###### Abstract

We describe the atomic database of the xstar spectral modeling code,
summarizing the systematic upgrades carried out in the past twenty years to
enable the modeling of K lines from chemical elements with atomic number
$Z\leq 30$ and recent extensions to handle high-density plasmas. Such plasma
environments are found, for instance, in the inner region of accretion disks
round compact objects (neutron stars and black holes), which emit rich
information about the system physical properties. Our intention is to offer a
reliable modeling tool to take advantage of the outstanding spectral
capabilities of the new generation of X-ray space telescopes (e.g., xrism and
athena) to be launched in the coming years. Data curatorial aspects are
discussed and an updated list of reference sources is compiled to improve the
database provenance metadata. Two xstar spin-offs—the ISMabs absorption model
and the uaDB database—are also described.

###### keywords:

xstar, atomic databases; atomic processes; line formation; X-rays; high-
density plasmas.

xx 1 5 Received: date; Accepted: date; Published: date The XSTAR Atomic
Database Claudio Mendoza 1,2, Manuel A. Bautista 1, Jérôme Deprince 3, Javier
A. García 4,
Efraín Gatuzz 5, Thomas W. Gorczyca 1, Timothy R. Kallman 6, Patrick Palmeri
3,
Pascal Quinet 3,7 and Michael C. Witthoeft 6,8 Claudio Mendoza, Manuel A.
Bautista, Jérôme Deprince, Javier A. García, Efraín Gatuzz, Thomas W. Gorczyca
Timothy R. Kallman, Patrick Palmeri, Pascal Quinet and Michael C. Witthoeft
Correspondence<EMAIL_ADDRESS>Tel.: +1-269-387-4935

##  1 Introduction

The xstar code computes the physical conditions and emission spectra of a
photoionized gas and has been widely used in astrophysics, most notably in
X-ray astronomy, for the past 20 years (Kallman and Bautista, 2001; Bautista
and Kallman, 2001). It assumes an ionizing radiation source surrounded by a
spherical gas shell that absorbs and transfers parts of this radiation to
finally emit a spectrum. From an input comprising the incident continuum,
shell thickness, elemental abundances, and gas density, the code computes the
ionization balance, level populations, and temperature to generate the gas
opacity and the emitted line and continuum fluxes. The computational model
determines simultaneously the gas state and radiation field at every point
from the source. To ensure convergence in local thermodynamic equilibrium
(LTE) conditions, it implements a detailed and consistent treatment of the
radiative (bound–bound, bound–free, and free–free) and collisional (electron-
impact excitation and ionization, electron–ion recombination, charge transfer
and three-body recombination) processes, which in turn depends on the accuracy
of the underlying database of atomic rate coefficients. Therefore, xstar is an
ideal platform to study data curation schemes for implementing and maintaining
application-based atomic databases.

Since 2001 we have been systematically computing for the xstar database the
atomic data required to model the K lines and edges in both cosmically
abundant and trace elements (Palmeri et al., 2002, 2003; Bautista et al.,
2003; Palmeri et al., 2003a, b; Bautista et al., 2004; Mendoza et al., 2004;
García et al., 2005; Juett et al., 2006; Palmeri et al., 2008a, b; Witthoeft
et al., 2009, 2011a, 2011b; Hasoglu et al., 2010; Palmeri et al., 2011;
Gorczyca et al., 2013; Hasoğlu et al., 2014; Palmeri et al., 2012, 2016;
Mendoza et al., 2017, 2018; Kallman et al., 2004; Palmeri et al., 2005;
Kallman et al., 2009; García et al., 2011; Gatuzz et al., 2013a, b, 2014,
2015, 2016, 2018, 2019, 2020; Deprince et al., 2018, 2019a, 2019b, 2020a,
2020b). These X-ray spectral features are prime candidates to devise
diagnostics to determine the plasma conditions and chemical abundances in a
wide variety of astronomical entities: interstellar, intergalactic, and intra-
cluster media; active galactic nuclei (AGN); X-ray binaries; supernova
remnants; stars; the Sun, and some solar planets and satellites. This long-
term collaboration has reached an important milestone, and the corresponding
upgrading of the xstar database with the new datasets has more than doubled
its volume, bringing to the fore a series of data curational problems we
discuss in this report. Our final goal is to groom xstar to take advantage of
the high spectral resolution (5 eV in the soft X-ray band $\sim 0.3{-}12$ keV)
and sensitivity of the microcalorimeter-based spectrometers in the joint
NASA/JAXA X-ray Imaging and Spectroscopy Mission (xrism) to be launched in
2022 and in the European Space Agency flagship Advanced Telescope for High-
ENergy Astrophysics (athena). As an example of the accuracy level we are
committed to, Figure 1 shows the xstar fit in the 6.50–6.60 keV region of the
spectrum of the Perseus Cluster taken by the hitomi space telescope before its
demise in 2016 (Hitomi Collaboration et al., 2016).

Figure 1: hitomi spectrum of the Perseus Cluster in the Fe xxv triplet
spectral region (6.50–6.60 keV) (Hitomi Collaboration et al., 2016) showing
the xstar fit (black line). With the higher resolution, the iconic He-like
triplet becomes a quartet and other Fe satellite lines begin to be detectable
(e.g., the bump at $\sim 6.51$ keV). Reproduced from the XSTAR home page.

We have recently introduced high-density ($n_{e}>10^{18}$ cm-3) effects in the
xstar database, which come into play in the reflection spectra of the inner
region of the accretion disks round compact objects (e.g., black-hole
candidates and neutron stars): continuum lowering (Deprince et al., 2018,
2019a, 2019b, 2020a, 2020b); dielectronic recombination (DR) suppression
(Nikolić et al., 2013, 2018); collisional ionization; three-body
recombination; and stimulated emission. Since the Fe abundance is a key
measure of line reprocessing in reflection models (García et al., 2016), we
are now in a good position to test if the neglect of such high-density effects
is responsible for the anomalously high abundances recurrently derived (García
et al., 2018). Regarding xstar database curation, the inclusion of high-
density effects presents serious difficulties that are now managed by pre-
processing the database at each density point. Since this pre-processing time
is generally long, a grid of pre-computed databases has been deployed that,
considering the data volumes involved, favors a cloud computing environment
for the xstar modeling of high-density plasmas.

Finally, the development of the xstar database has given rise to two spin-
offs: the ISMabs absorption model (Gatuzz et al., 2015) and the uaDB online
database. The former is the result of benchmarks of the theoretical
photoionization curves with observed K absorption in the interstellar medium
(ISM), which has led to the implementation of a reliable model of ISM K
absorption and to the matching of the theoretical K-line wavelengths with the
astronomically observed and laboratory measured values, the latter two not
always agreeing (e.g., O i (Kühn et al., 2020)). The uaDB database, on the
other hand, allows the public downloading of the xstar and other atomic rates
without having to intervene the code.

##  2 XSTAR Atomic Database

The xstar database comprises records of multilevel model ions (usually
referred to as ion targets) and data structures to derive the rates for the
atomic microprocesses that determine the ionization and excitation of the
plasma (Bautista and Kallman, 2001). The rate-type list is the following:

01.

Ground state ionization

03.

Bound–bound collision

04.

Bound–bound radiative

05.

Bound–free collision (level)

06.

Total recombination

07.

Bound–free radiative (level)

08.

Total recombination forcing normalization

09.

Two-photon decay

11.

Element data

12.

Ion data

13.

Level data

14.

Bound–bound radiative, superlevel – spectroscopic level

15.

Collisional ionization total rate

40.

Bound–bound collisional, superlevel – spectroscopic level

41.

Non-radiative Auger transition

42.

Inner-shell photoabsorption followed by autoionization.

For each ionic species $(Z;N)$ in the ranges $1\leq Z\leq 30$ and $1\leq N\leq
Z$, where $Z$ and $N$ are respectively the atomic and electron numbers, the
data for the target models and processes are contained in ASCII files labeled
$\mathtt{d}ion\mathtt{t}0dt$. The ion index $ion$ is defined as

$ion=Z(Z-1)/2+(Z-N)+1\ ,$ (1)

and $dt$ is the data type (see Appendix A for a complete list). Each
$\mathtt{d}ion\mathtt{t}0dt$ file contains integer, floating-point, and
character variables. For each release, the database is transcribed to a binary
FITS-format Greisen (2003); Pence et al. (2010) derived structure consisting
of three one-dimensional arrays (floating point, integer, and character) and a
pointer array, which are uploaded in main memory at runtime. This scheme
ensures portability, fast data uploading when the code is invoked, and single
data accesses in main memory during processing.

The xstar data curation strategy essentially follows two principles:

  1. 1.

Since the datasets are compiled from diverse sources, the original data
structures and units are kept in the database records to be transcribed and
unified at runtime. For instance, level energies are specified in eV but the
photoionization cross sections are usually tabulated in Rydbergs. Levels in
some atomic models are listed in intermediate coupling (fine structure) while
in other $LS$ terms are adopted. These format differences are accounted for by
defining data types, each of which adheres to its own rules for data
tabulation.

  2. 2.

As new data and processes are included in the database, new data types may be
defined. Thus, a photoionization cross sections can be specified in more than
one data type—valence shell and K shell, say—if the tabulation for each energy
region comes from different sources. They are then concatenated and adjusted
at runtime.

      6 13 0 4 6  8 0.0000000E+00  1.0000000E+00 ...  3 1 0 30  1 454 3s2.1S_0 %
      6 13 0 4 6 12 3.6651995E+01  1.0000000E+00 ...  3 3 1 30  2 454 3s1.3p1.3P_0 %
      6 13 0 4 6 12 3.8015000E+01  3.0000000E+00 ...  3 3 1 30  3 454 3s1.3p1.3P_1 %
      6 13 0 4 6 12 4.1638999E+01  5.0000000E+00 ...  3 3 1 30  4 454 3s1.3p1.3P_2 %
      6 13 0 4 6 12 5.6705005E+01  3.0000000E+00 ...  3 1 1 30  5 454 3s1.3p1.1P_1 %
      6 13 0 4 6 12 8.8177000E+01  1.0000000E+00 ...  3 3 1 30  6 454 3s0.3p2.3P_0 %
      6 13 0 4 6 12 8.9971999E+01  3.0000000E+00 ...  3 3 1 30  7 454 3s0.3p2.3P_1 %
      6 13 0 4 6 12 9.0909009E+01  5.0000000E+00 ...  3 3 1 30  8 454 3s0.3p2.3P_2 %
      6 13 0 4 6 12 9.5230001E+01  5.0000000E+00 ...  3 1 2 30  9 454 3s0.3p2.1D_2 %
      6 13 0 4 6 12 1.0956001E+02  1.0000000E+00 ...  3 1 0 30 10 454 3s0.3p2.1S_0 %
      6 13 0 4 6 16 1.0583000E+03  3.0000000E+00 ...  3 3 0 30 11 454 2p5.3s2.3p1.3S_1 %
      6 13 0 4 6 16 1.0607000E+03  5.0000000E+00 ...  3 3 2 30 12 454 2p5.3s2.3p1.3D_2 %
      6 13 0 4 6 16 1.0645000E+03  7.0000000E+00 ...  3 3 2 30 13 454 2p5.3s2.3p1.3D_3 %
      6 13 0 4 6 16 1.0654000E+03  3.0000000E+00 ...  3 1 1 30 14 454 2p5.3s2.3p1.1P_1 %
      6 13 0 4 6 16 1.0674000E+03  5.0000000E+00 ...  3 3 1 30 15 454 2p5.3s2.3p1.3P_2 %
      6 13 0 4 6 16 1.0766000E+03  1.0000000E+00 ...  3 3 1 30 16 454 2p5.3s2.3p1.3P_0 %
      6 13 0 4 6 16 1.0843000E+03  3.0000000E+00 ...  3 3 2 30 17 454 2p5.3s2.3p1.3D_1 %
      6 13 0 4 6 16 1.0895000E+03  3.0000000E+00 ...  3 3 1 30 18 454 2p5.3s2.3p1.3P_1 %
      6 13 0 4 6 16 1.0901000E+03  5.0000000E+00 ...  3 1 2 30 19 454 2p5.3s2.3p1.1D_2 %
      6 13 0 4 6 16 1.1029000E+03  1.0000000E+00 ...  3 1 0 30 20 454 2p5.3s2.3p1.1S_0 %
      6 13 0 4 6 20 1.2384461E+03  1.0000000E+00 ...  3 3 1 30 21 454 2s1.2p6.3s2.3p1.3P_0 %
      6 13 0 4 6 20 1.2391314E+03  3.0000000E+00 ...  3 3 1 30 22 454 2s1.2p6.3s2.3p1.3P_1 %
      6 13 0 4 6 20 1.2434606E+03  5.0000000E+00 ...  3 3 1 30 23 454 2s1.2p6.3s2.3p1.3P_2 %
      6 13 0 4 6 20 1.2457835E+03  3.0000000E+00 ...  3 1 1 30 24 454 2s1.2p6.3s2.3p1.1P_1 %
      6 13 0 4 6 24 9.7285003E+03  1.0000000E+00 ...  3 3 1 30 25 454 1s1.2s2.2p6.3s2.3p1.3P_0 %
      6 13 0 4 6 24 9.7293003E+03  3.0000000E+00 ...  3 3 1 30 26 454 1s1.2s2.2p6.3s2.3p1.3P_1 %
      6 13 0 4 6 24 9.7340004E+03  5.0000000E+00 ...  3 3 1 30 27 454 1s1.2s2.2p6.3s2.3p1.3P_2 %
      6 13 0 4 6 24 9.7373003E+03  3.0000000E+00 ...  3 1 1 30 28 454 1s1.2s2.2p6.3s2.3p1.1P_1 %
      6 13 0 4 6 10 6.6340128E+02  2.0000000E+00 ... 12 1 0 30 29 454 superlevel %
      6 13 0 4 6 14 1.0768748E+04  1.0000000E+00 ...  1 0 0 30 30 454 superlevel_[K] %
      6 13 0 4 6  9 6.9751000E+02  2.0000000E+00 ...  3 2 0 30 31 454 continuum %

Figure 2: Content of file $\mathtt{d}454\mathtt{t}006$ of the xstar database
listing the atomic model (data type $dt=06$ and rate type $rt=13$) for Mg-like
Zn xix ($ion=454$).

We show in Figure 2 the target model for Mg-like Zn xix complying with data
type $dt=06$ and contained in file $\mathtt{d}454\mathtt{t}006$. Each row is
headed by the integer tuple
$(dt,rt,0,N_{\mathrm{flt}},N_{\mathrm{int}},N_{\mathrm{chr}})$, where $dt$ is
the data type, $rt$ the rate type, $N_{\mathrm{flt}}$ the number of floating-
point parameters, $N_{\mathrm{int}}$ number of integer parameters, and
$N_{\mathrm{chr}}$ the length of the character string. As shown in the rate-
type list above, $rt=13$ identifies level data. The first and second floating-
point columns tabulate level energies (eV) and statistical weights $g=2J+1$
(the other two floating-point columns have been edited out). The second
integer tuple $(n,2S+1,L,Z,i,ion)$ lists: the $n$ principal quantum number of
the valence electron; the $2S+1$ spin multiplicity; the $L$ total orbital
angular momentum; the $Z$ element atomic number; the $i$ level index, and the
$ion$ identifier. The character string gives the level assignment
(configuration and spectroscopic term), the end of the record being indicated
with the $\%$ character. Records may span one arbitrary length line or
multiple lines in the ASCII file.

This ion representation presents some remarkable features. By looking at the
level $i$ index and assignment, the Zn xix model contains data attributes for
31 levels from the valence shell ($1\leq i\leq 10$), open L shell ($11\leq
i\leq 24$), and open K shell ($25\leq i\leq 28$), two superlevels
($i=29{-}30$), and a continuum level ($i=31$). The latter is associated to the
ionization potential of the ion. Therefore, the model comprises spectroscopic
bound levels, quasi-bound L- and K-vacancy resonances, and artificial levels.
The tabulation must identify the ground level with index 1 and the continuum
level with the highest index. Apart from this constraint, the levels are not
necessarily listed in energy order facilitating model upgrading, which simply
involves adding new levels at the end of the existing tabulation. The level-
assignment string has been carefully devised and used throughout to facilitate
searches based on filled shells, shell holes, $LS$ terms, and $J$ total
angular momenta.

All other data types follow similar data structures (floating point, integer,
and character) as those displayed in Figure 2. For instance, we show in Figure
3 an excerpt of file $\mathtt{d}454\mathtt{t}050$ containing radiative data
for the bound–bound transitions (upper level $k\leq 10$) in Zn xix. As before,
the first integer tuple prescribes the data and rate types $dt=050$ and
$rt=04$; three floating-point items; four integer items; and no character
strings. The floating-point tuple $(\lambda,gf(i,k),A(k,i))$ lists the
transition wavelength (Å), oscillator strength ($gf$-value), and transition
probability ($A$-value, s-1). The second integer tuple $(i,k,Z,ion)$ lists the
lower and upper levels of the transition, atomic number, and ion identifier.
By comparing the $i$ and $k$ transition indexes with the $i$ level indexes in
Figure 2, it may be seen that the tabulation includes both allowed and
forbidden transitions; e.g., the resonance transition $(i,k)=(1,5)$ and the
forbidden transition $(i,k)=(1,4)$. Importantly, every excited level in the
database must include a decay mechanism, radiative and/or collisional,
otherwise its population may grow out of bounds when modeling. The
$\mathrm{3s1.3p1.3P\\_0}$ metastable level ($i=2$) does not display a
radiative transition ($j=0\rightarrow 0$ radiative transitions are strictly
forbidden), and consequently, an alternative decay process must be provided in
a separate data type; e.g., electron-impact collisional de-excitation.

               50 4 0 3 4 0   3.2047230E+02  5.2260000E-03  1.1310000E+08 1  3 30 454  %
               50 4 0 3 4 0   2.0629320E+02  7.0930000E-01  3.7060000E+10 1  5 30 454  %
               50 4 0 3 4 0   2.4417010E+02  2.5340000E-01  2.8350000E+10 3  6 30 454  %
               50 4 0 3 4 0   4.2222080E+02  4.7650000E-03  1.7830000E+08 5  6 30 454  %
               50 4 0 3 4 0   2.2582420E+02  2.7330000E-01  1.1910000E+10 2  7 30 454  %
               50 4 0 3 4 0   2.3171380E+02  1.9730000E-01  8.1690000E+09 3  7 30 454  %
               50 4 0 3 4 0   2.4845700E+02  3.1050000E-01  1.1180000E+10 4  7 30 454  %
               50 4 0 3 4 0   3.8631020E+02  1.4800000E-03  2.2060000E+07 5  7 30 454  %
               50 4 0 3 4 0   2.2265070E+02  3.4070000E-01  9.1680000E+09 3  8 30 454  %
               50 4 0 3 4 0   2.3806620E+02  7.8830000E-01  1.8560000E+10 4  8 30 454  %
               50 4 0 3 4 0   3.6175990E+02  1.2440000E-01  1.2680000E+09 5  8 30 454  %
               50 4 0 3 4 0   2.0084360E+02  2.0630000E-02  6.8230000E+08 3  9 30 454  %
               50 4 0 3 4 0   2.1330280E+02  2.0500000E-01  6.0100000E+09 4  9 30 454  %
               50 4 0 3 4 0   3.0751030E+02  8.4760000E-01  1.1960000E+10 5  9 30 454  %
               50 4 0 3 4 0   1.7136220E+02  2.6040000E-03  5.9150000E+08 3 10 30 454  %
               50 4 0 3 4 0   2.4339670E+02  3.8770000E-01  4.3650000E+10 5 10 30 454  %
               50 4 0 3 4 0   2.9315000E+02  0.0000000E+00  9.5940000E+00 1  4 30 454  %

Figure 3: Excerpt of file $\mathtt{d}454\mathtt{t}050$ of the xstar database
listing the radiative transitions with upper level $k\leq 10$ (data type
$dt=50$ and rate type $rt=4$) for Mg-like Zn xix ($ion=454$).

Data type $dt=86$, listing the radiative and Auger widths for K-vacancy
levels, is also an interesting case as it involves transitions between
different ion-charge states (see Figure 4). The floating-point tuple
$(E(k_{N}),A_{a}(k_{N}),A_{a}(k_{N},i_{N-1}),A_{r}(k_{N}))$ lists: the energy
$E(k_{N})$ (relative to the ionization threshold) and total Auger width
$A_{a}(k_{N})$ of the $k_{N}$ level of the $N$-electron atom ($ion_{N}=454$);
the partial Auger width $A_{a}(k_{N},i_{N-1})$ leaving the ($N-1$)-electron
ion ($ion_{N-1}=455$) in the $i_{N-1}$ level; and the total radiative width
$A_{r}(k_{N})$ of the $N$-electron ion. The second integer tuple then
specifies $(i_{N-1},k_{N},Z,ion_{N-1},ion_{N})$. In this example the
$(N-1)$-electron ion is assumed to end up in its ground state ($i_{N-1}=1$)
after the Auger transition; however, this is not always the case as the Auger
transition may involve an excited end level of the $(N-1)$-electron ion. Such
partial Auger widths are not determined in some structure methods (e.g., hfr
(Cowan, 1981)) and in the $R$-matrix method (Berrington et al., 1995; Burke,
2011) that includes radiative and Auger damping through an optical model
potential (Gorczyca and Robicheaux, 1999).

     86 4 0 4 5 0   9.0309903E+03  1.1100000E+15  1.1100000E+15  1.1600000E+15 1 25 30 455 454 %
     86 4 0 4 5 0   9.0317903E+03  1.1000000E+15  1.1000000E+15  1.1800000E+15 1 26 30 455 454 %
     86 4 0 4 5 0   9.0364904E+03  1.1000000E+15  1.1000000E+15  1.1600000E+15 1 27 30 455 454 %
     86 4 0 4 5 0   9.0397903E+03  1.0800000E+15  1.0800000E+15  1.2900000E+15 1 28 30 455 454 %

Figure 4: Content of file $\mathtt{d}454\mathtt{t}086$ of the xstar database
listing the radiative and Auger widths (data type $dt=86$ and rate type
$rt=4$) for Mg-like Zn xix ($ion=454$).

Table 2 in Appendix B tabulates the number of levels for each ionic species
$(Z;N)$. It may be seen that most neutral and, in many cases, the singly
ionized systems are not well represented, indicating that xstar is mainly
destined to model photoionized plasmas for which such species have negligible
fractions. The number of levels in the ion models is never above 1000 to
enable practical runtimes when modeling, and the most relevant elements in the
astronomical soft X-ray band—N, O, Ne, Fe, and Ne—are singularly well treated.

As fully described in the original paper on the xstar database (Bautista and
Kallman, 2001), atomic datasets have been collected from a myriad of
individual sources and data compilations such as the NIST Atomic Spectra
Database (Kramida et al., 2020), TOPbase (Cunto et al., 1993), chianti (Dere
et al., 1997), ADAS, Iron Project (Hummer et al., 1993), and PP95 (Pradhan and
Peng, 1995). Major upgrades have been mainly concerned with the radiative and
dielectronic recombination data from the tabulations in AMDPP (Badnell et al.,
2003; Badnell, 2006) and from the systematic computations of atomic data for
K-line diagnostics summarized in Section 3. A complete data-provenance list is
given in Appendix C.

##  3 Computation of Atomic Data for K-line Diagnostics

Since xstar is widely used for spectral modeling in X-ray astrophysics, we
have dedicated a great effort to compute the atomic data to characterize K
lines in ionic species with $Z\leq 30$; namely, valence and K-vacancy level
energies, transition wavelengths, $A$-values, radiative and Auger widths, and
photoionization cross sections (Bautista et al., 2003; Palmeri et al., 2003a,
b; Bautista et al., 2004; Mendoza et al., 2004; García et al., 2005; Juett et
al., 2006; Palmeri et al., 2008a, b; Witthoeft et al., 2009, 2011a, 2011b;
Hasoglu et al., 2010; Palmeri et al., 2011, 2012; Gorczyca et al., 2013;
Hasoğlu et al., 2014; Palmeri et al., 2016; Mendoza et al., 2017, 2018). Due
to the lack of spectroscopic data to validate most ionic models, a multi-code
methodology was implemented right from the outset to compute the data and
estimate their accuracy. Structure data were computed with the
multiconfiguration codes hfr (Pauli Hamiltonian) (Cowan, 1981), autostructure
(Breit–Pauli Hamiltonian) (Eissner et al., 1974; Badnell, 2011), and grasp92
(Dirac–Coulomb–Breit Hamiltonian) (Parpia et al., 1996) and the
photoionization cross sections with the Breit–Pauli $R$-matrix suite of codes
(Berrington et al., 1995; Burke, 2011) and autostructure. Due to large target
models, the latter code was used to compute the photoionization cross sections
in the distorted-wave approximation for species in isoelectronic sequences
with electron number $19\leq N\leq 26$. Initial priority was given to ions
from the oxygen, nitrogen, and iron isonuclear sequences and then from
even-$Z$ elements, but those from odd-$Z$ and trace elements have been
recently completed.

In the calculations of accurate atomic data for K-line diagnostics, two key
effects must be considered in detail: radiative and Auger damping and orbital
relaxation. In Sections 3.1–3.2 we briefly go over these two processes and the
methods to include them in structure and scattering calculations.

Figure 5: Photoabsorption cross section of the $\mathrm{1s^{2}2s^{2}2p^{6}\
{}^{1}S}$ ground state of Ne-like Fe xvii in the K-edge region. Top panel:
undamped cross section. Bottom panel: damped (radiation and Auger) cross
section.

###  3.1 Radiative and Auger Damping

Let us consider an ion, say, with electron number $N\leq 10$. When a photon
promotes a K-shell electron to an excited Rydberg state

$h\nu+\mathrm{1s}^{2}\mathrm{2s}^{\lambda}\mathrm{2p}^{\mu}\longrightarrow\mathrm{1s2s}^{\lambda}\mathrm{2p}^{\mu}n\mathrm{p}\
,$ (2)

it subsequently decays via the radiative and Auger manifold

$\displaystyle\mathrm{1s2s}^{\lambda}\mathrm{2p}^{\mu}n\mathrm{p}$
$\displaystyle\stackrel{{\scriptstyle{\rm K}n}}{{\longrightarrow}}$
$\displaystyle\mathrm{1s}^{2}\mathrm{2s}^{\lambda}\mathrm{2p}^{\mu}+h\nu_{n}$
(3) $\displaystyle\stackrel{{\scriptstyle{\rm K}\alpha}}{{\longrightarrow}}$
$\displaystyle\mathrm{1s}^{2}\mathrm{2s}^{\lambda}\mathrm{2p}^{\mu-1}n\mathrm{p}+h\nu_{\alpha}$
(4) $\displaystyle\stackrel{{\scriptstyle{\rm KL}n}}{{\longrightarrow}}$
$\displaystyle\begin{cases}\mathrm{1s}^{2}\mathrm{2s}^{\lambda}\mathrm{2p}^{\mu-1}+e^{-}\\\
\mathrm{1s}^{2}\mathrm{2s}^{\lambda-1}\mathrm{2p}^{\mu}+e^{-}\end{cases}$ (5)
$\displaystyle\stackrel{{\scriptstyle{\rm KLL}}}{{\longrightarrow}}$
$\displaystyle\begin{cases}\mathrm{1s}^{2}\mathrm{2s}^{\lambda}\mathrm{2p}^{\mu-2}n\mathrm{p}+e^{-}\\\
\mathrm{1s}^{2}\mathrm{2s}^{\lambda-1}\mathrm{2p}^{\mu-1}n\mathrm{p}+e^{-}\\\
\mathrm{1s}^{2}\mathrm{2p}^{\mu-2}n\mathrm{p}+e^{-}\end{cases}$ (6)

dominated by K$\alpha$ radiative decay (Eq. 4) and KLL Auger spectator-
electron ionization (Eq. 6). Such channeling causes a damping effect (see
Figure 5) since the $\mathrm{1s2s}^{\lambda}\mathrm{2p}^{\mu}n\mathrm{p}$
resonances have broad and symmetric widths almost independent of $n$, which
must be taken into account when devising plasma diagnostics. In the $R$-matrix
method it is computationally intractable to treat this channel array from
first principles as it would involve target states with $n$p orbitals in an
ever increasing close-coupling expansion. Therefore, for the higher Rydberg
resonances, damping is neatly accounted for via an additional imaginary
potential $V_{\mathrm{opt}}=-i(\Gamma_{r}+\Gamma_{a})/2$ involving the total
radiative width $\Gamma_{r}$—as developed in the Hickman–Robicheaux formalism
Hickman (1984); Robicheaux et al. (1995) (which is essentially equivalent to
the Davies–Seaton formalism Davies and Seaton (1969))—and adapted to include
the total Auger width $\Gamma_{a}$ (Gorczyca and Robicheaux, 1999).

Figure 6: K-edge photoabsorption (full curve) and photoionization (dotted
curve) cross sections of Ca xv (C-like) as a function of photon energy. The
dashed curve gives the photoabsorption cross section convolved with a Gaussian
of 0.001 width. Reproduced from Figure 3 of (Witthoeft et al., 2009) with
permission of the AAS.

Due to their diagnostic importance, K$\alpha$ lines in the xstar database are
treated as bound–bound transitions and assigned wavelengths and $A$-values,
but the upper K-vacancy states also display Auger widths that lead to
autoionization (see Figures 2–4). However, the K resonances also appear in the
photoabsorption cross sections as shown in Figure 5 smearing the edge due to
their peculiarly symmetric and constant line profiles. As a result, the
K$\alpha$ resonances must be trimmed out from the partial photoionization
cross sections that are used to derive the rates so as not to count them
twice. However, it is more complicated to carry out this trimming procedure in
the L-edge region due to the piling of a large number of resonances converging
to closely spaced thresholds; thus some degree of double-counting is
practically unavoidable making the L edge less useful to devise plasma
diagnostics.

As shown in Figure 6, damping leads to a significant difference between
photoabsorption and photoionization, and in the xstar code both are needed:
the former to determine opacities and the latter to derive the photoionization
rates. However, the database essentially stores partial photoionization cross
sections; i.e., cross sections leaving the photoionized $(N-1)$-electron
system in specific states, and consequently, the difference between the total
photoabsorption and photoionization cross sections is assigned to
superlevel$\\_$[K] (see level $i=30$ in Figure 2).

Due to the large number of target levels in ions with electron number $N>20$,
their photoionization cross sections were computed using the simpler
distorted-wave method implemented in autostructure (Witthoeft et al., 2011b).
The level numbers for such ionic systems tabulated in Table 2 (Appendix B)
underwent considerable trimming to comply with the modeling specifications of
xstar, and hence, do not represent the attributes of the actual collision
targets. In autostructure, photoabsorption is conveniently treated as the sum
of two separate processes: photoionization and photoexcitation. However, the
complicated decay routes of K-vacancy states delineated in Eqs. (3–6) must be
explicitly included in the photoexcitation process, and were thus computed in
$LS$ coupling. Since xstar requires fine-structure partial photoionization
cross sections to determine rates, we decided to obviate the phototexcitation
process in ions with $Z\neq 26$ and $21\leq N\leq 26$ thus underestimating
their opacities, although the radiative and Auger decays of the
L$\alpha,\beta$ and K$\alpha,\beta$ lines from these systems will be
respectively taken into account in data types 50 and 86 (see Figures 3–4).

###  3.2 Orbital Relaxation

As shown in (Froese Fischer, 1977; Cowan, 1981), the photoionization of an
inner-shell electron leads to a relaxation of the outer electrons of the
ionized state due to a reduced screening of the atomic nuclear potential by
the reduced inner electron cloud; i.e., an increased effective charge
$Z_{\mathrm{eff}}$. For example, in the inner-shell photoionization of O i
$\mathrm{1s^{2}2s^{2}2p^{4}}$ to O ii $\mathrm{1s2s^{2}2p^{4}}$, the effective
charge experienced by a 2p electron in the initial and final states is a
complicated average screening including the other equivalent 2p electrons.
Nevertheless, by using hydrogenic considerations it is found that the electron
orbital energy ($E_{n}\sim-E_{R}~{}Z_{\mathrm{eff}}^{2}/n^{2}$) is more
tightly bound for the relaxed 2p electron, and the electron density is
concentrated closer to the nucleus ($r_{n}\sim
a_{0}~{}n^{2}/Z_{\mathrm{eff}}$).

To illustrate this phenomenon, we show in Figure 7 the outer 2p orbital in
both neutral oxygen and its K-vacancy ionized daughter, obtained from single-
configuration Hartree–Fock calculations (Froese Fischer, 1991; Froese Fischer
et al., 1997). Clearly the relaxed 2p orbital of the ionized O ii inner-shell
state differs significantly from the neutral O i 2p orbital, a difference that
needs to be accounted for in order to compute more accurate atomic transition
properties.

Figure 7: Probability density of the Hartree–Fock 2p orbital in the initial O
i $\mathrm{1s^{2}2s^{2}2p^{4}}$ ground state compared to the 2p orbital in the
final O ii $\mathrm{1s2s^{2}2p^{4}}$ K-vacancy state. The latter 2p electrons
are screened from the nucleus by one fewer inner-shell 1s electron, and are
therefore “relaxed” to more tightly bound orbitals.

In our hfr and autostructure structure calculations, orbital relaxation was
taken into account by adopting different non-orthogonal orbital bases for each
configuration. In most photoionization calculations, however, an orthonormal
orbital basis is used because of the relative simplicity in computing
transition and energy matrix elements. Relaxation then requires a substantial
multi-configurational wave-function description including additional orbitals
to account for the significant differences between initial- and final-state
orbitals. Thus, additional care must be taken in computing inner-shell
photoionization cross sections when compared to outer-shell photoionization as
discussed more fully in (Gorczyca et al., 2013).

##  4 Photoabsorption Cross-Section Benchmarks

Table 3 in Appendix C lists the reference sources for the computations of the
photoabsorption cross sections. Measurement of K absorption in the laboratory
and ISM enables useful benchmarks of the theoretical cross sections to improve
spectral accuracy. In the following sections we give a summary of these
procedures.

###  4.1 Carbon Sequence

Calculations of the atomic data to model the K-shell photoabsorption by carbon
ions were performed by (Hasoglu et al., 2010), and a benchmark was obtained
using Chandra X-ray high-resolution spectra (Gatuzz et al., 2018). The C ii
K$\alpha$ triplet as well as the C iii K$\alpha$ and K$\beta$ lines were
identified in the X-ray spectra of four super-soft sources. However, C i was
not modeled due to the presence of instrumental features at $\sim 43.6$ Å.

###  4.2 Oxygen Sequence

K-shell photoabsorption cross-sections for O i – O vii were computed by
(García et al., 2005), and comparisons of the theoretical resonance positions
with astronomical observations and laboratory measurements were carried out by
(Gatuzz et al., 2013a, b). The latter found that, due to a suspect
experimental energy calibration scale, the X-ray astronomical observations
provided a more reliable reference to perform the benchmark of the atomic
data. For O i, the K-edge cross section was re-examined in detail by (Gorczyca
et al., 2013) to yield a substantially improved version for the xstar atomic
database.

In an exhaustive study (Gorczyca et al., 2013), the K$\alpha$ ($1s\rightarrow
2p$) resonance in O i was examined with $R$-matrix and mchf calculations,
existing laboratory spectroscopic data, and several X-ray observational
assessments as summarized in Table 1. While practical $R$-matrix calculations
for multi-electron systems are better tailored for computing scattering and
atomic transition rates, they are less reliable in predicting the energy
differences between atomic states as compared to limited bound-state structure
calculations. ($R$-matrix calculations necessarily include all quasi-bound and
continuum final states, limiting a practical improvement the basis
description.) The $R$-matrix K$\alpha$ energy (Gorczyca et al., 2013) was
found to be $\sim 0.3$ eV higher than the final assessed observational value
of 527.37 eV. More complex mchf calculations, which were focused only on the
initial $\mathrm{1s^{2}2s^{2}2p^{4}}$ state and the final
$\mathrm{1s2s^{2}2p^{5}}$ state, converged downward to a value of 527.49 eV in
good agreement with the observations. On the other hand, the experiments
performed at the Advanced Light Source (ALS) were reporting a value of 526.79
eV (Stolte et al., 1997), a discrepancy of almost $-0.6$ eV. Considering the
reliability of the observational calibration and the convergence trend of the
mchf calculations, the X-ray observation was unconventionally chosen instead
of the laboratory measurement as the final resonance position in the atomic
absorption model.

Table 1: Comparison of observed, measured, and computed O i K$\alpha$ and K$\beta$ line energies (eV). Method | Source | $E(\mathrm{1s-2p})$ | $E(\mathrm{1s-3p})$ | $\Delta E$
---|---|---|---|---
Astronomical observations |  XMM-Neuwton, Mkn 421 (Gorczyca et al., 2013) | 527.30(5) | 541.95(28) | 14.65(33)
|  Chandra, 7 sources (Gorczyca et al., 2013) | 527.44(9) | 541.72(18) | 14.28(21)
|  Chandra, shifted (Gorczyca et al., 2013) | 527.26(9) |  |
|  Chandra, 11 sources (Liao et al., 2013) | 527.39(2) |  |
|  Chandra, 6 sources (Juett et al., 2004) | 527.41(18) | 541.77(40) | 14.36(58)
Laboratory measurements |  HZB (Leutenegger et al., 2020) | 527.26(4) | 541.645(12) |
|  ALS (McLaughlin et al., 2013a, b) | 526.79(4) | 541.19(4) | 14.40(8)
|  ALS (Stolte et al., 1997) | 526.79(4) | 541.20(4) | 14.41(8)
|  WSRC (Menzel et al., 1996) | 527.85(10) | 541.27(15) | 13.41(25)
|  Auger spectroscopy (Caldwell et al., 1994) | 527.20(30) |  |
mchf converged result |  mchf (Gorczyca et al., 2013) | 527.49 |  |

A further consideration in assessing the reliability of the ALS measurements
was that the absolute energy calibration relied on earlier molecular
measurements with uncertainty estimates that seemed questionable. Since the O
i study by (Gorczyca et al., 2013), new laboratory measurements have been
performed using an electron beam ion trap (EBIT) (Leutenegger et al., 2020) to
determine the K$\alpha$ resonance position at 527.6 eV, in good agreement with
the observations and the converged mchf result. This new measurement suggests
a recalibration of the ALS reference spectrum.

###  4.3 Neon

For neon the xstar atomic database includes the photoabsorption cross sections
by (Juett et al., 2006). A benchmark for Ne ii and Ne III was performed with
Chandra and XMM-Newton observations of the bright low-mass X-ray binaries
(LMXBs) Cygnus X–2 and XTE J1817-330 (Gatuzz et al., 2015). Column densities
were obtained for the cold (Ne i), warm (Ne ii, Ne iii), and hot (Ne vii, Ne
ix, Ne x) components of the ISM.

###  4.4 Magnesium

New photabsorption cross sections for Mg species were computed by (Hasoğlu et
al., 2014). X-ray XMM-Newton spectra of the LMXB GS 1826-238 were used to
perform a benchmark of the data. The resulting ionization fractions indicate
that Mg is predominantly ionized rather than in neutral form as also shown by
UV observations.

###  4.5 Silicon

High-resolution Chandra spectra in the Si K-edge region (6$-$7 Å) from 16
LMXBs were analyzed by (Gatuzz et al., 2020). The Si model included the Si i
photoabsorption cross sections computed by Gorczyca et al. (2020, in
preparation), while those for the ionized species were taken from (Witthoeft
et al., 2009). The absorption features identified in the spectra agreed with
the theoretical atomic data, even though the individual resonances of the
K$\alpha$ triplet could not be resolved. Although a model without dust
component was used, good data fits were obtained highlighting the need for
accurate modeling of the gaseous component before attempting to address the
solid component (Gatuzz et al., 2020).

##  5 High-Density Effects on Atomic Parameters

xstar needs to address spectra from high-density sources such as the X-ray
reflection from the inner region of the accretion disks round compact objects
($T_{e}\sim 10^{5}{-}10^{7}$ K and $n_{e}\sim 10^{18}{-}10^{22}$ cm-3) (García
et al., 2018; Fabian and Ross, 2010). This requires taking into account a
series of atomic processes usually neglected in plasma photoionization models,
which have been fully discussed by (Kallman et al., 2020) and recently
implemented in the code. We discuss in Sections 5.1–5.2 two of these
processes: continuum lowering and dielectronic recombination (DR) suppression,
since they implied definite modifications of the database design and
implementation.

###  5.1 Continuum Lowering

The density effects on the atomic thresholds (ionization potential and K
edge), K$\alpha$ wavelengths and $A$-values, and Auger rates of oxygen and
iron ions have been studied by (Deprince et al., 2018, 2019a, 2019b, 2020a).
The atom is assumed to be embedded in a weakly coupled plasma represented in
the mcdf method with a time-independent Debye–Hückel screened Dirac–Coulomb
Hamiltonian

$H^{DH}_{DC}=\sum_{i}c\vec{\alpha_{i}}\cdot\vec{p_{i}}+\beta_{i}c^{2}-\frac{Z}{r_{i}}e^{-\mu
r_{i}}+\sum_{i>j}\frac{1}{r_{ij}}e^{-\mu r_{ij}}\ ,$ (7)

where $r_{ij}=|\vec{r}_{i}-\vec{r}_{j}|$ and the plasma screening parameter
$\mu$ (inverse of the Debye shielding length $\lambda_{D}$) is given in atomic
units by

$\mu=\frac{1}{\lambda_{D}}=\sqrt{\frac{4\pi n_{e}}{kT_{e}}}\ .$ (8)

The density effects mainly cause a threshold lowering that increases with
$\mu$ (see Figure 8), which for the ionization potential in eV can be
approximated by the universal formula (Deprince et al., 2020)

$\Delta E_{0}=(-26.30\pm 0.08)\mu Z_{\mathrm{eff}}\ .$ (9)

In xstar, continuum lowering leads to density-dependent targets with reduced
numbers of levels, which must be derived at each density point causing a
severe overhead at runtime. This bottleneck can be mitigated by pre-computing
a $\mu$-grid of atomic databases but at the price of increasing the database
volume significantly ($\sim 10$ GB), thus hampering the familiar package
downloading procedure. Consequently, deployment strategies are being
considered in terms of cloud virtual machines.

Figure 8: Ionization potential lowering in Fe ix – Fe xxv as a function of
effective charge $Z_{\mathrm{eff}}=Z-N+1$ obtained with the mcdf method using
a Debye–Hückel screening potential. Red circles: $\mu=0.1$. Black circles:
$\mu=0.25$. Triangles: Debye–Hückel limit $\Delta
E_{0}^{\mathrm{DH}}=-27.2116\,\mu Z_{\mathrm{eff}}$. Reproduced from Figure 1
of (Deprince et al., 2020a) with permission from Astronomy & Astrophysics,
$\copyright$ESO.

###  5.2 DR Suppression

Rigorous collisional–radiative plasma modeling shows that DR is suppressed at
high densities (Badnell et al., 1993). To characterize DR plasma effects, we
have compared the heating and cooling rates in the ionization-
parameter–temperature plane

$-3\leq\log(\xi)\leq 3~{}\mathrm{erg\,cm\,s}^{-1}\quad\mathrm{and}\quad
3.5\leq\log(T)\leq 7.5~{}\mathrm{K}$ (10)

for xstar models with and without metal DR. We assume a power-law spectrum,
density $n_{e}=10^{10}$ cm-3, and luminosity $L=10^{32}$ erg s-1 (see Figure
9). The larger temperature differences occur in the interval
$1\leq\log(\xi)\leq 3$, where $T$ is lower by as much as 40% when DR is
excluded, and are caused by increases of the Fe average charge at
$\log(\xi)\approx 1.3$ and $\log(\xi)\approx 2.5$. As shown in Figure 9 (right
panel), the DR/noDR heating-rate ratio reaches a maximum at
$(\log(\xi),\log(T))\approx(1,6.3)$, where the dominant species with and
without DR are Fe xiii and Fe xvii, respectively. On the other hand, the
cooling-rate ratio reaches a maximum at $(\log(\xi),\log(T))\approx(-1,5.4)$
caused by a higher oxygen average charge when DR is excluded.

Figure 9: Cooling- and heating-rate ratios with and without DR obtained from
an xstar model with solar abundances, a power-law spectrum, density
$n_{e}=10^{10}$ cm-3, and luminosity $L=10^{32}$ erg s-1. Black dotted curve:
thermal temperature with DR. Red dotted curve: thermal temperature without DR.

Concerning the Fe anomalous overabundance derived from the reflection spectra
of accretion disks (García et al., 2018), we have computed the X-ray spectra
reflected from an optically thick atmosphere using the code xillver (García
and Kallman, 2010; García et al., 2013). The atmosphere is assumed to have
plane-parallel geometry and a constant gas density of $\log(n_{e})=18$ cm-3.
The ionization parameter is set to $\xi=4\pi\,F_{x}/n_{e}=32$ erg cm s-1
implying an illuminating flux of $F_{x}=3\times 10^{18}$ erg cm-2 s-1. The
ionization balance is calculated self-consistently using the routines and
atomic data from xstar setting all elemental abundances to their solar values.
It is found that metal DR suppression leads to significant changes in the
ionization state of the gas resulting in more ionized species. As shown in
Figure 10, there is a strong enhancement of the Fe xvii L lines and Fe xviii K
lines.

Figure 10: Reflected X-ray spectrum from an optically thick atmosphere modeled
using xillver with and without DR. A plane-parallel atmosphere with solar
abundances and density $\log(n_{e})=18$ cm-3 was assumed.

It is worth mentioning that continuum lowering is not taken into account in
this xillver test calculation since it is expected to have a noticeable impact
only at densities $n_{e}>10^{19}$ cm-3; the calculation was performed at
$n_{e}>10^{18}$ cm-3 to show that DR effects become conspicuous at lower
densities. Further characterization of high-density effects are reported in
(Kallman et al., 2020).

Density effects on DR and on the high-$n$ levels through continuum lowering
are taken into account in the xstar database via the rates into one or two
fictitious superlevels for each ion. The recombination rate onto the
superlevel is tabulated on a density–temperature grid and stored in data types
70 and 99 (see Appendix A). For the former, rates are tabulated on a log scale
while for the latter they are tabulated directly. The total recombination rate
onto the ion is the sum of the rate onto the superlevels plus the rates onto
the other levels that are treated explicitly; these are called the
“spectroscopic levels.” The recombination rates onto the superlevels are
chosen such that, when they are used to calculate a recombination rate and all
the rates are summed, the total recombination rate for the superlevel(s) plus
the spectroscopic levels adds to the total rate taken from one of the AMDPP
compilations (Badnell et al., 2003) where available or from (Aldrovandi and
Pequignot, 1973) otherwise. We apply density-dependent suppression factors to
the recombination rates onto the superlevel to take into account density
effects on radiative and dielectronic recombination. They are derived from a
general formula that depends on the isoelectronic sequence, charge, density,
and temperature (Nikolić et al., 2013, 2018).

The superlevels decay directly to the ground level without the emission of any
observable cascade radiation for ions with three or more electrons. The
exception is the decay of members of the H and He isoelectronic sequences for
which we use explicitly calculated cascade matrix calculations to treat the
decay of the superlevels to the spectroscopic levels (Bautista and Pradhan,
1998; Bautista, 2000). The superlevels are chosen to have energies close to
the continuum. We include both radiative and collisional transitions to the
ground level (and other levels in the case of H- and He-like ions).

##  6 Database Curation

The recent inclusion in the xstar database of atomic parameters for odd-$Z$
elements and trace elements with $Z=(21{-}25,27,29,30)$ (Palmeri et al., 2012,
2016; Mendoza et al., 2017, 2018) practically doubled the database volume when
compared with previous versions that used hydrogenic scaling for these
elements, bringing to the fore a series of curatorial problems. The database
upgrade was thus lengthy and demanding in detail. In Sections 6.1–6.4 we give
a brief account of some the issues encountered and steps taken to solve them.

###  6.1 Atomic Models

As shown in Table 9 of (Palmeri et al., 2012), the target models for ions with
atomic numbers $Z=(21{-}25,27,29,30)$ and electron number $19\leq N\leq Z-2$
include levels from the valence configurations
$\mu=\mathrm{3d}^{x}\mathrm{4s}^{y}$ and the L- and K-vacancy configurations
$\mathrm{3p}^{-1}\mu^{+1}$, $\mathrm{2p}^{-1}\mu^{+1}$, and
$\mathrm{1s}^{-1}\mu^{+1}$. The total number of target levels in each of these
species is larger than 500 and in some cases (e.g., $N=23$) close to 2000. It
was found that to model astrophysical plasmas in xstar with such large atomic
representations was impractical and with little tangible gains. We thus
excluded the levels belonging to $\mu$ configurations containing 4s orbitals;
specifically, $y=0$ in $\mu$ for $N>19$. This decision led to a reduction of
the number of target levels to a few hundreds and implied extensive level
renumbering for these sequences.

###  6.2 Metastable Levels

As discussed in Section 2, the xstar atomic models display occasional low-
lying metastable levels (e.g., the $\mathrm{3s1.3p1.3P\\_0}$ level in Mg-like
ions) with no radiative decay transitions. For such levels, alternative decay
mechanisms such as collisional de-excitation must be specified. However, for
ions with electron number $N>19$ and ground configuration $\mathrm{3d}^{x}$,
atomic models with a few hundred levels must be considered (see Section 6.1),
and leads to the appearance of unexpected metastable levels at fairly high
energies. Most of these levels were detected by running the code to look for
levels with anomalously large populations, which were then removed by hand
followed by level reordering.

###  6.3 Database Pointers

As previously mentioned, the raw xstar database consists of a list of ASCII
files labeled $\mathtt{d}ion\mathtt{t}0dt$, where $ion$ is the ion identifier
and $dt$ the data type. When the package is installed, these files are read
into three one-dimensional arrays (integer, real, and character variables) and
a set of pointers to be finally structured in a file under the binary FITS
format. At runtime, these arrays are read into main memory to be accessed
according to the user model. This data structure arrangement is efficient when
uploading from disk and during processing, but can be cumbersome in database
updating when new record types are created. Proficient nursing and testing are
required before the new version is released.

###  6.4 Metadata

The xstar database compiles atomic data computed to order and from a myriad of
other data sources. The data provenance of the first release was detailed in
(Bautista and Kallman, 2001), but since then the database has undergone
several mayor upgrades that have not been formally registered within its file
structure. One of the aims of the present paper is to create an up-to-date
data provenance blueprint to be included in the database using the FITS
metadata facilities.

In Table 3 of Appendix C we have tabulated an up-to-date list of data source
references including the original four- and five-letter mnemonics used for
identification in (Bautista and Kallman, 2001) and a new four-integer code to
be inserted in every database record. For this purpose we adopt the third
integer (currently displaying a zero) of the record heading tuple
$(dt,rt,0,N_{\mathrm{flt}},N_{\mathrm{int}},N_{\mathrm{chr}})$ described in
Section 2 to denote this provenance code.

###  6.5 Relational Integrity

As described in Section 2, the data in each $\mathtt{d}ion\mathtt{t}0dt$ file
are self-contained to simplify and speedup the calculation of a wide variety
of rates at runtime, but as a result this scheme obviates the relational
integrity of the database. For instance, the wavelengths displayed in file
$\mathtt{d}ion\mathtt{t}050$ (see Figure 3) are not automatically recalculated
if a level energy is updated in file $\mathtt{d}ion\mathtt{t}006$ (Figure 2).
The level attributes specified in the latter file are also repeated in several
other data types; e.g., the K-vacancy level energy in file
$\mathtt{d}ion\mathtt{t}086$ (Figure 4). The extent of this complication is
further illustrated in the list of data types in Appendix A. Data type 14
lists the ionization potential for every ionic species, but this datum is also
contained in the floating-point tuple of every level in data type 06. Some of
the level integer attributes of the latter data type are included in data
types dealing with the effective ion charge (57), photoionization cross
sections (49, 53, 85, and 88), superlevel recombination rates (70 and 99), and
satellite-level autoionization rates (72). This database model therefore can
make updating an involved process that is certainly error prone.

##  7 ISMabs

Although the main components of the ISM are neutral ionic species, the also
perceived existence of charged ions prompted us to develop a new ISM X-ray
absorption model (Gatuzz et al., 2015) referred to as ISMabs. It includes
atomic data for singly and doubly ionized species for cosmically abundant
elements, namely, H, He, C, N, O, Ne, Mg, Si, S, Ar, Ca, and Fe in addition to
the neutral systems. This model allows ion column densities to be determined
directly, and including ionized species has led to improved spectral fits when
compared with those only considering neutral systems. The completeness and
accuracy of the relevant atomic data are crucial to avoid misidentification
and misinterpretation of the absorption features detected in analyses of ISM
X-ray absorption spectra relying on fits based on Gaussian profiles. We have
performed with this model a detailed study of the X-ray absorption in the
local ISM by analyzing spectra from 24 Galactic sources. We have estimated the
fractions of neutral and singly and doubly ionized species of O, Ne, and Fe
confirming the dominance of the cold component and a pervasive low degree of
ionization (Gatuzz et al., 2016).

##  8 Universal Atomic Database (uaDB)

The collection of atomic data in xstar is comprised of data in many different
formats from many different sources. To assist in disseminating these data to
the larger community and to account for the addition of new data, the
Universal Atomic Database (uaDB) was developed. The uaDB is a mySQL database
hosted at NASA/GSFC accessed via its web site, and data can be queried based
on a number of properties such as ion and data type. The web page also
contains tools to help assess what data are available across ions or data
types. One such tool displays the type of data available on a grid of element
vs. ion (see Figure 11) while another displays all atomic lines present in a
given wavelength range.

Figure 11: Grid tool in uaDB.

The main features of uaDB are:

  * •

Each dataset contains a reference to the source paper(s)

  * •

Data are stored in the original format and units as published

  * •

Multiple entries can exist for the same quantity (e.g., theoretical vs.
measured energy levels)

  * •

The coupling scheme of atomic states is built into the database structure

  * •

Data collections exist that define a complete model; no duplicate data exist
within a collection.

All data in uaDB have a reference to the data source. The reference consists
of a link to the journal article where the data were obtained and to its entry
in NASA/ADS. The user is never more than a couple mouse clicks away from
reading the source article. Data are entered into uaDB in the same format and
with the same units as published. This means that, for example, some energy
levels are stored in eV and others in cm-1. The uaDB understands these units
and can internally convert them for data querying in an energy range. The uaDB
can also convert between quantities that differ by a statistical weight (e.g.,
$f$-values and $gf$-values) since it understands the level structure. We do
not modify published data in order to be as true as possible to the original
source and to help identify transcription errors. However, this can make it
more difficult to compare data from different sources. To help compare data,
tools are developed that can perform the necessary conversions.

When compiling a set of atomic data for modeling purposes, it is important to
have coverage; that is, for each state included in the model, a full set of
data connecting that state with other states is necessary. If there are data
allowing the population of a state to increase but no data to decrease it,
then the model as a whole will be flawed. Furthermore, if the atomic model
encompasses a large set of ions, it is difficult to obtain atomic data from
the literature of equal quality. We often need to combine level-resolved data
with term-resolved data to achieve coverage for an ion. To help with these
difficulties, uaDB has different coupling schemes built into its structure and
is aware of how different coupling schemes relate. Thus, when combining $LS$
states with $LSJ$, uaDB can detect if any states are being double-counted.
There are also routines for converting data from one coupling scheme to
another based on simple statistical weighting.

The uaDB currently contains the complete set of data included in xstar as well
as the level data from chianti. To assist in distinguishing these data, uaDB
defines collections. A collection is a dataset where there is no duplication
of values for the same quantity. Currently, in uaDB, the collection is just a
label that can be used to constrain a query, but in the future collections
could be created dynamically to construct a custom model.

##  9 Discussion and Conclusions

The present report describes in detail the updated version of the underlying
atomic database of the xstar photoionization code to replace the original
implementation of (Bautista and Kallman, 2001). We include complete lists of
the current rate types, data types (Appendix A), ionic models (Appendix B),
and source references (Appendix C). We summarize the systematic calculations
performed to characterize the metal K lines for astronomical X-ray spectral
modeling and recent extensions of the database, namely, continuum lowering and
dielectronic recombination suppression, to deal with high-density ($n_{e}\leq
10^{22}$ cm-3) plasmas. We have made an attempt to convey the intricacies
involved in the development and maintenance of an application-based atomic
database, which go way beyond the compilation of the data leading to
curatorial and integrity problems brought to the fore by the ever increasing
dataset volumes.

An important finding of this work is that the atomic models used to computed
the data are not necessarily suitable for plasma modeling, particularly for
ionic species with electron number $N>20$. Level-number trimming was necessary
to implement functional atomic representations for such systems although their
soundness in non-LTE modeling deserves further attention as the appearance of
unexpected metastable levels becomes an issue.

A further point worth emphasizing is that the xstar atomic database and output
files are structured under the FITS format specifications, which has been
established as the standard for astronomical datasets particularly those
associated to the new generation of telescopes. We believe that this
compliance will reduce user stress in intense data processing, which is bound
to take place at distributed data reservoirs rather than locally.

We have briefly recounted two projects that have emerged from the xstar
database, namely the ISMabs absorption model and the uaDB database. The former
has become an important initiative as it has led to benchmarks of the atomic
data with observations and laboratory measurements; however, it has not been a
smooth process as unexpected inaccuracies in the calibration of the laboratory
wavelength scale were detected and finally resolved (Gorczyca et al., 2013;
Leutenegger et al., 2020). This outcome has given us some confidence on the
identification of the spectral features and the accuracy of our atomic data.
The uaDB database model will become handy in future projects to disseminate
larger atomic data volumes associated with non-LTE modeling.

A question that remains unanswered is whether our efforts to ensure accuracy
and completeness for the xstar database are up to scratch to exploit the high
resolution and sensitivity expected from the microcalorimeter-based
spectrometers aboard the new X-ray space telescopes. The encouraging fit of
the showcase hitomi spectrum depicted in Figure 1 required a certain amount of
basic data manipulation, but at least it was manageable. Therefore, we
envision further database refinement in the short future to provide a reliable
modeling platform for high-resolution spectroscopy in a new era. In this
respect more laboratory benchmarks would be welcome.

conceptualization, C.M., M.A.B., T.R.K.; methodology, C.M., E.G., J.A.G.,
J.D., M.A.B., M.C.W., P.P., P.Q., T.R.K., and T.W.G.; software, C.M., E.G.,
J.A.G., M.A.B., M.C.W., P.P., T.R.K., and T.W.G.; validation, J.A.G., M.A.B.,
P.P., T.R.K.; formal analysis, C.M., E.G., J.A.G., J.D., M.A.B., M.C.W., P.P.,
P.Q., T.R.K., and T.W.G.; investigation, C.M., E.G., J.A.G., J.D., M.A.B.,
M.C.W., P.P., and, T.R.K.; validation, C.M., M.A.B., P.P., and T.R.K.;
resources, M.A.B., P.Q., T.R.K.; data curation, C.M., M.A.B., P.P., and T.R.K;
writing–original draft preparation, C.M., E.G., M.C.W., and T.R.K.;
writing–review and editing, C.M., E.G., J.A.G., J.D., M.A.B., M.C.W., P.P.,
P.Q., T.R.K., and T.W.G.; visualization, C.M., M.C.W., and T.R.K; supervision,
T.R.K.; project administration, M.A.B., P.Q., T.R.K.; funding acquisition,
J.A.G., P.P., P.Q., and T.R.K.

J.D. is a Research Fellow of the Belgian Fund for Research in Industry and
Agriculture (FRIA). P.P. & P.Q. are, respectively, Research Associate and
Research Director of the Belgian Fund for Scientific Research F.R.S.–FNRS.
Financial supports from these organizations as well as from the NASA
Astrophysics Research and Analysis Program (grants 12-APRA12-0070;
80NSSC17K0345) are gratefully acknowledged.

###### Acknowledgements.

We are grateful to Dr. Anil. K. Pradhan (Ohio State University) for access to
and space/time allocation at the Ohio Supercomputer Center and also to the
NASA Private Cloud at GSFC for access and virtual machine installation,
especially to Dr. Michael D. Moore for invaluable support. The authors declare
no conflict of interest. The following abbreviations are used in this
manuscript:
ADAS | Atomic Data and Analysis Structure
---|---
ADS | Astrophysics Data System
ALS | Advanced Light Source
AMDPP | Atomic and Molecular Diagnostic Processes in Plasmas
FITS | Flexible Image Transport System
GSFC | Goddard Space Flight Center
HZB | Helmholtz-Zentrum Berlin
IPNAS | Institut de Physique Nucléaire, Atomique et de Spectrométrie
LTE | Local Thermodynamic Equilibrium
MCHF | Multi-Configuration Hartree–Fock
NASA | National Aeronautics and Space Administration
NIST | National Institute of Standards and Technology
---|---
PP95 | Atomic Data for the Analysis of Emission Lines
WSRC | Wisconsin Synchrotron Radiation Center

##  Appendix A Data Types

01.

Radiative recombination rate coefficient of $N$-electron recombined ion
(Aldrovandi and Pequignot, 1973, 1976): $\mathtt{r1}=A_{\mathrm{rad}}$ (cm3
s-1); $\mathtt{r2}=\eta$; $\mathtt{i1}=ion_{N}$.

02.

H0 charge exchange rate coefficient of $N$-electron recombined ion (Kingdon
and Ferland, 1996): $\mathtt{r1}=a$ ($10^{-9}$ cm3 s-1); $\mathtt{r2}=b$;
$\mathtt{r3}=c$; $\mathtt{r4}=d$; $\mathtt{r5}=T_{1}$ (K); $\mathtt{r6}=T_{2}$
(K); $\mathtt{r7}=\Delta E/k$ ($10^{4}$ K); $\mathtt{i1}=ion_{N}$;
$\mathtt{s1}=$ recombining ion identifier.

06.

Data attributes of the $i$th level of $N$-electron ion: $\mathtt{r1}=E(i)$
(eV); $\mathtt{r2}=(2J+1)$; $\mathtt{r3}=\nu$ (effective quantum number);
$\mathtt{r4}=E(\infty)$ (eV); $\mathtt{i1}=n$; $\mathtt{i2}=(2S+1)$;
$\mathtt{i3}=L$; $\mathtt{i4}=Z$; $\mathtt{i5}=i$; $\mathtt{i6}=ion_{N}$;
$\mathtt{s1}=$ level configuration assignment.

07.

Dielectronic recombination rate coefficient of $N$-electron recombined ion
(Aldrovandi and Pequignot, 1973, 1976): $\mathtt{r1}=A_{\mathrm{di}}$ (cm3 s-1
K3/2); $\mathtt{r2}=B_{\mathrm{di}}$; $\mathtt{r3}=T_{0}$ (K);
$\mathtt{r4}=T_{1}$ (K); $\mathtt{i1}=ion_{N}$.

14.

Ionization potential of $N$-electron ion: $\mathtt{r1}=E(\infty)$ (eV);
$\mathtt{i1}=Z-N+1$; $\mathtt{i2}=Z$; $\mathtt{i3}=ion_{N}$; $\mathtt{s1}=$
ion identifier.

22.

Dielectronic recombination rate coefficient of the $N$-electron recombined ion
(Nussbaumer and Storey, 1986): $\mathtt{r1}=a$; $\mathtt{r2}=b$;
$\mathtt{r3}=c$; $\mathtt{r4}=d$; $\mathtt{r5}=e$; $\mathtt{r6}=f$;
$\mathtt{i1}=ion_{N}$.

30.

Total radiative recombination rate (hydrogenic) for $N$-electron recombined
ion (Gould and Thakur, 1970): $\mathtt{i1}=Z$; $\mathtt{i2}=ion_{N}$.

38.

Total radiative recombination rate coefficient of $N$-electron recombined ion
[http://amdpp.phys.strath.ac.uk/tamoc/DATA/RR/]: $\mathtt{r1}=A$ (cm3
s${}^{-1})$; $\mathtt{r2}=B$; $\mathtt{r3}=T_{0}$ (K); $\mathtt{r4}=T_{1}$
(K); $\mathtt{r5}=C$; $\mathtt{r6}=T_{2}$ (K); $\mathtt{i1}=Z$;
$\mathtt{i2}=N-1$; $\mathtt{i3}=M$; $\mathtt{i4}=W$; $\mathtt{i5}=ion_{N}$.

39.

Total dielectronic recombination rate coefficient of $N$-electron recombined
ion [http://amdpp.phys.strath.ac.uk/tamoc/DATA/DR/]:
$\mathtt{r1{-}rj_{max}}=(C(j),j=1,j_{\mathrm{max}})$ (cm3 s-1 K3/2);
$\mathtt{rj_{max+1}{-}rj_{2*max}}=(T(j),j=1,j_{\mathrm{max}})$ (K);
$\mathtt{i1}=Z$; $\mathtt{i2}=N-1$; $\mathtt{i3}=M$; $\mathtt{i4}=W$,
$\mathtt{i5}=ion_{N}$.

49.

Partial photoionization cross section of $i_{N}$th level of the $N$-electron
ion leaving the ($N-1$)-electron ion in the $k_{N-1}$th level:
$\mathtt{r1{-}rj_{2*max}}=(E(j),\sigma(E(j)),j=1,j_{\mathrm{max}})$ (Energy in
Ryd relative to $E(\infty)$, cross section in Mb); $\mathtt{i1}=n$;
$\mathtt{i2}=L$; $\mathtt{i3}=2J$; $\mathtt{i4}=Z$; $\mathtt{i5}=k_{N-1}$;
$\mathtt{i6}=ion_{N-1}$; $\mathtt{i7}=i_{N}$; $\mathtt{i8}=ion_{N}$.

50.

Line ($k-i$) radiation rates of $N$-electron ion: $\mathtt{r1}=\lambda$ (Å);
$\mathtt{r2}=gf(i,k)$; $\mathtt{r3}=A(k,i)$ (s-1); $\mathtt{i1}=i$ (lower
level); $\mathtt{i2}=k$ (upper level); $\mathtt{i3}=Z$; $\mathtt{i4}=ion_{N}$.

51.

Electron-impact effective collision strength for the $k-i$ transition of
$N$-electron ion (CHIANTI fit (Burgess and Tully, 1992; Dere et al., 1997)):
$\mathtt{r1}=\Delta E$ (Ryd); $\mathtt{r2}=C$;
$\mathtt{r3{-}r7}=(\Upsilon_{\rm red}(j),j=1,5)$ (reduced effective collision
strength); $\mathtt{i1}=it$ (transition type); $\mathtt{i2}=i$ (lower level);
$\mathtt{i3}=k$ (upper level); $\mathtt{i4}=Z$; $\mathtt{i5}=ion_{N}$.

53.

TOPbase partial photoionization cross section (resonance averaged) of
$i_{N}$th level of the $N$-electron ion leaving the ($N-1$)-electron ion in
the $k_{N-1}$th level:
$\mathtt{r1{-}rj_{2*max}}=(E(j),\sigma(E(j)),j=1,j_{\mathrm{max}})$ (Energy in
Ryd relative to $E(\infty)$, cross section in Mb); $\mathtt{i1}=n$;
$\mathtt{i2}=L$; $\mathtt{i3}=2J$; $\mathtt{i4}=Z$; $\mathtt{i5}=k_{N-1}$;
$\mathtt{i6}=ion_{N-1}$; $\mathtt{i7}=i_{N}$; $\mathtt{i8}=ion_{N}$.

54.

Radiative transition probability $A_{ki}$ for the $k-i$ transition of
$N$-electron ion computed by quantum defect theory (or hydrogenic):
$\mathtt{r1}=0.0E+0$; $\mathtt{i1}=i$ (lower level); $\mathtt{i2}=k$ (upper
level); $\mathtt{i3}=Z$; $\mathtt{i5}=ion_{N}$.

56.

Electron-impact effective collision strengths for the $k-i$ transition of
$N$-electron ion: $\mathtt{r1{-}rj_{max}}=(\log
T_{e}(j),j=1,j_{\mathrm{max}})$ (K);
$\mathtt{rj_{(max+1)}{-}rj_{(2*max)}}=(\Upsilon(T_{e}(j)),j=1,j_{\mathrm{max}})$
(effective collision strength); $\mathtt{i1}=i$ (lower level); $\mathtt{i2}=k$
(upper level); $\mathtt{i3}=Z$; $\mathtt{i5}=ion_{N}$.

57.

Effective ion charge for $i$th level of $N$-electron ion: $\mathtt{r1}=Z_{\rm
eff}$; $\mathtt{i1}=n$; $\mathtt{i2}=L$; $\mathtt{i3}=2J$; $\mathtt{i4}=Z$;
$\mathtt{i5}=i$; $\mathtt{i6}=ion_{N}$

59.

Partial photoionization cross section of $i_{N}$th level of the $N$-electron
ion leaving the ($N-1$)-electron ion in the $k_{N-1}$th level (Verner and
Yakovlev, 1995): $\mathtt{r1}=E(th)$ (eV); $\mathtt{r2}=E(0)$ (eV);
$\mathtt{r3}=\sigma(0)$ (Mb); $\mathtt{r4}=y(a)$; $\mathtt{r5}=P$;
$\mathtt{r6}=y(w)$; $\mathtt{i1}=N$; $\mathtt{i2}=n$ (shell principal quantum
number); $\mathtt{i3}=l$ (orbital quantum number of the subshell);
$\mathtt{i4}=k_{N-1}$; $\mathtt{i5}=ion_{N-1}$; $\mathtt{i6}=i_{N}$;
$\mathtt{i7}=ion_{N}$; $\mathtt{s1}=$ shell–ion identifier.

60.

Analytic fits for effective collision strengths in H-like ions (Callaway,
1994): $\mathtt{r1{-}rj_{max}}=$ coefficients; $\mathtt{i1}=i$ (lower level);
$\mathtt{i2}=k$ (upper level); $\mathtt{i3}=1$; $\mathtt{i8}=ion_{N}$;
$\mathtt{s1}=$ Transition.

62.

Analytic fits for effective collision strengths in H-like ions (Callaway,
1994): $\mathtt{r1{-}rj_{max}}=$ coefficients; $\mathtt{i1}=i$ (lower level);
$\mathtt{i2}=k$ (upper level); $\mathtt{i3}=1$; $\mathtt{i8}=ion_{N}$;
$\mathtt{s1}=$ Transition.

63.

Collisional transition probability $C_{ik}$ for $N$-electron ion computed by
quantum defect theory (or hydrogenic): $\mathtt{i1}=1$ $\mathtt{i2}=i$ (lower
level); $\mathtt{i3}=k$ (upper level); $\mathtt{i4}=Z$; $\mathtt{i5}=ion_{N}$.

66.

Fits to fine-structure collision strengths for He-like ions (Kato and
Nakazaki, 1989): $\mathtt{r1{-}rj_{max}}=$ coefficients; $\mathtt{i1}=i$
(lower level); $\mathtt{i2}=k$ (upper level); $\mathtt{i3}=Z$;
$\mathtt{i4}=ion_{N}$.

67.

Analytic fits for effective collision strengths in He-like ions (Keenan et
al., 1987): $\mathtt{r1{-}rj_{max}}=$ coefficients; $\mathtt{i1}=i$ (lower
level); $\mathtt{i2}=k$ (upper level); $\mathtt{i3}=Z$; $\mathtt{i4}=ion_{N}$.

68.

Analytic fits for effective collision strengths in He-like ions (Zhang and
Sampson, 1987): $\mathtt{r1{-}rj_{max}}=$ coefficients; $\mathtt{i1}=i$ (lower
level); $\mathtt{i2}=k$ (upper level); $\mathtt{i3}=Z$; $\mathtt{i8}=ion_{N}$.

69.

Fits to $LS$ collision strengths for He-like ions (Kato and Nakazaki, 1989):
$\mathtt{r1{-}rj_{max}}=$ coefficients; $\mathtt{i1}=i$ (lower level);
$\mathtt{i2}=k$ (upper level); $\mathtt{i3}=Z$; $\mathtt{i8}=ion_{N}$.

70.

Coefficients for recombination and photoionization cross sections of
superlevels: $\mathtt{r1{-}rj_{nd}}=(n_{e}(j),j=1,j_{nd})$;
$\mathtt{rj_{nd+1}{-}rj_{nd+nt}}=(T_{e}(j),j=1,j_{nt})$;
$\mathtt{rj_{nd+nt+1}{-}rj_{nd+nt+nt*nd}}=((\log\alpha(j,j^{\prime}),j^{\prime}=1,j^{\prime}_{nd}),j=1,j_{nt})$;
$\mathtt{rj_{nd+nt+nt*nd+1}-rj_{nd+nt+nt*nd+2*nx}}=(E(j),\sigma(j),j=1,j_{nx})$;
$\mathtt{i1}=nd$; $\mathtt{i2}=nt$; $\mathtt{i3}=nx$; $\mathtt{i4}=n$;
$\mathtt{i5}=L$; $\mathtt{i6}=2S+1$; $\mathtt{i7}=Z$; $\mathtt{i8}=k_{N-1}$;
$\mathtt{i9}=ion_{N-1}$; $\mathtt{i10}=i_{N}$; $\mathtt{i11}=ion_{N}$.

71.

Radiative transition rates from superlevels to spectroscopic levels:
$\mathtt{r1{-}rj_{nd}}=(n_{e}(j),j=1,j_{nd})$;
$\mathtt{rj_{nd+1}{-}rj_{nd+nt}}=(T_{e}(j),j=1,j_{nt})$;
$\mathtt{rj_{nd+nt+1}{-}rj_{nd+nt+nt*nd}}=((A(j,j^{\prime}),j^{\prime}=1,j^{\prime}_{nd}),j=1,j_{nt})$;
$\mathtt{r_{nd+nt+nt*nd+1}}=\lambda$ (Å); $\mathtt{i1}=nd$; $\mathtt{i2}=nt$;
$\mathtt{i3}=i$ (lower level); $\mathtt{i4}=k$ (upper level); $\mathtt{i5}=Z$;
$\mathtt{i6}=ion_{N}$.

72.

Autoionization rates for satellite levels: $\mathtt{r1}=A_{a}(k,i)$ (s-1);
$\mathtt{r2}=E(k)$ (eV above ionization limit); $\mathtt{r3}=(2J+1)$;
$\mathtt{i1}=(2S+1)$; $\mathtt{i2}=L$; $\mathtt{i3}=k$ (level);
$\mathtt{i4}=i$ (continuum level); $\mathtt{i5}=Z$; $\mathtt{i6}=ion_{N}$;
$\mathtt{s1}=$ level configuration.

73.

Fit to effective collision strengths for satellite levels of He-like ions
(Sampson et al., 1983): $\mathtt{r1{-}rj_{7}}=$ fit coefficients;
$\mathtt{i1}=i$ (lower level); $\mathtt{i2}=j$ (upper level); $\mathtt{i3}=Z$;
$\mathtt{i4}=ion_{N}$.

74.

Delta functions to add to photoionization cross sections to match ADF DR
rates: $\mathtt{r1}=E(\infty)$ (eV); $\mathtt{r1{-}rj_{m}}=(E(j),j=1,j_{m})$
(eV); $\mathtt{rj_{m+1}{-}rj_{2m}}=(f(j),j=1,j_{m})$ (cm2); $\mathtt{i1}=n$;
$\mathtt{i2}=L$; $\mathtt{i3}=2S+1$; $\mathtt{i4}=Z$; $\mathtt{i5}=k_{N-1}$;
$\mathtt{i6}=ion_{N-1}$; $\mathtt{i7}=i_{N}$; $\mathtt{i8}=ion_{N}$

75.

Autoionization rates for Fe xxiv satellites (Bautista et al., 2003):
$\mathtt{r1}=A_{a}(k,i)$ (s-1); $\mathtt{r2}=E(k)$ (eV above ionization
limit); $\mathtt{i1}=ion_{N}$, $\mathtt{i2}=k_{N}$; $\mathtt{i3}=ion_{N-1}$;
$\mathtt{i4}=i_{N-1}$; $\mathtt{i5}=ion_{N}$.

76.

Two-photon radiation rate for ($k-i$) transition of $N$-electron ion:
$\mathtt{r1}=A(k,i)$ (s-1); $\mathtt{i1}=i$ (lower level); $\mathtt{i2}=k$
(upper level); $\mathtt{i3}=1$; $\mathtt{i4}=ion_{N}$; $\mathtt{s1}=$
transition identifier.

77.

Collision transition rates from superlevels to spectroscopic levels:
$\mathtt{r1{-}rj_{nd}}=(n_{e}(j),j=1,j_{nd})$;
$\mathtt{rj_{nd+1}{-}rj_{nd+nt}}=(T_{e}(j),j=1,j_{nt})$;
$\mathtt{rj_{nd+nt+1}{-}rj_{nd+nt+nt*nd}}=((C(j,j^{\prime}),j^{\prime}=1,j^{\prime}_{nd}),j=1,j_{nt})$
(s-1); $\mathtt{rj_{nd+nt+nt*nd+1}}=\lambda$ (Å); $\mathtt{i1}=nd$;
$\mathtt{i2}=nt$; $\mathtt{i3}=i$ (lower level); $\mathtt{i4}=k$ (upper
level); $\mathtt{i5}=Z$; $\mathtt{i6}=ion_{N}$.

81.

Collision strengths for Fe xix (Bhatia et al., 1989):
$\mathtt{r1}=\Upsilon(k,i)$; $\mathtt{i1}=i$ (lower level); $\mathtt{i2}=k$
(upper level); $\mathtt{i3}=Z$; $\mathtt{i4}=ion_{N}$.

82.

Decay rates for Fe UTA (Gu et al., 2006): $\mathtt{r1}=\lambda$ (Å);
$\mathtt{r2}=E(k)$ (eV); $\mathtt{r3}=gf(i,k)$; $\mathtt{r4}=A_{r}(k,i)$
(s-1); $\mathtt{r5}=A_{a}(k,i)$ (s-1); $\mathtt{i1}=i$ (lower level);
$\mathtt{i2}=k$ (upper level); $\mathtt{i4}=ion_{N}$.

83.

Level data for Fe UTA (Gu et al., 2006): $\mathtt{r1}=E(i)$ (eV);
$\mathtt{r2}=(2J+1)$; $\mathtt{r3}=0.0$; $\mathtt{r4}=0.0$; $\mathtt{i1}=1$;
$\mathtt{i5}=i$ (level); $\mathtt{i6}=ion_{N}$; $\mathtt{s1}=$ level
configuration assignment.

85.

Photoionization cross sections for Fe ions obtained by summation of resonances
near the K edge (Palmeri et al., 2002): $\mathtt{r1}=Z_{\mathrm{eff}}$;
$\mathtt{r2}=E_{th}$ (Ryd); $\mathtt{r3}=f$; $\mathtt{r4}=\gamma$;
$\mathtt{r5}=$ scaling factor; $\mathtt{i1}=n$; $\mathtt{i2}=L$;
$\mathtt{i3}=2J$; $\mathtt{i4}=Z$; $\mathtt{i5}=k_{N-1}$;
$\mathtt{i6}=ion_{N-1}$; $\mathtt{i7}=i_{N}$; $\mathtt{i8}=ion_{N}$.

86.

Auger and radiative widths of $k_{N}$th K-vacancy level:
$\mathtt{r1}=E(k_{N})$ (eV, relative to $E(\infty)$);
$\mathtt{r2}=A_{a}(k_{N})$ (s-1); $\mathtt{r3}=A_{a}(k_{N},i_{N-1})$ (s-1);
$\mathtt{r4}=A_{r}(k_{N})$ (s-1); $\mathtt{i1}=i_{N-1}$; $\mathtt{i2}=k_{N}$;
$\mathtt{i3}=Z$; $\mathtt{i4}=ion_{N-1}$; $\mathtt{i5}=ion_{N}$.

88.

Photoionization cross section damped excess of $i_{N}$th level of the
$N$-electron ion leaving the ($N-1$)-electron ion in superlevel_[K] $k_{N-1}$:
$\mathtt{r1{-}rj_{max}}=(E(j),\sigma(E(j)),j=1,j_{\mathrm{max}})$ (Energy in
Ryd relative to $E(\infty)$, cross section in Mb); $\mathtt{i1}=n$;
$\mathtt{i2}=L$; $\mathtt{i3}=2J$; $\mathtt{i4}=Z$; $\mathtt{i5}=k_{N-1}$;
$\mathtt{i6}=i_{N}$; $\mathtt{i7}=ion_{N}$.

91.

APED line ($k-i$) radiation rates (Foster et al., 2012): $\mathtt{r1}=\lambda$
(Å); $\mathtt{r2}=0.0$; $\mathtt{r3}=A(k,i)$ (s-1); $\mathtt{i1}=i$ (lower
level); $\mathtt{i2}=k$ (upper level); $\mathtt{i3}=Z$; $\mathtt{i4}=ion_{N}$.

92.

APED collision strengths (Foster et al., 2012):
$\mathtt{r1{-}rj_{max}}=(T_{e}(j),j=1,j_{max})$ (K);
$\mathtt{rj_{max+1}{-}rj_{2*max}}=(\Upsilon(j),j=1,j_{max})$; $\mathtt{i1}=1$;
$\mathtt{i2}=i$ (lower level); $\mathtt{i3}=k$ (upper level); $\mathtt{i4}=Z$;
$\mathtt{i5}=ion_{N}$.

95.

Collisional ionization rates for $N$-electron ion (Bryans et al., 2006):
$\mathtt{r1}=E(th)$ (eV); $\mathtt{r2}=T_{0}$ (K);
$\mathtt{r3{-}rj_{max+2}}=(\rho(j),j=1,j_{max})$ (effective collision
strength); $\mathtt{i1}=i$ (level); $\mathtt{i5}=ion_{N}$.

98.

Electron-impact effective collision strengths for the $k-i$ transition of the
$N$-electron ion (CHIANTI fit (Burgess and Tully, 1992; Dere et al., 1997)):
$\mathtt{r1}=\Delta E$ (Ryd); $\mathtt{r2}=C$;
$\mathtt{r3{-}rj_{max+2}}=(\Upsilon_{\rm red}(j),j=1,max)$ (reduced effective
collision strength); $\mathtt{i1}=it$ (transition type); $\mathtt{i2}=i$;
$\mathtt{i3}=k$; $\mathtt{i4}=ion_{N}$.

99.

Coefficients for recombination and photoionization cross sections of
superlevels: $\mathtt{r1{-}rj_{nd}}=(n_{e}(j),j=1,j_{nd})$;
$\mathtt{rj_{nd+1}{-}rj_{nd+nt}}=(T_{e}(j),j=1,j_{nt})$;
$\mathtt{rj_{nd+nt+1}{-}rj_{nd+nt+nt*nd}}=((\alpha(j,j^{\prime}),j^{\prime}=1,j^{\prime}_{nd}),j=1,j_{nt})$;
$\mathtt{rj_{nd+nt+nt*nd+1}-rj_{nd+nt+nt*nd+2*nx}}=(E(j),\sigma(j),j=1,j_{nx})$;
$\mathtt{i1}=nd$; $\mathtt{i2}=nt$; $\mathtt{i3}=nx$; $\mathtt{i4}=n$;
$\mathtt{i5}=L$; $\mathtt{i6}=2S+1$; $\mathtt{i7}=Z$; $\mathtt{i8}=k_{N-1}$;
$\mathtt{i9}=ion_{N-1}$; $\mathtt{i10}=i_{N}$; $\mathtt{i11}=ion_{N}$.

##  Appendix B Ion Models

Table 2: Number of energy levels included in the xstar ion models.  N Z | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
1 | 33 | 33 | 33 | 33 | 33 | 33 | 33 | 33 | 33 | 33 | 33 | 33 | 33 | 33 | 33
2 |  | 46 | 32 | 32 | 32 | 56 | 58 | 241 | 52 | 54 | 52 | 58 | 52 | 58 | 52
3 |  |  | 3 | 3 | 3 | 26 | 43 | 43 | 22 | 43 | 22 | 43 | 22 | 43 | 22
4 |  |  |  | 3 | 3 | 22 | 53 | 53 | 43 | 79 | 43 | 79 | 43 | 79 | 43
5 |  |  |  |  | 3 | 22 | 58 | 163 | 53 | 163 | 53 | 163 | 53 | 163 | 53
6 |  |  |  |  |  | 8 | 61 | 79 | 53 | 79 | 53 | 79 | 53 | 79 | 53
7 |  |  |  |  |  |  | 82 | 34 | 34 | 34 | 34 | 34 | 63 | 34 | 34
8 |  |  |  |  |  |  |  | 19 | 3 | 19 | 19 | 19 | 57 | 19 | 19
9 |  |  |  |  |  |  |  |  | 3 | 118 | 7 | 7 | 7 | 7 | 7
10 |  |  |  |  |  |  |  |  |  | 4 | 3 | 46 | 46 | 46 | 50
11 |  |  |  |  |  |  |  |  |  |  | 3 | 24 | 4 | 60 | 42
12 |  |  |  |  |  |  |  |  |  |  |  | 3 | 4 | 57 | 31
13 |  |  |  |  |  |  |  |  |  |  |  |  | 3 | 18 | 55
14 |  |  |  |  |  |  |  |  |  |  |  |  |  | 3 | 3
15 |  |  |  |  |  |  |  |  |  |  |  |  |  |  | 3
N Z | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30
1 | 33 | 33 | 33 | 33 | 33 | 33 | 33 | 33 | 33 | 33 | 33 | 33 | 33 | 33 | 33
2 | 58 | 52 | 38 | 52 | 46 | 52 | 52 | 52 | 52 | 52 | 50 | 52 | 43 | 52 | 52
3 | 43 | 22 | 43 | 22 | 43 | 22 | 22 | 22 | 22 | 22 | 52 | 22 | 53 | 22 | 22
4 | 79 | 43 | 79 | 43 | 79 | 43 | 43 | 43 | 43 | 43 | 199 | 43 | 79 | 43 | 43
5 | 163 | 53 | 163 | 53 | 163 | 53 | 53 | 53 | 53 | 53 | 551 | 53 | 163 | 53 | 53
6 | 79 | 53 | 53 | 53 | 53 | 53 | 53 | 53 | 53 | 53 | 623 | 53 | 53 | 53 | 53
7 | 34 | 34 | 34 | 34 | 34 | 34 | 34 | 34 | 34 | 34 | 744 | 34 | 34 | 34 | 34
8 | 19 | 19 | 19 | 19 | 29 | 19 | 19 | 19 | 19 | 19 | 639 | 19 | 67 | 19 | 19
9 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 340 | 7 | 117 | 7 | 7
10 | 46 | 50 | 72 | 50 | 78 | 50 | 50 | 50 | 50 | 50 | 276 | 50 | 98 | 50 | 50
11 | 60 | 42 | 208 | 42 | 208 | 42 | 42 | 42 | 42 | 42 | 85 | 42 | 216 | 42 | 42
12 | 53 | 31 | 153 | 31 | 149 | 31 | 31 | 31 | 31 | 31 | 146 | 31 | 171 | 31 | 31
13 | 76 | 55 | 208 | 55 | 208 | 55 | 55 | 55 | 55 | 55 | 55 | 55 | 235 | 55 | 55
14 | 82 | 71 | 249 | 71 | 249 | 71 | 71 | 71 | 71 | 71 | 68 | 71 | 269 | 71 | 71
15 | 31 | 55 | 211 | 55 | 211 | 55 | 55 | 55 | 55 | 55 | 78 | 55 | 219 | 55 | 55
16 | 3 | 3 | 143 | 31 | 143 | 31 | 31 | 31 | 31 | 31 | 70 | 31 | 145 | 31 | 31
17 |  | 3 | 62 | 10 | 62 | 10 | 10 | 10 | 10 | 10 | 62 | 10 | 63 | 10 | 10
18 |  |  | 3 | 3 | 3 | 54 | 54 | 54 | 54 | 54 | 31 | 54 | 40 | 54 | 54
19 |  |  |  | 3 | 5 | 221 | 221 | 221 | 221 | 221 | 170 | 221 | 143 | 221 | 221
20 |  |  |  |  | 3 | 32 | 258 | 258 | 258 | 258 | 54 | 258 | 258 | 258 | 258
21 |  |  |  |  |  | 3 | 84 | 441 | 441 | 441 | 55 | 441 | 441 | 441 | 441
22 |  |  |  |  |  |  | 3 | 3 | 537 | 537 | 33 | 537 | 537 | 537 | 537
23 |  |  |  |  |  |  |  | 3 | 163 | 463 | 70 | 463 | 463 | 463 | 463
24 |  |  |  |  |  |  |  |  | 3 | 160 | 73 | 295 | 295 | 295 | 295
25 |  |  |  |  |  |  |  |  |  | 3 | 197 | 128 | 128 | 128 | 128
26 |  |  |  |  |  |  |  |  |  |  | 3 | 3 | 40 | 40 | 40
27 |  |  |  |  |  |  |  |  |  |  |  | 3 | 3 | 3 | 3
28 |  |  |  |  |  |  |  |  |  |  |  |  | 3 | 3 | 3
29 |  |  |  |  |  |  |  |  |  |  |  |  |  | 3 | 3
30 |  |  |  |  |  |  |  |  |  |  |  |  |  |  | 3

##  Appendix C Atomic Data Provenance

Table 3: Data provenance including the chianti (Dere et al., 1997), PP95 (Pradhan and Peng, 1995), and AMDPP (Badnell et al., 2003; Badnell, 2006) compilations. rt = rate type. dt = data type.  ID | Code | rt | dt | $\mathbf{(Z;N)}$ | References
---|---|---|---|---|---
ac81 | 1000 | 3 | 56 | $(8;1)$ | (Abu-Salbi and Callaway, 1981)
ac92 | 1001 | 3 | 56 | $(2;1)$ | (Aggarwal et al., 1992)
ak91 | 1002 | 3 | 56 | $(6;1)$ | (Aggarwal and Kingston, 1991a)
ak91a | 1003 | 3 | 56 | $(10;1)$ | (Aggarwal and Kingston, 1991b)
ak92 | 1004 | 3 | 56 | $(14;1)$ | (Aggarwal and Kingston, 1992a)
ak92a | 1005 | 3 | 56 | $(20;1)$ | (Aggarwal and Kingston, 1992b)
ak93 | 1006 | 3 | 56 | $(26;1)$ | (Aggarwal and Kingston, 1993)
ba00 | 1007 | 4 | 50 | $(28;2)$ | (Bautista, 2000)
bm98 | 1008 | 3 | 56 | $(26;15)$ |  (Binello et al., 1998), chianti ((Flower, 1977; Tayal et al., 1987))
bn00 | 1009 | 3 | 56 | $(26;20)$ |  (Berrington et al., 2000), chianti ((Keenan and Norrington, 1987))
bp98 | 1010 | 3 | 56 | $(26;25)$ | (Bautista and Pradhan, 1998)
ch00 | 1011 | 3 | 51 |  $(10;7)$, $(20;8)$, $(26;16)$, $(28;14)$ |  chianti ((Gau and Henry, 1977))
ch00 | 1012 | 4 | 50 |  $(6,7,8;4)$, $(12,14;5)$,$(20;8)$, |  chianti ((Gau and Henry, 1977))
|  |  |  |  $(26;6,12,14{-}18)$, $(28;14)$ |
ch01 | 1013 | 3 | 51 | $(6,7;3)$ |  chianti ((Gau and Henry, 1977))
ch01 | 1014 | 4 | 50 | $(6,7;3)$ |  chianti ((Wiese et al., 1966; Martin et al., 1993))
ch02 | 1015 | 4 | 50 | $(8,10,12,14,16,18,20,26,28;3)$ |  chianti ((Zhang et al., 1990; Martin et al., 1993))
ch02 | 1016 | 3 | 51 | $(8,10,12,14,16,18,20,28;3)$ |  chianti ((Zhang et al., 1990))
ch04 | 1017 | 3 | 51 | $(6;4)$ |  chianti ((Berrington et al., 1985, 1989))
ch04 | 1018 | 4 | 50 | $(10,12,16;4)$ |  chianti ((Muehlethaler and Nussbaumer, 1976; Sampson et al., 1984; Zhang and Sampson, 1992))
ch05 | 1019 | 3 | 51 | $(7;4)$ |  chianti ((Ramsbottom et al., 1994))
ch05 | 1020 | 4 | 50 | $(14,18,26;4)$ |  chianti ((Gau and Henry, 1977; Sampson et al., 1984))
ch06 | 1021 | 3 | 51 | $(8;4)$ |  chianti ((Kato et al., 1990; Zhang and Sampson, 1992))
ch06 | 1022 | 4 | 50 | $(20,28;4)$ |  chianti ((Muehlethaler and Nussbaumer, 1976; Zhang and Sampson, 1992))
ch07 | 1023 | 3 | 51 | $(10,12,14,16,18,20,26,28;4)$ |  chianti ((Sampson et al., 1984; Zhang and Sampson, 1992))
ch07 | 1024 | 4 | 50 | $(6;5)$ |  chianti ((Dankwort and Trefftz, 1978; Nussbaumer and Storey, 1981; Lennon et al., 1985)), nist
ch08 | 1025 | 3 | 51 | $(6;5)$ |  chianti ((Blum and Pradhan, 1992))
ch08 | 1026 | 4 | 50 | $(7;5)$ |  chianti ((Nussbaumer and Storey, 1979; Stafford et al., 1993))
ch09 | 1027 | 4 | 50 | $(8,10;5)$ |  chianti ((Dankwort and Trefftz, 1978))
ch09 | 1028 | 3 | 51 | $(7;5)$ |  chianti ((Stafford et al., 1994a, b))
ch10 | 1029 | 4 | 50 | $(16,18,20;5)$ |  chianti ((Dankwort and Trefftz, 1978; Bhatia et al., 1986))
ch10 | 1030 | 3 | 51 | $(8,10,12,14,16,18,20,26;5)$ |  chianti ((Zhang et al., 1994))
ch11 | 1031 | 3 | 51 | $(28;5)$ |  chianti ((Sampson et al., 1986))
ch11 | 1032 | 4 | 50 | $(26;5)$ |  chianti ((Sampson et al., 1990))
ch12 | 1033 | 4 | 50 | $(28;5)$ |  chianti ((Dankwort and Trefftz, 1978; Bhatia et al., 1986; Sampson et al., 1986))
ch12 | 1034 | 3 | 51 | $(7;6)$ |  chianti ((Stafford et al., 1994a, b))
ch13 | 1035 | 4 | 50 | $(7;6)$ |  chianti ((Gau and Henry, 1977; Bell et al., 1995))
ch13 | 1036 | 3 | 51 | $(8;6)$ |  chianti ((Aggarwal, 1983, 1985; Bhatia and Kastner, 1993; Lennon and Burke, 1994))
ch14 | 1037 | 4 | 50 | $(8;6)$ |  chianti ((Bhatia and Kastner, 1993))
ch14 | 1038 | 3 | 51 | $(10;6)$ |  chianti ((Aggarwal, 1984; Bhatia and Doschek, 1993a; Lennon and Burke, 1994))
ch15 | 1039 | 4 | 50 | $(10,12,14;6)$ |  chianti ((Bhatia and Doschek, 1993a, b))
ch15 | 1040 | 3 | 51 | $(12;6)$ |  chianti ((Bhatia and Doschek, 1995))
ch16 | 1041 | 3 | 51 | $(14;6)$ |  chianti ((Bhatia and Doschek, 1993a, b)
ch16 | 1042 | 4 | 50 | $(16;6)$ |  chianti ((Bhatia and Kastner, 1987),)
ch17 | 1043 | 4 | 50 | $(18;6)$ |  chianti ((Dere et al., 1979)
ch17 | 1044 | 3 | 51 | $(16;6)$ |  chianti ((Mason and Bhatia, 1978; Bhatia and Kastner, 1987))
ch18 | 1045 | 3 | 51 | $(18;6)$ |  chianti ((Dere et al., 1979))
ch18 | 1046 | 4 | 50 | $(20;6)$ |  chianti ((Froese Fischer and Saha, 1985))
Table 2: – continued ID | Code | rt | dt | $\mathbf{(Z;N)}$ | References
---|---|---|---|---|---
ch19 | 1047 | 3 | 51 | $(20;6)$ |  chianti ((Aggarwal et al., 1991a, b))
ch19 | 1048 | 4 | 50 | $(12,14,16,18,20;7)$ |  chianti ((Bhatia and Mason, 1980))
ch20 | 1049 | 4 | 50 | $(26;7)$ |  chianti ((Bhatia et al., 1989))
ch20 | 1050 | 3 | 51 | $(26;6)$ |  chianti ((Mason et al., 1979; Aggarwal, 1991))
ch21 | 1051 | 4 | 50 | $(14,16,18;8)$ |  chianti ((Bhatia et al., 1979))
ch21 | 1052 | 3 | 51 | $(8;7)$ |  chianti ((McLaughlin and Bell, 1994))
ch22 | 1053 | 3 | 51 | $(12,14,16,18,20;7)$ |  chianti ((Bhatia and Mason, 1980))
ch22 | 1054 | 4 | 50 | $(26;8)$ |  chianti ((Loulergue et al., 1985))
ch23 | 1055 | 3 | 51 | $(26;7)$ |  chianti ((Bhatia and Mason, 1980; Bhatia et al., 1989))
ch24 | 1056 | 4 | 50 | $(12,14,16,20;9)$ |  chianti ((Blackford and Hibbert, 1994)), nist
ch24 | 1057 | 3 | 51 | $(10,12;8)$ |  chianti ((Butler and Zeippen, 1994))
ch25 | 1058 | 3 | 51 | $(14,16,18;8)$ |  chianti ((Bhatia et al., 1979),)
ch25 | 1059 | 4 | 50 | $(26,28;9)$ |  chianti ((Sampson et al., 1991; Cornille et al., 1992; Blackford and Hibbert, 1994))
ch26 | 1060 | 4 | 50 | $(14;10)$ |  chianti ((Bhatia et al., 1985))
ch26 | 1061 | 3 | 51 | $(26;8)$ |  chianti ((Loulergue et al., 1985))
ch27 | 1062 | 4 | 50 | $(16;10)$ |  chianti ((Hibbert et al., 1993))
ch27 | 1063 | 3 | 51 | $(10;9)$ |  chianti ((Saraph and Tully, 1994))
ch28 | 1064 | 3 | 51 | $(12;9)$ |  chianti ((Mohan et al., 1988))
ch28 | 1065 | 4 | 50 | $(18,20,28;10)$ |  chianti ((Zhang et al., 1987; Hibbert et al., 1993))
ch29 | 1066 | 4 | 50 | $(26;10)$ |  chianti ((Bhatia and Doschek, 1992))
ch29 | 1067 | 3 | 51 | $(14;9)$ |  chianti ((Mohan and Le Dourneuf, 1990; Saraph and Tully, 1994))
ch30 | 1068 | 3 | 51 | $(16;9)$ |  chianti ((Mohan et al., 1987; Saraph and Tully, 1994))
ch30 | 1069 | 4 | 50 | $(12,14,16,18,20,26,28;11)$ |  chianti ((Wiese et al., 1966; Sampson et al., 1990))
ch31 | 1070 | 4 | 50 | $(14;12)$ |  chianti ((Gau and Henry, 1977; Dufton et al., 1983))
ch31 | 1071 | 3 | 51 | $(20,26;9)$ |  chianti ((Mason, 1975; Saraph and Tully, 1994))
ch32 | 1072 | 3 | 51 | $(14;10)$ |  chianti ((Bhatia et al., 1985))
ch32 | 1073 | 4 | 50 | $(16,18,20,28;12)$ |  chianti ((Christensen et al., 1986)), nist
ch33 | 1074 | 4 | 50 | $(14;13)$ |  chianti ((Gau and Henry, 1977; Lanzafame, 1994))
ch33 | 1075 | 3 | 51 | $(16;10)$ |  chianti ((Mohan et al., 1990))
ch34 | 1076 | 4 | 50 | $(16;13)$ |  chianti ((Bhatia et al., 1980; Dufton et al., 1982))
ch34 | 1077 | 3 | 51 | $(18,20,28;10)$ |  chianti ((Zhang et al., 1987))
ch35 | 1078 | 3 | 51 | $(26;10)$ |  chianti ((Bhatia and Doschek, 1992))
ch35 | 1079 | 4 | 50 | $(26;13)$ |  chianti ((Fischer and Liu, 1986))
ch36 | 1080 | 4 | 50 | $(26;19)$ |  chianti ((Czyzak and Krueger, 1966; Fawcett, 1989)), nist
ch36 | 1081 | 3 | 51 | $(12,14,16,18,20,28;11)$ |  chianti ((Sampson et al., 1990))
ch37 | 1082 | 3 | 51 | $(14;12)$ |  chianti ((Dufton and Kingston, 1989))
ch37 | 1083 | 4 | 50 | $(26;20)$ |  chianti ((Nussbaumer et al., 1982))
ch38 | 1084 | 3 | 51 | $(16,18,20,28;12)$ |  chianti ((Christensen et al., 1986))
ch39 | 1085 | 3 | 51 | $(14;13)$ |  chianti ((Dufton and Kingston, 1991))
ch40 | 1086 | 3 | 51 | $(16;13)$ |  chianti ((Bhatia et al., 1980; Bhadra and Henry, 1980; Dufton et al., 1982))
ch41 | 1087 | 3 | 51 | $(26;18)$ |  chianti ((Fawcett and Mason, 1991; Mason, 1994))
ch42 | 1088 | 3 | 51 | $(26;19)$ |  chianti ((Czyzak and Krueger, 1966; Pindzola et al., 1989))
ch43 | 1089 | 3 | 51 | $(26;14)$ |  chianti ((Fawcett and Mason, 1989; Mason, 1994))
cj94 | 1090 | 3 | 56 | $(1;1)$ | (Callaway, 1994; Aggarwal and Kingston, 1991a)
cp99 | 1091 | 4 | 50 | $(26;21)$ | (Chen and Pradhan, 1999)
cp99 | 1092 | 3 | 56 | $(26;21)$ | (Chen and Pradhan, 1999)
eg99 | 1093 | 3 | 56 | $(26;11)$ | (Dufton and Kingston, 1989; Eissner et al., 1999a)
ei99 | 1094 | 3 | 56 | $(26;12)$ | (Gau and Henry, 1977; Eissner et al., 1999b)
fe01 | 1095 | 4 | 50 | $(26;25)$ | (Garstang, 1962; Nussbaumer and Storey, 1988; Giridhar and Arellano Ferro, 1995)
fe10 | 1096 | 3 | 56 | $(26;17)$ | (Gau and Henry, 1977; Pelan and Berrington, 1995)
fe24 | 1097 | 3 | 56 | $(26;3)$ | (Zhang et al., 1990; Berrington and Tully, 1997)
gr58 | 1098 | 4 | 50 | $(26;23)$ | (Garstang, 1958)
im | 1099 | 3 | 63 |  $(7,12,16,18,28;1)$, $(7;2)$ | Impact parameter method
kh84 | 1100 | 4 | 50 | $(2;2)$ | (Kono and Hattori, 1984)
km87 | 1101 | 3 | 56 | $(10,14,1;2)$ | (Sampson et al., 1983; Goett et al., 1983; Keenan et al., 1987; Zhang and Sampson, 1987)
kn89 | 1102 | 3 | 69 | $(6;2)$ | (Kato and Nakazaki, 1989)
Table 2: – continued ID | Code | rt | dt | $\mathbf{(Z;N)}$ | Reference
---|---|---|---|---|---
kn89b | 1103 | 3 | 69 | $(2,8,12,20;2)$ | (Goett et al., 1983; Sampson et al., 1983; Kato and Nakazaki, 1989)
kn89c | 1104 | 3 | 69 | $(26;2)$ | (Goett et al., 1983; Sampson et al., 1983; Kato and Nakazaki, 1989)
mg05 | 1105 | 4 | 50 | $(12;8)$ |  PP95 ((Kaufman and Sugar, 1986)), (Nussbaumer and Rusca, 1979; Nussbaumer and Storey, 1981; Mendoza, 1983)
ne01 | 1106 | 4 | 50 | $(10;7)$ |  (Gau and Henry, 1977), PP95 ((Zeippen, 1982; Kaufman and Sugar, 1986))
ne02 | 1107 | 4 | 50 | $(10;8)$ |  (Gau and Henry, 1977), PP95((Mendoza, 1983; Kaufman and Sugar, 1986))
np96 | 1108 | 4 | 50 | $(26;24)$ | (Nahar, 1996)
ny01 | 1109 | 4 | 50 | $(7;7)$ | (Butler and Zeippen, 1984; Bautista, 1999a, b)
ox01 | 1110 | 4 | 50 | $(8;6)$ |  PP95 ((Moore, 1985; Kaufman and Sugar, 1986)), chianti ((Bhatia and Kastner, 1993))
ox02 | 1111 | 4 | 50 | $(8;7)$ |  (Gau and Henry, 1977), PP95 ((Zeippen, 1982; Kaufman and Sugar, 1986))
ox03 | 1112 | 4 | 50 | $(8;8)$ |  (Bautista, 1999a, b), PP95((Mendoza, 1983; Kaufman and Sugar, 1986)
pb95 | 1113 | 3 | 56 | $(18,20;17)$ | (Pelan and Berrington, 1995)
pp01 | 1114 | 4 | 50 | $(6;6)$ |  PP95 ((Nussbaumer and Storey, 1981; Nussbaumer and Rusca, 1979; Kaufman and Sugar, 1986))
pp01 | 1115 | 3 | 56 | $(6;6)$ |  PP95((Pequignot and Aldrovandi, 1976; Johnson et al., 1987; Thomas and Nesbet, 1975))
pp02 | 1116 | 3 | 56 | $(7;7)$ |  PP95((Dopita et al., 1976; Berrington and Burke, 1981))
pp03 | 1117 | 3 | 56 | $(8;8)$ |  PP95((LeDourneuf and Nesbet, 1976; Berrington and Burke, 1981))
pp04 | 1118 | 3 | 56 | $(16;14)$ |  PP95 ((Mendoza, 1983; Johnson et al., 1987; Johnson and Kingston, 1987))
pp05 | 1119 | 4 | 50 | $(18,20;16)$ |  PP95((Mendoza, 1983; Kaufman and Sugar, 1986))
pp05 | 1120 | 3 | 56 |  $(18;14)$, $(20;19)$ |  PP95 ((Mendoza, 1983))
pp06 | 1121 | 3 | 56 | $(18;15)$ |  PP95 ((Zeippen et al., 1987))
pp06 | 1122 | 4 | 50 |  $(10;9)$, $(20;17)$ |  PP95 ((Kaufman and Sugar, 1986))
pp07 | 1123 | 3 | 56 | $(18,20;16)$ |  PP95 ((Krueger and Czyzak, 1970))
pp07 | 1124 | 4 | 50 | $(16;14)$ |  PP95 ((Mendoza and Zeippen, 1982; Kaufman and Sugar, 1986; Hayes, 1986))
pp08 | 1125 | 4 | 50 | $(18;15)$ |  PP95 ((Mendoza and Zeippen, 1982; Kaufman and Sugar, 1986))
pp09 | 1126 | 4 | 50 | $(18;17)$ |  PP95 ((Mendoza, 1983))
pp10 | 1127 | 4 | 50 | $(20;19)$ |  PP95 ((Fuhr and Wiese, 1990))
pp11 | 1128 | 4 | 50 | $(18;14)$ |  PP95((Dufton et al., 1982; Kaufman and Sugar, 1986))
rb96 | 1129 | 3 | 56 | $(16;15)$ |  (Ramsbottom et al., 1996), chianti ((Cai and Pradhan, 1993))
sm00 | 1130 | 3 | 51 | $(26;13)$ | (Storey et al., 2000)
ss01 | 1131 | 4 | 50 | $(16;15)$ | (Gau and Henry, 1977)
ss96 | 1132 | 3 | 56 | $(18,20;13)$ | (Saraph and Storey, 1996)
tb93 | 1133 | 4 | 50 | $(6,7,8,10,12,14,16,18,20,26;2)$ | (Cunto et al., 1993)
zh96 | 1134 | 3 | 56 | $(26;24)$ | (Zhang, 1996)
zp97 | 1135 | 3 | 56 | $(26;23)$ | (Zhang and Pradhan, 1997)
zs87 | 1136 | 3 | 56 | $(18,28;2)$ | (Zhang and Sampson, 1987)
bm01 | 1137 | 3 | 56 | $(26;3)$ | (Bautista et al., 2003)
bm01 | 1138 | 4 | 50 | $(26;3)$ | (Bautista et al., 2003)
bm02 | 1139 | 3 | 56 | $(26;4{-}10)$ | (Bautista et al., 2004)
pm01 | 1140 | 4 | 50 | $(26;4{-}9)$ | (Palmeri et al., 2003a)
pm02 | 1141 | 4 | 50 | $(26;18{-}25)$ | (Palmeri et al., 2003b)
mk01 | 1142 | 4 | 50 | $(26;10{-}17)$ | (Mendoza et al., 2004)
gm01 | 1143 | 4 | 50 | $(8;2{-}8)$ | (García et al., 2005)
gk01 | 1144 | 4 | 50 | $(7;1{-}7)$ | (García et al., 2009)
pm03 | 1145 | 4 | 50 | $(16;2{-}16)$ | (Palmeri et al., 2006)
pq01 | 1146 | 4 | 50 | $(10,12,14,16,18,20;2{-}Z)$ | (Palmeri et al., 2008a)
pq02 | 1147 | 4 | 50 | $(28;2{-}27)$ | (Palmeri et al., 2008b)
pq03 | 1148 | 4 | 50 | $(14;2{-}13)$ | (Palmeri et al., 2011)
pq04 | 1149 | 4 | 50 | $(9,11,15,17,19;2{-}(Z-1))$ | (Palmeri et al., 2012)
|  |  |  | $(21{-}25,27,29,30;2{-}(Z-1))$ |
mb01 | 1150 | 3 | 56 | $(9,11,15,17,19;3{-}(Z-2))$ | Unpublished
fj01 | 1151 | 3 | 56 | $(26;2,3)$ | (Foster et al., 2012)
fj01 | 1152 | 4 | 50 | $(26;2,3)$ | (Foster et al., 2012)
gu01 | 1153 | 4 | 50 | $(26;11{-}25)$ | (Gu et al., 2006)
gu01 | 1154 | 13 | 6 | $(26;11{-}25)$ | (Gu et al., 2006)

Table 2: – continued ID | Code | rt | dt | $\mathbf{(Z;N)}$ | Reference
---|---|---|---|---|---
kf01 | 1155 | 5 | 25 |  $(3{-}5,21,29,30;2)$, | (Kingdon and Ferland, 1996)
|  |  |  |  $(6{-}8,16;(Z-3){-}Z)$, |
|  |  |  |  $(10,12,14,16,18;(Z-2){-}Z)$, |
|  |  |  |  $(26,28;(Z-2){-}Z)$, |
|  |  |  | $(20;(Z-1){-}Z)$ |
bb01 | 1156 | 5, 15 | 95 | $(1{-}30;1{-}Z)$ | (Bryans et al., 2006)
tb01 | 1157 | 7 | 53 |  $(1{-}30;1)$, $(21{-}25,27{-}30;2)$, | Hydrogenic
|  |  |  | $(28;3{-}10,21{-}26,28)$ |
tb02 | 1158 | 7 | 53 | $(2{-}20,26;2)$ | (Fernley et al., 1987)
tb03 | 1159 | 7 | 53 | $(6,7,8,10,12,14,16,18,20,26;3)$ | (Peach et al., 1988)
tb04 | 1160 | 7 | 53 | $(6,7,8,10,12,14,16,18,20,26;4)$ | (Tully et al., 1990)
tb05 | 1161 | 7 | 53 | $(6,7,8,10,12,14,16,18,20,26;5)$ | (Fernley et al., 1999)
tb06 | 1162 | 7 | 53 | $(6,7,8,10,12,14,16,18,20,26;6)$ | (Luo and Pradhan, 1989)
tb07 | 1163 | 7 | 53 | $(7,8,10,12,14,16,18,20,26;7)$ | (Cunto et al., 1993)
tb08 | 1164 | 7 | 53 | $(8,10,12,14,16,18,20,26;8)$ | (Cunto et al., 1993)
tb09 | 1165 | 7 | 53 | $(10,12,14,16,18,20,26;9)$ | (Cunto et al., 1993)
tb10 | 1166 | 7 | 53 | $(10,12,14,16,18,20,26;10)$ | (Hibbert and Scott, 1994)
tb11 | 1167 | 7 | 53 | $(14,18,20,26;11)$ | (Cunto et al., 1993)
tb12 | 1168 | 7 | 53 | $(26;12)$ | (Butler et al., 1993)
tb13 | 1169 | 7 | 53 | $(26;13)$ | (Mendoza et al., 1995)
tb14 | 1170 | 7 | 53 | $(14,26;14)$ | (Nahar and Pradhan, 1993; Cunto et al., 1993)
tb15 | 1171 | 7 | 53 |  $(16;16)$, $(18;18)$, $(26;15{-}21)$ | (Cunto et al., 1993)
tb16 | 1172 | 7 | 53 | $(26;22)$ | (Bautista, 1996)
tb17 | 1173 | 7 | 53 | $(26;23)$ | (Bautista and Pradhan, 1997)
tb18 | 1174 | 7 | 53 | $(26;24)$ | (Nahar and Pradhan, 1996)
tb19 | 1175 | 7 | 53 | $(26;25)$ | (Nahar and Pradhan, 1994)
tb20 | 1176 | 7 | 53 | $(26;26)$ | (Bautista, 1997)
tb21 | 1177 | 7 | 53 | $(28;27)$ | (Bautista, 1999a)
vy01 | 1178 | 1, 7 | 59 |  $(3,4,5,9,11,15,17,19,21{-}25;1{-}Z)$, | (Verner and Yakovlev, 1995)
|  |  |  |  $(27,29,30;1{-}Z)$, $(13;1,2,12,13)$, |
|  |  |  |  $(14;14)$, $(16;16)$, $(18;18)$, |
|  |  |  |  $(20;18,29,30)$, $(26;19{-}25)$, $(28;21{-}28)$ |
kp01 | 1179 | 7 | 53 | $(26;3{-}26)$ | (Palmeri et al., 2002; Bautista et al., 2003, 2004; Kallman et al., 2004)
gg01 | 1180 | 7 | 53 | $(6;3{-}6)$ | (Hasoglu et al., 2010; Gatuzz et al., 2018)
gm01 | 1181 | 7 | 53 | $(8;3{-}8)$ | (García et al., 2005)
gg02 | 1182 | 7 | 49 | $(8;6{-}8)$ | (Gorczyca et al., 2013; Gatuzz et al., 2013a, b)
gk01 | 1183 | 7 | 53 | $(7;3{-}7)$ | (García et al., 2009)
wk01 | 1184 | 7 | 49 | $(10,12,14,16,18,20;3{-}10)$ | (Witthoeft et al., 2009)
gg03 | 1185 | 7 | 49 | $(10;8{-}10)$ | (Gorczyca, 2000; Juett et al., 2006; Gatuzz et al., 2015)
wk02 | 1186 | 7 | 49 | $(12,14,16,18,20;11{-}17)$ | (Witthoeft et al., 2011a)
gg04 | 1187 | 7 | 49 | $(12;3{-}12)$ | (Hasoğlu et al., 2014)
wk03 | 1188 | 7 | 49 | $(13;3{-}11)$ | (Witthoeft et al., 2013)
wk04 | 1189 | 7 | 49 | $(28;3{-}20)$ | (Witthoeft et al., 2011b)
tr01 | 1190 | 7 | 49 |  $(9;3{-}(Z-2))$, $(15,17,19;3{-}11)$ | (Palmeri et al., 2016)
|  |  |  | $(21{-}25,27,29,30;3{-}11)$ |
tr02 | 1191 | 7 | 49 |  $(15,17,19;12{-}(Z-2))$, | (Mendoza et al., 2017)
|  |  |  | $(21{-}25,27,29,30;12{-}18)$ |
tr03 | 1192 | 7 | 49 |  $(21{-}25,27;19{-}(Z-2))$, | (Mendoza et al., 2018)
|  |  |  |  $(28;21{-}26)$, $(29,30;19{-}26)$ |
ap01 | 1193 | 8 | 1 |  $(3{-}30;2)$, $(15{-}30;14{-}Z)$ | (Aldrovandi and Pequignot, 1973, 1976)
ap01 | 1194 | 8 | 7 |  $(3{-}5;2{-}Z)$, $(7,21,29,30;2)$, | (Aldrovandi and Pequignot, 1973, 1976)
|  |  |  | $(13{-}25,27{-}30;13{-}Z)$ |
ad01 | 1195 | 8 | 38 |  $(3{-}12;3{-}Z)$, $(13{-}30;3{-}13)$ |  AMDPP ((Badnell, 2006))
ad01 | 1196 | 8 | 39 |  $(3{-}13;3{-}Z)$, $(14{-}30;3{-}12)$, |  AMDPP ((Badnell et al., 2003))
|  |  |  |  $(26,28;13{-}20)$, $(26;21{-}26)$ |
ns01 | 1197 | 8 | 22 |  $(13;13)$, $(14;13,14)$ | (Nussbaumer and Storey, 1986)
gt01 | 1198 | 8 | 30 | $(1{-}30;1)$ | (Gould and Thakur, 1970)

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