\documentclass{aa}
\usepackage{psfig,amsmath,ifthen}
\usepackage[dvips]{graphicx}

\newcommand{\lsto}[3]{% short-cut for LS Term odd
                        \ensuremath{^{#1}\mathrm{#2}^\text{o}_{\text{#3}}}}

\newcommand{\lste}[3]{% short-cut for LS Term
                        \ensuremath{^{#1}\mathrm{#2}_{\text{#3}}}}

\begin{document}

\title{Atomic Data from the IRON Project
\thanks{ The full  datasets are available in electronic form
at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5)
or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/.
}}
\subtitle{I. Electron-impact excitation of $n=3,4$ levels 
          of Fe$^{19+}$}
\author{M. C. Witthoeft\inst{1} \and G. Del Zanna\inst{2} \and
       N. R. Badnell\inst{1}
       }
\institute{Department of Physics, University of Strathclyde, 
           Glasgow, G4 0NG, UK \and 
	          MSSL,  University College London, Holmbury St., 
           Mary  Dorking, RH5 6NT, UK 
          }
\date{Received <date> / Accepted <date>}


\abstract
{ 
We present results for the electron-impact excitation of N-like Fe.  
$R$-matrix theory using an intermediate-coupling frame transformation method
is used to obtain level-resolved collision strengths.
Separate calculations are performed using different target expansions.
The first is a 215 level calculation which has the 2$l^5$, 2s$^2$ 2p$^2$ 3$l$, 
and 2s 2p$^3$ 3$l$ configurations while the second calculation also includes 
the levels from the 2s$^2$ 2p$^2$ 4$l$ configurations for a total of 302
levels.
The effect of the additional resonant enhancement of the larger calculation
is explored and compared with a previous IRON Project report and other, more 
recent, calculations.
Some errors were found in the previous IRON Project work which are corrected
and superceded by this report.
As a final comparison, we model an astrophysical plasma using the present
calculations and previous work.
}
\maketitle

\newpage

\section{Introduction}

The purpose of the IRON Project (Hummer et al., 1993) is to perform large-scale
electron-scattering calculations for ions of astophysical importance.
The current work, as a part of this effort, extends the previous IRON Project
calculation (IP XLIX) on N-like Fe by Butler \& Zeippen (2001).
This older work was an 86 level Breit-Pauli $R$-matrix calculation which 
included the $2l^5$, 2s$^2$ 2p$^2$ 3$l$, and select 2s 2p$^3$ 3$l$ levels.
Originally, the goal of this work was to extend these calculations to include
transitions to all 2s 2p$^3$ 3$l$ and 2s$^2$ 2p$^2$ 4$l$ levels using the 
intermediate-coupling frame transformation (ICFT) method.
This is thought necessary because we have found in other cases 
(e.g. Fe$^{17+}$; Witthoeft et al., 2005) that the inclusion of $n=4$ levels 
changed the ion population considerably.
However, this work also corrects an error found in the Butler \& Zeippen work, 
which will be discussed in detail later.

The Fe$^{19+}$ system produces a large number of spectral lines observed from 
the X-rays to the UV.
A considerable number of 2s$^2$ 2p$^3$ -- 2s$^2$ 2p$^2$ 3d transitions are 
observed in the X-rays, in particular at high densities (laser spectra), but 
also in astrophysical spectra (solar flares, active stars).
The 2s$^2$ 2p$^3$ -- 2s 2p$^4$ transitions are prominent in EUV spectra of 
solar flares (e.g. Kastner et al. 1974), active stars and Tokamaks (e.g. 
Stratton et al. 1984), and can be used to measure electron densities. 
The forbidden 2s$^2$ 2p$^3$ transitions show up as prominent lines in the UV 
(cf. Kucera et al. 2000).

Besides the previous IRON Project calculation, McLaughlin \&  Kirby (2001) 
performed a 23-level Breit-Pauli $R$-matrix calculation primarily focused on
transitions between the $2l^5$ levels. 
The effective collision strengths for these transitions are currently included 
in the CHIANTI database.
Most recently, a large distorted wave calculation to $n=5$ was carried out by 
Landi \& Gu (2006) where resonance effects were included for configurations 
with $n \leq 3$.
This work was aimed at providing accurate effective collision strengths at
higher temperatures and is also included in the current version of the 
CHIANTI database (v. 5; Landi et al., 2006).

The rest of the paper is organized as follows.  In Sec. 2, we outline the
calculation details and perform structure comparisons with other calculations
and measurements.  Analysis of the effective collision strengths with previous
calculations is performed in Sec. 3 along with a look at level populations
and line intensities. 
Finally, we summarize our results in Sec. 4.


\section{Calculation \& Structure}

The present work consists of two $R$-matrix calculations.  
The first, referred to hereafter as the 3$l$ calculation, contains the 
following configurations: 2s$^2$ 2p$^3$, 2s 2p$^4$, 2p$^5$, 2s$^2$ 2p$^2$ 3$l$,
2s 2p$^3$ 3$l$ with $l$=0,1,2. 
The second calculation, we will call 4$l$, extends the 3$l$ target expansion 
by including the 2s$^2$ 2p$^2$ 4$l$ configurations with $l$=0-3.
The smaller calculation has 120 LS terms and 215 fine-structure levels while 
the 4$l$ calculation has 284 terms and 302 levels.
The structure of each calculation was determined using AUTOSTRUCTURE 
(Badnell, 1986) where radial scaling parameters were used to minimize the 
equally-weighted sum of all LS term energies in the Thomas-Fermi approximation.
These scaling parameters are given in Table \ref{tab:lambda} for both 
calculations.

\begin{table}
\centering
\caption{ Radial scaling parameters used in AUTOSTRUCTURE. }
\begin{tabular}{ | c  c  c |}
\hline
                & $n=3$  & $n=4$  \\
\hline
$\lambda_{1\text{s}}$  & 1.4112 & 1.4149 \\
$\lambda_{2\text{s}}$  & 1.3257 & 1.3452 \\
$\lambda_{2\text{p}}$  & 1.2550 & 1.2709 \\
$\lambda_{3\text{s}}$  & 1.2388 & 1.2307 \\
$\lambda_{3\text{p}}$  & 1.1850 & 1.1772 \\
$\lambda_{3\text{d}}$  & 1.2619 & 1.2466 \\
$\lambda_{4\text{s}}$  &    -   & 1.2308 \\
$\lambda_{4\text{p}}$  &    -   & 1.1814 \\
$\lambda_{4\text{d}}$  &    -   & 1.2425 \\
$\lambda_{4\text{f}}$  &    -   & 1.2870 \\
\hline
\end{tabular}
\label{tab:lambda}
\end{table}

The energy levels for the 4$l$ calculation are shown in Fig.~\ref{fig:elev}, 
split by configuration.
Within each $nl$-configuration, the levels are further split, increasing from 
left-to-right, by the angular momentum of the valence electron.
There is a lot of overlap between the  2s$^2$ 2p$^2$ 3$l$ and 2s 2p$^3$ 3$l$
levels but the 2s$^2$ 2p$^2$ 4$l$ levels are well separated from the rest.
Due to the overlap of the $n$=3 levels, the configuration and term of each
level are not reliable labels for identification.  
When comparing the collision strengths from different calculations it is 
important to identify the levels by only the total angular momentum, parity,
and energy order while ignoring the configuration and term labels.

\begin{figure}
\includegraphics[width=6cm,angle=270]{Figs/fig1.ps}
\caption{
Energy levels in Ry for the 4$l$ calculation from AUTOSTRUCTURE.  For each
$nl$-configuration, the levels are further split by the angular momentum of 
the valence electron, increasing from left-to-right.
}
\label{fig:elev}
\end{figure}

In Table \ref{tab:elev} are listed the 4$l$ level energies for the 2$l^5$ and
2s$^2$ 2p$^2$ 3$l$ configurations, together with NIST v. 3\footnote{The full 
list of energies is available on-line}.
As the 3$l$ energies agree well with the 4$l$ energies, they are not included 
in the table.
For the 2$l^5$ levels, we find good agreement with the NIST values,
as well as previous calculations by Butler \& Zeippen (2001) 
and McLaughlin \& Kirby (2001).
The energies of the recent distorted wave calculation of Landi \& Gu (2006) 
show better agreement with observations for these levels, presumably because 
of the larger target expansion (they include 725 levels).
A comparison of level energies in the higher configurations is shown in 
Fig.~\ref{fig:ecomp}.
Here, we plot the percentage difference of the present 3$l$ calculation energies, 
observed energies listed in CHIANTI and NIST, and the energies of Landi \& Gu 
(2006), with the present 4$l$ calculation.
As previously mentioned, there is very good agreement between the energies of
the present 3$l$ and 4$l$ calculations. 
However, the additional $n=4$ configurations lead to a slight improvement of 
the 4$l$ energies compared to the 3$l$ calculation for these higher levels.
Generally speaking, the energies of the 4$l$ calculation are between 0.2 and 
0.4\% higher than the observed energies.
For the 2s$^2$ 2p$^2$ 4$l$ levels, the agreement between the 4$l$ calculation 
energies and the NIST energies is worse, but still under 1\%.
The agreement between the energies of the present calculation and those of 
Landi \& Gu is also between 0.2 and 0.4\% for the higher levels.
The Landi \& Gu energies are in better agreement with the observed energies for 
most of these levels.
Overall, the energy differences seen between the calculations are small and in 
good agreement with observations.
While the location of spectral features are shifted due to these differences, 
the overall magnitude of the collision strengths should not be affected since 
the energy-order of the levels is correct with few exceptions.
Also, due to the fact that these energy differences are small, we expect that
the level mixing is accurate.

\begin{figure}
\includegraphics[width=6cm,angle=270]{Figs/fig2.ps}
\caption{
Percent difference of the 3$l$ and Landi \& Gu (2006) calculations, and the 
observed energies from NIST and CHIANTI, with the present 4$l$ calculation.
}
\label{fig:ecomp}
\end{figure}

It is also useful to check oscillator strengths and A-values to get a better 
idea of the accuracy of our structure.  In Table \ref{tab:gf}, the $gf$-values 
of the 3$l$ and 4$l$ calculations for transitions from the ground level to the 
2s$^2$ 2p$^2$ 3s/3d levels are compared with the Case B calculation of 
Mason \& Bhatia (1983). 
Generally, we see good agreement between the calculations for all transitions 
with few exceptions, in particular the transitions to the higher levels.
In Table \ref{tab:list}, we include A-value comparisons for the
strongest transitions and find excellent agreement with NIST and a recent
calculation of Jonauskas et al. (2005).  
We do find, however, some large, and surprising, differences with our 
A-values and those of a previous IRON Project report by Nahar (2004). 
This will be further discussed in Section 3.2.


\begin{table*}
\centering
\caption{
Energy levels of the 2$l^5$ and 2s$^2$ 2p$^2$ 3$l$ configurations for the
present 4$l$ calculation, compared to NIST (v. 3).  
For the 2s$^2$ 2p$^2$ 3$l$ levels, we use only the valence electron as a label 
to save space.  
Gaps in the level-index sequence indicate the presence of a level from another 
configuration.
All energies are given in Ry.
}
\begin{tabular}{| c c c c | c c c c | c c c c |}
\hline
idx & conf & 4l & NIST & idx & conf & 4l & NIST & idx & conf & 4l & NIST\\
\hline
   1  & 2s$^2$ 2p$^3$ \lsto{4}{S}{3/2}     &   0.000  &   0.000  &  25  & 3p \lsto{2}{S}{1/2}  &  67.798  &   --  &   50  & 3d \lste{4}{D}{3/2}  &  70.779  &    --    \\
   2  & 2s$^2$ 2p$^3$ \lsto{2}{D}{3/2}     &   1.294  &   1.263  &  26  & 3p \lsto{4}{P}{3/2}  &  68.074  &   --  &   51  & 3d \lste{4}{D}{7/2}  &  70.809  &    --    \\
   3  & 2s$^2$ 2p$^3$ \lsto{2}{D}{5/2}     &   1.674  &   1.605  &  27  & 3p \lsto{4}{D}{5/2}  &  68.150  &   --  &   52  & 3d \lste{2}{F}{5/2}  &  70.824  &    --    \\
   4  & 2s$^2$ 2p$^3$ \lsto{2}{P}{1/2}     &   2.411  &   2.372  &  28  & 3p \lsto{4}{P}{1/2}  &  68.266  &   --  &   53  & 3d \lste{4}{F}{9/2}  &  70.839  &    --    \\
   5  & 2s$^2$ 2p$^3$ \lsto{2}{P}{3/2}     &   3.005  &   2.946  &  29  & 3p \lsto{4}{P}{5/2}  &  68.352  &   --  &   55  & 3p \lsto{2}{P}{1/2}  &  71.016  &    --    \\
   6  & 2s 2p$^4$ \lste{4}{P}{5/2}         &   6.906  &   6.859  &  30  & 3p \lsto{2}{D}{3/2}  &  68.453  &   --  &   56  & 3d \lste{4}{P}{5/2}  &  71.142  &  71.097  \\
   7  & 2s 2p$^4$ \lste{4}{P}{3/2}         &   7.519  &   7.478  &  31  & 3p \lsto{4}{D}{7/2}  &  68.551  &   --  &   57  & 3p \lsto{2}{P}{3/2}  &  71.143  &    --    \\
   8  & 2s 2p$^4$ \lste{4}{P}{1/2}         &   7.720  &   7.677  &  32  & 3s \lste{2}{S}{1/2}  &  68.762  &   --  &   58  & 3d \lste{4}{P}{3/2}  &  71.248  &  71.097  \\
   9  & 2s 2p$^4$ \lste{2}{D}{3/2}         &   9.615  &   9.501  &  33  & 3p \lsto{4}{S}{3/2}  &  68.764  &   --  &   59  & 3d \lste{2}{P}{1/2}  &  71.267  &    --    \\
  10  & 2s 2p$^4$ \lste{2}{D}{5/2}         &   9.780  &   9.644  &  34  & 3p \lsto{2}{P}{3/2}  &  68.992  &   --  &   60  & 3d \lste{4}{P}{1/2}  &  71.329  &    --    \\
  11  & 2s 2p$^4$ \lste{2}{S}{1/2}         &  11.014  &  10.892  &  35  & 3p \lsto{2}{D}{5/2}  &  69.037  &   --  &   61  & 3d \lste{2}{F}{7/2}  &  71.455  &  71.261  \\
  12  & 2s 2p$^4$ \lste{2}{P}{3/2}         &  11.475  &  11.322  &  36  & 3p \lsto{2}{P}{1/2}  &  69.213  &   --  &   63  & 3d \lste{2}{D}{3/2}  &  71.675  &  71.616  \\
  13  & 2s 2p$^4$ \lste{2}{P}{1/2}         &  12.371  &  12.211  &  38  & 3p \lsto{2}{F}{5/2}  &  69.710  &   --  &   64  & 3d \lste{2}{D}{5/2}  &  71.690  &  71.471  \\
  14  & 2p$^5$ \lsto{2}{P}{3/2}            &  18.030  &  17.809  &  39  & 3d \lste{4}{F}{3/2}  &  69.791  &   --  &   67  & 3d \lste{2}{G}{7/2}  &  72.028  &    --    \\
  15  & 2p$^5$ \lsto{2}{P}{1/2}            &  19.037  &  18.790  &  40  & 3p \lsto{2}{F}{7/2}  &  69.833  &   --  &   68  & 3d \lste{2}{G}{9/2}  &  72.179  &    --    \\
  16  & 3s \lste{4}{P}{1/2}                &  65.403  &    --    &  41  & 3p \lsto{2}{D}{3/2}  &  69.910  &   --  &   69  & 3d \lste{2}{D}{3/2}  &  72.300  &  72.163  \\
  17  & 3s \lste{4}{P}{3/2}                &  65.996  &    --    &  42  & 3d \lste{4}{F}{5/2}  &  70.010  &   --  &   70  & 3d \lste{2}{D}{5/2}  &  72.346  &  72.109  \\
  18  & 3s \lste{2}{P}{1/2}                &  66.288  &    --    &  43  & 3p \lsto{2}{D}{5/2}  &  70.086  &   --  &   71  & 3d \lste{2}{P}{1/2}  &  72.483  &    --    \\
  19  & 3s \lste{4}{P}{5/2}                &  66.402  &    --    &  44  & 3p \lsto{2}{P}{1/2}  &  70.150  &   --  &   74  & 3d \lste{2}{F}{7/2}  &  72.552  &  72.309  \\
  20  & 3s \lste{2}{P}{3/2}                &  66.704  &    --    &  45  & 3d \lste{2}{P}{3/2}  &  70.458  &   --  &   79  & 3d \lste{2}{S}{1/2}  &  72.798  &    --    \\
  21  & 3p \lste{4}{D}{1/2}                &  67.236  &    --    &  46  & 3d \lste{4}{F}{7/2}  &  70.474  &   --  &   80  & 3d \lste{2}{P}{3/2}  &  72.808  &  72.601  \\
  22  & 3p \lste{4}{D}{3/2}                &  67.629  &    --    &  47  & 3d \lste{4}{D}{1/2}  &  70.521  &   --  &   81  & 3d \lste{2}{F}{5/2}  &  72.813  &  72.746  \\
  23  & 3s \lste{2}{D}{5/2}                &  67.629  &    --    &  48  & 3d \lste{4}{D}{5/2}  &  70.550  &   --  &   85  & 3d \lste{2}{D}{5/2}  &  73.507  &  73.330  \\
  24  & 3s \lste{2}{D}{3/2}                &  67.721  &    --    &  49  & 3p \lsto{2}{P}{3/2}  &  70.655  &   --  &   86  & 3d \lste{2}{D}{3/2}  &  73.602  &    --    \\
\hline
\end{tabular}
\label{tab:elev}
\end{table*}

\begin{table*}
\centering
\caption{ 
Comparison of $gf$-values of the present calculations with the Case B 
calculation of Mason \& Bhatia (1983) for transitions to 2s$^2$ 2p$^2$ 3s/3d 
levels from the ground level.  The indices, $i$ and $j$, are the energy-ordered 
level indices of the 4$l$ calculation.
}
\begin{tabular}{| c c c c c c |}
\hline
 $i$ & $j$ & $j$ level & 4$l$ & 3$l$ & Mason \& Bhatia \\
\hline
 1 & 16 & 2s$^2$ 2p$^2$ 3s $^4$P$_{1/2}$ & 7.610E-02 & 7.433E-02 & 6.768E-02 \\
 1 & 17 & 2s$^2$ 2p$^2$ 3s $^4$P$_{3/2}$ & 1.221E-01 & 1.177E-01 & 1.157E-01 \\
 1 & 18 & 2s$^2$ 2p$^2$ 3s $^2$P$_{1/2}$ & 4.978E-05 & 3.703E-05 & 4.511E-05 \\
 1 & 19 & 2s$^2$ 2p$^2$ 3s $^4$P$_{5/2}$ & 1.843E-01 & 1.763E-01 & 1.809E-01 \\
 1 & 20 & 2s$^2$ 2p$^2$ 3s $^2$P$_{3/2}$ & 1.602E-03 & 1.433E-03 & 1.506E-03 \\
 1 & 23 & 2s$^2$ 2p$^2$ 3s $^2$D$_{5/2}$ & 5.793E-03 & 5.458E-03 & 6.375E-03 \\ 
 1 & 24 & 2s$^2$ 2p$^2$ 3s $^2$D$_{3/2}$ & 8.727E-04 & 8.536E-04 & 1.041E-03 \\
 1 & 32 & 2s$^2$ 2p$^2$ 3s $^2$S$_{1/2}$ & 2.228E-05 & 2.535E-05 & 2.060E-05 \\
 1 & 39 & 2s$^2$ 2p$^2$ 3d $^4$F$_{3/2}$ & 7.624E-02 & 7.665E-02 & 6.978E-02 \\
 1 & 42 & 2s$^2$ 2p$^2$ 3d $^4$F$_{5/2}$ & 3.999E-01 & 4.043E-01 & 3.844E-01 \\
 1 & 45 & 2s$^2$ 2p$^2$ 3d $^2$P$_{3/2}$ & 2.207E-01 & 2.178E-01 & 2.100E-01 \\
 1 & 47 & 2s$^2$ 2p$^2$ 3d $^4$D$_{1/2}$ & 3.231E-02 & 3.234E-02 & 3.076E-02 \\
 1 & 48 & 2s$^2$ 2p$^2$ 3d $^4$D$_{5/2}$ & 5.085E-01 & 5.166E-01 & 5.008E-01 \\
 1 & 50 & 2s$^2$ 2p$^2$ 3d $^4$D$_{3/2}$ & 5.139E-02 & 5.276E-02 & 5.188E-02 \\
 1 & 52 & 2s$^2$ 2p$^2$ 3d $^2$F$_{5/2}$ & 7.316E-01 & 7.225E-01 & 6.980E-01 \\
 1 & 56 & 2s$^2$ 2p$^2$ 3d $^4$P$_{5/2}$ & 1.969E+00 & 1.947E+00 & 2.043E+00 \\
 1 & 58 & 2s$^2$ 2p$^2$ 3d $^4$P$_{3/2}$ & 1.997E+00 & 1.981E+00 & 2.031E+00 \\
 1 & 59 & 2s$^2$ 2p$^2$ 3d $^2$P$_{1/2}$ & 2.175E-01 & 2.161E-01 & 1.926E-01 \\
 1 & 60 & 2s$^2$ 2p$^2$ 3d $^4$P$_{1/2}$ & 9.142E-01 & 9.059E-01 & 9.521E-01 \\
 1 & 63 & 2s$^2$ 2p$^2$ 3d $^2$D$_{3/2}$ & 1.696E-02 & 2.152E-02 & 2.052E-02 \\
 1 & 64 & 2s$^2$ 2p$^2$ 3d $^2$D$_{5/2}$ & 2.128E-01 & 2.160E-01 & 1.690E-01 \\
 1 & 69 & 2s$^2$ 2p$^2$ 3d $^2$D$_{3/2}$ & 1.897E-02 & 1.891E-02 & 1.223E-02 \\
 1 & 70 & 2s$^2$ 2p$^2$ 3d $^2$D$_{5/2}$ & 1.012E-02 & 7.927E-03 & 1.698E-02 \\
 1 & 71 & 2s$^2$ 2p$^2$ 3d $^2$P$_{1/2}$ & 1.146E-02 & 1.109E-02 & 1.124E-03 \\
 1 & 79 & 2s$^2$ 2p$^2$ 3d $^2$S$_{1/2}$ & 1.138E-02 & 1.148E-02 & 1.129E-02 \\
 1 & 80 & 2s$^2$ 2p$^2$ 3d $^2$P$_{3/2}$ & 1.080E-02 & 1.036E-02 & 9.000E-03 \\
 1 & 81 & 2s$^2$ 2p$^2$ 3d $^2$F$_{5/2}$ & 1.872E-02 & 1.769E-02 & 4.929E-03 \\
 1 & 85 & 2s$^2$ 2p$^2$ 3d $^2$D$_{5/2}$ & 8.887E-04 & 1.027E-03 & 1.789E-03 \\
 1 & 86 & 2s$^2$ 2p$^2$ 3d $^2$D$_{3/2}$ & 7.473E-06 & 2.701E-06 & 3.257E-05 \\
\hline
\end{tabular}
\label{tab:gf}
\end{table*}


The scattering calculations were performed using the intermediate-coupling 
frame transformation (ICFT) method (see Griffin et al., 1998) which employs 
multi-channel quantum defect theory (MQDT) to obtain level-resolved collision 
strengths from a term-resolved $R$-matrix calculation.
Both calculations include the mass-velocity, spin-orbit, and Darwin 
relativistic corrections.
The 3$l$ and 4$l$ calculations use 20 and 30 continuum basis functions 
respectively.
In the $R$-matrix inner region, exchange effects were included for $J$=0-10 for 
the 3$l$ calculation and $J$=0-12 for the 4$l$ calculation.
This range is extended to $J$=40 for both calculations using a non-exchange 
approximation. 
A further top-up of the collision strengths to infinite $J$ was added using the 
Burgess sum rule (see Burgess, 1974) for dipole transitions and a geometric 
series for the non-dipole transitions (see Badnell \& Griffin, 2001).
In the outer region, an energy mesh of 10$^{-5}$ $z^2$ Ry (where $z$=19 for 
N-like Fe) was used in the resonance region of the exchange calculation.
A mesh of 10$^{-3}$ $z^2$ Ry was used beyond the resonance region of the 
exchange calculation and over the entire energy range of the non-exchange 
calculation up to an energy of 420 Ry, or near 3.5 times the ionization 
threshold.  
The fine energy mesh used in the resonance region is not small enough to fully 
resolve all of the resonances, however, as discussed by Badnell \& Griffin 
(2001), this mesh is small enough to accurately sample the small width 
resonances.
Effective collision strengths are then obtained by convoluting the collision 
strengths with a Maxwellian distribution, where interpolation to 
infinite-energy points is used to calculate the effective collision strengths 
beyond our energy range.
The infinite-energy collision strengths are calculated for dipole and allowed
transitions within AUTOSTRUCTURE (see Whiteford et al., 2001).

\section{Results}
\subsection{Comparison of Effective Collision Strengths}

The primary purpose of this work is to improve on the previous IRON Project 
calculation by Butler \& Zeippen (2001), following the findings of our 
previous work on Fe$^{17+}$ (Witthoeft et al., 2006).
However, errors have been found in the high-energy collision strengths of some 
transitions calculated by Butler \& Zeippen, where large ``jumps'' in the 
collision strength can be seen just beyond the resonance region.
These discontinuous ``jumps'' are caused by the incorrect matching of the levels
of the low-energy collision strengths with those of the high-energy collision 
strengths (Butler, 2005; private communication).
An example of this is shown in Fig.~\ref{fig:omg1-19}, along with the 
collision strengths for the two present calculations. 
For these transitions, the high temperature effective collisions strengths 
will be unphysically enhanced (or suppressed in the case of ``drops'' in the 
collision strength) in the Butler \& Zeippen calculation.
Between the two present calculations, we see that the 4$l$ resonances extend 
to much larger energy than the 3$l$ calculation.
However, note that we are plotting the logarithm of the collision strength, so 
the magnitude of these extra resonances is actually small compared to the 3$l$ 
resonances and will have a small effect on the effective collision strength
for this transition.
The differences between the two present calculations at low temperatures is 
primarily due to differences in the $n=3$ resonance structure.

\begin{figure}
\includegraphics[width=6cm,angle=270]{Figs/fig3.ps}
\caption{
Collision strength for the transition to 2s$^2$ 2p$^2$ 3s $^4$P$_{5/2}$
from the ground level.  From top to bottom, the results shown are from 
Butler \& Zeippen (2001), the 3$l$ calculation, and the 4$l$ calculation.
}
\label{fig:omg1-19}
\end{figure}

In light of the errors in the Butler \& Zeippen calculation, our primary 
comparison will be with those data currently included in the CHIANTI database. 
For transitions between the 2$l^5$ levels, we will compare with the 23-level 
Breit-Pauli $R$-matrix calculation of McLaughlin \& Kirby (2001).
For transitions to the higher levels we will compare with the recent distorted 
wave calculation (up to $n=5$) of Landi \& Gu (2006), where the approximate 
effects of the $n \leq 3$ resonances have been included.
Comparisons will be made at the peak abundance temperature for photo-ionized 
plasmas, $T \approx 4 \times 10^5$ K (Kallman \& Bautista, 2001), and 
collision-dominated plasmas, $T \approx 1 \times 10^7$ K 
(Mazzotta et al., 1998).

\begin{table*}
\centering
\caption{ 
Effective collision strengths of the present 3$l$ and 4$l$ calculations
compared with those of McLaughlin and Kirby (2001) (denoted as M\&K).  
Values are given at the peak abundance temperatures of photo-ionized plasmas 
and collision-dominated plasmas.
}
\begin{tabular}{| c | c c c | c c c |}
\hline
  & &  T = 4 $\times$ 10$^5$ K &  &  & T = 1.2 $\times$ 10$^7$ K &   \\
 $i$-$j$ & 3$l$ & 4$l$  & M\&K & 3$l$ & 4$l$  & M\&K \\
\hline
 1-2 & 1.10E-1 & 1.19E-1 & 9.08E-2 & 5.11E-2 & 5.04E-2 & 4.59E-2 \\
 1-3 & 7.53E-2 & 8.35E-2 & 6.31E-2 & 5.05E-2 & 4.80E-2 & 4.63E-2 \\
 1-4 & 2.34E-2 & 2.32E-2 & 1.76E-2 & 1.72E-2 & 1.51E-2 & 1.47E-2 \\
 1-5 & 3.81E-2 & 4.25E-2 & 3.71E-2 & 2.63E-2 & 2.65E-2 & 2.20E-2 \\
 2-3 & 1.14E-1 & 1.15E-1 & 8.92E-2 & 8.40E-2 & 8.81E-2 & 6.59E-2 \\
 2-4 & 9.90E-2 & 9.79E-2 & 5.27E-2 & 3.95E-2 & 3.95E-2 & 3.80E-2 \\
 2-5 & 9.25E-2 & 9.22E-2 & 4.58E-2 & 5.20E-2 & 5.38E-2 & 4.06E-2 \\
 3-4 & 5.11E-2 & 5.12E-2 & 3.40E-2 & 3.35E-2 & 3.14E-2 & 3.19E-2 \\
 3-5 & 2.02E-1 & 1.87E-1 & 1.02E-1 & 9.60E-2 & 9.35E-2 & 8.40E-2 \\
 4-5 & 4.89E-2 & 4.70E-2 & 3.60E-2 & 3.82E-2 & 4.08E-2 & 2.94E-2 \\
\hline
\end{tabular}
\label{tab:mclaugh}
\end{table*}

In Table \ref{tab:mclaugh}, we compare the effective collision strengths of the 3$l$ 
and 4$l$ calculations with the Breit-Pauli $R$-matrix calculation of McLaughlin 
\& Kirby (2001).
There is generally very good agreement between the 3$l$ and 4$l$ calculations 
at both temperatures.
Interestingly, the agreement is slightly better for most transitions at the 
high temperature, despite the extra resonant enhancement present in the 4$l$ 
calculation.  
This is most likely due to the fact that the background of the 3$l$ calculation 
is slightly higher than the 4$l$ calculation for all but two of these 
transitions.  
The agreement between the present calculations and those of McLaughlin \& Kirby 
are at the 30\% level (on average) for the lower temperature and the 15\% level 
for the high temperature.  
The background collision strengths at high energies between McLaughlin \& 
Kirby's calculation and our own is in good agreement, so the differences in 
the Table \ref{tab:mclaugh} are most likely due to resonance effects.
We would expect there to be better agreement between McLaughlin \& Kirby and 
our 3$l$ calculation, since they included only the 2$l^5$ and 2s$^2$ 2p$^2$ 
3$l$ configurations in their calculation, but this is not always the case.
The most probable reason for the difference is due to the resonance resolution 
of the two calculations.  
In the McLaughlin \& Kirby calculation, an energy mesh of 10$^{-4}$ $z^2$ Ry 
was used in the resonance region whereas a mesh of 10$^{-5}$ $z^2$ Ry is used 
in the present work.
This is confirmed by the better agreement between the calculations at the 
higher temperature where the resonance contribution to the effective collision 
strength is smaller.

Next we will look at the transitions to the 2s$^2$ 2p$^2$ 3$l$ levels from the 
ground level.  
At near the peak abundance temperature for collision-dominated plasmas 
($T=1.2 \times 10^7$ K), 
the agreement between the present calculations and 
those of a recent distorted wave calculation of Landi \& Gu (2006) agree at the 
10\% level for the strongest transitions.  
For several of the weaker transitions, however, we find that the present 
calculations give results more than a factor of two greater than the distorted
wave calculation.
Landi \& Gu provide effective collision strengths down to a temperature 
of 1.1 $\times$ 10$^6$ K, where we find that the differences between 
the calculations are larger overall.
This is probably due to the approximate treatment of the resonances in 
the distorted wave calculations.
In Fig. \ref{fig:upsrat}, we compare the 4$l$ calculation with the results
of Landi \& Gu at a temperature of 1.2 $\times$ 10$^6$ K by plotting the ratio
of the 4$l$ effective collision strength to that of Landi \& Gu versus the
magnitude of the 4$l$ collision strength.
We show only the ratios for the transitions between the ground level and
the 2s$^2$ 2p$^2$ 3$l$ levels in the figure; triangles denote 3s transitions,
stars are for 3p transitions, and the boxes mark the 3d transitions.
The agreement with the stronger transitions to the 2s$^2$ 2p$^2$ 3d levels is 
still quite good, but the 4$l$ calculations give consistantly larger results
for the transitions to the 2s$^2$ 2p$^2$ 3s and 2s$^2$ 2p$^2$ 3p levels.
The strongest transition to each configuration has been circled and labeled
according to the energy-ordered index of the 4$l$ calculation (see Table 
\ref{tab:elev}).

\begin{figure}
\includegraphics[width=6cm,angle=270]{Figs/fig4.ps}
\caption{
The ratio of the effective collision strengths of the present 4$l$ calculation
to the Landi \& Gu results at a temperature of 1.2 $\times$ 10$^6$ K.
Only transitions between the ground level and the levels belonging to the
2s$^2$ 2p$^2$ 3$l$ configurations are plotted.
The triangles show transitions to the 3s levels, the stars are 3p
levels, and the boxes are the 3d levels.
The dotted curves mark differences of a factor of two.
The strongest transition to each configuration has been circled
and labeled according to the energy-ordered index of the 4$l$ calculation
for further discussion.
}
\label{fig:upsrat}
\end{figure}

In Fig.~\ref{fig:ups1-19} is shown the effective collision strength for the 
strongest 2s$^2$ 2p$^2$ 3s transition from the ground level which has a level 
label of $^4$P$_{5/2}$.
Included in the figure are the results from the 3$l$ calculation (long-dash), 
the 4$l$ calculation (solid), Butler \& Zeippen (2001) (dot), and Landi \& Gu 
(2006) (dot-dash).
At high temperatures, we see very good agreement between the present 
calculations and those of Landi \& Gu. 
However, due to the error apparent in Fig.~\ref{fig:omg1-19}, the 
Butler \& Zeippen results are too large by more than a factor of two.
At low temperatures, all of the calculations disagree due to differences in the
resonance structure.
We would expect that the 3$l$ results be in good agreement with the Butler
\& Zeippen results at low temperatures due to a similar target expansion, but 
this is not the case.
The differences are most likely caused by a combinations of factors, namely 
the incorrect high-energy behavior of the Butler \& Zeippen results and
that their energy mesh was five times coarser in the resonance region than the
present calculations.

\begin{figure}
\includegraphics[width=6cm,angle=270]{Figs/fig5.ps}
\caption{
Effective collision strength for the transition to 2s$^2$ 2p$^2$ 3s 
$^4$P$_{5/2}$ from the ground level.  
The solid and dotted curves are the 4$l$ and 3$l$ calculations, respectively.  
The dashed curve is the result from Butler \& Zeippen (2001) and the dot-dashed 
curve is the result of Landi \& Gu (2006).
}
\label{fig:ups1-19}
\end{figure}

The strongest 2s$^2$ 2p$^2$ 3p transition has a level label of $^4$S$_{3/2}$.
The effective collision strength for this transition is plotted in 
Fig.~\ref{fig:ups1-33} where, again, we see very good agreement with the 
present calculations and those of Landi \& Gu at high temperatures. 
The Butler \& Zeippen results are also in very good agreement at high 
temperatures as the error we saw in the background of the previous transition 
does not occur here.
As there is very good agreement between the backgrounds of all the calculations,
the discrepancy at low temperatures must be due to resonances.
The Landi \& Gu results show little resonant enhancement while there is an 
increasing effect for the Butler \& Zeippen, 3$l$, and 4$l$ results, 
respectively.

\begin{figure}
\includegraphics[width=6cm,angle=270]{Figs/fig6.ps}
\caption{
Effective collision strength for the transition to 2s$^2$ 2p$^2$ 3p 
$^4$S$_{3/2}$ from the ground level. 
The curve identifications are the same as in Fig.~\ref{fig:ups1-19}.
}
\label{fig:ups1-33}
\end{figure}

As the transitions to the 2s$^2$ 2p$^2$ 3d levels have little resonant 
enhancement, the agreement between the present calculations and those of Landi 
\& Gu is good at all temperatures. 
Shown in Fig.~\ref{fig:ups1-56} is the transition to the 2s$^2$ 2p$^2$ 3d
$^4$P$_{5/2}$ level, where we see that the Landi \& Gu results are slightly 
higher than the present calculations (which are in excellent agreement with 
each other) over the entire temperature range.
The results of Butler \& Zeippen agree very well with the present calculations 
at the lower temperatures, but fall off faster than the other 
calculations at higher temperatures due to the error discussed previously.

\begin{figure}
\includegraphics[width=6cm,angle=270]{Figs/fig7.ps}
\caption{
Effective collision strength for the transition to 2s$^2$ 2p$^2$ 3d 
$^4$P$_{5/2}$ from the ground level. 
The curve identifications are the same as in Fig.~\ref{fig:ups1-19}.
}
\label{fig:ups1-56}
\end{figure}

Finally, we examine the 1-61 transition, which is also identified in 
Fig.~\ref{fig:upsrat}, where level 61 is labeled as 2s$^2$ 2p$^2$ 3d 
$^2$F$_{7/2}$ in all the calculations.
This transition stands out as it is the only one where the results of 
Landi \& Gu are significantly larger than for the present calculations.  
In Fig.~\ref{fig:ups1-61}, we show the effective collision strength for this 
transition and it appears that the Landi \& Gu results are for a different 
type of transition than for the results of the other calculations.
This level is highly mixed with the $^4$D$_{7/2}$ and $^2$G$_{7/2}$ levels, 
according to the 4$l$ calculation.
When plotted, however, the effective collision strengths for the transitions 
to these levels resemble that of the 1-61 transition for the present 
calculations and not that of Landi \& Gu.
After performing larger structure calculations, we are unable to to find 
another level that is highly mixed with level 61 that might explain the 
differences seen for this transition.

\begin{figure}
\includegraphics[width=6cm,angle=270]{Figs/fig8.ps}
\caption{
Effective collision strength for the transition to 2s$^2$ 2p$^2$ 3d 
$^2$F$_{7/2}$ from the ground level. 
The curve identifications are the same as in Fig.~\ref{fig:ups1-19}.
}
\label{fig:ups1-61}
\end{figure}


\subsection{Transition probabilities and line intensities}

We have calculated level populations with the 4$l$ dataset assuming 
steady-state conditions at a temperature where  Fe$^{19+}$ has peak abundance 
in collisional-ionization equilibrium (T $\approx$ 10$^{7}$ K).
We have selected only the brightest transitions in the low-density  regime 
(10$^{12}$ cm$^{-3}$), applicable to most astrophysical plasmas and 
low-density laboratory plasmas such as tokamaks. 
The results are shown in Table~\ref{tab:list}, where we have compared our 
transition probabilities with those in the NIST (v. 3) compilation, those 
calculated by Jonauskas et al. (2005), and within the IRON Project report of 
Nahar (2004). 
The A-values of Jonauskas et al. (2005) were calculated using the relativistic 
structure code, GRASP, and included the lowest 700 levels (up to n=5) in the 
multi-configuration Dirac-Fock (MCDF) approach. 
Nahar (2004) used the Breit-Pauli R-matrix (BPRM) codes 
(Berrington et al., 1995) to calculate the dipole-allowed transitions and 
SUPERSTRUCTURE (Eissner et al. 1974) for the forbidden transitions, where  
a correction to observed energies was also included.
We find there is excellent agreement (within 10\%) of our results with the 
NIST and Jonauskas et al. (2005) values.
Finer refinements (such as the use of  observed energies) are still 
possible, but would only change our results slightly. 
We therefore recommend, for consistancy, that our A-values are used together 
with our collision rates.
On the other hand, we find significant discrepancies with the BPRM values of 
Nahar (2004).
For the strongest transitions, listed in Table~\ref{tab:list}, the differences 
are within a factor of two, however, for weaker transitions differences are 
much larger as already shown in Table~6 of  Nahar (2004).
These differences are noted and discussed by Jonauskas et al. (2005). 

A second important step in our assessment of the data concerns the line 
intensities. 
First, we wanted to assess the effects that the inclusion of $n=4$ levels has 
on the level balance of the ion. 
Second, it is important to check what the effects are from the few erroneous 
collision strengths in  Butler \& Zeippen results. 
Third, we wanted to compare our results with those of Landi \& Gu.
In Table~\ref{tab:list}, we list our (normalized) line intensities, compared 
with those obtained with the Landi \& Gu and the  Butler \& Zeippen datasets, 
as included in CHIANTI v. 5 and 4 respectively (with the exclusion of 
ionization/recombination corrections and the inclusion of proton excitations 
within the ground configuration).
It turns out that, at the peak temperature, the results of Landi \& Gu are very 
close to ours (within 10\%) with few exceptions (for example, the transition 
from level 61 where we noted large disagreement in the effective collision 
strength).
Larger discrepancies with the  Landi \& Gu results are found at higher 
densities and lower temperatures.

We find that larger differences are found with the Butler \& Zeippen data 
overall, but, in most cases, still within 20\%. 
Significant exceptions listed in Table~\ref{tab:list} are clearly due to the 
erroneous ``jumps'' of the high energy collision strenths in the 
Butler \& Zeippen calculation.
Finally, we have found that the inclusion of the $n=4$ levels did not 
significantly affect the line intensities for this ion at the peak abundance
temperature for collisionally-ionized plasmas

A complete benchmark on identifications, observed wavelengths and diagnostic 
possibilities for astrophysical and laboratory plasmas is beyond the scope of 
this paper, however, a few comments are worth mentioning here. 
The forbidden transitions within the 2s$^2$ 2p$^3$ ground configurations are 
strong in solar flares, as shown in Kucera et al. (2000). 
As the same authors point out, these lines can potentially be very useful in 
the cross-calibration of instruments observing the 300-2700~\AA\ spectral 
range (as long as densities are below 10$^{11}$).
The 2s$^2$ 2p$^3$--2s$^2$ 2p$^2$ 3d transitions are prominent in the X-ray 
spectra of solar flares and active stars. One particular strong
transition,
2-64 ($^2$D$_{3/2}$--$^2$D$_{5/2}$), is an useful density 
diagnostic when observed in conjunction with one of the other transitions to 
the ground state. Fig.~\ref{fig:ratio2} shows one example, with the 
measurement from an SMM spectrum of a solar flare (Landi \& Phillips 2005).
In this particular case,  
an electron density of approximately 10${^{12.6}}$ cm$^{-3}$ is obtained.

The  2s$^2$ 2p$^3$--2s 2p$^4$ lines are also  prominent in solar flares, 
however most of them are blended with lines from other ions. Notably, the 1-6 
line with the resonance of Fe$^{22+}$.
As already found by previous authors, the 1-7 (121.845~\AA) and 2-9 
(110.627~\AA) lines are notable exceptions, and their ratio is an excellent 
density diagnostic. Fig.~\ref{fig:ratio} shows that our results are in close 
agreement (30\%) with the measurements of Stratton et al. (1984).

\begin{figure}
\includegraphics[width=6cm,angle=90]{Figs/fig_ratio2.ps}
\caption{Theoretical ratio of the 1-56 $^4$S$_{3/2}$--$^4$P$_{5/2}$ 
(12.845~\AA) vs. 2-64 $^2$D$_{3/2}$--$^2$D$_{5/2}$ 
as a function of electron density, calculated at $T=10^7$ K.
The box is the measurement of Landi \& Phillips (2005).
}
\label{fig:ratio2}
\end{figure}



\begin{figure}
\includegraphics[width=6cm,angle=90]{Figs/fig_ratio.ps}
\caption{Theoretical ratio of the $^4$S$_{3/2}$--$^4$P$_{3/2}$ 
(121.845~\AA) vs. the $^2$D$_{3/2}$--$^2$D$_{3/2}$  (110.627~\AA)
as a function of electron density, calculated at $T=10^7$ K.
The box is the measurement of Stratton et al. (1984), with 
30\% error bars.}
\label{fig:ratio}
\end{figure}


\begin{table*}
\centering
\caption{List of all the most prominent lines in Fe$^{19+}$.
Columns 3,4,5 indicate the theoretical line intensities (photons) 
calculated with the present $4l$ dataset, the dataset of Landi \&
Gu (L05), and that of Butler \& Zeippen (BZ01). 
The intensities have been calculated assuming 
steady-state conditions, in the low density regime (10$^{12}$ cm$^{-3}$)
at T= 10$^{7}$ K, and are normalised to the intensity of the 
strongest transition.
Colummns 6,7,8,9 give, respectively,
our A-values, those in the NIST database (v. 3), those in 
Jonauskas et al. (2005 - J05) and in Nahar (2004 - N04). 
Notable differences are marked with asterisks}
\begin{tabular}{ll c c c  c c c c l }
\hline
 $i$-$j$ & Terms   &  $I$& $I$(L05) & $I$(BZ01) & $A_{ji}$ & $A_{ji}$(NIST) & $A_{ji}$(J05) & $A_{ji}$(N04) & \\
\hline

% The relative intensities  (photons)  $Int=N_{j} A_{ji}/N_{\rm e}$ are normalised to 2.1e-11

\multicolumn{10}{c}{ 2s$^2$ 2p$^3$--2s$^2$ 2p$^3$} \\


    % 300.001-20000 �
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    % 721.558  2s$^2$ 2p$^3$--2s$^2$ 2p$^3$
1-2 &  $^4$S$_{3/2}$--$^2$D$_{3/2}$   & 7.3 & 6.8 & 6.3   & 1.6 10$^{4}$ &  -  & 1.6 10$^{4}$ &1.4 10$^{4}$ & \\

    % 567.866  2s$^2$ 2p$^3$--2s$^2$ 2p$^3$
1-3 &  $^4$S$_{3/2}$--$^2$D$_{5/2}$   & 2.8 & 2.9 & 2.6   & 1.3 10$^{3}$ & 1.3 10$^{3}$ &1.2 10$^{3}$ &1.1 10$^{3}$  & \\

    % 384.209  2s$^2$ 2p$^3$--2s$^2$ 2p$^3$
1-4 &  $^4$S$_{3/2}$--$^2$P$_{1/2}$   & 1.2 & 1.2 & 1.1   & 3.3 10$^{4}$ &  -  & 3.1 10$^{4}$& 3.0 10$^{4}$ & \\

    % 309.294  2s$^2$ 2p$^3$--2s$^2$ 2p$^3$
1-5 &  $^4$S$_{3/2}$--$^2$P$_{3/2}$   & 0.69 & 0.62 & 0.61   & 3.1 10$^{4}$ & 2.9 10$^{4}$ &3.0 10$^{4}$ & 2.9 10$^{4}$ & \\

    % 541.336  2s$^2$ 2p$^3$--2s$^2$ 2p$^3$
2-5 &  $^2$D$_{3/2}$--$^2$P$_{3/2}$   & 1.0 & 0.91 & 0.87   & 4.6 10$^{4}$ & 4.5 10$^{4}$ &4.3 10$^{4}$ & 4.3 10$^{4}$& \\

    % 2666.03  2s$^2$ 2p$^3$--2s$^2$ 2p$^3$
2-3 &  $^2$D$_{3/2}$--$^2$D$_{5/2}$   & 1.2 & 1.1 & 0.89   & 5.8 10$^{2}$ & 2.9 10$^{4}$ & 4.3 10$^{2}$& 4.2 10$^{2}$ & \\

    % 679.260  2s$^2$ 2p$^3$--2s$^2$ 2p$^3$
3-5 &  $^2$D$_{5/2}$--$^2$P$_{3/2}$   & 0.26 & 0.26 & 0.24   & 1.2 10$^{4}$ &  -  & 1.2 10$^{4}$ & 1.2 10$^{4}$ & \\

    % 821.787  2s$^2$ 2p$^3$--2s$^2$ 2p$^3$
2-4 &  $^2$D$_{3/2}$--$^2$P$_{1/2}$   & 0.22 & 0.23 & 0.21   & 6.0 10$^{3}$ &  -  & 5.9 10$^{3}$&  6.1 10$^{3}$ & \\

\hline
\multicolumn{10}{c}{2s$^2$ 2p$^3$--2s$^2$ 2p$^2$ 3d} \\

    % 1-30 �
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    % 12.827  2s$^2$ 2p$^3$--2s$^2$ 2p$^2$ 3d
1-58 &  $^4$S$_{3/2}$--$^4$P$_{3/2}$   & 1.0 & 1.1 & 0.95   & 2.0 10$^{13}$ & 2.1 10$^{13}$ & 2.05 10$^{13}$ &1.4 10$^{13}$ * & \\

    % 12.845  2s$^2$ 2p$^3$--2s$^2$ 2p$^2$ 3d
1-56 &  $^4$S$_{3/2}$--$^4$P$_{5/2}$   & 0.90 & 0.95 & 0.82   & 1.3 10$^{13}$ &  -  & 1.3 10$^{13}$ & 1.3 10$^{13}$ & \\

    % 12.812  2s$^2$ 2p$^3$--2s$^2$ 2p$^2$ 3d
1-60 &  $^4$S$_{3/2}$--$^4$P$_{1/2}$   & 0.43 & 0.45 & 0.41   & 1.9 10$^{13}$ &  -  &1.8 10$^{13}$ & - & \\

    % 12.951  2s$^2$ 2p$^3$--2s$^2$ 2p$^2$ 3d
1-48 &  $^4$S$_{3/2}$--$^4$D$_{5/2}$   & 0.29 & 0.29 & 0.26   & 3.4 10$^{12}$ &  -  & 3.1 10$^{12}$ & - & \\


    % 12.905  2s$^2$ 2p$^3$--2s$^2$ 2p$^2$ 3d
% 1-53 in J05 and in Gu ? 
1-52 &  $^4$S$_{3/2}$--$^2$F$_{5/2}$   & 0.25 &  0.28  & 0.22   & 4.9 10$^{12}$ &  -  & 5.1 10$^{12}$ & - & \\


    % 13.052  2s$^2$ 2p$^3$--2s$^2$ 2p$^2$ 3d
1-42 &  $^4$S$_{3/2}$--$^4$F$_{5/2}$   & 0.23 & 0.25 & 0.21   & 2.6 10$^{12}$ &  -  &2.7 10$^{12}$ & & \\


    % 13.405  2s 2p$^4$--2s 2p$^3$ 3d
% 6-111 in J05 and in Gu
%6-112 &  $^4$P$_{5/2}$--$^4$D$_{7/2}$   & 0.22 &  0.24  &  -    & 8.8 10$^{12}$ &  -  & 8.5 10$^{12}$ & - & \\


    % 13.140  2s$^2$ 2p$^3$--2s$^2$ 2p$^2$ 3d
% 2-53 in J05 
2-52 &  $^2$D$_{3/2}$--$^2$F$_{5/2}$   & 0.15 &  -  & 0.14   & 3.0 10$^{12}$ &  -  & 2.7 10$^{12}$ & - & \\



    % 13.091  2s$^2$ 2p$^3$--2s$^2$ 2p$^2$ 3d
3-61 &  $^2$D$_{5/2}$--$^2$F$_{7/2}$   & 6.4 10$^{-2}$ & 0.53 * & 4.9 10$^{-2}$ *  & 6.8 10$^{12}$ &  -  &7.0 10$^{12}$ & & \\

\hline

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\multicolumn{10}{c}{ 2s$^2$ 2p$^3$--2s$^2$ 2p$^2$ 3s}\\

    % 13.781  2s$^2$ 2p$^3$--2s$^2$ 2p$^2$ 3s
1-19 &  $^4$S$_{3/2}$--$^4$P$_{5/2}$   & 0.16 & 0.21 * & 0.36 *  & 1.1 10$^{12}$ &  -  & 1.1 10$^{12}$& 1.2 10$^{12}$& \\

    % 13.844  2s$^2$ 2p$^3$--2s$^2$ 2p$^2$ 3s
1-17 &  $^4$S$_{3/2}$--$^4$P$_{3/2}$   & 9.8 10$^{-2}$ & 0.11 & 0.22 *  & 1.1 10$^{12}$ &  -  &1.1 10$^{12}$ & - & \\

    % 13.972  2s$^2$ 2p$^3$--2s$^2$ 2p$^2$ 3s
1-16 &  $^4$S$_{3/2}$--$^4$P$_{1/2}$   & 6.9 10$^{-2}$ & 8.5 10$^{-2}$ & 0.13 *  & 1.3 10$^{12}$ &  -  & 1.3 10$^{12}$ & 3.6 10$^{11}$ * & \\

    % 14.123  2s$^2$ 2p$^3$--2s$^2$ 2p$^2$ 3s
3-19 &  $^2$D$_{5/2}$--$^4$P$_{5/2}$   & 4.0 10$^{-2}$ & 5.4 10$^{-2}$ & 9.7 10$^{-2}$ *  & 2.8 10$^{11}$ &  -  &2.8 10$^{11}$ & 2.8 10$^{11}$ & \\

\hline

    % 30.001-300 �
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\multicolumn{10}{c}{2s$^2$ 2p$^3$--2s 2p$^4$}\\

    % 132.840  2s$^2$ 2p$^3$--2s 2p$^4$
1-6 &  $^4$S$_{3/2}$--$^4$P$_{5/2}$   & 15. & 15. & 14.   & 1.2 10$^{10}$ & 1.3 10$^{10}$ & 1.2 10$^{10}$&  1.2 10$^{10}$& \\

    % 121.845  2s$^2$ 2p$^3$--2s 2p$^4$
1-7 &  $^4$S$_{3/2}$--$^4$P$_{3/2}$   & 11. & 11. & 10.   & 1.8 10$^{10}$ & 1.9 10$^{10}$ & 1.7 10$^{10}$&  1.37 10$^{10}$ * & \\

    % 118.680  2s$^2$ 2p$^3$--2s 2p$^4$
1-8 &  $^4$S$_{3/2}$--$^4$P$_{1/2}$   & 5.4 & 5.4 & 5.2   & 2.0 10$^{10}$ & 2.1 10$^{10}$ & 1.9 10$^{10}$& 1.3 10$^{10}$ & \\

    % 93.781  2s$^2$ 2p$^3$--2s 2p$^4$
3-12 &  $^2$D$_{5/2}$--$^2$P$_{3/2}$   & 1.3 & 1.2 & 1.2   & 9.8 10$^{10}$ & 1.0 10$^{11}$ &  9.7 10$^{10}$ &  9.3 10$^{10}$& \\

    % 113.349  2s$^2$ 2p$^3$--2s 2p$^4$
3-10 &  $^2$D$_{5/2}$--$^2$D$_{5/2}$   & 1.1 & 1.0 & 0.81   & 3.1 10$^{10}$ & 3.3 10$^{10}$ & 3.0 10$^{10}$ & 2.9 10$^{10}$& \\

    % 110.627  2s$^2$ 2p$^3$--2s 2p$^4$
2-9 &  $^2$D$_{3/2}$--$^2$D$_{3/2}$   & 0.89 & 0.70 * & 0.64 *  & 4.1 10$^{10}$ & 4.3 10$^{10}$ & 4.0 10$^{10}$& 2.5 10$^{10}$ * & \\

    % 162.815  2s$^2$ 2p$^3$--2s 2p$^4$
2-6 &  $^2$D$_{3/2}$--$^4$P$_{5/2}$   & 0.65 & 0.64 & 0.63   & 5.5 10$^{8}$ &  -  & 5.2 10$^{8}$ &  5.2 10$^{8}$ & \\

    % 94.643  2s$^2$ 2p$^3$--2s 2p$^4$
2-11 &  $^2$D$_{3/2}$--$^2$S$_{1/2}$   & 0.22 & 0.17 * & 0.15 *  & 4.4 10$^{10}$ & 4.5 10$^{10}$ & 4.3 10$^{10}$&3.4 10$^{10}$ * & \\

    % 90.594  2s$^2$ 2p$^3$--2s 2p$^4$
2-12 &  $^2$D$_{3/2}$--$^2$P$_{3/2}$   & 0.19 & 0.18 & 0.17   & 1.4 10$^{10}$ & 1.5 10$^{10}$ &1.5 10$^{10}$ & 1.4 10$^{10}$& \\

    % 98.355  2s$^2$ 2p$^3$--2s 2p$^4$
5-13 &  $^2$P$_{3/2}$--$^2$P$_{1/2}$   & 0.16 & 7.8 10$^{-2}$ * & 8.0 10$^{-2}$ *  & 9.3 10$^{10}$ & 9.6 10$^{10}$ &8.3 10$^{10}$ & - & \\


    % 106.961  2s$^2$ 2p$^3$--2s 2p$^4$
4-11 &  $^2$P$_{1/2}$--$^2$S$_{1/2}$   & 0.18 & 0.14 * & 0.12 *  & 3.6 10$^{10}$ & 3.7 10$^{10}$ & 3.6 10$^{10}$ &3.4 10$^{10}$ & \\


    % 173.405  2s$^2$ 2p$^3$--2s 2p$^4$
3-6 &  $^2$D$_{5/2}$--$^4$P$_{5/2}$   & 0.29 & 0.28 & 0.28   & 2.4 10$^{8}$ &  -  & 2.2 10$^{8}$ & 2.4 10$^{8}$ & \\

    % 136.052  2s$^2$ 2p$^3$--2s 2p$^4$
5-10 &  $^2$P$_{3/2}$--$^2$D$_{5/2}$   & 0.20 & 0.19 & 0.15   & 5.8 10$^{9}$ & 6.0 10$^{9}$ & 5.6 10$^{9}$ &  5.4 10$^{9}$& \\

    % 101.819  2s$^2$ 2p$^3$--2s 2p$^4$
4-12 &  $^2$P$_{1/2}$--$^2$P$_{3/2}$   & 0.12 & 0.11 & 0.10   & 8.9 10$^{9}$ & 9.1 10$^{9}$ & 8.6 10$^{9}$ &8.4 10$^{9}$ & \\

    % 108.803  2s$^2$ 2p$^3$--2s 2p$^4$
5-12 &  $^2$P$_{3/2}$--$^2$P$_{3/2}$   & 0.13 & 0.12 & 0.11   & 9.5 10$^{9}$ & 9.4 10$^{9}$ & 9.4 10$^{9}$ &  1.1 10$^{10}$& \\

\hline

\multicolumn{10}{c}{2s 2p$^4$--2p$^5$}\\

    % 111.579  2s 2p$^4$--2p$^5$
10-14 &  $^2$D$_{5/2}$--$^2$P$_{3/2}$   & 0.12 & 1.2 10$^{-2}$ * & 7.1 10$^{-3}$ *  & 4.1 10$^{10}$ & 4.3 10$^{10}$ & 4.1 10$^{10}$& 3.9 10$^{10}$ & \\


\hline
\end{tabular}
\label{tab:list}
\end{table*}


\section{Summary}
Two ICFT $R$-matrix calculations  were performed for the electron-impact 
excitation of Fe$^{19+}$.
This work expands upon, and corrects an error in, the previous IRON Project
work by Butler \& Zeippen (2001).
Effective collision strengths for all 45,451 transitions of the larger
calculation have been archived.  
We find excellent agreement of our collision strengths with the recent
work of Landi \& Gu (2006) at high temperatures, but there are significant
differences at lower temperatures where resonant enhancement plays a larger
role.
We find little difference in level populations between our results and
the work of Landi \& Gu for a low density N-like Fe plasma at 10$^7$ K.
We have clearly shown the importance of running extensive checks and 
comparisons with other calculations.
Not only has the error in the Butler \& Zeippen results been discovered and
rectified, but we also note some large differences of our A-values with the
work of Nahar (2004).
However, we are confident in the soundness of our A-values from comparisons 
with both NIST and the calculation of Jonauskas et al. (2005).

\begin{acknowledgements}
This work has been funded by PPARC grant PPA/G/S2003/00055.
GDZ acknowledges support from PPARC and warmly thanks DAMTP,
University of Cambridge for the hospitality.
\end{acknowledgements}


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