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%|  Spectral lines
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\newcommand{\SOHO}{\mbox{SOHO}}       % SOlar Heliospheric Observatory
\newcommand{\CDS}{\mbox{CDS}}         % Coronal Diagnostic Spectrometer
\newcommand{\NIS}{\mbox{NIS}}         % Normal Incidence Spectrometer
\newcommand{\GIS}{\mbox{GIS}}         % Grazing Incidence Spectrometer
\newcommand{\SUMER}{\mbox{SUMER}}     % Solar UV Measurement of Emitted Radiation
\newcommand{\SERTS}{\mbox{SERTS}}     %  Goddard Solar Extreme
				%  Ultraviolet Research Telescope and Spectrograph

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\newcommand{\SXT}{\mbox{SXT}}         % " Soft X-ray Telescope
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%|  Electron density et al.
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\def\rsun{R$_\odot$}

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\begin{document}

\title{Benchmarking atomic data for astrophysics: \ion{Fe}{x}}

\author{G. Del Zanna
\inst{1}  
\and
K. A. Berrington
\inst{2}
\and 
H. E. Mason
\inst{1}  
}
\institute{
Department of Applied Mathematics and Theoretical Physics,
University of Cambridge, Cambridge UK
\and {School of Science and Mathematics, Sheffield Hallam University, Sheffield S1 1WB, UK}
}

\offprints{G. Del Zanna \\ (G.Del-Zanna@damtp.cam.ac.uk)}

\date{\today}

%\titlerunning{ }

\abstract{
Available atomic data for \ion{Fe}{x} ($n=3$ configurations)
are assessed and where necessary new data are calculated, 
in order to build an accurate model ion, hence to determine 
level populations and spectral line intensities.
%
The theoretical data are benchmarked against 
well-calibrated spectroscopic observations of the solar corona and 
laboratory measurements. Our approach focuses on the brightest spectral
lines, and uses both wavelengths and line intensities for the 
line identifications. 
%
Although many previous line identifications are confirmed,
some are rejected and new ones are proposed, in addition 
the presence of blends is highlighted.
%
Our analysis procedure provides both an estimate of the 
uncertainties in the atomic data and also indicates which 
spectral lines are best as diagnostics or  
for instrument calibration. 
%
The agreement between theoretical and experimental data which we
achieve with our new model ion is extremely good.
%
\keywords{Sun: corona -- Techniques: spectroscopic }
}


\maketitle


\section{ Introduction }

This paper is the first in a series which aims to provide 
assessed sets of atomic data for the analysis of astrophysical spectra.
The results will be presented on an ion by ion basis.
The approach used will be similar for all ions studied.
Atomic data are gathered from different sources. 
These data are assessed 
and integrated to form a model ion. Level populations 
and spectral line intensities are calculated and compared to 
experimental data (both solar and laboratory). 
The approach is very practical since both 
the intensities and wavelengths for the brightest spectral 
lines are compared to all available observations.
In this way, the identifications of the brightest spectral lines 
from each ion can be assessed and in addition the accuracy of
the atomic data can be evaluated.


Our method assumes a steady-state collisionally-ionised 
optically-thin plasma, so is particularly suitable for example for 
direct comparisons with spectroscopic observations of stellar 
coronae. However, the assessment method for each ion
is based on a discussion of atomic energy levels, 
weighted oscillator strengths ($gf$ values), 
spontaneous radiative decay rates ($A$ values),  
electron (proton) collisional excitation rates,
and is therefore of interest for wider astrophysical applications.


In recent years, a vast amount of high-resolution spectroscopic 
observations in the XUV have been produced  by instruments on-board 
the SOHO, HST-STIS, Chandra, FUSE, XMM-Newton satellites. It is therefore 
timely to focus on the EUV (150-900 \AA), UV (900-2000 \AA)
and soft X (5-150 \AA) wavelength ranges.

The completeness of available atomic data in the EUV is very good, 
since almost all the brightest lines in the spectra have been identified.
For example, \cite{delzanna01_cdscal} compared 
SOHO Coronal Diagnostic Spectrometer (CDS) spectra of different 
solar features in the 150--780 \AA\ range 
with simulated spectra calculated with the 
CHIANTI\footnote{http://www.chianti.rl.ac.uk/} atomic database.
The sensitivity of the 
SOHO CDS  has however revealed that a host of weaker 
lines are not yet identified (see for example \citealt{brooks_etal:99}).
In the UV, quite a few bright lines remain unidentified, as shown in 
SOHO Solar UV Measurement of Emitted Radiation (SUMER)
spectra (see, e.g., \citealt{feldman_etal:97}, and references therein). 
In the X-rays, the situation is somewhat different. 
The lines from the \ion{H}{i} and  \ion{He}{i} isoelectronic
sequences and their satellites are well known. 
Most of the rest of the  bright lines are produced by 
 \ion{Fe}{xvii-xxiv} ions, for which good atomic data 
has been lacking until recently (see \citealt{dere_etal:01} for a 
review of published atomic data). 
It is of no surprise that a large number of 
lines are either unidentified or have a questionable
identification (see for example the spectral line list 
in \citealt{phillips_etal:99}).

The issue of completeness of atomic data is extremely important,
for two main reasons. 
First, even at the highest spectral resolution, many spectral lines are 
blended to some degree. Indeed, most of the lines 
useful for density diagnostics (see \citealt{mason_monsignori:94}
for a review) are weak and therefore particularly prone 
to problems with blending.
%
Second, as the number of levels in a model ion increases, so does 
the number of predicted spectral lines. 
In some wavelength ranges (mainly the X-ray range), 
the pseudo-continuum 
created by the  superposition of weak lines can 
be comparable to the real continuum 
emission (as produced by e.g. free-free, free-bound transitions).


It is important to remember that a great number  of current
line identifications are based on early (50's to 70's or even earlier) 
observations of the solar corona in eclipses and with 
rockets and satellites.
These data were supplemented by a large amount of 
laboratory data. 
At that time, the calculations of radiative 
data were in a reasonably good state,
while the calculations of collisional excitation 
data has improved dramatically over the years
(see for example Iron Project 
\footnote{http://www.usm.uni-muenchen.de/people/ip/iron-project.html} 
and UK Rmax\footnote{http://amdpp.phys.strath.ac.uk/UK\_RmaX}
collaborations). 

It is now important to use the most accurate atomic 
calculations for each ion and to benchmark these data 
against the observations and laboratory measurements.
The aim of this series of papers is to do this 
in a comprehensive way, 
using the method described below in Sect.\ref{sec:method}.
Our method aims to: 
a) build a model ion that 
includes the most important configurations;
b) compare both calculated and observed line intensities and
wavelengths in a quantitative way;
c) consider all the brightest lines, spanning 
a broad spectral range;
d) use a variety of sources of experimental data, 
calibrated independently from the atomic data.
Special attention is paid in our method 
to spectral line identifications based on 
our semi-empirical adjustment of the energy levels, 
and on the calculated intensities. 
%
Hence,  it is  possible to assess the 
accuracy of the atomic calculations, identify 
blends, and to suggest the best diagnostic lines 
to be used. Some estimates of the uncertainties on the  
atomic data are also provided as a by-product.

%
In this series of papers, we do not aim to review of all 
the observational data (e.g. wavelength measurements
and line identifications) and theoretical data that 
are available for each ion, since the literature is too extensive.
We have selected those data which we consider to be most reliable 
and appropriate.
%
A critical review of the current status of 
theoretical and experimental data that are 
available for benchmarking is presented in Sect.\ref{sec:method}.
This section also describes the standard procedures we adopt 
to build our ion models. 

Much can be learnt from spectroscopic observations of
the solar corona. This series of papers starts with the 
\ion{Fe}{viii-xvi} ions and focuses on the
EUV range, since many new R-matrix calculations have 
recently been performed on these ions.

\ion{Fe}{x} is by far the most important coronal ion, but
surprisingly, many of the transitions in \ion{Fe}{x} remain 
unidentified, so the energy level values are still uncertain. 
%
Given the complexity of this ion, it is of no surprise that 
the status of the collisional 
calculations was unsatisfactory until recently, 
when \cite{pelan_berrington:01} published new 
R-matrix calculations for the $n=3$ levels.
It is therefore natural to start the series with 
\ion{Fe}{x}, which is discussed in Sect.\ref{sec:fe_10}.
Conclusions and further work needed on this ion are presented in
Sect.\ref{sec:concl}.


\section{Method and available data}
\label{sec:method}

The {\it first step} is to collect and/or
calculate  all the collisional and radiative 
rates  which are needed to calculate the level population 
for the ion, including all the relevant processes
and configurations.

The {\it second step} is to calculate the level populations.
The end result is  $N_j (N_{\rm e}, T_{\rm e})$, the 
population of level $j$ relative to the total $N(X^{+r})$
number density of the ion $X^{+r}$, as  a function of the electron
temperature and density.
An important part of the process is to examine the metastable levels 
(if present),  assess their effect, and make sure that all the 
important rates are included.
%
Then, the line intensities, $I_{\rm th}$,proportional to $N_j A_{ji}$,
can be calculated, where 
$A_{ji}$ is the spontaneous transition probability 
from the upper level $j$ to the lower level $i$.

The {\it third step} is to find which transitions
correspond to the brightest intensities, 
and to search all the available observations 
for possible identifications.
We then compare calculated and observed $I_{\rm ob}$
intensities in a comprehensive way, by plotting the values 

\begin{equation}
F_{ji}= { I_{\rm ob}  N_{\rm e} \over N_j(N_{\rm e}, T_0)  \;A_{ji}}
\end{equation}
as a function of electron density,  calculated 
at a fixed temperature $T_0$.
%
In this method, we make the assumption that
most of the emission from the individual ion 
originates from an approximately iso-density region and 
that temperature effects in the intensity ratios 
are negligible. In order to have agreement between calculated and 
observed intensities, all the $F_{ji}$ curves 
should either overlap (if the transitions originate 
form the same upper level or have a similar density 
behaviour),  or cross at one point (if the ratios are 
density sensitive).  

This method is described in more detail in 
\cite{delzanna02_aumic}, where it 
was used to critically revise a large amount of 
published work on spectral diagnostics in stellar transition 
regions.
%
This approach  has  the following advantages 
over the individual line ratio technique:
a) it gives a global view of all the lines;
b) it can directly confirm the accuracy of relative 
 $A$-values when branching ratios are observed;
c) it shows which lines are obvious blends; 
d) it shows which combination of lines are 
  best for density measurements;
e) it clearly shows at which density regimes 
  the diagnostic lines can be used.
%
We note that 
temperature effects can be important for some ions,
however, these are normally second order  effects,
compared to the uncertainties in the instrument 
calibration and in the atomic data.
%
Also, we note that only the relative, and not the absolute
$F_{ji}$ values are used. Unless otherwise stated,
the plots of the $F_{ji}$ values will be on the same scale,
a factor of ten. (***Giulio - what does this mean??***)
The plots of $F_{ji}$ provide an immediate visual pointer
to problematic identifications.

The {\it fourth step} is to identify 
the blends whenever possible, and then to 
semi-empirically adjust all the energy levels 
using the identified 
transitions (normally the brightest lines).
Then, and this is a crucially important step, 
these adjusted energy values are used to  
re-calculate the radiative data using the SUPERSTRUCTURE program
(***Ref***). 
We then return again to the second step, 
in order to identify all the spectral lines 
(not just the strongest ones) that should be 
observable, and to provide a set of best 
wavelengths for all the lines in the model ion.

The above procedure is novel and non-standard. It provides
a much more accurate model ion than can be provided
by a completely ab-initio method, which uses only theoretical wavelengths,
rather than adjusted wavelengths and intensity ratios.  Below we summarise
some of the main difficulties in performing such an assessment method.


\subsection{Atomic data sources}

It is a non-trivial task to collect all the collisional and radiative 
rates  which are needed to build a model ion. 
%
The only atomic  database that freely provides a comprehensive 
collection of published data from different sources 
 on  energy levels, wavelengths,
radiative transition probabilities and electron/proton
 excitation data for almost all ions of astrophysical 
interest is CHIANTI.  
In reality CHIANTI is an atomic package, in the sense that
the atomic data are integrated in a suite of programs that calculate 
level populations, line emissivities, etc.
The package is kept up-to-date, provides 
extensive references to the original sources, and has 
associated papers (\citealt[v.1]{dere97}, 
 \citealt[v.2]{landi99b}; 
\citealt[v.3]{dere_etal:01};
\citealt[v.4]{young_etal03}) that describe the model ions.
%
In a number of cases, collisional data from different 
sources are rescaled, interpolated and merged, and radiative data 
are either collected from various sources, or 
calculated {\it ab initio} using SUPERSTRUCTURE.


Many other good atomic databases exist, but often they:
only contain data from one source;
 only provide a subset of all the atomic data that 
are needed to build 
an ion model (e.g. just radiative or collisional data);
 are not kept up-to-date;
 do not clearly reference the sources;
 refer to unpublished work.
%
%A notable exception is the 
%Iron project database\footnote{www}, that however 
%only includes Fe ions and is lacking some 
%radiatve data.
%
%CHIANTI gathers togehter atomic data from 
%a range of sources. 


CHIANTI contains a vast amount of atomic data gathered from a range of
sources. These most reliable data available are selected and stored in a 
reduced/compact form. It is important to benchmark these
data aginst solar and laboratory spectra, to confirm their
accuracy. This is a time consumming and laborious process.
%
In order to provide an assessment of the atomic 
data for the coronal Fe ions it is necessary 
review what data are available both in CHIANTI and beyond.


\subsubsection{Energy levels and wavelengths}

In the literature, it is common to use as reference 
values the energies   
available from the National Institute of Science and
Technology (NIST) Atomic Spectra Database 
(see \citealt{nist}, but also 
monographs such as \citealt{kelly:87}, and
\citealt{shirai_etal:00}).
In turn, these compilations rely, 
at least for the complex Fe ions,
on the original studies performed mostly in the 
60's and 70's (or earlier), and they do not always have 
the best values.
For example, there has been a great deal of 
experimental and theoretical work since the 70's, 
that has not always been included in  
these compilations.
%Unfortunately, NIST does not provide references to 
%the single energy levels. These, together with the 
%observed wavelengths, are provided in the monographs 
%instead. 
%
In some cases we have found energies 
which are not consistent 
with the reported wavelengths, or with the observed 
ones.
In other cases, as for \ion{Fe}{x} and \ion{Fe}{xi},
some energies are only known 
 relative to particular levels within a configuration,
 but not relative to the ground level, so many line
identifications are uncertain. This information 
needs to be taken into account when benchmarking the 
data.
%
In the present series, we have therefore 
decided to re-assess the level energies, by reviewing
the original line identifications and derived energies.
The most recent studies are also included. 
%

\subsubsection{Theoretical energies}


In the past three decades, several sophisticated atomic 
structure codes have been written,
and a large amount of data published.
%
However, the results often only
pertain to a subset of the important configurations
that produce spectral lines, 
 and provide significant differences in level energies.
 The energy differences between the various calculations are 
often much larger than the fine-structure splittings, 
and this creates uncertainty in the level ordering and in turn 
on the line identifications.
The size of the differences is particularly sensitive to 
which configurations have been included.
Even the most complex 
{\it ab initio} calculations are not good enough 
to match the observations, and the predicted
wavelengths are often off by a few \AA.
For this reason, a large number of 
spectral lines are still unidentified.
Within the CHIANTI package, these lines are considered to be
`unobserved', and do not normally appear in the 
simulated spectra, although the model ions actually 
predict some of them to be as bright as other 
`observed' (identified) lines.

As an example, we 
consider the \ion{Fe}{x} energies recently calculated by 
two groups.  
\cite{dong_etal99} have performed a multi-configuration
Dirac-Fock (MCDF) calculation using the well-known
GRASP92 code of I. Grant for the lowest 3 
configurations (31 fine-structure levels). As the same authors 
notice, the differences with the available 
observed energies is up to 8000 cm$^{-1}$, which 
results e.g. in a displacement of the strongest  \ion{Fe}{x} 
transition (observed at 174.53 \AA) by more than 2 \AA.  
%
\cite{deb_etal02} have used the well-known 
CIV3 structure code of A. Hibbert and calculated 
radiative data for the lowest 4 configurations 
by considering configuration interaction (CI) 
between 30 configurations (up to $n=4$) 
that included one-, two-, and three-electron 
excitations with respect to the ground, for a 
total of 1351 levels.
As in the case of the \cite{dong_etal99} calculation,
the agreement with observations for the lower-energy 
states is reasonably good, while for the rest, 
differences are large. For the 
strongest \ion{Fe}{x} transition, the difference is about 19000 cm$^{-1}$,
producing a displacement of  6 \AA.
Such large displacements mean that the target 
wavefunctions are  not well enough described, hence also the radiative 
 data that are calculated are not accurate.

% From a practical point of view, 
%they mean that wavelengths calculated ab initio 
%are not reliable

In this paper we adopt the  
Term Energy Correction (TEC) procedure 
(see, e.g. \citealt{zeippen_etal:77};
 \citealt{nussbaumer_storey:78}),  applied within the 
SUPERSTRUCTURE code (SS, see
 \citealt{eissner_etal:74}; \citealt{nussbaumer_storey:78}).
%
Basically, empirical corrections
 to the LS energies are used to modify the 
non-relativistic Hamiltonian matrix, which 
is then used together with the 
Breit-Pauli relativistic correction 
to solve the eigenvalue problem and 
obtain the fine-structure energies.
%
Empirical corrections to the LS energies 
have been applied here 
 whenever one fine-structure level has a known 
energy. If more than one is available, an average is used.
If only one level within one 
configuration is known, a single correction to 
the entire configuration is applied. 
Experience shows that if the right configurations are 
used, the TEC within each configuration are approximately
(say within 500 cm$^{-1}$) the same. The situation 
improves when high-$n$ configurations are considered. 
The use of  TEC values improves the calculation of 
the line strengths.
We note that semi-empirical adjustments within an 
atomic structure code have been (and are) commonly applied 
in the literature (see, e.g. the extensive work of 
\citealt{bromage_etal:77} on \ion{Fe}{x,xi}),
 but are not the rule.


Ions such as \ion{Fe}{x} are particularly 
complex because of the strong mixing between levels 
having the same J-value and parity. 
Information on level mixing is important because 
it can help to assess which level assignments 
are most uncertain. This information  
is not always provided in the literature. 



\subsubsection{Radiative data}

The Einstein coefficients that are needed to build an ion model 
are the electric-dipole allowed (E1) and the 
`forbidden' ones: magnetic dipole (M1), magnetic 
quadrupole (M2) and electric quadrupole (E2).

A first problem is one of completeness. 
To build an ion model, $A$-values 
for {\it all} the transitions are needed.
As in the case of the energy levels and wavelengths,
the NIST database only provides radiative data 
(often not up-to-date) for a 
few transitions. 
The number of measured $A$-values, based for example 
on laboratory measurements of level lifetimes, is increasing but 
still very limited, so we still have to 
rely on theoretical calculations.
In turn, published calculations often only report 
a subset of 
all the $A$-values, normally just 
dipole allowed and some forbidden transitions.


A second problem is one of accuracy.
Fortunately, atomic structure calculations, 
in particular for the E1 transitions, can be quite 
accurate and usually give consistent results
with the laboratory measurements. 
However line strengths for forbidden transitions are less relaible 
and more susceptible to the configurations used.
The importance of adding the right configurations 
has been emphasised by many authors.
(see, for example, the discussion on the \ion{Fe}{x} case in 
\cite{berrington_etal:01}).


Even if the line strengths are quite accurate, 
the  transition rates that are published in the 
literature are often poor, because theoretical energies, instead of 
the experimental ones, are used.
%
For E1 transitions, the rates are proportional to the 
cube of the energy difference, so the error is often not 
too large.
However, for the quadrupole E2 and M2 transitions 
(that have a dependence on the fifth power),
the errors introduced by using theoretical 
energies can be significant.
%
Again considering \ion{Fe}{x}, for example, the
$A$-values published by \cite{dong_etal99} and \cite{deb_etal02} 
could have been much improved if observed energies had been used.
\cite{dong_etal99} calculates a value of 65 s$^{-1}$ 
for the famous forbidden line within the ground, against 
a commonly-accepted value of  69 s$^{-1}$.

In this paper, the iterative procedure outlined above 
is implemented, in order to obtain the best 
 energies and line strengths. 
Then, the adjusted energies based on the observed wavelength
values are used to calculate the $A$-values 
of E1, E2, M1, and M2 transitions in intermediate coupling
with SUPERSTRUCTURE.


\subsubsection{Collisional data}

As in the case of the radiative data, the number 
and type of configurations included in the 
scattering calculations strongly affects the results.

In the case of the data calculated in the 
distorted wave (DW) approximation, 
the  practical approach suggested by 
\cite{flower_nussbaumer:74}, for dipole allowed transitions, 
is adopted here. 
The procedure is to  rescale the 
collision strengths  $\Omega$ with the ratio of the 
oscillator strengths $f$  and the energy differences
$\Delta E$ (for the allowed transitions):

\beq
\Omega' = {\Delta E \over \Delta E'} {f' \over f} \Omega 
\eeq

This is a procedure is sometimes used within 
CHIANTI, and it seems to work quite well. 
Once the collision strengths have been rescaled, the 
maxwellian-averaged collision strengths are 
calculated.

A large number of R-matrix calculations 
have recently become available. They normally 
provide more accurate collision data than the DW calculations.
However, if the target is not well represented,
and the contribution from important resonances
have been left out, the results have limited accuracy.

\subsection{Experimental data}



Despite the large number of solar observations and laboratory measurements, 
very few of these studies have sufficient spectral resolution,
completeness and accuracy to allow reliable line identifications to be made.
Indeed, very few solar observations have an accurate calibration,
even though this is a fundamental requirement for any 
scientific analysis of spectroscopic data.  

When assessing which solar observations are suitable for benchmarking
atomic data, it is necessary to investigate the way in which these
spectra have been calibrated. Only rarely is an independent calibration
source used. Even then the ground calibration can differ from the
in-flight calibration. Frequently, atomic data (assumed to be
insensitive to density or temperature) are used to calibrate solar
spectra. In several cases, instrument calibrations have been
found to be incorrect using available atomic data. 
It is not straightforward to use these spectra to benchmark 
new atomic data.
It is necessary to step back and take a more comprehensive
view of available solar and laboratory spectra, 
to search for consistencies and
inconsistencies between the atomic data and solar spectra. A
re-assessment of the available calibration is sometimes required.
In this series of papers, we shall study individual ions, but first it
is necessary to survey the most important high- to medium-resolution 
spectroscopic observations relevant to our study.

\subsubsection{Solar spectra in the EUV-UV}

\cite{behring_etal:72} 
published a line list based on a LASP rocket flight
that observed the entire Sun in the  60-385 \AA\ region with 
high-resolution (0.06 \AA).
\cite{behring_etal:76} have presented similar results,
covering the 160-770 \AA\ range.
In both studies, 
the wavelengths of the lines were accurately measured,
but  intensities were only
approximate and lines were mainly identified upon their 
wavelengths. 
We normally adopt their wavelengths, since they are still
the most accurate ones that are available.
%
Many previous studies exist  (see, e.g.,
the  review of \citealt{mason_monsignori:94}),
 but they were either 
of lower-resolution or lower-sensitivity, or not
calibrated in intensity.

\cite{malinovsky_heroux:73}
 presented  an integrated-Sun spectrum 
covering the 50-300 \AA\ range with a medium resolution (0.25 \AA),
taken with  a grazing-incidence spectrometer  flown on a
rocket in 1969.
The spectrum was photometrically calibrated, and still,
quite surprisingly,  
represent the best available spectrum in the EUV 150--300 \AA\ range.
These authors were among the first 
 to confirm or reject previous  identifications
using line intensity estimates and not just wavelengths.

%\cite{firth74} (1974) give a line list in the 140-870 \AA\ range,
%based on U.K. rocket observations, with 0.17 \AA\ resolution.

%Kastner et al. (1974), 66-171 \AA

Many other line lists have been published, but are 
normally biased toward high-temperature lines, and are not 
useful for benchmarking ions such as \ion{Fe}{x}.
For example, \cite{dere:78} presented a list of line 
identifications based on all the flare
observations of the NRL SO82-A instrument aboard Skylab, in the 171-630 \AA\
range, with 0.1 \AA\ resolution. 


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

The  ESA/NASA Solar and Heliospheric Observatory
(\SOHO) 
has produced a wealth of spectral data with the 
 \CDS, \SUMER,
and the Ultraviolet Coronagraph Spectrometer (\UVCS).
%Details of the instruments can be found 
%in a special issue (Vol. 162) of the  Solar Physics journal (1995).
%
The \CDS\ covers a wide  wavelength range (150 -- 780 \AA),
with nine channels, distributed between a Normal
Incidence (\NIS) and a Grazing Incidence (\GIS) Spectrometer.
% Details can be found in 
%\cite{harrison95} and \cite{delzanna_thesis99}.
\SUMER\ is a 
normal incidence spectrometer in the 500 to 1610 \AA\ band
with high spectral resolution.
\UVCS\ has  performed off-limb (2--10 \rsun\ from Sun centre)
spectroscopic observations in the 940-1350 \AA\ range.
The spectral resolution for \UVCS\ is somewhat lower than \SUMER\.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


There has been a great deal of work 
by different groups to obtain a consistent 
radiometric calibration of all the instruments on-board \SOHO\
(\citealt{SOHO-calib:02}) to an accuracy of 30-50\%.
Atomic data can be and have been used to cross-check and 
improve some of the instrument calibrations.
For example, the CHIANTI atomic  data were used to show that 
the ground calibration of the \CDS\ channels was
in error by factors of up to two 
(cf. \citealt{delzanna01_cdscal}). The CDS instrument 
calibration has been revised based on several studies,
including those using rocket flights.
It should be noted that 
the in-flight calibration of the  \NIS-2 channel 
is based on a single in-flight cross-calibration with 
a coarse spectrum produced by an EGS  
rocket flight launched in May 1997.
The  in-flight calibration of the  \NIS-1 channel 
also  relies on a single cross-calibration study 
(\citealt{thomas99}) based on the \SERTS-97 flight. 
The only \GIS\ in-flight calibration 
(\cite{delzanna01_cdscal}) was obtained with the use of 
CHIANTI atomic data, some of which are now under review
in this series of papers.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

The Goddard Solar Extreme Ultraviolet
Research Telescope and Spectrograph (\SERTS) 
 has been flown several times since 1989, 
and has  produced both non overlapping spectroheliograms
and stigmatic spectra of excellent spectral resolution.
%
The \SERTS-89 (\citealt{thomas_neupert:94})
covered  the 170-225 \AA\ range in second order and the 
235-450 \AA\ range in first order.
The \SERTS-89 and \SERTS-97 were radiometrically 
calibrated on the ground against 
primary standards and in theory could be used for the benchmark. 
However, \cite{young_etal:98}, when  performing a detailed 
benchmark of CHIANTI atomic data on the 
\SERTS-89 spectrum, found  major 
inconsistencies  (by factors of 2) in the calibration 
of the second order lines and of the 400-450 \AA\ region.
These inconsistencies have been confirmed 
in \cite{delzanna_thesis99}, where a $DEM$ analysis 
was performed in order to assess line blending 
in the \SERTS-89 spectrum.
The \SERTS-97 flight  only covered a narrow
wavelength region, and presents  some  discrepancies 
both in the cross-calibration with CDS 
(see \citealt{delzanna01_cdscal}),
and in the \SERTS-97 line intensities themselves. 

The \SERTS-95 spectra 
(\citealt{brosius_etal:98b}) covered the 
171-225 \AA\ band in  second-order,
and the 235-335  \AA\ region in first order
with excellent spectral resolution 
(FWHM= 0.03, 0.05 \AA\ respectively).
However, atomic data (\CHIANTI\ version 1.01) were
actually used by \cite{brosius_etal:98a}  to  calibrate the 
\SERTS-95 spectra.



In summary, very few medium- or 
high-resolution radiometrically-calibrated EUV spectra 
exist which are useful for benchmarking atomic data.
%
The \CDS\ data, although extremely valuable,
cannot at the moment be reliably 
used to benchmark atomic data. 
The  calibration of the \SUMER\ 
instrument should also undergo rigorous checking before 
its spectra can be used for this purpose with confidence.
%
Only part of the \SERTS-89 data together with 
the \cite{malinovsky_heroux:73} spectrum can be used
with any confidence.
%
The calibration problems will not necessarily improve
in the future, since 
multilayer technology (successfully tested 
in the \SERTS-95,97 flights)  will be used in most
future missions such as SOLAR-B EIS. 
This technology  has the advantage of offering high sensitivities,
however the responsivities typically drop by one
order of magnitude in just a few \AA, hence 
a small error in the calibration can have a huge effect.
Since no in-flight calibration sources will be flown,
these instruments will most probably need to be calibrated using
accurate atomic data. Hence, it is essential that we have
confidence in the most recent atomic data for 
the coronal iron ions.

%multilayer-coated toroidal diffraction grating


\subsubsection{Coronal forbidden lines}

The visible coronal forbidden lines have been observed 
during total solar eclipses since 1869 (see for example 
\citealt{aly_etal:62})). A notable study is 
that of \cite{jefferies_etal:71},
which provided calibrated 
intensities of all the lines observed on the ground during 
the 1965 eclipse in the 3000--11000 \AA\ range.
Rockets were used to
extend the wavelength range of the eclipse observations
(see, e.g. \citealt{gabriel_etal:71} for the 1970 eclipse,
850--2190 \AA\).

Information on the forbidden lines was
further improved with the Skylab ATM 
NRL S082B spectrograph, which recorded a large number 
of lines. \cite{sandlin_etal:77} provided an extensive
and accurate list of calibrated line intensities 
in the 970--2650 \AA\ range.
Further details 
were presented by \cite{sandlin_tousey:79}.
\cite{feldman_doschek:77} also provided a list of 
forbidden lines in the 1170--2650 \AA\ range.


A large number of coronal  forbidden lines have 
been observed with the SOHO SUMER instrument 
in the  in the 500--1600 \AA\ range 
(see, e.g., \citealt{feldman_etal:97}), and some still await 
identification.
A few of these lines have also been observed with UVCS 
(see, e.g., \citealt{raymond_etal:97}).

We note that measurements and identifications of 
coronal forbidden lines are important, since energy level 
separations can be measured with high accuracy ($\simeq$1 cm$^{-1}$).

\subsubsection{Laboratory data in the XUV-visible}


Many tokamak and laser-produced high-resolution spectra
have been published, but they mainly focus on 
high-temperature plasmas, more relevant to solar flare spectra.
Since the pioneering work by
{Edl{\' e}n} in the 1930's (see e.g. 
\citealt{edlen:37b} on \ion{Fe}{x}), there have been several other 
laboratory studies.
%
A lot of work was carried out at the 
Culham laboratory (UK) in the 60-70s by a group 
of researchers (see, e.g. for \ion{Fe}{x} in the EUV:
\citealt{fawcett_gabriel:65}; \citealt{gabriel_etal:65};
 \citealt{fawcett_gabriel:66}; \citealt{gabriel_etal:66};
\citealt{bromage_etal:77})


More recently. papers based on beam-foil spectroscopy 
or electron beam ion traps have produced very useful
spectral data for the 
identifications of lines from \ion{Fe}{viii-xiv}
(see, e.g. \citealt{jupen_etal:93};
\citealt{trabert_etal:03};
\citealt{lepson_etal:02};
 and the references therein).

The main advantage of laboratory data over solar observations
is that they 
tend to be relatively free of blending from different elements,
although significant blending between adjacent 
ionisation stages is still present.
However, the spectral resolution is often 
poor, line intensities are not normally calibrated,
and their interpretation can be even more complex than 
in the case of the solar corona.

Another important contribution of laboratory 
studies is the measurement of lifetimes and 
$A$ values, which are now becoming available in the 
literature. 
However, the few available  measurements 
are not always consistent with each other.
Hence, these data can only provide a limited benchmark 
for the moment.



\section{Model ion for \ion{Fe}{x}}
\label{sec:fe_10}

In this paper, we restrict our discussion to the 
 main $n=3$ spectroscopic configurations in \ion{Fe}{x} 
(c1: 3s$^2$ 3p$^5$,  c2: 3s 3p$^6$,  c3: 3s$^2$3p$^4$ 3d, c4: 3s 3p$^5$3d),
which produce 54 levels, and the majority of the brightest 
lines from the EUV to the infrared.
%
Although many other \ion{Fe}{x}  lines  
have been observed in laboratory and astrophysical X-ray
spectra, a 
discussion on the X-rays ($n>3$) is left to a future paper.
The reason for this is that no reliable R-matrix 
or DW calculations are currently available, only  
the approximate calculations of \cite{malinovsky_etal:80}.

%orb[2s 2]\orb[2p 2]\orb[3s ]

\begin{table}[!htbp]
\caption{The configurations used to calculate the radiative data 
within SS. The configurations are ordered according to their 
relative energies, and grouped by odd or even parity.}
\begin{center}
%\scriptsize
\footnotesize
%\tiny
%\normalsize
\begin{tabular}{lclcl}
\hline\noalign{\smallskip}
\hline\noalign{\smallskip}
   &          odd  &    &  even      &  \\
\hline\noalign{\smallskip}
c1 & 3s$^2$ 3p$^5$ & c2 &  3s 3p$^6$ &  \\
c4 &  3s 3p$^5$ 3d & c3 &  3s$^2$ 3p$^4$ 3d & \\
c5 &  3s$^2$ 3p$^3$ 3d$^2$ & c6 &  3s$^2$ 3p$^2$ 3d$^3$ &  \\
c10 &  3s 3p$^3$ 3d$^3$ &  c7 &  3s$^2$ 3p$^4$ 4s &  \\
c11 &  3s$^2$ 3p$^4$ 4p &   c8  & 3s 3p$^4$ 3d$^2$ &  \\
c13 &  3s 3p$^5$ 4s &  c9  & 3p$^6$ 3d &  \\
c15 &  3s$^2$ 3p$^4$ 4f & c12 &  3s$^2$ 3p$^4$ 4d &  \\
    &                  &    c14 &  3s 3p$^5$ 4p &  \\
\noalign{\smallskip}
\hline
\end{tabular}
\end{center}
\normalsize
\label{tab:conf}
\end{table}
% Table~\ref{tab:conf}


\begin{figure}[!htbp]
\centerline{\epsfig{file=gf.ps, width=7cm,angle=90 }}
  \caption{A plot of the $gf$ values 
from the \cite{bhatia_doschek:95} DW calculation
 for all the dipole-allowed  transitions to the 
3s 3p$^5$ 3d levels  vs.
the values scaled using the SS results ($gf'$).
    The corrections are quite large.}
  \label{fig:gf}
\end{figure}
% Fig.~\ref{fig:gf}



Various calculations of collision strengths exist in the literature,
as discussed by \cite{pelan_berrington:01}. The first comprehensive
study of the lowest three cofigurations of \ion{Fe}{x} was published by  
***Ref Mason (1975), MNRAS, 170,  651***), using the DW
approximation. Subsequently, R-matrix calculations were provided by 
\cite{mohan_etal:94} and \cite{tayal:01}. 
However, both these calculations had limitations which render them
unsuitable for our benchmark study.
The former omitted some important resonance contributions
(see \citealt{pelan_berrington:95})
while the latter omitted the spectroscopically-important 
 $^4$F$_j$ and $^2$F$_j$ metastable levels.
In both cases only collisional excitations from the first 
two configurations were published. 
As we shall see below,
neglecting collisional processess involving the metastable levels in
3s$^2$3p$^4$ 3d configuration significantly affects 
the level population even at moderate densities. 
This is important for all coronal ions with metastable levels.

The method outlined in Sect.\ref{sec:method} was applied iteratively
a few times, using the following atomic data:
a) the R-matrix collisional data for the excitations between 
the levels in the first two configurations (c1, c2) 
and the levels in c3,  %remainder of the  31 levels (c1,c2,c3)
 published in \cite{pelan_berrington:01};
b) R-matrix collisional data for the remaining excitations between all 
the levels in c1, c2 and c3 (31 levels). These data have been 
recalculated by us using the same 
codes and specifications as those described in
\cite{pelan_berrington:01}
(given in the Appendix of this paper);
c) scaled energies obtained from SUPERSTRUCTURE, derived from the 
assessment of the solar and laboratory spectra (**listed in table 1**);
d) new $A$ and $gf$ values for all transitions calculated with 
 SUPERSTRUCTURE using semi-empirically adjusted energies 
(**listed in table 2**);
e) the  \cite{bhatia_doschek:95} data for the 
3s 3p$^5$3d configuration, rescaled using the 
SUPERSTRUCTURE results. Fig.~\ref{fig:gf} gives an indication of 
the adjustments required.


Table~\ref{tab:conf} lists the set of configurations 
we finally adopted for our SUPERSTRUCTURE (SS) calculation, 
after a number of tests had been run.
These tests confirmed the importance of including configurations
with orbitals 3d$^2$ and  3d$^3$ 
(as discussed in \citealt{berrington_etal:01})
in order to have accurate $gf$ values and energies.  

Table~\ref{tab:levels} lists the results for the 
54 levels, ordered according to the 
energies $E_{\rm CC}$ of the target for the collisional calculations.
This table also lists SS level mixing information, together with 
the energies  $E_{\rm obs}$ which we propose in this paper
to be the best set. We have obtained these from the solar and 
laboratory observations. For comparisons, the 
$E_{\rm NIST}$ values reported in NIST, and 
the set of scaled SS values $E_{\rm SS}$ are also listed.
Two main points are worth noting. First, there is strong level mixing
for the majority of levels. Second, there is good agreement 
between the scaled SS energies and the observed ones.
We also note that in many cases the observed energies 
differ the NIST values.

Table~\ref{tab:lines} lists the radiative data 
($gf$ and $A$ values) for the most important transitions.
The $gf$ values compare well with those calculated by 
\cite{pelan_berrington:01}, and the 
$A$ values are in good agreement with the few 
values reported by \cite{shirai_etal:00},
as shown in Table~\ref{tab:lines}, and with the 
few laboratory measurements.
The lifetimes of a few levels have been measured
and these values are compared with 
our predicted values in Table~\ref{tab:lifetimes}.
Considering all the uncertainties involved, and 
the scatter in the measurements, 
there seems to be good agreement. 
Uncertainties in the calculated $A$ values are 
roughly estimated as 10\% for allowed 
transitions and 10-20\% for the forbidden ones.
Notable exceptions are the $A$ values for the 
doublet 3s$^2$3p$^5$ 
$^2$P$_{3/2,1/2}^{\rm o}$--3s 3p$^6$ $^2$S$_{1/2}^{\rm e}$ 
(1,2-3), that are $\simeq$20\% higher in \cite{shirai_etal:00}.
Note that the values reported here imply a 
lifetime of 0.21 ns for the 3s 3p$^6$ $^2$S$_{1/2}$ level, 
in better agreement with the measurement of 0.27$\pm$0.2 ns by
\cite{trabert:96},  compared to the 0.18 ns value 
reported by \citealt{shirai_etal:00}.
The R-matrix results of \cite{pelan_berrington:01} give
0.24  ns, in even better 
agreeement with the laboratory data.
The quantities useful 
for radiometric calibration are not the 
absolute $A$ values, but the branching ratios.
For this doublet,
\cite{trabert:96}  reports a branching ratio of 
2.4$\pm$0.3, which compares very well with the value 
2.26 calculated with SUPERSTRUCTURE.


\begin{table*}[!htbp]
\caption{Measured and predicted lifetimes for some of the 
 levels in \ion{Fe}{x}. 
Measured values from
M0: \cite{moehs_etal:00}; M1: \cite{moehs_etal:01};
T6: \cite{trabert:96}; T2: \cite{trabert_etal:02}; 
T3: \cite{trabert_etal:03}.
The predicted values have been calculated here
with SUPERSTRUCTURE and adjusted energies.
Note the excellent agreement for the metastable
3s$^2$3p$^4$ 3d levels.
}
\begin{center}
%\footnotesize
\begin{tabular}{llccl}
\hline\noalign{\smallskip}
\hline\noalign{\smallskip}
i  & Upper level  & measured (ms) & this work (ms) &  \\
\hline\noalign{\smallskip}

2  & 3s$^2$3p$^5$  $^2$P$_{1/2}^{\rm o}$           & 13.64$\pm$0.25 (M1) & 14.5 & \\
3  & 3s 3p$^6$     $^2$S$_{1/2}^{\rm e}$           & 2.7$\pm$0.2
10$^{-7}$ (T6) & 2.1 10$^{-7}$ & \\
8  & 3s$^2$3p$^4$ ($^3$P) 3d $^4$F$_{9/2}^{\rm e}$ & 
110$\pm$5 (T3) -- 85.7$\pm$9.2 (M0) &  89.2 & \\
10 & 3s$^2$3p$^4$ ($^3$P) 3d $^4$F$_{7/2}^{\rm e}$ & 
58$\pm$10 (T2) -- 93$\pm$30 (M0) & 75.3 & \\
18 & 3s$^2$3p$^4$ ($^3$P) 3d $^2$F$_{7/2}^{\rm e}$ & 16$\pm$1.6 (T2) & 12.4 & \\
20 & 3s$^2$ 3p$^4$ ($^1$D) 3d $^2$G$_{9/2}^{\rm e}$ & 17.8$\pm$3.1 (M0) & 13.7  & \\
24 & 3s$^2$3p$^4$ ($^1$D) 3d $^2$F$_{7/2}^{\rm e}$ & 4.6$\pm$0.4 (T2) & 4.8 & \\ 

\noalign{\smallskip}
\hline
\end{tabular}
\end{center}
\normalsize
\label{tab:lifetimes}
\end{table*}
% Table~\ref{tab:lifetimes}




\subsection{Level balance}


A detailed discussion of the main spectral identificatons 
for each of the levels is 
essential in our procedure. This is in turn dependent on 
the level populations and line intensity calculations.

The ion level balance has been calculated using the 
collisional and radiative data described above.
Additionally, proton excitations and photo-excitations 
can be important processes for the forbidden transitions taking place
between levels within the same configuration.
For the proton rates, the data calculated by  \cite{bely_faucher:70}
 as included in CHIANTI v.4 have been used here.
%
For the photo-excitation, a simple 6000~K
 blackbody radiation field and spherical
symmetry have been assumed, as described in \cite{young_etal03}.
However, the addition of these two processes only 
slightly affects the  \ion{Fe}{x} level balance,
for the observations considered here.

What is extremely important is the inclusion of all 
the excitations and de-excitations from all the levels, 
in particular from the metastable levels. Even at the 
relatively low densities characteristic of the quiet solar corona, 
these levels have a significant fraction of the ion 
populations.
Fig.~\ref{fig:balance} and Tables~\ref{tab:pop},\ref{tab:pop1-3}
show the  populations of the  most spectroscopically-important levels,
calculated with the inclusion of all collisional 
excitations (Fig.~\ref{fig:balance} (top)) and without collisional
excitations within the c3 (Fig.~\ref{fig:balance} (bottom)).
The effect of including collisional processes connected with the
metastable levels is clearly shown. 
For example, at a density of 1.0 10$^{10}$ \cmt
level 3 has its population underestimated by 50\%, if 
only excitations from the 
first 3 levels are included in the calculation.
This would lead to  the underestimation of the intensity of the 
bright doublet 3s$^2$3p$^5$ $^2$P$_{3/2,1/2}$--3s 3p$^6$
$^2$S$_{1/2}$, observed at 345.7, 365.5 \AA.


Table~\ref{tab:pop} also compares the level populations 
 calculated by \cite{bhatia_doschek:95} and 
\cite{pelan_berrington:01} at a density of 10$^{10}$ \cmt.
The differences between the  results 
are due not only to the different 
collisions strengths included in the three models, but also 
to the different $A$ values.
Perhaps the most notable feature of the new R-matrix 
calculations is the fact that, because of the 
resonances,  the population of the 
3s 3p$^6$ $^2$S$_{1/2}$ level is $\simeq$ 50\% lower 
compared to the value calculated by \cite{bhatia_doschek:95}, 
as noted by \cite{pelan_berrington:01}.
This results in a variation of $\simeq$ 50\% between 
the relative intensities of the lines arising from the 
3s 3p$^6$ $^2$S$_{1/2}$ level (345.7, 365.5 \AA),
and those arising from  the 3s$^2$3p$^4$ 3d levels.


%This applies not only to \ion{Fe}{x}, but also to all the ions 
%that have metastable levels.

\begin{figure}[!htbp]
\centerline{\epsfig{file=fe_10_v5_pop1.ps, width=7cm,angle=90 }}
\centerline{\epsfig{file=fe_10_v5_only1-3_pop1.ps, width=7cm,angle=90 }}
  \caption{The fractional level populations of the ground and 
the metastable levels using the present model, with 
all excitations included (top), and with only excitations from the 
first 3 levels included (bottom). Note the large differences
in the metastable level populations, which in turn also 
affect the entire level balance of the ion 
(see Tables~\ref{tab:pop},\ref{tab:pop1-3}).  }
  \label{fig:balance}
\end{figure}
% Fig.~\ref{fig:balance}

%Calculated: 29/Aug/03 16:27:57
\begin{table}
\caption{Level populations calculated with the present model,
including all excitations between all the 54 levels.
Only the most spectroscopically-important levels are listed.
 The first two columns list the 
 values $N_{j}$ [cm$^{-3}$] calculated  at different densities
(10$^{8}$, 10$^{10}$ \cmt, see Fig.~\ref{fig:balance}).
The last two columns report, for comparison, the values calculated 
by \cite{bhatia_doschek:95} [BD] and \cite{pelan_berrington:01} [PB] 
at a density of 10$^{10}$ \cmt. The metastable levels are marked M.} 
\begin{center}
\scriptsize
%\footnotesize
%\tiny
%\normalsize
\begin{tabular}{@{}cccrrl@{}}
\hline\noalign{\smallskip}
\hline\noalign{\smallskip}
      & Present      &  Present      & BD & PB & \\ \hline
 i    & 1.0 10$^{8}$ & 1.0 10$^{10}$  & 1.0 10$^{10}$ & 1.0 10$^{10}$ & \\ \hline
\hline 
1 & 0.98 & 0.67 &                  0.72 & 0.62 & \\ 
2 & 8.2 10$^{-3}$ & 0.19 &          0.14 & 0.17 & \\ 
8 & 3.8 10$^{-3}$ & 4.0 10$^{-2}$ & 4.2 10$^{-2}$ & 8.7 10$^{-2}$ & M \\ 
5 & 2.0 10$^{-3}$ & 3.1 10$^{-2}$ & 2.9 10$^{-2}$ & 4.1  10$^{-2}$ & M \\ 
10 & 1.3 10$^{-3}$ & 2.0 10$^{-2}$ & 1.9 10$^{-2}$ & 3.7 10$^{-2}$ & M \\ 
18 & 3.9 10$^{-4}$ & 1.7 10$^{-2}$ & 2.0  10$^{-2}$ & 1.6  10$^{-2}$ & M \\ 
20 & 2.5 10$^{-4}$ & 1.4 10$^{-2}$ & 1.3 10$^{-2}$ & 1.3  10$^{-2}$ & M \\ 
21 & 2.0 10$^{-4}$ & 1.2 10$^{-2}$ & 1.3 10$^{-2}$ & 1.1  10$^{-2}$ & M \\ 
24 & 6.7 10$^{-5}$ & 5.3 10$^{-3}$ & 4.8 10$^{-3}$ & 3.9  10$^{-3}$ & M \\ 
4 & 4.3 10$^{-9}$ & 5.1 10$^{-7}$ & 1.5 10$^{-7}$ & 3.7 10$^{-7}$ &  \\ 
6 & 1.4 10$^{-9}$ & 1.7 10$^{-7}$ &  1. 10$^{-7}$ & 1.2 10$^{-7}$ & \\ 
22 & 6.1 10$^{-10}$ & 8.3 10$^{-8}$ & 5.7 10$^{-8}$ & 4.5 10$^{-7}$ & \\ 
17 & 3.0 10$^{-10}$ & 3.7 10$^{-8}$ &  1.2 10$^{-8}$ &  1.3 10$^{-8}$ & \\ 
19 & 1.1 10$^{-10}$ & 1.6 10$^{-8}$ & 5.4  10$^{-9}$  & 1.3  10$^{-8}$ & \\ 
15 & 3.6 10$^{-11}$ & 3.8 10$^{-9}$ &  2.3 10$^{-9}$ & 2.2 10$^{-9}$ &\\ 
13 & 2.2 10$^{-11}$ & 2.7 10$^{-9}$ &  1.7 10$^{-9}$ & 6.3 10$^{-9}$ &\\ 
3 & 1.7 10$^{-11}$ & 1.4 10$^{-9}$ & 1.9 10$^{-9}$ & 1.4 10$^{-9}$ & \\ 
43 & 9.7 10$^{-12}$ & 7.1 10$^{-10}$ &   &  &  \\ 
44 & 4.0 10$^{-12}$ & 2.9 10$^{-10}$ &   &  &  \\ 
30 & 3.6 10$^{-12}$ & 2.5 10$^{-10}$ & 2.2 10$^{-10}$ & 2.1 10$^{-10}$  & \\ 
28 & 2.4 10$^{-12}$ & 1.7 10$^{-10}$ & 1.7 10$^{-10}$ & 3.2 10$^{-12}$? & \\ 
45 & 1.4 10$^{-12}$ & 1.2 10$^{-10}$ &   &  &  \\ 
27 & 1.2 10$^{-12}$ & 9.4 10$^{-11}$ & 8.4 10$^{-11}$ & 7.8 10$^{-11}$ & \\ 
29 & 3.2 10$^{-13}$ & 5.9 10$^{-11}$ & 3.9 10$^{-11}$ & 4.9  10$^{-11}$ & \\ 
31 & 1.6 10$^{-13}$ & 9.8 10$^{-11}$ & 6.3  10$^{-11}$ & 7.5  10$^{-11}$ & \\ 
\noalign{\smallskip}
\hline
\end{tabular}
\end{center}
\normalsize
\label{tab:pop}
\end{table}
%Table~\ref{tab:pop}


\begin{table}
\caption{Same as Table~\ref{tab:pop}, but with level
 populations calculated only including excitations from the 
first three levels, at 10$^{8}$, 10$^{10}$ \cmt, see
 Fig.~\ref{fig:balance}.
}
\begin{center}
\scriptsize
%\footnotesize
%\tiny
%\normalsize
\begin{tabular}{@{}cccl@{}}
\hline\noalign{\smallskip}
\hline\noalign{\smallskip}
 i    & 1.0 10$^{8}$ & 1.0 10$^{10}$  & \\ 
\hline 
1 & 0.98 & 0.46 &  \\ 
2 & 8.2 10$^{-3}$ & 0.13 &  \\ 
8 & 4.1 10$^{-3}$ & 0.19 &  \\ 
5 & 2.1 10$^{-3}$ & 0.10 &  \\ 
10 & 1.4 10$^{-3}$ & 7.1 10$^{-2}$ &  \\ 
18 & 3.9 10$^{-4}$ & 2.1 10$^{-2}$ &  \\ 
20 & 2.4 10$^{-4}$ & 1.3 10$^{-2}$ &  \\ 
21 & 2.0 10$^{-4}$ & 1.3 10$^{-2}$ &  \\ 
24 & 6.6 10$^{-5}$ & 3.7 10$^{-3}$ &  \\ 
4 & 4.2 10$^{-9}$ & 2.3 10$^{-7}$ &  \\ 
6 & 1.3 10$^{-9}$ & 8.3 10$^{-8}$ &  \\ 
22 & 6.0 10$^{-10}$ & 4.2 10$^{-8}$ &  \\ 
17 & 2.9 10$^{-10}$ & 1.6 10$^{-8}$ &  \\ 
19 & 1.1 10$^{-10}$ & 7.0 10$^{-9}$ &  \\ 
15 & 3.5 10$^{-11}$ & 2.0 10$^{-9}$ &  \\ 
13 & 2.2 10$^{-11}$ & 1.5 10$^{-9}$ &  \\ 
3 & 1.6 10$^{-11}$ & 9.9 10$^{-10}$ &  \\ 
43 & 9.7 10$^{-12}$ & 4.5 10$^{-10}$ &  \\ 
44 & 4.0 10$^{-12}$ & 1.9 10$^{-10}$ &  \\ 
30 & 3.6 10$^{-12}$ & 1.7 10$^{-10}$ &  \\ 
28 & 2.4 10$^{-12}$ & 1.1 10$^{-10}$ &  \\ 
45 & 1.4 10$^{-12}$ & 8.2 10$^{-11}$ &  \\ 
27 & 1.2 10$^{-12}$ & 6.4 10$^{-11}$ &  \\ 
29 & 3.2 10$^{-13}$ & 3.9 10$^{-11}$ &  \\ 
31 & 1.5 10$^{-13}$ & 6.5 10$^{-11}$ &  \\ 
\noalign{\smallskip}
\hline
\end{tabular}
\end{center}
\normalsize
\label{tab:pop1-3}
% Table~\ref{tab:pop1-3}
\end{table}


\subsection {\ion{Fe}{x}: energy levels and line identifications}


For \ion{Fe}{x} many of the identifications in the past have been 
based on wavelength correspondence and $gf$ values, or on 
approximate estimates of line intensities.
It is virtually impossible to list in detail all the
line identifications proposed, discussed, or rejected 
in the literature. Only the most notable studies for 
the configurations included here are discussed. 
We note that studies 
of the variations of the wave number intervals along
isoelectronic sequences are normally used for spectral 
line classification. Indeed this method has allowed 
the identification of many of the brightest lines in 
\ion{Fe}{x}.
On the other hand, weaker lines are more difficult to 
identify for the complex Fe ions, because of their 
level separations and mixing effects.

\subsubsection{The forbidden transitions}

\cite{edlen:42}, upon suggestion 
from  \cite{grotrian:39}, identified the famous 
bright red coronal forbidden line at 6374.6 \AA\
as the \ion{Fe}{x} transition $^2$P$_{3/2}$--$^2$P$_{1/2}$ 
within the ground configuration. 

The transition array 3s$^2$ 3p$^5$--3s$^2$ 3p$^4$ 3d
produces the brightest \ion{Fe}{x} lines.
\cite{gabriel_etal:65} and \cite{gabriel_etal:66}
first identified three of the lines
for this transition array.
A further six lines were identified by \cite{fawcett_gabriel:66},
while others were later identified by \cite{bromage_etal:77}.

The transition array 
3s$^2$ 3p$^4$ 3d--3s 3p$^5$ 3d produces weaker lines.
\cite{smitt:77} was the first to propose the identification
of some lines for this transition array, but no details on the laboratory
spectra were provided. Other laboratory observations of 
these lines have not been found in the literature. 
We shall see later that the \cite{smitt:77} identifications 
of this transition array are rejected here.


Transitions within the 3s$^2$ 3p$^4$ 3d configuration
produce some bright forbidden lines.
\cite{edlen:69}, on the basis of wavelength 
correspondences,  suggested 5 
possible identifications, of which only one (3454.2 \AA)
turned out to be correct. 
%
\cite{jordan:71} used the 1970 eclipse observations 
described by \cite{gabriel_etal:71} to suggest 
a possible identification of the 1918.3 \AA\ line,
using both  wavelength and line intensity correspondences.
\cite{mason_nussbaumer:77} performed a detailed 
calculation of  level populations
 and line intensities. This allowed a number of new 
identifications to be proposed on firmer ground.
%
\cite{mason_nussbaumer:77} proposed the identifications of
the 1918.3, 3454.2  \AA\ lines, and suggested
possible identifications for the 
1428.7, 1603.3,  3533.6, 4311.8 \AA\ lines.
%
\cite{smitt:77} confirmed the identifications of 
\cite{mason_nussbaumer:77}, further identifying other 
 transitions and suggesting a few more
that should have been observed.
%
\cite{edlen_smitt:78} made very approximate 
intensity calculations to confirm and extend the 
identifications presented in \cite{smitt:77}.
%
%We shall confirm all the  identifications
%proposed by \cite{mason_nussbaumer:77} but not all 
%those proposed by \cite{smitt:77} or \cite{edlen_smitt:78}.
%
%Not all the identifications proposed by 
%\cite{edlen_smitt:78} and \cite{smitt:77} turn out 
%to be correct though. 

We note that all the above studies provided only
the relative energies for some of the levels within the 
3s$^2$ 3p$^4$ 3d configuration and not their position
with respect to the ground level.

\subsubsection{The metastable levels}

The results of our model ion are compared with the 
observations of the 3s$^2$ 3p$^5$ and  3s$^2$ 3p$^4$ 3d forbidden lines,
in Figs.~\ref{fig:jefferies71},\ref{fig:sandlin77b},\ref{fig:fd77}.
%
Considering
all the uncertainties in the observations, we can
confirm all the identifications proposed by 
\cite{mason_nussbaumer:77}. Also, we confirm most of the identifications 
proposed by the other authors, 
%(e.g. \citealt{jordan:71, mason_nussbaumer:77, edlen_smitt:78})
with the notable exception of the 1582.35 \AA\ 
line that is obviously not due to the 
10-24 transition, as previously suggested 
(see, e.g., \citealt{smitt:77}; \citealt{edlen_smitt:78};
\citealt{sandlin_tousey:79}).
Doubts about this identifications have been 
expressed by \cite{bhatia_doschek:95}, but
no direct comparisons with observations were provided.


\begin{figure}[!htbp]
\centerline{\epsfig{file=fe_10_jefferies71.ps, width=6.5cm,angle=90 }}
  \caption{The $F_{ji}$ curves relative to a 
coronal condensation observed from the ground 
at 1.02 \rsun\  during 
the 1965 solar eclipse (\citealt{jefferies_etal:71}).}
  \label{fig:jefferies71}
\end{figure}
% Fig.~\ref{fig:jefferies71}


\begin{figure}[!htbp]
\centerline{\epsfig{file=fe_10_sandlin77b.ps, width=6.5cm,angle=90 }}
  \caption{The $F_{ji}$ curves relative to the  
Skylab ATM observations 40\arcsec above an active 
region reported by  \cite{sandlin_etal:77}.
Note that the ordinate of the plot spans more than three orders
 of magnitude. 
The line observed at 1582 \AA\ cannot obviously 
be ascribed to the 10-24 \ion{Fe}{x} transition, which 
is more than two orders of magnitude weaker than the 
observed line.}
  \label{fig:sandlin77b}
\end{figure}
% Fig.~\ref{fig:sandlin77b}

\begin{figure}[!htbp]
\centerline{\epsfig{file=fe_10_fd77.ps, width=6.5cm,angle=90 }}
  \caption{The $F_{ji}$ curves relative to the 
 Skylab ATM observations reported by \cite{feldman_doschek:77}.
Note that the ordinate of the plot spans three orders
 of magnitude.
}
  \label{fig:fd77}
\end{figure}
% Fig.~\ref{fig:fd77}


Figs.~\ref{fig:jefferies71},\ref{fig:sandlin77b},\ref{fig:fd77}
and show that the energies of the 
 3s$^2$ 3p$^4$ 3d levels ultimately depend on the 
position of the 4, 5 ($^4$D$_{5/2, 7/2}$) levels,
 which could be regarded as uncertain until the present work. 
%
In fact, the energies of the levels 4-7 ($^4$D$_j$) have only been suggested 
in the literature. \cite{smitt:77} was the first to tentatively  
assign an energy of 388708 \cm to both levels 4 and 5.
The energies of the higher levels were assigned by 
\cite{edlen_smitt:78} and subsequent authors (see NIST listings) 
by assuming the \cite{smitt:77} suggestion to be correct.


Level 5 ($^4$D$_{7/2}$) is metastable, and can 
only decay to the ground via the M2 transition 1-5. 
This line is the fourth strongest line in the EUV spectrum
of \ion{Fe}{x}, and would easily have been identified if it 
were not for the fact that it falls in a region 
(250--270 \AA) which is crowded 
with lines that all have dubious identifications.


The position of level 5 could be 
established by knowing the energy of level 4
($^4$D$_{5/2}$), for example by considering the 1-4 E1 transition.
In fact, these two levels are predicted to be close.
\cite{deb_etal02} predict the $^4$D$_{5/2, 7/2}$ levels to be 
separated (although inverted) by 21 \cm, while our SS results
predict a splitting of approximately 70 \cm. 
%
Fortunately, good observational evidence on the splitting 
of this term was given by 
\cite{sandlin_tousey:79} (see Table~\ref{tab:lines}).
The authors report a strong 
component at 1603.21 \AA\ (the 5-21 line) 
and a weaker one at 1603.35 \AA (the 4-21 line), which  result in an energy
difference of 5 \cm. We adopt this value here.
Similarly, \cite{sandlin_tousey:79} report 
an asymmetry in the red wing of the 1918.25 \AA\ line,
consistent with the splitting and intensities of the 
5-18 and 4-18 transitions.


The relative  position of level 5 is well-constrained by the
observed 5-8 (3454.9 \AA) and 8-24 (1463.5 \AA) transitions. 
%
The 5-24 is predicted to be the 
fourth strongest forbidden line (see Table~\ref{tab:lines}), 
and should be easily observable at approximately 1028 \AA, as already 
noted by \cite{smitt:77}. 
%
Indeed there is a strong line reported 
by \cite{feldman_etal:97} and observed at 1028.02 \AA\ in the 
SUMER spectra. It is listed as the \ion{Fe}{x} 5-24
transition, probably based on the suggestion of \cite{smitt:77}.
%
It turns out that the 4-24 transition should have an intensity
of about 0.3 of the 5-24 one, and so the line 
observed at 1028.02 \AA\ should be instead a blend of 
both  5-24 and  4-24 transitions, since no other nearby 
lines are reported by \cite{feldman_etal:97}.
%
We have calibrated 
the intensities of the 1028.02 \AA\ and the 
1463.5 \AA\ lines
reported by \cite{feldman_etal:97}
with the standard SUMER calibration (the published data
are not calibrated).
The associated $F_{ji}$ values are displayed in Fig.~\ref{fig:sumer}.
A puzzling aspect is the fact that the line intensities 
 would be in better agreement with theory by 
assuming that the 1028.02 \AA\ is simply due to the 
 5-24 transition. A further assessment should include 
a critical review of the line intensities and the  SUMER calibration.

\begin{figure}[!htbp]
\centerline{\epsfig{file=fe_10_feldman97.ps, width=6.5cm,angle=90 }}
  \caption{The $F_{ji}$ curves relative to the 
 SUMER observations of \cite{feldman_etal:97}.}
  \label{fig:sumer}
\end{figure}
% Fig.~\ref{fig:sumer}


A great aid in the identification of the 
$^4$D$_j$ levels  comes from the 
beam-foil spectroscopy. For example,  \cite{jupen_etal:93} 
presented an \ion{Fe}{ix-xi} spectrum in the 200-270 \AA\ range
measured  18ns after the excitation took place.
%
A simple prediction with our model ion of the relative line intensities
after 18ns, based on calculated level lifetimes, 
is in  good agreement with their observations.
After 18ns, all the levels with short lifetimes have decayed.
%
The $^4$D$_{7/2}$ level has such a long lifetime that
 the 1-4 line is the dominant
transition (as already suggested by \citealt{jupen_etal:93}). 
Unfortunately, however, the beam-foil spectra 
had a $\simeq$ 1-2 \AA\ resolution, and only provided
an approximate  position  around  257 \AA.
We note that \cite{smitt:77} suggested a value of 257.263 \AA.


%Having established the approximate position 
%of the $^4$D$_{5/2}$ level using beam-foil spectroscopy, the next step is to 
%identify the position of level 5 ($^4$D$_{7/2}$).


In conclusion, having established a consistency between the brightest
transitions connected to the 3s$^2$ 3p$^4$ 3d levels,
we are still left with at least five candidates  for the strong  EUV 
1-5  transition in the high-resolution solar spectra of 
 \cite{behring_etal:76}. Note that the 1-5  transition
 must be blended with the 1-4 one.
The blend could correspond to the relatively bright lines observed at
256.686 \AA\ (blended with a \ion{S}{xiii} line); 
256.925 \AA; 257.262 \AA\;
257.392 \AA\ (normally identified as an \ion{Fe}{xiv} line)
but probably blended with an unidentified line);
257.547 \AA (possibly due to \ion{Fe}{xi}).
%Details on the will be provided elsewhere.
We note that with  medium-resolution ($\simeq$ 0.3 \AA) spectroscopy
as in the \cite{malinovsky_heroux:73} spectrum, 
the latter three spectral lines are blended.  


We confirm the identification of 257.262 \AA
observed by \cite{behring_etal:76} as the blend of
the $^2$P$_{3/2}$--$^4$D$_{5/2, 7/2}$ transitions, 
in agreement with the identification of 257.257 \AA
given by \cite{thomas_neupert:94} and \cite{young_etal:98}, 
based on the \SERTS-89 spectrum.
\cite{brosius_etal:98b}  observed this line with
\SERTS-95 at  257.246 \AA, but identified it 
as due to a blend of \ion{Fe}{x} and \ion{Si}{ix}.


\subsubsection{150-250 \AA}

The brightest \ion{Fe}{x} lines are found in the 150-300 \AA\ region;
174.534, 177.242, 184.543, 190.0 \AA. Fig.~\ref{fig:malinovsky}
shows an excellent agreement between our present model and the
\cite{malinovsky_heroux:73} data. 


\begin{figure}[!htbp]
\centerline{\epsfig{file=fe_10_malinovsky.ps, width=6.5cm,angle=90 }}
  \caption{The $F_{ji}$ curves relative to the full-Sun spectrum of \cite{malinovsky_heroux:73}.
Note that the intensities of the  257.26 and 182.3 \AA\ lines have
  been rescaled taking into account the known blends.
The 190.04 \AA\ line is obviously blended.  }
  \label{fig:malinovsky}
\end{figure}
% Fig.~\ref{fig:malinovsky}


The notable features are:
\noindent
a) an excellent agreement for the 
bright 174.534, 177.242, 184.543 \AA\ lines;

\noindent
b) as noted by previous authors, the 2-31 transition is an excellent 
density diagnostic for the quiet solar corona.
Its intensity suggests a log \Ne=8.8 \cmt, in excellent 
agreement with the electron densities derived from other ions.

\noindent
c) The blend of the 1-5 and 1-4 transitions
is a good density diagnostic for active regions 
(for log \Ne $>$ 9 \cmt). 
We have included this blend in Fig.~\ref{fig:malinovsky},
by measuring the line intensity
from the \cite{malinovsky_heroux:73} spectrum (it was not 
listed by the authors), and by assuming that 
the \ion{Fe}{x} blend contributes by 40\% 
to this very strong line.

\noindent
d) The bright 184.54, 190.04 \AA\ lines 
form a branching ratio, and could therefore be useful
for instrument calibration.

\noindent
e) The  190.04 \AA\ line (labelled 7 in Fig.~\ref{fig:malinovsky})
1s problematic. In medium-resolution spectra,
the bright 190.04 \AA\ line is not due to \ion{Fe}{x}, as often
reported.  The calibrated  theta-pinch  laboratory 
spectra of \cite{datla_etal:75} 
also shows the same type of blending (labelled 3 in Fig.~\ref{fig:datla}). 
The blend should therefore be ascribed to another iron ion, 
probably \ion{Fe}{ix} or \ion{Fe}{xi}.
%
%Indeed \cite{behring_etal:76} reported 
%two other nearby lines,  at 189.940 and 
%189.733 \AA, the first  unknown and the second 
%probably due to \ion{Fe}{xi} as will be discussed elsewhere. 
%

f) The 2-28 line (182.308 \AA) is very weak and blended 
in medium-resolution spectra  with the \ion{Fe}{xi} 182.167 \AA\
line (see, e.g., \citealt{behring_etal:76})
 According to theory, the contribution 
of the 2-28 \ion{Fe}{x} transition to the 
observed line should only be 8\%, as Fig.~\ref{fig:malinovsky}
shows.
%


\begin{figure}[!htbp]
\centerline{\epsfig{file=datla_2.ps, width=6.5cm,angle=90 }}
  \caption{The $F_{ji}$ curves relative to the  theta-pinch  laboratory 
spectra of \cite{datla_etal:75}, second case, 
tube filled with helium.
The estimated electron density and temperature 
at the time of peak intensity of the discharge were
\Ne=1 10$^{16}$ \cmt and \Te= 1.1 MK.
The intensities of the 1-30 and 1-28 transitions 
were corrected by \cite{datla_etal:75} for optical depth.
Note the good agreement between theory and 
observations, with the exception of 
 the 2-27 line, which is clearly blended.
}
  \label{fig:datla}
\end{figure}
% Fig.~\ref{fig:datla}


Most of the other weaker \ion{Fe}{x} transitions, which fall in the 
220-240 \AA\ wavelength range (see Table~\ref{tab:lines}),
remain relatively unexplored, at least with high-resolution 
solar observations. 
Many conflicting identifications have been proposed. 
Some new identifications are proposed here. 
However, it should be noted that, according to our 
model calculations, none of these transitions are  
spectroscopically important. 
The intensities  of these lines have been measured from the 
\cite{malinovsky_heroux:73} spectrum. 
It turns out that the observed lines are 3-5 times brighter than our 
calculated intensities, hence all these lines are still to be
considered tentatively identified.

\subsubsection{250-400 \AA}

The 3s 3p$^6$ configuration produces 
two bright lines observed at 345.7, 365.5 \AA.
These lines form a branching ratio,
and are therefore an excellent way of constraining 
an instrument calibration between those wavelengths. 
%
Care must be used, however, since 
the 365.543~\AA\ line is strongly blended with a 
bright \ion{Ne}{v} line in
solar on-disc observations (see, 
\citealt{young_etal:98}, \citealt{delzanna01_cdscal}).


\begin{figure}[!htbp]
\centerline{\epsfig{file=nisat_off.ps, width=6.5cm,angle=90 }}
\centerline{\epsfig{file=fe_10_serts89.ps, width=6.5cm,angle=90 }}
  \caption{Top: a solar CDS off-limb 
spectrum (\citealt{delzanna_thesis99}) with the newly identified line at 337.27 \AA.
Bottom: $F_{ji}$ curves relative to the \SERTS-89 calibrated data, 
which confirm this identification, togehter with the 
identification of the important $^2$P$_{3/2}$--$^4$D$_{5/2, 7/2}$ 
blend, observed at 257.257 \AA.
Other lines of the transition array are blended with other lines.
Note that the lines indicate  log \Ne =9.5 [\cmt],
in agreement with results from other ions (\citealt{young_etal:98}). 
Also note that the 365.543~\AA\ line is a well-known blend with a 
\ion{Ne}{v} line.
}
  \label{fig:nisat_off}
\end{figure}
% Fig.~\ref{fig:nisat_off}

The situation for the  3s 3p$^5$ 3d configuration 
is considerably worse, since to date no level energy 
has been established with certainty. 
NIST reports values for the $^4$F$_J$ (35-38) levels, based 
on the identifications proposed by \cite{smitt:77}.
Unfortunately, no details about the 
observations were given. The brightest line 
should be due to the 5-35 transition,  supposedly at 324.7 \AA.
The second brightest would then be the
8-35 at 358.4 \AA, followed by  4-36 (321.8 \AA)
and 5-34 (355.5 \AA). 
All these identifications were rejected by 
\cite{brooks_etal:99} using SOHO/CDS-NIS 
observations. 

We have also used various CDS-NIS 
observations (\citealt{delzanna_thesis99}) to check 
these identifications (Fig.~\ref{fig:nisat_off}). 
We agree with the 
conclusions of \cite{brooks_etal:99} and reject 
these identifications, since the calculated intensity values
are much smaller than the observed ones. 
% 
We tentatively 
identified the brightest 5-35 line
with the weak line observed at 329.94 \AA\
(\citealt{brooks_etal:99} also report an unidentified line at 
329.9 \AA).


What is surprising is that the line we 
predict as the third brightest 
\ion{Fe}{x} line in the 300-400 \AA\ wavelength range 
(the 18-43 transition)  has never been identified. 
We identify it as the previously unidentified
line observed in CDS spectra at 337.27 \AA (see Fig.~\ref{fig:nisat_off}).
%
This line, being relatively bright, is reported 
in most published solar spectra. 
The identification of this and other lines of the 
transition array is confirmed by the intensities 
obtained with the CDS calibration presented in 
\cite{delzanna01_cdscal}. However, the CDS calibration 
still needs further improvement.

To confirm this identification we also use the 
calibrated \SERTS-89 data of \cite{thomas_neupert:94}.
\cite{thomas_neupert:94} identify this line, observed at 
337.238 \AA,  with an \ion{Ar}{viii} transition. 
However, according to the \ion{Ar}{viii} atomic model present in 
CHIANTI v.4, this line should have an intensity 
1/10 of a self-blend of three \ion{Ar}{viii} transitions 
at $\simeq$ 260.3 \AA. \cite{thomas_neupert:94} do not 
report any lines at those wavelengths in their 
spectrum, hence the 337.238 \AA\ line cannot be due to 
\ion{Ar}{viii}. A similar argument applies to 
the nearby 338.181 \AA\ line, also identified as due to 
\ion{Ar}{viii}.

Instead, the intensity of the 18-43 line agrees very well with the 
intensity of the nearby 1-3 line,
as shown in  Fig.~\ref{fig:nisat_off}.
Also,  other weaker lines produced by the $^2$F$_{J}$ 
levels (43-44) can be identified as blending other lines.
The 21-43 would contribute 15\% to the blend of 
\ion{Mg}{vi} and \ion{Fe}{xi}. The 18-44 would blend
by 30\% a \ion{Ne}{iii} line, while the 17-43 
would contribute by 40\% to the observed line.
Note that the energies of the 3s 3p$^5$ 3d 
levels were obtained by applying a single 
correction to the entire configuration, so 
the wavelengths of the lines originating
from these levels could be further be refined, if for example
laboratory data were available.


Fig.~\ref{fig:nisat_off} 
also confirms, on a quantitative basis, the 
identification of the important $^2$P$_{3/2}$--$^4$D$_{5/2, 7/2}$ 
blend. 
The $F_{ji}$ curves indicate  log \Ne =9.5 \cmt,
in excellent agreement with results 
from other ions which will be reported in further papers in this series.
Note that \cite{young_etal:98} obtained a lower density,
log \Ne =9.0 \cmt, using the CHIANTI model.

%**********************************************************************
%*******************GIULIO THIS IS AS FAR AS I GOT TODAY***************
%**********************************************************************


\subsubsection{Calibration in the 150-400 \AA\ range}


\begin{figure}[!htbp]
\centerline{\epsfig{file=cds_fe_10_v5.ps, width=6.5cm,angle=90 }}
\centerline{\epsfig{file=cds_fe_10_v4.ps, width=6.5cm,angle=90 }}
  \caption{The $F_{ji}$ curves relative to a 
 CDS NIS/GIS off-limb spectrum (\citealt{delzanna01_cdscal}),
covering the 150-380 \AA\ range. 
Top: results with the present model; bottom: results obtained with the 
data in CHIANTI v.3. 
Note the good agreement, in both cases, 
between the lines (1 to 7) observed in the GIS 1 channel.
Also note the large variation of the 345.7 \AA\ line (8),
due to inclusion of 
resonance effects in the R-matrix calculations.
}
  \label{fig:cds_fe_10}
\end{figure}
% Fig.~\ref{fig:cds_fe_10}


There is virtually no independently-calibrated medium-resolution
solar spectrum that spans the entire 150-400 \AA\ range
and that could be used to benchmark the 
relative intensities between lines originating from the 
3s 3p$^6$ and 3s$^2$3p$^4$3d configurations.
The laboratory data of \cite{datla_etal:75} indicate 
good agreement with the present model ion.

This  benchmark is important for instrument calibration.
%
Atomic data from \ion{Fe}{x-xii} (CHIANTI v.3) were used by 
\cite{delzanna01_cdscal} to derive the relative \NIS-1 \GIS-1 
calibration.
The brightest \ion{Fe}{x} lines 
are in fact observed in the \GIS-1 channel 
(150--210 \AA),
while the 1-2,1-3 doublet is observed
with the \NIS-1 detector (308--380 \AA).
These lines can be used for instrument calibration because
they are bright and have a similar density dependence.
%
It is interesting to note that \cite{delzanna01_cdscal}
reported an inconsistency between the \ion{Fe}{x} lines 
and those from the other ions, 
a clear indication of a problem in the collision strengths
calculations.
As already mentioned, the new calculations, having  increased 
the collision strengths for level 3, produce a $\simeq$50\%
variation in the predicted ratio between the  
1-2,1-3 doublet  and the other bright lines observed in \GIS-1, 
as shown in  Fig.~\ref{fig:cds_fe_10}.
This variation  substantially improves the agreement with the 
results obtained from the other ions.
A very similar situation has occurred with 
\ion{Fe}{xii}, as new R-matrix calculations 
show (P. Storey, priv. comm.).
Work is in progress to revise the relative NIS/GIS calibration.

      
Fig.~\ref{fig:cds_fe_10} also shows other interesting points.
First, that 
the internal \GIS-1 calibration obtained by \cite{delzanna01_cdscal}
was very good. In fact, there is good agreement 
between the \GIS-1 lines and the present model.
%
Second, that  the CHIANTI v.3 data for \ion{Fe}{x}
are close to those presented here.
 CHIANTI v.3 contained  DW 
collision strengths of \cite{bhatia_doschek:95}
scaled by P. Young with radiative data calculated with SS.



\section{Conclusions and further work}
\label{sec:concl}

Despite the large amount of theoretical and 
experimental studies produced in the literature,
complete sets of accurate atomic and experimental data 
are still missing for many ions that are important 
for astrophysical applications.
%
Very few data, both on the theoretical and 
observational side, are complete enough to 
allow a proper benchmark of the atomic data 
to be performed.

%Still a lot more work needs to be done,
%even on the line identification issue.


We have shown the importance of building a 
complete ion model to predict line intensities 
to be compared to observations.
For complex ions  with many metastable levels 
such as \ion{Fe}{x}, it is necessary to include all 
the populating and de-populating processes when 
calculating the level balance. 

For complex ions with strong level mixing such as 
\ion{Fe}{x}, it is important to apply the method 
of adjusting empirically the energy levels and 
use the adjusted values for the radiative calculations. 
This in turn helps the line identification problem.


A comprehensive benchmark of  \ion{Fe}{x}
atomic data against  well-calibrated 
observations has been performed.
The assessment  takes into account 
both wavelength coincidences and line intensities 
and is done for the first time in a comprehensive way.
%
The method atopted allowed us to confirm most previous 
identifications on a quantitative basis,
but also to reject some, and suggest new ones. 
We have suggested the best lines to be used for 
density diagnostic and instrument calibration 
purposes.

The assesment also indicated the presence of many 
blends, and allowed uncertainties on the atomic data 
to be estimated.
For the cases free of blends, the agreement between theoretical and
experimental data is excellent.

Further work is needed, to identify with certainty 
the weaker transitions.
Also, further work is needed to re-calculate the 
collision strengths for the 3s 3p$^5$ 3d 
configuration with  better wavefunctions, 
and to properly calculate collision strengths for 
 the $n=4,5$ levels, which produce a host
of transitions in the X-rays.



\begin{acknowledgements}

Support from  PPARC is acknowledged. \\
We thank P.J. Storey for providing an updated version of 
SUPERSTRUCTURE, and P.R. Young for useful 
comments on the manuscript.


\end{acknowledgements}

\bibliographystyle{aa}
%\bibliography{bib}
\bibliography{paper2}


\appendix

%Table~\ref{tab:lines}
%Table~\ref{tab:levels}

\section{Further details about level identifications}


We now provide further comments about level identifications 
and on the details listed in Tables~\ref{tab:levels},~\ref{tab:lines}
The splitting of the ground  $^2$P term is well known 
because of the famous red coronal line, observed at 6374 \AA.
The position of level 3, the 3s 3p$^6$ $^2$S$_{1/2}^e$ (mixed
with level 27), is also well known 
because of the strong 1-3, 1-2 transitions accurately measured by 
\cite{behring_etal:76}. 

Levels 4,5 have already been  discussed.
The other two $^4$D levels, 6,7, are not important 
spectroscopically. The 1-6 E1 line is weak and 
is blended.


The lowest of the   $^4$F terms,  $^4$F$_{9/2}$, is also a metastable level
and only decays to the $^4$D$_{7/2}$ via the second-brightest forbidden 
line observed at 3454.2 \AA. This in turn constraints the energies 
of the other fine-structure $^4$F$_J$ levels.
Level 9 is strongly mixed and still unidentified, but is not spectroscopically important.
The   $^4$F$_{7/2}$ should produce a strong line around 2934 \AA, 
in a spectral region not covered by previous observations.
%This line was probably not observed because of poor sensitivity.
The $^4$F$_{5/2}^e$ (level 11) mainly decays via a weak E1 transition
to the ground, located at 234.35 \AA\ and blended with \ion{He}{ii} 
in solar spectra. $^4$F$_{3/2}^e$ is identified here with the 
weak 1-12 observed by \cite{behring_etal:76} at 233.445 \AA.

Levels 13-16 are  not spectroscopically important. 
A riddle of different  values have been proposed by 
various authors.
%\cite{jupen} suggested a value of 428002 \cm.

Level 17, the $^4$P$_{5/2}^e$, is strongly mixed. 
It should decay with a weak but measurable line at approximately 226 \AA.
Two possible choices are the lines observed at 225.856 and 226.320 \AA.
The first choaice is adopted. Note that \cite{bromage_etal:77}
predicts the line to be observed at 225.29 \AA, but did not
identify this line with any observed ones.

Level 18, ($^2$F$_{7/2}^e$) is metastable and decays via
the strong M1 5-18 transition observed at 1918.25 \AA.
The weaker 8-18 line %should have a wavelength of 4313.5 \AA,
has been observed at 4312 \AA.
The interesting fact about level 18 is that 
the 1-18 M2 transitions is weak but should be measurable.
If its wavelength can be measured accurately, 
it would solve the problem of not knowing all the energies 
of the  3s$^2$ 3p$^4$ 3d levels (relative to the ground).

Level 19 is strongly mixed, but should produce a measurable line
  around 226 \AA, of similar intensity as the 1-17.
 Again there are many options,
the most probable seems the line observed at 226.998 \AA.
\cite{bromage_etal:77} predicted the line to be at 
226.45 \AA\ but identified it with a laboratory line observed 
at 226.31 \AA.
\cite{jupen_etal:93} identifies the 1-19 line instead  with 
a laboratory line observed at 225.163.

Levels 20,21 ($^2$G$_{9/2, 7/2}$) are both metastable. 
The first decays via the strong forbidden line
8-20 observed at  3020.1. The second via the 10-21 
observed at  3533.6 \AA.

Level 22 ($^2$F$_{5/2}^e$)  should produce an observable 
1-22 line around 220 \AA, a region with many unidentified lines.
In agreement with \cite{jupen_etal:93}, this level is assigned 
according to the line observed at 220.247 \AA.
It is interesting to note that  \cite{bromage_etal:77} 
predicted the 1-22 line at 220.12 but tentatively 
identified it with a line at 220.882.


Level 23 also has an uncertain identification. 
Most probably, the 1-23 transition (weaker than the 
1-22) is the line 
observed at 207.449 \AA. \cite{bromage_etal:77} 
predicts the line at 207.58 \AA\ and tentatively 
identified it with a line observed at 209.776 \AA.
 \cite{jupen_etal:93} identifies it with a laboratory 
line observed at 207.444 \AA, in agreement with 
our suggestion.

Level 24 ($^2$F$_{7/2}$) is metastable and not
strongly mixed. The decay to level 8 is via the 
forbidden line observed at 1463.49~\AA.


Level 26 is possibly identified by \cite{jupen_etal:93}
with a laboratory line observed at 193.715 \AA.

Levels 27-31 produce the strongest lines in the 
 \ion{Fe}{x} spectrum, and their energies are 
accurately known. 
Surprisingly, as in many other cases, the 
values reported by NIST do not agree with the 
published literature 
(we adopt the accurate wavelengths 
of \citealt{behring_etal:76}).


The  3s 3p$^5$ 3d levels have some mixing, as indicated in 
Table~\ref{tab:levels}, in particular with 
  3s$^2$ 3p$^3$ 3d$^2$ (c5) levels.
Aside from a few lines already discussed, most 
of the 3s 3p$^5$ 3d levels produce very weak lines.
The energy of all the levels was obtained by 
applying a single correction (-17200 \cm) to the 
entire configuration.
Hence, the wavelengths of the lines originating
from these levels can further be refined.

\begin{table*}
\caption{The details of the most important 4 configurations in 
\ion{Fe}{x}. The percentage of level mixing ($>$10\%) is indicated
in second column. For example, level 27 is mixed with 
level 3 of configuration c2 by 23\%.
$E_{\rm obs}$ indicates the best energies (\cm)
proposed in this work. The uncertainties are only indicative,
but derived from assessing the reliability of line identifications.
The following columns indicate the differences between  
$E_{\rm obs}$ and the energies from NIST, the collisional 
calculations, and the scaled SS values. 
Levels are ordered according to the 
energies $E_{\rm CC}$ of the  collisional calculations.
}
%Calculated: 29/Aug/03 12:10:53
\begin{center}
%\scriptsize
\footnotesize
%\tiny
%\normalsize
\begin{tabular}[c]{@{}|rlcrrrrr|@{}}

 i &  Configuration & Term & $E_{\rm obs}$ & $\Delta E_{\rm NIST}$ & $\Delta E_{\rm CC}$  &  $\Delta E_{\rm SS}$ &\\ \hline
\hline

1 & 3s$^2$ 3p$^5$(96\%) & $^2$P$_{3/2}^{\rm o}$ &          0.0$\pm$0 & 0 & $+$0 &    &  \\
2 & 3s$^2$ 3p$^5$(96\%) & $^2$P$_{1/2}^{\rm o}$ &      15683.1$\pm$1 & 0 & $+$912 & $-$149  &  \\
3 & 3s 3p$^6$(72\%) +27(c3 24\%) & $^2$S$_{1/2}^{\rm e}$ &     289236.0$\pm$5 & -13 & $+$517 & $-$7  &  \\
4 & 3s$^2$ 3p$^4$ ($^3$P)  3d(93\%) & $^4$D$_{5/2}^{\rm e}$ &     388713.5$\pm$50 & 4.5 & $-$4255 & $+$29  &  \\
5 & 3s$^2$ 3p$^4$ ($^3$P)  3d(94\%) & $^4$D$_{7/2}^{\rm e}$ &     388708.0$\pm$50 & -1 & $-$4371 & $-$123  &  \\
6 & 3s$^2$ 3p$^4$ ($^3$P)  3d(92\%) & $^4$D$_{3/2}^{\rm e}$ &     390019.0$\pm$50 & -31 & $-$4047 & $+$173  &  \\
7 & 3s$^2$ 3p$^4$ ($^3$P)  3d(93\%) & $^4$D$_{1/2}^{\rm e}$ &     391554.0$\pm$50 & -1 & $-$3829 & $+$179  &  \\
8 & 3s$^2$ 3p$^4$ ($^3$P)  3d(92\%) & $^4$F$_{9/2}^{\rm e}$ &     417652.0$\pm$10 & -1 & $-$6263 & $-$247  &  \\
9 & 3s$^2$ 3p$^4$ ($^1$D)  3d(42\%) +29(50\%) & $^2$P$_{1/2}^{\rm e}$ &     418456.0$\pm$100 &  -  & $-$6776 &    &  \\
10 & 3s$^2$ 3p$^4$ ($^3$P)  3d(88\%) & $^4$F$_{7/2}^{\rm e}$ &     422785.0$\pm$20 & -10 & $-$5848 & $-$130  &  \\
11 & 3s$^2$ 3p$^4$ ($^3$P)  3d(95\%) & $^4$F$_{5/2}^{\rm e}$ &     426776.0$\pm$50 & 13 & $-$5369 & $+$18  &  \\
12 & 3s$^2$ 3p$^4$ ($^3$P)  3d(84\%) & $^4$F$_{3/2}^{\rm e}$ &     428366.0$\pm$50 & 68 & $-$4767 & $+$307  &  \\
13 & 3s$^2$ 3p$^4$ ($^1$D)  3d(47\%) +28(36\%) & $^2$P$_{3/2}^{\rm e}$ &     426676.0$\pm$100 & -5252 & $-$7005 &    &  \\
14 & 3s$^2$ 3p$^4$ ($^3$P)  3d(95\%) & $^4$P$_{1/2}^{\rm e}$ &     433576.0$\pm$100 & -1224 & $-$6909 &    &  \\
15 & 3s$^2$ 3p$^4$ ($^1$D)  3d(27\%) +12(10\%) +31(25\%) +25(24\%) & $^2$D$_{3/2}^{\rm e}$ &     433140.0$\pm$100 & -1474 & $-$7455 &    &  \\
16 & 3s$^2$ 3p$^4$ ($^3$P)  3d(78\%) & $^4$P$_{3/2}^{\rm e}$ &     438538.0$\pm$100 &  -  & $-$6666 &    &  \\
17 & 3s$^2$ 3p$^4$ ($^3$P)  3d(48\%) +19(11\%) +30(12\%) +26(19\%) & $^4$P$_{5/2}^{\rm e}$ &     442760.0$\pm$50 & 907 & $-$4858 & $-$161  &  \\
18 & 3s$^2$ 3p$^4$ ($^3$P)  3d(50\%) +21(30\%) & $^2$F$_{7/2}^{\rm e}$ &     440839.0$\pm$5 & -1 & $-$6999 & $-$163  &  \\
19 & 3s$^2$ 3p$^4$ ($^1$D)  3d(21\%) +30(15\%) +26(11\%) +17(46\%) & $^2$D$_{5/2}^{\rm e}$ &     440532.0$\pm$50 &  -  & $-$9061 & $+$52  &  \\
20 & 3s$^2$ 3p$^4$ ($^1$D)  3d(92\%) & $^2$G$_{9/2}^{\rm e}$ &     450754.0$\pm$5 & 3 & $-$7070 & $-$55  &  \\
21 & 3s$^2$ 3p$^4$ ($^1$D)  3d(62\%) +18(25\%) & $^2$G$_{7/2}^{\rm e}$ &     451083.0$\pm$5 & -1 & $-$6850 & $-$18  &  \\
22 & 3s$^2$ 3p$^4$ ($^3$P)  3d(72\%) +23(20\%) & $^2$F$_{5/2}^{\rm e}$ &     454036.0$\pm$100 & 1306 & $-$6312 & $-$128  &  \\
23 & 3s$^2$ 3p$^4$ ($^1$D)  3d(76\%) +22(17\%) & $^2$F$_{5/2}^{\rm e}$ &     482046.0$\pm$50 &  -  & $-$7382 & $-$94  &  \\
24 & 3s$^2$ 3p$^4$ ($^1$D)  3d(78\%) +18(17\%) & $^2$F$_{7/2}^{\rm e}$ &     485982.0$\pm$10 & -1 & $-$7287 & $-$52  &  \\
25 & 3s$^2$ 3p$^4$ ($^1$S)  3d(57\%) +15(35\%) & $^2$D$_{3/2}^{\rm e}$ &     511905.0$\pm$100 & 105 & $-$7701 &    &  \\
26 & 3s$^2$ 3p$^4$ ($^1$S)  3d(49\%) +19(42\%) & $^2$D$_{5/2}^{\rm e}$ &     516222.0$\pm$50 &  -  & $-$7664 & $+$100  &  \\
27 & 3s$^2$ 3p$^4$ ($^1$D)  3d(70\%) +3(c2 23\%) & $^2$S$_{1/2}^{\rm e}$ &     541897.0$\pm$10 & 18 & $-$13264 & $+$34  &  \\
28 & 3s$^2$ 3p$^4$ ($^3$P)  3d(50\%) +13(39\%) & $^2$P$_{3/2}^{\rm e}$ &     564208.0$\pm$10 & 10 & $-$12461 & $-$114  &  \\
29 & 3s$^2$ 3p$^4$ ($^3$P)  3d(43\%) +9(51\%) & $^2$P$_{1/2}^{\rm e}$ &     569882.0$\pm$50 & -103 & $-$12494 & $-$366  &  \\
30 & 3s$^2$ 3p$^4$ ($^3$P)  3d(66\%) +19(18\%) +26(10\%) & $^2$D$_{5/2}^{\rm e}$ &     572964.0$\pm$20 & 10 & $-$14240 & $-$96  &  \\
31 & 3s$^2$ 3p$^4$ ($^3$P)  3d(61\%) +15(21\%) & $^2$D$_{3/2}^{\rm e}$ &     586254.0$\pm$20 & 10 & $-$13570 & $+$67  &  \\
32 & 3s 3p$^5$ ($^3$P)  3d(83\%) & $^4$P$_{1/2}^{\rm o}$ &     659450.0$\pm$100 &  -  & $-$51397 &    &  \\
33 & 3s 3p$^5$ ($^3$P)  3d(82\%) & $^4$P$_{3/2}^{\rm o}$ &     662081.0$\pm$100 &  -  & $-$51576 &    &  \\
34 & 3s 3p$^5$ ($^3$P)  3d(81\%) & $^4$P$_{5/2}^{\rm o}$ &     666799.0$\pm$100 &  -  & $-$51811 &    &  \\
35 & 3s 3p$^5$ ($^3$P)  3d(85\%) +(c5 10\%) & $^4$F$_{9/2}^{\rm o}$ &     691789.0$\pm$30 & -4872 & $-$38891 & $+$584  &  \\
36 & 3s 3p$^5$ ($^3$P)  3d(83\%) +(c5 10\%) & $^4$F$_{7/2}^{\rm o}$ &     694075.0$\pm$100 & -5417 & $-$39596 &    &  \\
37 & 3s 3p$^5$ ($^3$P)  3d(82\%) +(c5 10\%) & $^4$F$_{5/2}^{\rm o}$ &     697075.0$\pm$100 & -5510 & $-$39601 &    &  \\
38 & 3s 3p$^5$ ($^3$P)  3d(83\%) +(c5 10\%) & $^4$F$_{3/2}^{\rm o}$ &     699761.0$\pm$100 & -5669 & $-$39528 &    &  \\
39 & 3s 3p$^5$ ($^3$P)  3d(80\%) & $^4$D$_{7/2}^{\rm o}$ &     726572.0$\pm$100 &  -  & $-$40444 &    &  \\
40 & 3s 3p$^5$ ($^3$P)  3d(79\%) & $^4$D$_{5/2}^{\rm o}$ &     728166.0$\pm$100 &  -  & $-$40540 &    &  \\
41 & 3s 3p$^5$ ($^3$P)  3d(81\%) & $^4$D$_{1/2}^{\rm o}$ &     727905.0$\pm$100 &  -  & $-$40898 &    &  \\
42 & 3s 3p$^5$ ($^3$P)  3d(80\%) & $^4$D$_{3/2}^{\rm o}$ &     728367.0$\pm$100 &  -  & $-$40673 &    &  \\
43 & 3s 3p$^5$ ($^3$P)  3d(74\%) +(c5 11\%) & $^2$F$_{7/2}^{\rm o}$ &     737368.0$\pm$30 &  -  & $-$55850 & $+$14  &  \\
44 & 3s 3p$^5$ ($^3$P)  3d(40\%) +46(38\%) & $^2$F$_{5/2}^{\rm o}$ &     750547.0$\pm$100 &  -  & $-$45639 &    &  \\
45 & 3s 3p$^5$ ($^3$P)  3d(73\%) & $^2$D$_{3/2}^{\rm o}$ &     748033.0$\pm$100 &  -  & $-$51352 &    &  \\
46 & 3s 3p$^5$ ($^3$P)  3d(40\%) +44(37\%) & $^2$D$_{5/2}^{\rm o}$ &     742719.0$\pm$100 &  -  & $-$59222 &    &  \\
47 & 3s 3p$^5$ ($^1$P)  3d(24\%) +54(38\%) +(c5 27\%) & $^2$P$_{1/2}^{\rm o}$ &     761445.0$\pm$100 &  -  & $-$65660 &    &  \\
48 & 3s 3p$^5$ ($^1$P)  3d(36\%) +53(20\%) +(c5 24\%) & $^2$P$_{3/2}^{\rm o}$ &     769389.0$\pm$100 &  -  & $-$65535 &    &  \\
49 & 3s 3p$^5$ ($^1$P)  3d(54\%) +(c5 14\%) & $^2$F$_{5/2}^{\rm o}$ &     789756.0$\pm$100 &  -  & $-$81210 &    &  \\
50 & 3s 3p$^5$ ($^1$P)  3d(53\%) +(c5 14\%) & $^2$F$_{7/2}^{\rm o}$ &     793796.0$\pm$100 &  -  & $-$78424 &    &  \\
51 & 3s 3p$^5$ ($^1$P)  3d(33\%) +(c5 14\%) & $^2$D$_{3/2}^{\rm o}$ &     818742.0$\pm$100 &  -  & $-$80623 &    &  \\
52 & 3s 3p$^5$ ($^1$P)  3d(46\%) +(c5 19\%) & $^2$D$_{5/2}^{\rm o}$ &     820906.0$\pm$100 &  -  & $-$79277 &    &  \\
53 & 3s 3p$^5$ ($^3$P)  3d(55\%) +(c5 20\%) & $^2$P$_{3/2}^{\rm o}$ &     862268.0$\pm$100 &  -  & $-$111848 &    &  \\
54 & 3s 3p$^5$ ($^3$P)  3d( 4\%) +47(54\%) +(c5 22\%) & $^2$P$_{1/2}^{\rm o}$ &     861499.0$\pm$100 &  -  & $-$113761 &    &  \\

\hline
\end{tabular}
\end{center}
\normalsize
\label{tab:levels}
%Table~\ref{tab:levels}
\end{table*}


\begin{table*}
\caption{Details of the brightest lines in \ion{Fe}{x}. 
The lines are grouped in three wavelength ranges  
(150--300; 300--900 ; 900--20000 \AA), and 
ordered according to their calculated intensity at 
10$^8$ \cmt.
 Two  $N_{j}/N_{\rm e} A_{ji}$  values,  
calculated at 10$^8$, 10$^{10}$ \cmt and 
 normalised to 6.6 10$^{-9}$, are shown in columns 2,3.
Columns 4,5 show the  $gf$ and $A$ values calculated 
in this work. Column 6  (S 2000) shows, for comparison, the few
NIST $A$ values compiled by \cite{shirai_etal:00}
(values not available are indicated with a `-'; lines 
not reported are indicated with `N'; lines 
reported with a different identification with `Ni').
The last two columns show the wavelengths corresponding to the 
best energies and the scaled SS energies of Table~\ref{tab:levels}.
The uncertainties on the proposed wavelengths are only indicative,
since they are derived from the  uncertainties 
assigned to the energies.
}
%Calculated: 29/Aug/03 12:14:13
%cutoff=0.01 cutoff=0.0015 cutoff=0.005 cutoff=0.001
\begin{center}
%\scriptsize
\footnotesize
%\tiny
%\normalsize
\begin{tabular}[c]{@{}cccrccrcrrl@{}}
\hline\noalign{\smallskip}
\hline\noalign{\smallskip}
 i-j    &  $N_{j}/N_{\rm e} A_{ji}$ &  $N_{j}/N_{\rm e} A_{ji}$ & $gf$
 & $A_{ji}$ (s$^{-1}$) &  $A_{ji}$ (s$^{-1}$) & T & Term  & $\lambda_{\rm obs}$(\AA) & $\lambda_{\rm th}$(\AA)   & \\ \hline
   & 1.0 10$^{8}$ & 1.0 10$^{10}$ & & & S 2000  & & & & \\ 
% 150-300 \AA 
\hline 

1-30 & 1.0 & 0.68 & 4.99 & 1.8 10$^{11}$ &  1.8 10$^{11}$          & E1  & $^2$P$_{3/2}^{\rm o}$-$^2$D$_{5/2}^{\rm e}$ & 174.531$\pm$0.006 & 174.50 & \\ 
1-28 & 0.55 & 0.38 & 2.82 & 1.5 10$^{11}$ &   -                    & E1  & $^2$P$_{3/2}^{\rm o}$-$^2$P$_{3/2}^{\rm e}$ & 177.240$\pm$0.003 & 177.20 & \\ 
1-27 & 0.22 & 0.18 & 1.30 & 1.3 10$^{11}$ & 1.2 10$^{11}$          & E1  & $^2$P$_{3/2}^{\rm o}$-$^2$S$_{1/2}^{\rm e}$ & 184.537$\pm$0.003 & 184.55 & \\ 
1-5 & 0.14 & 2.3 10$^{-2}$ & - & 47.      &   -                    & M2  & $^2$P$_{3/2}^{\rm o}$-$^4$D$_{7/2}^{\rm e}$ & 257.263$\pm$0.033 & 257.18 & \\ 
2-27 & 6.5 10$^{-2}$ & 5.3 10$^{-2}$ & 0.40 & 3.7 10$^{10}$ & 4.2 10$^{10}$ & E1  & $^2$P$_{1/2}^{\rm o}$-$^2$S$_{1/2}^{\rm e}$ & 190.037$\pm$0.004 & 190.10 & \\ 
2-29 & 5.6 10$^{-2}$ & 0.10 & 1.12 & 1.2 10$^{11}$ &  -                &  E1  & $^2$P$_{1/2}^{\rm o}$-$^2$P$_{1/2}^{\rm e}$ & 180.441$\pm$0.017 & 180.37 & \\ 
2-31 & 4.1 10$^{-2}$ & 0.26 & 3.18 & 1.7 10$^{11}$ &  1.7 10$^{11}$  & E1  & $^2$P$_{1/2}^{\rm o}$-$^2$D$_{3/2}^{\rm e}$ & 175.263$\pm$0.006 & 175.33 & \\ 
1-4 & 3.2 10$^{-2}$ & 3.8 10$^{-2}$ & 2.9 10$^{-4}$ & 4.9 10$^{6}$ & -& E1  & $^2$P$_{3/2}^{\rm o}$-$^4$D$_{5/2}^{\rm e}$ & 257.259$\pm$0.033 & 257.28 & \\ 
1-17 & 2.6 10$^{-2}$ & 3.3 10$^{-2}$ & 2.7 10$^{-3}$ & 5.8 10$^{7}$ & Ni &         E1  & $^2$P$_{3/2}^{\rm o}$-$^4$P$_{5/2}^{\rm e}$ & 225.856$\pm$0.026 & 225.77 & \\ 
1-19 & 2.3 10$^{-2}$ & 3.2 10$^{-2}$ & 6.2 10$^{-3}$ & 1.3 10$^{8}$ & N &        E1  & $^2$P$_{3/2}^{\rm o}$-$^2$D$_{5/2}^{\rm e}$ & 226.998$\pm$0.026 & 227.02 & \\ 
1-29 & 1.8 10$^{-2}$ & 3.3 10$^{-2}$ & 0.33 & 3.6 10$^{10}$ &   - &       E1  & $^2$P$_{3/2}^{\rm o}$-$^2$P$_{1/2}^{\rm e}$ & 175.475$\pm$0.015 & 175.36 & \\ 
1-22 & 2.1 10$^{-2}$ & 2.9 10$^{-2}$ & 1.0 10$^{-3}$ & 2.3 10$^{7}$ & Ni & E1  & $^2$P$_{3/2}^{\rm o}$-$^2$F$_{5/2}^{\rm e}$ & 220.247$\pm$0.049 & 220.18 & \\ 
2-28 & 1.5 10$^{-2}$ & 1.1 10$^{-2}$ & 8.2 10$^{-2}$ & 4.1 10$^{9}$ & -& E1  & $^2$P$_{1/2}^{\rm o}$-$^2$P$_{3/2}^{\rm e}$ & 182.307$\pm$0.004 & 182.32 & \\ 
1-23 & 1.5 10$^{-2}$ & 2.2 10$^{-2}$ & 5.6 10$^{-3}$ & 1.5 10$^{8}$ & Ni & E1  & $^2$P$_{3/2}^{\rm o}$-$^2$F$_{5/2}^{\rm e}$ & 207.449$\pm$0.022 & 207.41 & \\ 
1-18 & 1.6 10$^{-2}$ & 7.0 10$^{-3}$ & - & 27.                      & N &   M2  & $^2$P$_{3/2}^{\rm o}$-$^2$F$_{7/2}^{\rm e}$ & 226.840$\pm$0.003 & 226.76 & \\ 
1-11 & 1.6 10$^{-2}$ & 2.3 10$^{-2}$ & 2.0 10$^{-3}$ & 4.1 10$^{7}$ & 2.2 10$^{7}$ & E1 & $^2$P$_{3/2}^{\rm o}$-$^4$F$_{5/2}^{\rm e}$ & 234.315$\pm$0.027 & 234.32 & \\ 
1-15 & 1.2 10$^{-2}$ & 1.3 10$^{-2}$ & 7.3 10$^{-3}$ & 2.3 10$^{8}$ & -&   E1  & $^2$P$_{3/2}^{\rm o}$-$^2$D$_{3/2}^{\rm e}$ & 230.872$\pm$0.053 & 230.87 & \\ 
1-13 & 1.2 10$^{-2}$ & 1.5 10$^{-2}$ & 1.2 10$^{-2}$ & 3.6 10$^{8}$ & N &  E1  & $^2$P$_{3/2}^{\rm o}$-$^2$P$_{3/2}^{\rm e}$ & 234.370$\pm$0.055 & 234.37 & \\ 
1-6 & 1.3 10$^{-2}$ & 1.7 10$^{-2}$ & 2.5 10$^{-4}$ & 6.4 10$^{6}$ & - &   E1  & $^2$P$_{3/2}^{\rm o}$-$^4$D$_{3/2}^{\rm e}$ & 256.398$\pm$0.033 & 256.51 & \\ 
2-9 & 1.2 10$^{-2}$ & 1.1 10$^{-2}$ & 4.2 10$^{-3}$ & 2.3 10$^{8}$ & N &  E1  & $^2$P$_{1/2}^{\rm o}$-$^2$P$_{1/2}^{\rm e}$ & 248.279$\pm$0.062 & 248.37 & \\ 
%\hline 
% 300-900 \AA 
\hline 
1-3 & 8.3 10$^{-2}$ & 7.2 10$^{-2}$ & 0.12 & 3.3 10$^{9}$ &   3.9 10$^{9}$ & E1  & $^2$P$_{3/2}^{\rm o}$-$^2$S$_{1/2}^{\rm e}$ & 345.738$\pm$0.006 & 345.73 & \\ 
2-3 & 3.7 10$^{-2}$ & 3.2 10$^{-2}$ & 5.8 10$^{-2}$ & 1.5 10$^{9}$ & 1.7 10$^{9}$ & E1 & $^2$P$_{1/2}^{\rm o}$-$^2$S$_{1/2}^{\rm e}$ & 365.560$\pm$0.008 & 365.75 & \\ 
18-43 & 2.0 10$^{-2}$ & 1.5 10$^{-2}$ & 0.18 & 1.3 10$^{9}$        & N & E1  & $^2$F$_{7/2}^{\rm e}$-$^2$F$_{7/2}^{\rm o}$ & 337.235$\pm$0.040 & 337.44 & \\ 
21-43 & 7.8 10$^{-3}$ & 5.7 10$^{-3}$ & 7.7 10$^{-2}$ & 5.3 10$^{8}$ & N &  E1  & $^2$G$_{7/2}^{\rm e}$-$^2$F$_{7/2}^{\rm o}$ & 349.302$\pm$0.043 & 349.34 & \\ 
18-44 & 7.1 10$^{-3}$ & 5.1 10$^{-3}$ & 0.11 & 1.1 10$^{9}$ & N & E1  & $^2$F$_{7/2}^{\rm e}$-$^2$F$_{5/2}^{\rm o}$ & 322.885$\pm$0.110 & 323.06 & \\ 
9-45 & 4.1 10$^{-3}$ & 3.4 10$^{-3}$ & 0.10 & 1.9 10$^{9}$ & N & E1  & $^2$P$_{1/2}^{\rm e}$-$^2$D$_{3/2}^{\rm o}$ & 303.419$\pm$0.184 & 303.42 & \\ 
17-43 & 4.4 10$^{-3}$ & 3.3 10$^{-3}$ & 4.2 10$^{-2}$ & 3.0 10$^{8}$ & N & E1  & $^4$P$_{5/2}^{\rm e}$-$^2$F$_{7/2}^{\rm o}$ & 339.434$\pm$0.092 & 339.64 & \\ 
13-44 & 3.5 10$^{-3}$ & 2.6 10$^{-3}$ & 4.9 10$^{-2}$ & 5.7 10$^{8}$ & N &  E1  & $^2$P$_{3/2}^{\rm e}$-$^2$F$_{5/2}^{\rm o}$ & 308.765$\pm$0.191 & 308.77 & \\ 
22-44 & 3.7 10$^{-3}$ & 2.7 10$^{-3}$ & 6.1 10$^{-2}$ & 6.0 10$^{8}$ &N & E1  & $^2$F$_{5/2}^{\rm e}$-$^2$F$_{5/2}^{\rm o}$ & 337.256$\pm$0.228 & 337.40 & \\ 
15-47 & 3.0 10$^{-3}$ & 2.1 10$^{-3}$ & 8.3 10$^{-2}$ & 3.0 10$^{9}$ &N &  E1  & $^2$D$_{3/2}^{\rm e}$-$^2$P$_{1/2}^{\rm o}$ & 304.595$\pm$0.186 & 304.59 & \\ 
22-45 & 3.3 10$^{-3}$ & 2.8 10$^{-3}$ & 0.11 & 1.5 10$^{9}$ &N & E1  & $^2$F$_{5/2}^{\rm e}$-$^2$D$_{3/2}^{\rm o}$ & 340.140$\pm$0.232 & 340.29 & \\ 
5-35 & 3.0 10$^{-3}$ & 8.1 10$^{-3}$ & 0.43 & 2.7 10$^{9}$ & Ni &  E1  & $^4$D$_{7/2}^{\rm e}$-$^4$F$_{9/2}^{\rm o}$ & 329.945$\pm$0.087 & 330.72 & \\ 
\hline 
% 900-20000 \AA 
%\hline 
1-2 & 0.87 & 0.20 & - & 69.                     & 69. &  M1  & $^2$P$_{3/2}^{\rm o}$-$^2$P$_{1/2}^{\rm o}$ & 6376.3$\pm$0.4 & 6316.1 & \\ 
5-8 & 6.6 10$^{-2}$ & 6.9 10$^{-3}$ & - & 11.   & 12. &  M1  & $^4$D$_{7/2}^{\rm e}$-$^4$F$_{9/2}^{\rm e}$ & 3454.9$\pm$7.2 & 3440.2 & \\ 
5-18 & 1.5 10$^{-2}$ & 6.6 10$^{-3}$ & - & 26.  & -   &  M1  & $^4$D$_{7/2}^{\rm e}$-$^2$F$_{7/2}^{\rm e}$ & 1918.2$\pm$2.0 & 1916.8 & \\ 
8-20 & 2.2 10$^{-2}$ & 1.3 10$^{-2}$ & - & 58.  & 55. &  M1  & $^4$F$_{9/2}^{\rm e}$-$^2$G$_{9/2}^{\rm e}$ & 3021.0$\pm$1.4 & 3038.6 & \\ 
5-24 & 6.9 10$^{-3}$ & 5.4 10$^{-3}$ & - & 67.  & N   &  M1  & $^4$D$_{7/2}^{\rm e}$-$^2$F$_{7/2}^{\rm e}$ & 1028.0$\pm$0.6 & 1028.8 & \\ 
5-10 & 1.7 10$^{-2}$ & 2.5 10$^{-3}$ & - & 8.5  & N   &  M1  & $^4$D$_{7/2}^{\rm e}$-$^4$F$_{7/2}^{\rm e}$ & 2934.5$\pm$6.0 & 2933.9 & \\ 
8-24 & 7.8 10$^{-3}$ & 6.1 10$^{-3}$ & - & 76.  & 70. &  M1  & $^4$F$_{9/2}^{\rm e}$-$^2$F$_{7/2}^{\rm e}$ & 1463.5$\pm$0.4 & 1467.7 & \\ 
5-21 & 5.9 10$^{-3}$ & 3.4 10$^{-3}$ & - & 19.  & 20. &  M1  & $^4$D$_{7/2}^{\rm e}$-$^2$G$_{7/2}^{\rm e}$ & 1603.2$\pm$1.4 & 1605.9 & \\ 
4-21 & 2.9 10$^{-3}$ & 1.7 10$^{-3}$ & - & 9.2  & -   &  M1  & $^4$D$_{5/2}^{\rm e}$-$^2$G$_{7/2}^{\rm e}$ & 1603.3$\pm$1.4 & 1602.1 & \\ 
4-24 & 1.8 10$^{-3}$ & 1.4 10$^{-3}$ & - & 18.  & N   &  M1  & $^4$D$_{5/2}^{\rm e}$-$^2$F$_{7/2}^{\rm e}$ & 1028.1$\pm$0.6 & 1027.2 & \\ 
10-21 & 5.8 10$^{-3}$ & 3.3 10$^{-3}$ & - & 18. & 14. &  M1  & $^4$F$_{7/2}^{\rm e}$-$^2$G$_{7/2}^{\rm e}$ & 3533.8$\pm$3.1 & 3547.8 & \\ 
8-18 & 6.3 10$^{-3}$ & 2.7 10$^{-3}$ & - & 11.  & -   &  M1  & $^4$F$_{9/2}^{\rm e}$-$^2$F$_{7/2}^{\rm e}$ & 4312.8$\pm$2.8 & 4328.4 & \\ 
4-18 & 2.6 10$^{-3}$ & 1.1 10$^{-3}$ & - & 4.3  & -   &  M1  & $^4$D$_{5/2}^{\rm e}$-$^2$F$_{7/2}^{\rm e}$ & 1918.4$\pm$2.0 & 1911.4 & \\ 
5-20 & 1.9 10$^{-3}$ & 1.1 10$^{-3}$ & - & 5.0  & 4.  &  M1  & $^4$D$_{7/2}^{\rm e}$-$^2$G$_{9/2}^{\rm e}$ & 1611.7$\pm$1.4 & 1613.5 & \\ 
10-18 & 4.3 10$^{-3}$ & 1.8 10$^{-3}$ & - & 7.1 & -   &  M1  & $^4$F$_{7/2}^{\rm e}$-$^2$F$_{7/2}^{\rm e}$ & 5538.9$\pm$7.7 & 5528.7 & \\ 

%11-24 & 1.1 10$^{-3}$ & 8.6 10$^{-4}$ & - & 11. &          M1  & $^4$F$_{5/2}^{\rm e}$-$^2$F$_{7/2}^{\rm e}$ & 1689.0$\pm$1.7 & 1687.0 & \\ 
%11-18 & 3.7 10$^{-3}$ & 1.6 10$^{-3}$ & - & 6.1 &          M1  & $^4$F$_{5/2}^{\rm e}$-$^2$F$_{7/2}^{\rm e}$ & 7110.9$\pm$27.9 & 7020.1 & \\ 
%10-20 & 1.8 10$^{-3}$ & 1.0 10$^{-3}$ & - & 4.8 &          M1  & $^4$F$_{7/2}^{\rm e}$-$^2$G$_{9/2}^{\rm e}$ & 3575.4$\pm$3.2 & 3585.0 & \\ 
%8-21 & 1.3 10$^{-3}$ & 7.7 10$^{-4}$ & - & 4.3 &          M1  & $^4$F$_{9/2}^{\rm e}$-$^2$G$_{7/2}^{\rm e}$ & 2991.2$\pm$1.3 & 3011.9 & \\ 
%8-10 & 8.5 10$^{-3}$ & 1.3 10$^{-3}$ & - & 4.2 &          M1  & $^4$F$_{9/2}^{\rm e}$-$^4$F$_{7/2}^{\rm e}$ & 19481.8$\pm$114.5 & 19937.1 & \\ 
%4-10 & 1.1 10$^{-3}$ & 1.6 10$^{-4}$ & - & 0.54 &          M1  & $^4$D$_{5/2}^{\rm e}$-$^4$F$_{7/2}^{\rm e}$ & 2935.0$\pm$6.0 & 2921.3 & \\ 
%11-21 & 1.0 10$^{-3}$ & 5.9 10$^{-4}$ & - & 3.3 &          M1  & $^4$F$_{5/2}^{\rm e}$-$^2$G$_{7/2}^{\rm e}$ & 4114.0$\pm$9.3 & 4107.8 & \\ 
%18-21 & 1.8 10$^{-3}$ & 1.1 10$^{-3}$ & - & 5.9 &          M1  & $^2$F$_{7/2}^{\rm e}$-$^2$G$_{7/2}^{\rm e}$ & 9761.8$\pm$9.5 & 9901.9 & \\ 
%18-20 & 1.8 10$^{-3}$ & 1.0 10$^{-3}$ & - & 4.7 &          M1  & $^2$F$_{7/2}^{\rm e}$-$^2$G$_{9/2}^{\rm e}$ & 10085.7$\pm$10.2 & 10197.2 & \\ 

\noalign{\smallskip}
\hline
\end{tabular}
\end{center}
\normalsize
\label{tab:lines}
\end{table*}
%Table~\ref{tab:lines}


\end{document}

