table gives electron-impact broadening (Stark broadening) 
Full Widths at Half Intensity Maximum (W) for Sc IV  spectral lines, for a
perturber density of 10$^{17}$ cm$^{-3}$ and temperatures from 10 000
to 160 000 K. Also are given multiplet numbers and wavelengths from NIST database \citep{Kr17}
and $3kT/2\Delta E$ for $T$ = 20 000 K, where $\Delta E$ is the energy difference 
between closest perturbing level and the closer of initial and final levels.}
\label{tab:2}       % Give a unique label
% For LaTeX tables use
\centering
\begin{tabular}{crrrr}
\hline 
Transition  & T(K) & W[\AA]&W[10$^{12}$ s$^{-1}$]\\
\hline
 
  Sc IV  3s$^2$3p$^5$4s$^1$P$^o$-3s$^2$3p$^5$4p$^1$P  &     10000.&  0.0735&  0.294\\
           (Mult. 100)          &     20000.&  0.0519&  0.208\\
         2171.2 \AA     &     40000.&  0.0367&  0.147\\
  3kT/2$\Delta$E= 0.541     &     80000.&  0.0260&  0.104\\
                     &    160000.&  0.0194&  0.0776\\
\hline                         
  Sc IV  3s$^2$3p$^5$4s$^1$P$^o$-3s$^2$3p$^5$4p$^1$D   &    10000.&  0.0802&  0.337\\
            (Mult. 101)          &    20000.&  0.0621&  0.260\\
         2119.0 \AA      &    40000.&  0.0479&  0.201\\
  3kT/2$\Delta$E= 0.526      &    80000.&  0.0399&  0.167\\
                      &   160000.&  0.0344&  0.144\\
\hline
  Sc IV  3s$^2$3p$^5$4s$^1$P$^o$-3s$^2$3p$^5$4p$^1$S   &    10000.&  0.0472&  0.321\\
            (Mult. 102)          &    20000.&  0.0334&  0.227\\
         1665.9 \AA      &    40000.&  0.0240&  0.163\\
  3kT/2$\Delta$E= 0.453      &    80000.&  0.0180&  0.122\\
                      &   160000.&  0.0146&  0.0989\\
\hline                         
  Sc IV  3s$^2$3p$^5$4s$^3$P$^o_2$-3s$^2$3p$^5$4p$^3$S$_1$  &    10000.&  0.0964&  0.271\\
           (Mult. 85)           &    20000.&  0.0682&  0.192\\
         2586.9 \AA       &    40000.&  0.0482&  0.136\\
  3kT/2$\Delta$E= 0.606      &    80000.&  0.0344&  0.0969\\
                      &   160000.&  0.0272&  0.0765\\
\hline                         
  Sc IV  3s$^2$3p$^5$4s$^3$P$^o_1$-3s$^2$3p$^5$4p$^3$S$_1$  &    10000.&  0.104 &  0.274\\
           (Mult. 85)           &    20000.&  0.0737&  0.194\\
         2678.0 \AA      &    40000.&  0.0521&  0.137\\
  3kT/2$\Delta$E= 0.606      &    80000.&  0.0373&  0.0980\\
                      &   160000.&  0.0295&  0.0774\\
\hline                         
  Sc IV  3s$^2$3p$^5$4s$^3$P$^o_0$-3s$^2$3p$^5$4p$^3$S$_1$  &    10000.&  0.125 &  0.279\\
           (Mult. 85)           &    20000.&  0.0886&  0.197\\
         2906.5 \AA      &    40000.&  0.0626&  0.140\\
  3kT/2$\Delta$E= 0.606      &    80000.&  0.0451&  0.101\\
                      &   160000.&  0.0357&  0.0797\\

                         
\hline
\end{tabular}
\end{table*}

\section*{RESULTS AND DISCUSSION}
  
Stark widths (FWHM) of six Sc IV spectral lines, broadened by collisions with electrons, have been calculated using 
Eqs. (1-4) wihin the frame of MSE method \citep{Di80, Po01b}. Energy levels and ionization energy needed for their 
calculations have been taken from \citet{Su85}. 

In Table 1, the  results of our MSE calculations of Stark widths (FWHM) for six spectral lines
broadened by electron-impacts, for a perturber density of 10$^{17}$
cm$^{-3}$ and for a set of temperatures from 10 000 K to 160 000 K, are shown. 
The chosen temperature range is of interest in astrophysics, laboratory plasma, fusion research, technology and for lasers 
and laser produced plasma. If one needs perturber densities lower than  10$^{17}$
cm$^{-3}$ the extrapolation is linear. For higher perturber densities extrapolation is linear if the influence of Debye 
screening is negligible or reasonably small. In Table 1 are also given the observed wavelength and the multiplet number from 
the NIST database \citep{Kr17}. It is shown as well the quantity 3$kT/2\Delta E$, representing the ratio of the average energy of 
free electrons, $E = 3kT/2$, and the energy difference of initial or final and the closest perturbing level, $\Delta E$. It is calculated 
for $T$=20 000 K in the following way:


$$\Delta E = {\rm Max}[E/\Delta E_{i,i'}, E/\Delta E_{f,f'}, \Delta E_{n_i,n_i+1}, \Delta E_{n_f,n_f+1}] \eqno(5)$$
 
This ratio shows which collisions are dominant. $3kT/2\Delta E = 1$ is the threshold for the corresponding inelastic
transition. If it is lower than one, elastic collisions are dominant and it is so called low temperature limit. If it is
large, say larger than 50, high temperature limit approximation can be applied.


The calculated triplets belong to the same  4s$^3$P$^o$-4p$^3$S multiplet, singlets to the same 
4s$^1$P$^o$-4p$^1$L (L=S, P, D) supermultiplet and all calculated transitions to the same, 4s-4p transition array. 
\citet{Wi82} concluded after examination of regularities and similarities in plasma broadened spectral line widths that
line widths in angular frequency units in multiplets usually agree within a few per cent, in supermultiple within about 30 per cent and within a
transition array within about 40 per cent. The obtained here results give us an opportunity to check the similarities 
of Stark line widths within multiplet, supermultiplet
and transition array for Sc IV in order to see if they could be used for derrivation of missing values. 
The transformation of the Stark widths expressed in \AA-units to the widths in angular frequency units 
may be performed by the following formula:


$$W(\mathring{A})=\frac{\lambda ^{2}}{2\pi c}W(s^{-1}), \eqno(6)$$
 

\noindent where $c$ is the speed of light.

From Table 1 we obtained that within the Sc IV 4s$^3$P$^o$-4p$^3$S multiplet the smalest Stark width value is 2.87\% smaller from largest
at $T$=10 000 K and 4.02\% at $T$=160 000 K. Within Sc IV  4s$^1$P$^o$-4p$^1$L (L=S, P, D) supermultiplet, the smallest W is 12.76\% smaller from the 
largest one at $T$=10 000 K and 46.11\% at $T$=160 000 K. For 4s-4p transition array these values are 19.58\% and 46.88\%. We can conclude that in average,
these values are in agreement with \citet{Wi82} conclusions and that disagreement increases with the increase of temperature.


 
 If we have Stark width value for one member of multiplet, supermultiplet or transition array, the 
 needed width for another member, can be obtained with the help of the expression:


$$W_{1}=\left( \frac{\lambda _{1}}{\lambda }\right) ^{2}W. \eqno(7)$$
 

\noindent Here, with $W$$_{1}$ is denoted the corrected width,
for the spectral line with the wavelength $\lambda$$_{1}$, and $\lambda$ is the
wavelength of the line for which we have the Stark width value $W$.

The Stark FWHM for Sc IV spectral lines obtained within the modified semiempirical method and shown 
in Table 1, will be also implemented in
the \textsc{STARK-B} database \citep{starkb, Sah15}, created first of all for the investigations, modelling
and diagnostics of the plasma of stellar atmospheres,but useful also for the diagnostics of laboratory plasmas, investigation of laser produced and 
inertial fusion plasma as well as for plasma technologies.

We want to draw attention that  \textsc{STARK-B} database is one of the databases which enter also in the Virtual
Atomic and Molecular Data Center - VAMDC \citep{vamdc,Rixon11, Dub16}, created in order to enable an efficacious search and mining of atomic and molecular data.
 scattered in different databases and to make more convenient their adequate use. VAMDC portal with 30 databases with atomic and molecular data, 
 including STARK-B, is on the web site: http://portal.vamdc.org/.


\section*{CONCLUSION}

Within the frame of MSE method we have calculated Stark widths
for six Sc IV spectral lines broadened by collisions with electrons.
The obtained data are used to check similarities of Stark widths within a
multiplet, supermultiplet and transition array. Also the Stark widths for six Sc IV spectral lines 
will be implemented in STARK-B database. Other theoretical as well as  experimental
data for Stark broadening of Sc IV spectral lines do not exist, so that we hope  that
the obtained results will be of interest, for various problems, especially in stellar physics and
laboratory plasma diagnostics. 

\section*{ACKNOWLEDGEMENTS}

 
This work is  a part of the project 176002 "Influence of
collisional processes on astrophysical plasma line shapes"
supported by the Ministry of Education, Science and Technological
Development of Serbia.

\begin{thebibliography}{43}
\expandafter\ifx\csname natexlab\endcsname\relax\def\natexlab#1{#1}\fi

\bibitem[{Adelman \& Pintaldo (2000)}]{Ad00}
Adelman, S.~J., \& Pintaldo, O. 2000, Elemental abundance analyses with 
Complejo Astronomico El Leoncito REOSC echelle spectrograms. IV. Extensions of nine previous analyses, 
Astronomy and Astrophysics, 354, 899--903 .

\bibitem[{Adelman {et~al.}(2001) Adelman, Snow, Wood, Ivans, Sneden, Ehrenfreund, \& Foing}]{Ad01}
Adelman, S.~J., Snow, T.~P., Wood, E.~L., Ivans, I.~I., Sneden, C., Ehrenfreund, P. \& Foing, B.~H.
2001, An elemental abundance analysis of the mercury manganese star HD 29647, Monthly Notices of the 
Royal Astronomical Society, 328~(4), 1144--1150.

\bibitem[{Bates \& Damgaard(1949)}]{b10}
Bates, D.~R. \& Damgaard, A. 1949, The Calculation of the Absolute Strengths of
  Spectral Lines, Philosophical Transactions of the Royal Society of London.
  Series A. Mathematical and Physical Sciences,  242~(842), 101--122.

\bibitem[{Beauchamp {et~al.}(1997) Beauchamp, Wesemael, \& Bergeron}]{Be97}
Beauchamp, A., Wesemael, F., \& Bergeron, P. 1997, Spectroscopic Studies of DB
  White Dwarfs: Improved Stark Profiles for Optical Transitions of Neutral
  Helium, Astrophysical Journal Supplement,  108, 559--573.

\bibitem[{Csillag \& Dimitrijevi\' c (2004)}]{Cs04}
Csillag, L. \& Dimitrijevi\'c, M.~S. 2004, On the Stark broadening of the 537.8
  nm and 441.6 nm Cd+ lines excited in a hollow cathode laser discharge,
  Applied Physics B: Lasers and Optics,  78~(2), 221--223.
  
\bibitem[{Dimitrijevi\'c (2003)}]{Di03} 
Dimitrijevi\'c M. S., 2003, Stark broadening in Astrophysics (Applications of Belgrade School
Results and collaboration of former Soviet republics), Astronomical and Astrophysical 
Transactions, 22, 389--412. 

\bibitem[{Dimitrijevi\'c \& Konjevi\'c (1980)}]{Di80}
Dimitrijevi\'c, M.~S. \& Konjevi\'c, N. 1980, Stark widths of doubly- and
  triply-ionized atom lines., Journal of Quantitative Spectroscopy \& Radiative
  Transfer,  24, 451--459.
  
\bibitem[{Dimitrijevi\'c \& Kr\v{s}ljanin (1986)}]{Di86}
Dimitrijevi\'c, M.~S. \& Kr\v{s}ljanin, V. 1986, Electron-impact shifts of ion
  lines - Modified semiempirical approach, Astronomy and Astrophysics,  165,
  269--274.

\bibitem[{Dimitrijevi\'c \& Popovi\'c (2001)}]{Di01}
Dimitrijevi\'c, M.~S. \& Popovi\'c, L. \v{C}. 2001, Modified Semiempirical Method,
  Journal of Applied Spectroscopy,  68~(6), 893--901.
  
\bibitem[{Dimitrijevi\'{c} \& Sahal-Br\'{e}chot (1992)}]{Di92}
Dimitrijevi\'{c}, M.~S., \& Sahal-Br\'{e}chot, S. 1992, Stark broadening of 
spectral lines of multicharged ions of astrophysical interest. V. Sc III 
and Ti IV lines, Astronomy and Astrophysics Supplement Series,  95, 121--128.
 
\bibitem[{Dimitrijevi\'{c} \& Sahal-Br\'{e}chot (1998{\natexlab{a}})}]{Di98a}
Dimitrijevi\'{c}, M.~S., \& Sahal-Br\'{e}chot, S. 1998a, Stark broadening of 
spectral lines of multicharged ions of astrophysical interest. XXI. Sc X, Sc XI, 
Ti XI and Ti XII spectral lines, Astronomy and Astrophysics Supplement Series,  
131, 143--144.
  
\bibitem[{Dimitrijevi\'{c} \& Sahal-Br\'{e}chot (1998{\natexlab{b}})}]{Di98b}
Dimitrijevi\'{c}, M.~S., \& Sahal-Br\'{e}chot, S. 1998a, Stark broadening parameter 
tables for Sc X, Sc XI, Ti XI and Ti XII, Serbian Astronomical Journal, 157, 39--64.

\bibitem[{Dimitrijevi\'c \& Sahal-Br\'echot(2014)}]{Di14}
Dimitrijevi\'c, M.~S. \& Sahal-Br\'echot, S. 2014, On the
  Application of Stark Broadening Data Determined with a Semiclassical
  Perturbation Approach, Atoms,  2, 357--377.
  
 \bibitem[{Dubernet {et~al.} (2016) Dubernet, Antony, Ba, Babikov, Bartschat,
  Boudon, Braams, Chung, Daniel, \& Delahaye}]{Dub16}
Dubernet, M.~L., Antony, B.~K., Ba, Y.~A., {et~al.} 2016, The virtual atomic
  and molecular data centre (VAMDC) consortium, Journal of Physics B: Atomic,
  Molecular and Optical Physics,  49~(7), 074003.

\bibitem[{Dubernet {et~al.}(2010) Dubernet, Boudon, Culhane, Dimitrijevi\'c,
  Fazliev, Joblin, Kupka, Leto, Le~Sidaner, \& Loboda}]{vamdc}
Dubernet, M.~L., Boudon, V., Culhane, J.~L., {et~al.} 2010, Virtual atomic and
  molecular data centre, Journal of Quantitative Spectroscopy \& Radiative
  Transfer,  111~(15), 2151--2159.

\bibitem[{Elabidi \& Sahal-Br\'echot (2011)}]{El11}
Elabidi, H., \& Sahal-Br\'echot, S. 2011, Checking the dependence on the upper 
level ionization potential of electron impact widths using quantum calculations,
European Physical Journal D, 61, 285--290.

\bibitem[{Dufour {et~al.} (2011) Dufour, Ben Nessib, Sahal-Br\'{e}chot \& Dimitrijevi\'{c}}]{Dufour11} 
Dufour, P., Ben Nessib, N., Sahal-Br\'{e}chot, S., Dimitrijevi\'{c}, M. S. 2011, 
Stark Broadening of Carbon and Oxygen Lines in Hot DQ White Dwarf Stars: Recent Results and Applications, 
Baltic Astronomy, 20, 511--515.

\bibitem[{Gaisinski \& Oks (1983)}]{Ga83} 
Gaisinsky I. M. \& Oks E. A. 1983, in Energy Levels and Transition Probabilities in Atoms and Ions, 
Akademiya Nauk SSSR, Otdelenie Obshchej Fiziki i Astronomii, Nauchnyj Sovet po Spektroskopii, Moscow, 212.   

\bibitem[{Gornushkin {et~al.}(1999) Gornushkin, King, Smith, Omenetto, \&
  Winefordner}]{Go99}
Gornushkin, I.~B., King, L.~A., Smith, B.~W., Omenetto, N., \& Winefordner,
  J.~D. 1999, Line broadening mechanisms in the low pressure laser-induced
  plasma, Spectrochimica Acta, Part B: Atomic Spectroscopy,  54~(8), 1207--1217

\bibitem[{Griem (1968)}]{Griem68}
Griem, H.~R. 1968, Semiempirical Formulas for the Electron-Impact Widths and 
Shifts of Isolated Ion Lines in Plasmas, Physical Review, 165~(1), 258-266.
  
\bibitem[{Griem (1974)}]{Griem74}
Griem, H.~R. 1974, Spectral line broadening by plasmas (New York: Academic
  Press, Inc.)

\bibitem[{Griem (1992)}]{Gr92}
Griem, H.~R. 1992, Plasma spectroscopy in inertial confinement fusion and soft
  x-ray laser research, Physics of Fluids,  4~(7), 2346--2361.

\bibitem[{Hoffman {et~al.} (2006) Hoffman, Szyma\'nski, \& Azharonok}]{Ho05}
Hoffman, J., Szyma\'nski, Z., \& Azharonok, V. 2006, Plasma Plume Induced
  During Laser Welding of Magnesium Alloys, AIP Conference Proceedings,  812,
  469--472.
  
\bibitem[{Kahraman Alicavus {et~al.} (2017) Kahraman Alicavus, Niemczura, Poli\'nska, Helminiak, 
Lampens, Molenda-\.Zakowicz, Ukita, \&Kambe}]{Ka17}  
Kahraman Alicavus, F., Niemczura, E., Poli\'nska, M., Helminiak, K.~G., Lampens, P., 
Molenda-\.Zakowicz, J., Ukita, N., \& Kambe, E. 2017, High-resolution spectroscopy and abundance 
analysis of $\delta$ Scuti stars near the $\gamma$ Doradus instability strip, 
Monthly Notices of the Royal Astronomical Society, 470~(4), 4408--4420. 

\bibitem[{Keane {et~al.} (1990) Keane, Lee, Hammel, Osterheld, Suter, Calisti, Khelfaoui, 
Stamm, Talin}]{Ke90} 
Keane, C.~J., Lee, R.~W., Hammel, B.~A., Osterheld, A.~L., Suter, L.~J., Calisti, A., Khelfaoui, F.,
Stamm, R., Talin, B. 1990, Line broadening of Ne-like xenon as a diagnostic for high-density implosion 
experiments, Review of Scientific Instruments, 61~(10), 2780--2782.

\bibitem[{Konjevi\'c(1999)}]{Ko99}
Konjevi\'c, N. 1999, Plasma broadening and shifting of non-hydrogenic spectral
  lines: present status and applications, Physics Reports,  316~(6), 339--401.
  
\bibitem[{Kramida {et~al.}(2017) Kramida, Ralchenko, Reader, NIST ASD Team }]{Kr17}  
Kramida, A., Ralchenko, Yu., Reader, J., and NIST ASD Team 2017, NIST Atomic Spectra Database 
(ver. 5.5.1), [Online]. Available: https://physics.nist.gov/asd [2017, November 18]. 
National Institute of Standards and Technology, Gaithersburg, MD.
 
\bibitem[{Milovanovi\'c {et~al.}(2004)Milovanovi\'c, Dimitrijevi\'c, Popovi\'c,
  \& Simi\'c}]{Mi04}
Milovanovi\'c, N., Dimitrijevi\'c, M.~S., Popovi\'c, L.~\v{C}., \& Simi\'c, Z.
  2004, Importance of collisions with charged particles for stellar UV line
  shapes: Cd III, Astronomy and Astrophysics,  417, 375--380.

\bibitem[{Oertel \& Shomo(1968)}]{Oer68}
Oertel, G.~K. \& Shomo, L.~P. 1968, Tables for the Calculation of Radial
  Multipole Matrix Elements by the Coulomb Approximation, Astrophysical
  Journal Supplement,  16, 175--218.
  
\bibitem[{Pel\'aez {et~al.} (2009)}]{Pe09} 
Pel\'aez, R. J., \'Ciri\v san, M., Djurovi\'c, S., Aparicio, J. A., Mar, S., 2009,
Stark broadening measurements of low-intensity singly and doubly ionized xenon spectral 
lines, Astronomy and Astrophysics, 507~(3), 1697--1705.
  
\bibitem[{Popovi\'c \& Dimitrijevi\'c (1996)}]{Po96}
Popovi\'c, L. \v C., \& Dimitrijevi\'c, M.~S. 1996, Stark widths for astrophysically 
important ns-np transitions in Sc II, Y II and Zr II spectra, Astronomy and 
  Astrophysics Supplement Series, 120, 373--374.

\bibitem[{Popovi\'c \& Dimitrijevi\'c (1997)}]{Po97}
Popovi\'c, L. \v C., \& Dimitrijevi\'c, M.~S. 1997, Stark broadening parameter tables 
for Xe II, Sc II, Y II and Zr II, Bulletin Astronomique de Belgrade, 155, 159--163.

\bibitem[{Popovi\'c {et~al.} (2001) Popovi\'c, Simi\' c, Milovanovi\' c \& Dimitrijevi\'c}]{Po01b} 
Popovi\'c, L.~\v C ., Simi\' c, S., Milovanovi\' c, N., Dimitrijevi\'c, M.~S. 2001, Stark 
Broadening Effect in Stellar Atmospheres: Nd II Lines, Astrophysical Journal Supplement Series, 
135~(1), 109--114.

\bibitem[{Rauch {et~al.}(2007)Rauch, Ziegler, Werner, Kruk, Oliveira, Van~de
  Putte, Mignani, \& Kerber}]{Rauch07}
Rauch, T., Ziegler, M., Werner, K., {et~al.} 2007, High-resolution FUSE and HST
  ultraviolet spectroscopy of the white dwarf central star of Sh 2-216,
  Astronomy and Astrophysics,  470~(1), 317--329.
  
\bibitem[{Richou \& Molitor (1970)}]{Ri70} 
Richou J. \& Molitor A., 1970, Determination of the electron density of a xenon plasma, 
created in a shock tube, by laser interferometry and spectroscopy, Comptes Rendus de L'Acad\'emie
de Science, Serie B, 271, 753--756.  

\bibitem[{Rixon {et~al.}(2011) Rixon, Dubernet, Piskunov, Walton, Mason,
  Le~Sidaner, Schlemmer, Tennyson, Akram, \& Benson}]{Rixon11}
Rixon, G., Dubernet, M.~L., Piskunov, N., {et~al.} 2011, VAMDC—The Virtual
  Atomic and Molecular Data Centre—A New Way to Disseminate Atomic and
  Molecular Data—VAMDC Level 1 Release, AIP Conference Proceedings,  1344,
  107--115.

  \bibitem[{Sahal-Br\'echot {et~al.} (2017) Sahal-Br\'echot, Dimitrijevi\'c, \&
Moreau}]{starkb}
Sahal-Br\'echot, S., Dimitrijevi\'c, M.~S., \& Moreau, N. 2017, STARK-B database, [online]. 
Available: http://stark-b.obspm.fr [November 12, 2017]. Observatory of Paris, LERMA and 
Astronomical Observatory of Belgrade

\bibitem[{Sahal-Br\'echot {et~al.} (2015) Sahal-Br\'echot, Dimitrijevi\'c,
  Moreau, \& Ben~Nessib}]{Sah15}
Sahal-Br\'echot, S., Dimitrijevi\'c, M.~S., Moreau, N., \& Ben~Nessib, N. 2015,
  The STARK-B database VAMDC node: a repository for spectral line broadening
  and shifts due to collisions with charged particles, Physica Scripta,  50,
  054008.

\bibitem[{Seidel {et~al.} (2001) Seidel, Wrubel, Roston, Kunze}]{Se01} 
Seidel S., Wrubel Th., Roston G., Kunze H.-J. 2001, Line profile measurements of 
($^4$S)6s$^5$S-($^4$S)6p$^5$P transitions of Xe III, Journal of Quantitative 
Spectroscopy and Radiative Transfer, 71~(2-6), 703--709.

\bibitem[{Simi\'{c} {et~al.} (2009) Simi\'{c}, Dimitrijevi\'{c}, \&
  Kova\v{c}evi\'{c}}]{Simic09}
Simi\'{c}, Z., Dimitrijevi\'{c}, M.~S., \& Kova\v{c}evi\'{c}, A. 2009, Stark
  broadening of spectral lines in chemically peculiar stars: Te I lines and
  recent calculations for trace elements, New Astronomy Review,  53~(7-10),
  246--251.

\bibitem[{Simi\'{c} {et~al.}(2005{\natexlab{a}})Simi\'{c}, Dimitrijevi\'{c},
  Milovanovi\'c, \& Sahal-Br\'echot}]{Si05b}
Simi\'{c}, Z., Dimitrijevi\'{c}, M.~S., Milovanovi\'c, N., \& Sahal-Br\'echot,
  S. 2005{\natexlab{a}}, Stark broadening of Cd I spectral lines, Astronomy and
  Astrophysics,  441~(1), 391--393.

\bibitem[{Simi\'{c} {et~al.}(2005{\natexlab{b}})Simi\'{c}, Dimitrijevi\'{c},
  Popovi\'{c}, \& Da\v{c}i\'c}]{Si05a}
Simi\'{c}, Z., Dimitrijevi\'{c}, M.~S., Popovi\'{c}, L.~\v {C}., \& Da\v{c}i\'c, M.
  2005{\natexlab{b}}, Stark Broadening of F III Lines in Laboratory and Stellar
  Plasma, Journal of Applied Spectroscopy,  72~(3), 443--446.

\bibitem[{Simi\'{c} {et~al.}(2006)Simi\'{c}, Dimitrijevi\'{c}, Popovi\'{c}, \&
  Da\v{c}i\'c}]{Si06}
Simi\'{c}, Z., Dimitrijevi\'{c}, M.~S., Popovi\'{c}, L.~\v {C}., \& Da\v{c}i\'c, M.
  2006, Stark broadening parameters for Cu III, Zn III and Se III lines in
  laboratory and stellar plasma, New Astronomy,  12~(3), 187--191.
  
\bibitem[{Sobel'man (1979)}]{So79}
Sobel'man, I. I. 1979, Atomic Spectra and Radiative Transitions, (Berlin: Springer-Verlag).

\bibitem[{Sorge {et~al.}(2000)Sorge, Wierling, R\"opke, Theobald, Sauerbrey, \&
  Wilhein}]{So00}
Sorge, S., Wierling, A., R\"opke, G., {et~al.} 2000, Diagnostics of a
  laser-induced dense plasma by hydrogen-like carbon spectra, Journal of
  Physics B: Atomic, Molecular and Optical Physics,  33~(16), 2983--3000.
  
\bibitem[{Sugar \& Corliss (1985)}]{Su85}
Sugar, J., \& Corliss, C. 2004, Atomic Energy Levels of the Iron-Period Elements: 
Potassium through Nickel, Journal of Physical and Chemical Reference Data,  14, 
Supplement 2, 1--664. 

\bibitem[{Tankosi\'{c} {et~al.}(2003)Tankosi\'{c}, Popovi\'c, \&
  Dimitrijevi\'{c}}]{Ta03}
Tankosi\'{c}, D., Popovi\'c, L.~\v {C}., \& Dimitrijevi\'{c}, M.~S. 2003, The
  electron-impact broadening parameters for Co III spectral lines, Astronomy
  and Astrophysics,  399, 795--797.

\bibitem[{Torres {et~al.}(2006)Torres, van~de Sande, van~der Mullen, Gamero, \&
  Sola}]{To06}
Torres, J., van~de Sande, M.~J., van~der Mullen, J. J. A.~M., Gamero, A., \&
  Sola, A. 2006, Stark broadening for simultaneous diagnostics of the electron
  density and temperature in atmospheric microwave discharges, Spectrochimica
  Acta, Part B: Atomic Spectroscopy,  61~(1), 58--68.

\bibitem[{Van~Regemorter {et~al.}(1979)Van~Regemorter, Hoang~Binh, \&
  Prud'homme}]{Van79}
Van~Regemorter, H., Hoang~Binh, D., \& Prud'homme, M. 1979, Radial transition
  integrals involving low or high effective quantum numbers in the Coulomb
  approximation, Journal of Physics B: Atomic, Molecular and Optical Physics,
  12, 1053--1061.
  
\bibitem[Wiese \& Konjevi\'c (1982)]{Wi82}
Wiese, W. L.\& Konjević, N. 1982, Regularities and similarities in plasma broadened spectral line widths (Stark widths), 
Journal of Quantitative Spectroscopy and Radiative Transfer, 28, 185--198. 
 
\bibitem[{Wieser {et~al.} (1997) Wieser, Murnick, Ulrich, Huggins, Liddle, Brown}]{Wi97} 
Wieser, J., Murnick, D.~E., Ulrich, A., Huggins, H.~A., Liddle, A., Brown, W.~L. 1997, 
Vacuum ultraviolet rare gas excimer light source, Review of Scientific Instruments, 68~(3), 
1360-1364.
  

\end{thebibliography}
\end{document}

