\documentclass{utns}  
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\usepackage{graphicx}
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\begin{document} 

   \title{ON THE STARK BROADENING OF K III AND Ca IV SPECTRAL LINES}
   
   \author{MILAN S. DIMITRIJEVI\'C
          \inst{1}\fnmsep\thanks{Corresponding author: {mdimitrijevic@aob.rs}} 
                          }

   \institute{Astronomical Observatory, Volgina 7, 11060 Belgrade,
Serbia
         \and
  Sorbonne Université, Observatoire de Paris, Université PSL, CNRS, LERMA, F-92190, Meudon, France}
 
  \abstract{Stark full widths at half maximum (FWHM) for ten multiplets of doubly charged potassium ion (K III),
  and 35 multiplets of triply charged calcium ion (Ca IV) have been calculated for electron density of 
  10$^{17}$ cm$^{-3}$ by using the symplified modified semiempirical (SMSE) method. The calculations were 
  performed for temperatures from 5 000 K to 80 000 K, for K III and for temperatures from 10 000 K to 160 000 K for Ca IV,
  for broadening by collisions with electrons. The results obtained here will be implemented in the STARK-B 
database which is a memeber of Virtual atomic and molecular data center (VAMDC).}

   \keywords{Stark broadening,
   	spectral lines,
   	line profiles,
   	K III, Ca IV.}

   \maketitle
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\section*{INTRODUCTION}

Data on Stark broadening, or broadening of spectral lines by collisions with charged particles 
due to Stark effect in a fluctuating electric microfield are needed in many research fields in astrophysics, 
for laboratory plasma diagnostics, for design of lasers and investigations of laser produced plasma, in inertial 
fusion research as well
as for different technologies which use plasmas, like light industry, and cutting,
welding and melting metals using lasers.

Line  broadening data for as much as possible larger number of spectral lines is needed because  we do not
know  {\it a priori} the chemical composition of a stellar atmosphere. Stark broadening research of the lines
of trace elements is also needed because with the development of space astronomy, instruments like Goddhard High Resolution 
Spectrograph (GHRS) on Hubble Space Telescope, produce spectral line profiles with unpreceded resolution and accuracy
and with modern computers all calculations become more and more easier. 
                                    
K III and Ca IV lnes are the two successive members of the Chlorine isoelectronic sequence. \citet{Fr95} underline 
the importance of atomic data for them in fusion research as well as 
for estimating the energy loss through impurity ions. Stark broadening data for their
spectral lines are needed for laboratory plasma diagnostics, in astophysics, for fusion plasma research
and in plasma physics.

Since there is no neither experimental nor theoetical data  for Stark broadening of K III and Ca IV spectral lines,
here are calculated Stark full widths at half maximum (FWHM) for 10 multiplets of K III,
and 35 of Ca IV by using the simplified modified semiempirical method \citep{Di87}, since a sufficiently 
complete set of atomic data, needed for a more sophysticated calculation does not exist.

The obtained results will be included in the STARK-B \citep{Sah15, starkb}, a database for Stark widths and shifts of
spectral lines broadened by collisions with charged particles.


\section{SYMPLIFIED MSE FORMULA}

When there is no data for more sophysticated theoretical methods, or when data for a lot of spectral 
lines are needed, what is the case especially in astrophysics e.g. for model atmosphere or radiative transfer calculations,
 might be very useful the simplified modified se\-mi\-em\-pi\-ri\-cal formula \citep{Di87} for Stark widths of isolated, singly, 
and multiply  charged ion  lines. This formula may be used in the case when  the nearest atomic energy 
level  ($j'=i'$ or $f'$), having an allowed  dipol transition from or to the initial  ($i$)  or   final  ($f$)  energy level 
of the considered spectral line,  is far enough, so that   the  condition 
$x_{\rm jj\prime }= E/\vert E_{\rm j\prime }-E_{\rm j}\vert \le 2$ 
is  satisfied. Than, full width  at  half   maximum   is  given   as \citep{Di87}: 


$$W(\AA ) = 2.2151\times  10^{-8} {\lambda ^2 ({\rm cm}) N({\rm cm^{-3}})
\over T^{1/2}({\rm K})} (0.9 - {1.1\over Z})\times$$

$$\times \sum\limits _{\rm j = i,f} 
 ({3n_{\rm j}^\ast \over 2Z})^2 (n_{\rm j}^{\ast 2} - \ell _{\rm j}^2  - \ell 
 - 1).\eqno(1)$$


In the upper equation, $ N$ and $ T$  are  the  electron  density  and  
temperature, $ E = 3kT/2$ is the energy of perturbing electron, 
$Z-1$ is the ionic charge, $n$ the effective principal quantum 
number and $\lambda$ is the transition wavelength.  
   
\begin{table*}
\caption{This table gives electron-impact broadening (Stark broadening) 
Full Widths at Half Intensity Maximum (W) for K III  spectral lines, for a
perturber density of 10$^{17}$ cm$^{-3}$ and temperatures from 5 000
to 80 000 K. The configuration is 3s$^2$3p$^4$($^3$P)n$\ell$. Also is  given quantity $3kT/2\Delta E$ 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:1}       % Give a unique label
% For LaTeX tables use


\centering
\begin{tabular}{crrrr}
\hline 
Transition  & T(K) & W[\AA]&3kT/2$\Delta$E\\
\hline

  K III  3d$^2$F-4p$^2$D$^o$   &    5000.& 0.732E-01 &  2.98\\    
         $\lambda$ = 2366.6 \AA  &        10000. & 0.518E-01 &  5.95\\    
                       &   20000.&  0.366E-01 &  11.9 \\   
                       &   40000.&  0.259E-01 &  23.8   \\ 
                       &   80000.&  0.183E-01 &  47.6    \\
\hline


 K III  4s$^2$P-4p$^2$D$^o$    &   5000.&  0.328     &  2.98    \\
         $\lambda$ = 3312.2 \AA  &        10000.&  0.232      & 5.95\\    
                       &   20000.&  0.164     &  11.9\\    
                       &   40000.&  0.116     &  23.8  \\  
                       &   80000.&  0.820E-01 &  47.6    \\
\hline


  K III  4s$^2$P-4p$^2$P$^o$   &    5000.&  0.311     &  1.89    \\
        $\lambda$ = 3205.3 \AA   &       10000.&  0.220      & 3.78\\    
                       &   20000.&  0.155      & 7.56\\    
                       &   40000.&  0.110      & 15.1  \\  
                       &   80000.&  0.777E-01  & 30.2    \\
\hline


  K III  4p$^2$D$^o$-5s$^2$P    &    5000.&   1.23      & 2.98    \\
         $\lambda$ = 5070.3 \AA  &        10000.&  0.873      & 5.95 \\   
                       &   20000.&  0.617       &11.9    \\
                       &   40000.&  0.436       &23.8    \\
                       &   80000.&  0.309       &47.6    \\
\hline


  K III  4p$^2$P$^o$-5s$^2$P    &    5000.&   1.38       &1.89    \\
         $\lambda$ = 5342.9 \AA  &        10000.&  0.976       &3.78   \\ 
                       &   20000.&  0.690       &7.56    \\
                       &   40000.&  0.488       &15.1    \\
                       &   80000.&  0.345       &30.2    \\
\hline


  K III  4p$^2$D$^o$-3d$^2$D    &    5000.&  0.182       &2.98    \\
         $\lambda$ = 1678.3 \AA  &        10000.&  0.129       &5.95\\
                       &   20000.&  0.911E-01   &11.9    \\
                       &   40000.&  0.644E-01   &23.8    \\
                       &   80000.&  0.456E-01   &47.6    \\
\hline


  K III  4p$^2$P$^o$-3d$^2$D    &    5000.&  0.190       &1.89    \\
         $\lambda$ = 1707.1 \AA  &        10000.&  0.134 &      3.78  \\  
                       &   20000.&  0.948E-01   &7.56    \\
                       &   40000.&  0.670E-01   &15.1    \\
                       &   80000.&  0.474E-01   &30.2    \\

\hline


  K III  4s$^4$P-4p$^4$P$^o$    &    5000. & 0.310     & 0.176    \\
         $\lambda$ = 3376.2 \AA   &       10000.&  0.219  &    0.352    \\
                       &   20000. & 0.155      &0.704    \\
                       &   40000. & 0.110       &1.41    \\
                       &   80000. & 0.776E-01   &2.82    \\
\hline


  K III  4s$^4$P-4p$^4$D$^o$    &    5000. & 0.256      &0.176    \\
         $\lambda$ = 3006.0 \AA   &       10000.&  0.181   &   0.352    \\
                       &   20000. & 0.128     & 0.704    \\
                       &   40000. & 0.905E-01 &  1.41    \\
                       &   80000. & 0.640E-01 &  2.82    \\
\hline


  K III  4s$^4$P-4p$^4$S$^o$    &    5000. & 0.203    &  0.176    \\
         $\lambda$ = 2601.3 \AA   &       10000.&  0.144    &  0.352    \\
                       &   20000. & 0.102     & 0.704    \\
                       &   40000. & 0.719E-01 &  1.41    \\
                       &   80000. & 0.508E-01 &  2.82   \\
                       
\hline
\end{tabular}
\end{table*}

\begin{table*}
\caption{This table gives electron-impact broadening (Stark broadening) 
Full Widths at Half Intensity Maximum (W) for Ca IV  spectral lines, for a
perturber density of 10$^{17}$ cm$^{-3}$ and temperatures from 10 000
to 160 000 K. Also is  given quantity $3kT/2\Delta E$, 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]&3kT/2$\Delta$E\\
\hline

  Ca IV ($^3$P)3d$^4$D-($^3$P)4p$^4$P$^o$   &   10000. & 0.401E-02 & 0.270\\    
        $\lambda$ = 773.3 \AA     &     20000.&  0.284E-02 & 0.539\\    
                       &   40000. & 0.201E-02 &  1.08\\    
                       &   80000. & 0.142E-02 &  2.16\\    
                       &  160000. & 0.100E-02 &  4.31\\    
\hline

  Ca IV ($^3$P)3d$^4$D-($^3$P)4p$^4$D$^o$  &   10000. & 0.402E-02 & 0.239 \\   
         $\lambda$ = 745.2 \AA    &      20000.&  0.284E-02 & 0.479\\    
                       &   40000. & 0.201E-02 & 0.958    \\
                       &   80000. & 0.142E-02 &  1.92    \\
                       &  160000. & 0.100E-02 &  3.83    \\
\hline

  Ca IV ($^3$P)3d$^4$F-($^3$P)4p$^4$D$^o$    &   10000. & 0.548E-02 & 0.239    \\
         $\lambda$ = 858.2 \AA    &      20000.&  0.387E-02  &0.479\\    
                       &   40000. & 0.274E-02 & 0.958    \\
                       &   80000. & 0.194E-02 &  1.92    \\
                       &  160000. & 0.137E-02 &  3.83    \\
\hline

  Ca IV ($^3$P)3d$^4$P-($^3$P)4p$^4$P$^o$    &   10000. & 0.663E-02 & 0.270    \\
          $\lambda$ = 971.7 \AA   &       20000.&  0.469E-02  &0.539\\    
                       &   40000. & 0.332E-02  & 1.08    \\
                       &   80000. & 0.235E-02  & 2.16    \\
                       &  160000. & 0.166E-02  & 4.31    \\
\hline

  Ca IV ($^3$P)3d$^4$P-($^3$P)4p$^4$D$^o$   &   10000. & 0.650E-02  &0.239    \\
          $\lambda$ = 927.7 \AA   &       20000.&  0.460E-02&  0.479\\    
                       &   40000. & 0.325E-02  &0.958    \\
                       &   80000. & 0.230E-02  & 1.92    \\
                       &  160000. & 0.163E-02  & 3.83    \\
\hline

  Ca IV ($^3$P)3d$^4$P-($^3$P)4p$^4$S$^o$    &   10000. & 0.636E-02  &0.206    \\
          $\lambda$ = 871.4 \AA   &       20000.&  0.450E-02 & 0.413\\    
                       &   40000. & 0.318E-02  &0.826    \\
                       &   80000. & 0.225E-02  & 1.65    \\
                       &  160000. & 0.159E-02  & 3.30    \\
\hline

  Ca IV ($^3$P)4s$^4$P-($^3$P)4p$^4$P$^o$   &   10000.  &0.112      &0.270    \\
         $\lambda$ = 2586.1 \AA   &       20000.&  0.794E-01  &0.539\\    
                       &   40000. & 0.561E-01  & 1.08    \\
                       &   80000. & 0.397E-01  & 2.16    \\
                       &  160000. & 0.281E-01  & 4.31    \\
\hline

  Ca IV ($^3$P)4s$^4$P-($^3$P)4p$^4$D$^o$    &   10000. & 0.913E-01  &0.270    \\
         $\lambda$ = 2295.8 \AA   &       20000.&  0.645E-01&  0.539\\    
                       &   40000. & 0.456E-01  & 1.08    \\
                       &   80000. & 0.323E-01  & 2.16    \\
                       &  160000. & 0.228E-01  & 4.31    \\
\hline

  Ca IV ($^3$P)4s$^4$P-($^3$P)4p$^4$S$^o$    &   10000. & 0.711E-01  &0.270    \\
         $\lambda$ = 1979.5 \AA   &       20000.&  0.503E-01 & 0.539\\    
                       &   40000. & 0.355E-01  & 1.08    \\
                       &   80000. & 0.251E-01  & 2.16    \\
                       &  160000. & 0.178E-01  & 4.31    \\
\hline

  Ca IV ($^3$P)3d$^2$F-($^3$P)4p$^2$D$^o$    &   10000. & 0.701E-02  &0.284    \\
          $\lambda$ = 937.1 \AA   &       20000.&  0.495E-02  &0.567\\    
                       &   40000. & 0.350E-02  & 1.13    \\
                       &   80000. & 0.248E-02  & 2.27    \\
                       &  160000. & 0.175E-02  & 4.54    \\
\hline

  Ca IV ($^3$P)3d$^2$P-($^3$P)4p$^2$D$^o$   &   10000. & 0.476E-01  &0.284    \\
         $\lambda$ = 2231.7 \AA   &       20000.&  0.336E-01&  0.567\\    
                       &   40000. & 0.238-01  & 1.13    \\
                       &   80000. & 0.168E-01  & 2.27    \\
                       &  160000. & 0.119E-01   &4.54    \\

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

\begin{table*}
\renewcommand\thetable{2}
\caption{Continued.}
\label{tab:3}       % Give a unique label
% For LaTeX tables use

\centering
\begin{tabular}{crrrr}
\hline 
Transition  & T(K) & W[\AA]&3kT/2$\Delta$E\\
\hline

Ca IV($^3$P)3d$^2$P-($^3$P)4p$^2$P$^o$   &   10000. & 0.486E-01  &0.289    \\
         $\lambda$ = 2264.9 \AA   &       20000.&  0.344E-01 & 0.578\\    
                      &    40000. & 0.243E-01   &1.16    \\
                      &    80000.&  0.172E-01   &2.31    \\
                      &   160000.&  0.122E-01   &4.62    \\
\hline

  Ca IV ($^3$P)3d$^2$P-($^3$P)4p$^2$S$^o$   &    10000.&  0.428E-01 & 0.259    \\
         $\lambda$ = 2071.5 \AA   &       20000.&  0.303E-01 & 0.518\\    
                      &    40000. & 0.214E-01  & 1.04    \\
                      &    80000. & 0.151E-01  & 2.07    \\
                      &   160000. & 0.107E-01  & 4.15    \\
\hline

  Ca IV ($^3$P)3d$^2$P-($^3$P)4p$^2$D$^o$   &    10000. & 0.729E-01  &0.284    \\
         $\lambda$ = 2715.7 \AA   &       20000.&  0.516E-01&  0.567\\    
                      &    40000. & 0.365E-01  & 1.13\\    
                      &    80000. & 0.258E-01  & 2.27\\    
                      &   160000. & 0.182E-01  & 4.54\\    
\hline

  Ca IV ($^3$P)3d$^2$P-($^3$P)4p$^2$P$^o$  &    10000. & 0.750E-01  &0.289\\    
         $\lambda$ = 2765.1 \AA   &       20000.&  0.531E-01 & 0.578\\    
                      &    40000. & 0.375E-01  & 1.16    \\
                      &    80000. & 0.265E-01  & 2.31    \\
                      &   160000. & 0.188E-01  & 4.62    \\
\hline

  Ca IV ($^3$P)4s$^2$P-($^3$P)4p$^2$D$^o$   &    10000. & 0.136      &0.284    \\
         $\lambda$ = 2720.8 \AA   &       20000.&  0.965E-01  &0.567\\    
                      &    40000. & 0.682E-01  & 1.13    \\
                      &    80000. & 0.482E-01  & 2.27    \\
                      &   160000. & 0.341E-01  & 4.54    \\
\hline

  Ca IV ($^3$P)4s$^2$P-($^3$P)4p$^2$P$^o$ &    10000. & 0.141      &0.289    \\
         $\lambda$ = 2770.3 \AA   &       20000.&  0.996E-01  &    0.578\\    
                      &    40000. & 0.704E-01  & 1.16    \\
                      &    80000. & 0.498E-01  & 2.31    \\
                      &   160000. & 0.352E-01  & 4.62    \\
\hline

  Ca IV ($^3$P)4s$^2$P-($^3$P)4p$^2$S$^o$  &    10000. & 0.117      &0.284    \\
         $\lambda$ = 2486.3 \AA   &       20000.&  0.824E-01&  0.567\\    
                      &    40000. & 0.583E-01  & 1.13    \\
                      &    80000. & 0.412E-01  & 2.27    \\
                      &   160000. & 0.291E-01  & 4.54    \\
\hline

  Ca IV ($^1$D)3d$^2$P-($^1$D)4p$^2$D$^o$  &    10000. & 0.729E-02  &0.229    \\
          $\lambda$ = 730.6 \AA   &       20000.&  0.516E-02&  0.457\\    
                      &    40000. & 0.365E-02  &0.915    \\
                      &    80000. & 0.258E-02  & 1.83    \\
                      &   160000. & 0.182E-02  & 3.66    \\
\hline

  Ca IV ($^1$D)3d$^2$P-($^1$D)4p$^2$P$^o$   &    10000. & 0.721E-02  &0.219    \\
          $\lambda$ = 720.4 \AA   &       20000.&  0.510E-02 & 0.439\\    
                      &    40000. & 0.361E-02  &0.877    \\
                      &    80000. & 0.255E-02  & 1.75    \\
                      &   160000. & 0.180E-02  & 3.51    \\
\hline

  Ca IV ($^1$D)3d$^2$D-($^1$D)4p$^2$D$^o$  &    10000. & 0.876E-02  &0.262    \\
          $\lambda$ = 813.2 \AA   &       20000.&  0.620E-02&  0.523\\    
                      &    40000. & 0.438E-02  & 1.05    \\
                      &    80000. & 0.310E-02  & 2.09    \\
                      &   160000. & 0.219E-02  & 4.19    \\
\hline

  Ca IV ($^1$D)3d$^2$P-($^1$D)4p$^2$D$^o$   &    10000. & 0.839E-02  &0.229    \\
          $\lambda$ = 776.9 \AA   &       20000.&  0.593E-02&  0.457\\    
                      &    40000. & 0.419E-02  &0.915    \\
                      &    80000. & 0.297E-02  & 1.83    \\
                      &   160000. & 0.210E-03  & 3.66    \\
\hline

  Ca IV ($^1$D)3d$^2$P-($^1$D)4p$^2$P$^o$   &    10000. & 0.828E-02  &0.219    \\
          $\lambda$ = 765.3 \AA   &       20000.&  0.585E-02 & 0.439\\    
                      &    40000. & 0.414E-02  &0.877    \\
                      &    80000. & 0.293E-02  & 1.75    \\
                      &   160000. & 0.207E-02  & 3.51    \\
\hline

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

\begin{table*}
\renewcommand\thetable{2}
\caption{Continued.}
\label{tab:4}       % Give a unique label
% For LaTeX tables use

\centering
\begin{tabular}{crrrr}
\hline 
Transition  & T(K) & W[\AA]&3kT/2$\Delta$E\\
\hline



  Ca IV ($^1$D)3d$^2$G-($^1$D)4p$^2$F$^o$  &    10000. & 0.965E-02  &0.262    \\
          $\lambda$ = 848.5 \AA   &       20000.&  0.682E-02  &0.523\\    
                      &    40000. & 0.483E-02  & 1.05    \\
                      &    80000. & 0.341E-02  & 2.09    \\
                      &   160000. & 0.241E-02  & 4.19    \\
\hline

  Ca IV ($^1$D)3d$^2$F-($^1$D)4p$^2$F$^o$   &    10000. & 0.141E-01  &0.262    \\
         $\lambda$ = 1002.2 \AA   &       20000.&  0.996E-02&  0.523\\    
                      &    40000. & 0.704E-02  & 1.05    \\
                      &    80000. & 0.498E-02  & 2.09    \\
                      &   160000. & 0.352E-02  & 4.19    \\
\hline

  Ca IV ($^1$D)3d$^2$F-($^1$D)4p$^2$D$^o$  &    10000. & 0.132E-01  &0.229    \\
          $\lambda$ = 947.7 \AA   &       20000.&  0.932E-02 & 0.457\\    
                     &     40000. & 0.659E-02  &0.915    \\
                     &     80000. & 0.466E-02  & 1.83    \\
                     &    160000. & 0.329E-02  & 3.66    \\
\hline

  Ca IV ($^1$D)3d$^2$S-($^1$D)4p$^2$P$^o$ &     10000.  &0.373E-01  &0.219    \\
         $\lambda$ = 1490.4 \AA    &      20000.&  0.263E-01  &0.439\\    
                     &     40000.  &0.186E-01  &0.877    \\
                     &     80000.  &0.132E-01  & 1.75    \\
                     &    160000.  &0.931E-02  & 3.51    \\
\hline

  Ca IV ($^1$D)4s$^2$D-($^1$D)4p$^2$F$^o$ &     10000.  &0.108      &0.262    \\
         $\lambda$ = 2509.5 \AA    &      20000.&  0.764E-01&  0.523\\    
                     &     40000.  &0.540E-01  & 1.05    \\
                     &     80000.  &0.382E-01  & 2.09    \\
                     &    160000.  &0.270E-01  & 4.19    \\
\hline

  Ca IV ($^1$D)4s$^2$D-($^1$D)4p$^2$D$^o$   & 10000. &0.856E-01  &0.262    \\
        $\lambda$ =  2193.5 \AA    &      20000.&  0.606E-01&  0.523\\    
                         & 40000.  &0.428E-01   &1.05    \\
                         & 80000. & 0.303E-01   &2.09    \\
                         &160000. & 0.214E-01   &4.19    \\
\hline

  Ca IV ($^1$D)4s$^2$D-($^1$D)4p$^2$P$^o$    & 10000. & 0.798E-01  &0.262    \\
         $\lambda$ = 2103.6 \AA   &       20000.&  0.564E-01&  0.523\\    
                        &  40000. & 0.399E-01 & 1.05    \\
                        &  80000. & 0.282E-01 &  2.09    \\
                        & 160000. & 0.200E-01 &  4.19    \\
\hline

  Ca IV ($^1$D)4p$^2$F$^o$-($^1$D)5s$^2$D   &  10000. & 0.126     & 0.262    \\
         $\lambda$ = 2091.3 \AA   &       20000.&  0.892E-01 & 0.523\\    
                        &  40000. & 0.631E-01  & 1.05    \\
                        &  80000. & 0.446E-01  & 2.09    \\
                        & 160000. & 0.315E-01  & 4.19    \\
\hline

  Ca IV ($^1$D)4p$^2$D$^o$-($^1$D)5s$^2$D    &  10000. & 0.167      &0.260    \\
         $\lambda$ = 2376.7 \AA   &       20000.&  0.118      &0.520\\    
                       &   40000. & 0.836E-01  & 1.04    \\
                       &   80000. & 0.591E-01  & 2.08    \\
                       &  160000. & 0.418E-01  & 4.16    \\
\hline

 Ca IV ($^1$D)4p$^2$P$^o$-($^1$D)5s$^2$D    &   10000. & 0.185      &0.260    \\
         $\lambda$ = 2492.0 \AA   &       20000.&  0.131  &    0.520\\    
                       &   40000. & 0.927E-01   &1.04    \\
                       &   80000. & 0.655E-01   &2.08    \\
                       &  160000. & 0.463E-01   &4.16    \\
\hline

  Ca IV ($^1$S)3d$^2$D-($^1$S)4p$^2$P$^o$   &   10000. & 0.628E-02  &0.244    \\
          $\lambda$ = 912.0 \AA   &       20000.&  0.444E-02&  0.488\\    
                       &   40000. & 0.314E-02  &0.976 \\   
                       &   80000. & 0.222E-02  & 1.95   \\ 
                       &  160000. & 0.157E-02  & 3.90    \\
\hline

  Ca IV ($^1$S)4s$^2$S-($^1$S)4p$^2$P$^o$ &   10000. & 0.953E-01  &0.244    \\
         $\lambda$ = 2339.8 \AA   &       20000.&  0.674E-01 & 0.488\\    
                       &   40000. & 0.476E-01  &0.976    \\
                       &   80000. & 0.337E-01  & 1.95    \\
                       &  160000. & 0.238E-01  & 3.9\\
                       
\hline
\end{tabular}
\end{table*}



\section*{RESULTS AND DISCUSSION}
  
By using the symplified modified semiempirical (SMSE) method  \citep{Di87}, Stark full widths at half maximum 
(FWHM) for 10 multiplets of K III and 35 multiplets of Ca IV have been 
calculated for electron density of 10$^{17}$ cm$^{-3}$ and for temperatures from 5 000 K to 80 000 K in the case of K III while 
for Ca IV the chosen temperature range was from 10 000 K to 160 000 K. Calculations were performed for broadening of spectral
lines by collisions with electrons. Energy levels and ionization energies needed for the corresponding 
calculations have been taken from \citet{Su85, Sa08, Kr18} in the case of K III and from \citet{Su85, Kr18} in the case of Ca IV.
The data for energy levels are incomplete for any more sophysticated calculation but using them, SMSE method, who needs less atomic data,
can be applied.

\begin{table}
\renewcommand\thetable{3}
\caption{This table gives electron-impact broadening (Stark broadening) Full Widths at Half Intensity Maximum (W) 
for K III  4s$^{(2S+1)}$P-4p$^{2S+1}$L$^o$ (L=S, P, D) supermultiplet, for a perturber density of 10$^{17}$ cm$^{-3}$ 
and temperature of 10 000 K, in [\AA] and in [$10^{12}$s$^{-1}$] units.}
\label{tab:8}       % Give a unique label
% For LaTeX tables use

\centering
\begin{tabular}{crrr}
\hline 
Transition  & T(K) &  W[\AA]&W[10$^{12}$ s$^{-1}$]\\
\hline

 K III  4s$^2$P-4p$^2$D$^o$    &   10000.&  0.232     &  0.398    \\
         $\lambda$ = 3312.2 \AA  &        &       & \\    
\hline


  K III  4s$^2$P-4p$^2$P$^o$   &    10000.&  0.220     &  0.403    \\
        $\lambda$ = 3205.3 \AA   &      &    &\\    
\hline


  K III  4s$^4$P-4p$^4$P$^o$    &    10000. & 0.219     & 0.362    \\
         $\lambda$ = 3376.2 \AA   &      &  &   \\
\hline


  K III  4s$^4$P-4p$^4$D$^o$    &    10000. & 0.181      &0.377    \\
         $\lambda$ = 3006.0 \AA   &      &   &    \\
 \hline


  K III  4s$^4$P-4p$^4$S$^o$    &    10000. & 0.144   &  0.401    \\
         $\lambda$ = 2601.3 \AA   &      &    &   \\
                       
\hline
\end{tabular}
\end{table}


The results of our calculations of Stark widths for K III spectral lines are shown in Table 1 and for Ca IV in Table 2. 
The extrapolation to lower perturber densities is linear while for higher extrapolation is linear to densities where the 
influence of Debye screening is negligible or reasonably small. The wavelengths presented in Tables 1 and 2 are the calculated ones from the averaged
energy levels for multiplet so that they differ from the observed ones. In the last column is shown the quantity 3$kT/2\Delta E$, which represents
the ratio of the average energy of 
free electrons, $E = 3kT/2$, and the energy difference between the initial or final and the closest perturbing level,and is taken the 
larger of such values for initialand final level.

$$\Delta E = {\rm Max}[E/\Delta E_{i,i'}, E/\Delta E_{f,f'}] \eqno(2)$$
 
This ratio is the validity condition for the used method. If $3kT/2\Delta E = 1$, it 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, and the applied method is completely 
convenient and valid. If it is larger than one the inelastic collisions start to play more and more important role with its increase
and the method underestimates the real value. However, since the Stark width decrease monotonically with the increase of temperature, 
if we look at the value of Stark width at lower temperatures, where the condition given by Eq. (2) is satisfied, and the obtained value 
for the needed temperature, the right value is between these limits, so that we have a rough estimate for it.

The Stark widths obtained here, enable to check the similarities of these line broadning parameters  
within a supermultiplet and transition array. If such similarities exist, they could be used for derrivation of missing values,
on the basis of the known ones. Namely, \citet{Wi82} found that Stark line widths in angular frequency units in a supermultiplet
usually agree within about 30 per cent and within a transition array within about 40 per cent. We will check this for K III,
belonging to the chlorine isoelectronic sequence, for the supermltiplet 4s$^{(2S+1)}$P-4p$^{2S+1}$L$^o$ (L=S, P, D).
In order to do so we should transform the Stark widths expressed in \AA-units to the widths in angular frequency units, what can be 
done by the following formula:


$$W(\mathring{A})=\frac{\lambda ^{2}}{2\pi c}W(s^{-1}), \eqno(3)$$
 

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


The values in \AA \- and in s$^{-1}$ are presented in Table 3. We can see that for values in \AA \- the highest value in 
supermultiplet is 52\% higher from the lowest and in transition array 61\%, but this is because of the influence of wavelength. In s$^{-1}$
units, when the width is liberated from this influence, the maximal value in both supermultiplet and transition array is only 11\% 
larger from the smaller one what is well within the limits found by  \citet{Wi82}. 

The Stark widths obtained here for K III and Ca IV spectral lines will be included in
the \textsc{STARK-B} database \citep{Sah15, starkb}, one of the databases which enter also in the european Virtual
Atomic and Molecular Data Center - VAMDC \citep{vamdc,Rixon11, Dub16}, which can be found on the web site  http://portal.vamdc.org/.


\section*{CONCLUSION}

By using the SMSE method we have calculated Stark widths
for 10 K III and 35 Ca IV  multiplets as a function of temperature. 
The presented widths are also used to check how similar they are within a
 supermultiplet and transition array. These data will be implemented in STARK-B database. 
 Since other experimental or theoretical data for these ions do not exist it is not
 possible to make a comparison with other results. 
 The data obtained in this work may be of interest for stellar physics, plasma diagnostics and inertial fusion reearch.  

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\end{document}

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