# Critically Evaluated Atomic Data for Au IV Spectrum 111Released on Oct 01,
2021

Aashna Zainab Department of Physics, Aligarh Muslim University, Aligarh, UP
202002, India  K. Haris Department of Physics, Aligarh Muslim University,
Aligarh, UP 202002, India  Sébastien Gamrath Physique Atomique et
Astrophysique, Université de Mons, B-7000 Mons, Belgium  Pascal Quinet
Physique Atomique et Astrophysique, Université de Mons, B-7000 Mons, Belgium
IPNAS, Université de Liège, B-4000 Liège, Belgium  A. Tauheed Department of
Physics, Aligarh Muslim University, Aligarh, UP 202002, India K. Haris
<EMAIL_ADDRESS><EMAIL_ADDRESS>
(Received ****; Revised *****; Accepted ****)

###### Abstract

The spectral investigation of the triply ionized gold (Au IV) has been carried
out in the wavelength region of 500–2106 Å. The gold spectra were photographed
at the National Institute of Standards and Technology (NIST, USA) on a 10.7-m
normal incidence vacuum spectrograph (NIVS) using a sliding spark source as
well as on a 3-m NIVS at the Antigonish laboratory in Canada with a triggered
spark source. Our analysis is theoretically supported by the pseudo-
relativistic Hartree-Fock (HFR) formalism with superposition of configuration
interactions implemented in Cowan’s suite of codes. Radiative transition
parameters are also calculated using HFR+CPOL (core-polarization effects)
model and multiconfiguration Dirac-Hartree-Fock (MCDHF) approach, and their
comparisons are used to evaluate the transition rate data. All the previously
reported levels of the $5d^{8}$, $5d^{7}6s$, and $5d^{7}6p$ configurations are
confirmed, except one and three are newly established. The missing
${}^{1}S_{0}$ level of $5d^{8}$ is now established at 55277.8 cm-1. A total of
981 observed lines (E1-type) classified to 1031 transitions, including 133
newly identified, enabled us to optimize 139 energy levels. Several
astrophysically important transitions, forbidden (M1- and E2-types) lines of
$5d^{8}$ and $5d^{7}6s$, are provided with their Ritz wavelengths and
radiative parameters. A critically evaluated set of energy levels, observed
and Ritz wavelengths along with their uncertainties, transition rates, and
uniformly-scaled intensities of Au IV lines have been presented. Also, large
scale atomic data to compute opacity of Au IV in the kilonova ejecta have been
supplemented in this work.

atomic data – techniques: spectroscopic – instrumentation: spectrographs –
methods: laboratory: atomic – methods: data analysis – ultraviolet: general

††journal: ApJS

##  1 Introduction

The high resolution spectra of chemically peculiar stars obtained with the
Goddard High Resolution Spectrograph on-board Hubble Space Telescope rekindled
the interest in the spectroscopy of high-_Z_ elements. The rich spectrum of
the Hg-Mn $\chi$ Lupi stars is made up of the spectra of singly- and doubly-
ionized elements with empty 4 _d_ \- and 5 _d_ -sub-shells whose atomic
structures are quite complex (Leckrone et al., 1993). To obtain an accurate
data-set for these elements, it was proposed that their spectral research must
be supported by the energy parameters regularities in their iso-electronic
sequence (Wyart et al., 1993a). Consequently, Wahlgren et al. (1995)
summarized the elemental abundances of Pt, Au, and Hg in these chemically
peculiar stars, and Au abundances were estimated from the observation of a few
selected lines of Au II and Au III. The Au I and Au II have simple structures,
however, the spectrum of Au III and those of its higher charge stages are very
dense, and they overlap each other. In such cases, spectroscopic analysis of
adjacent charge states is highly useful and aids the accurate line
identification for the spectrum under investigation. Besides, the laboratory
studies of heavier elements ($Z\geq 54$) including gold have also gained high
astrophysical interest after the detection of the gravitational waves by the
LIGO–Virgo collaboration as its observations ‘GW170817’ and the followed
kilonova ‘AT2017gfo’ support the hypothesis that neutron star mergers (NSM)
can account for the nucleosynthesis of these heavy elements by r-process
(Abbott et al., 2017; Kasen et al., 2017; Kajino et al., 2019). To explain and
model the observed AT2017gfo spectra, large sets of calibrated atomic data are
needed for elements beyond iron-peak ($Z>30$) including data on their
ionization species (II–V). In this regard, large-scale atomic data for
computing the bound-bound opacities of r-process ejecta elements have been
given by Kasen et al. (2017); Tanaka et al. (2018); Fontes et al. (2020);
Tanaka et al. (2020), however, data for neutral gold (Au) and its ions (Au
II–IV) were only included in the work of Tanaka et al. (2020). Recently,
Bromley et al. (2020) and McCann et al. (2022) have provided more calibrated
atomic data for Au I–III ions, and Gillanders et al. (2021) used these data
together with data on Pt I–III to estimate Au/Pt abundances in the ejecta of
AT2017gfo for photospheric and nebular phases. For photospheric modeling, data
on allowed electric-dipole transitions could be important, whereas, Gillanders
et al. (2021) had manifested that the accurate data on radiative parameters of
forbidden lines are important to interpret the observed kilonova AT2017gfo
spectra of late-epochs, $t\geq$ +3 d and/or of NSM ejecta with low
temperatures and densities. Besides these, transition rates of electric and
magnetic dipole transitions in Au IV were reported by Taghadomi et al. (2022)
using GRASP code calculations. These authors also showed the expansion opacity
of Au IV for kilonova ejecta at time t = 1 day and for temperature T = 3700 K
and density $\rho$ = 10-13 g/cm3.

In terms of astrophysical observations, the presence of gold (Au I-II) has
been confirmed in the environments of various astrophysical objects, however,
so far only its allowed transitions are detected and no forbidden lines are
observed yet in the spectra of astrophysical objects (see details in Wahlgren
et al., 1995; Gillanders et al., 2021). It should be noted that at present
radiative parameters of forbidden transitions are reported only for Au I–III
spectra, and no such data are available for the Au IV. Also, our survey on
forbidden spectrum of Au IV shows that its several lines fall in the visible-
IR (0.5 to 28 $\mu$m) operating region of the recently launched James Webb
Space Telescope (JWST), and the role of the JWST will be instrumental for the
future kilonovae observations in the IR region (Bartos et al., 2016) as
similar to observations made by the Spitzer Space Telescope for the ‘GW170817’
NSM event (Villar et al., 2018; Wu et al., 2019; Kasliwal et al., 2022).
Therefore, from laboratory to astrophysics, accurate data on energy levels,
wavelengths, intensities, and transition rates are greatly needed for various
applications (Wahlgren, 2011), including estimating the abundances of
r-process elements in the kilonova ejecta (Vieira et al., 2023). These data
are also used for improving the accuracy of theoretical calculations of
complex atoms/ions. Thus, the present work aims to provide critically
evaluated spectral data for triply-ionized gold (Au IV) belonging to the 5 _d_
-series elements.

Au IV is a member of Os I iso-electronic sequence. Its ground configuration is
[Xe] $4f^{14}5p^{6}5d^{8}$, which consists of 9 energy levels;
${}^{3}F_{4,3,2}$, ${}^{3}P_{2,1,0}$, ${}^{1}D_{2}$, ${}^{1}G_{4}$ and
${}^{1}S_{0}$ among which ${}^{3}F_{4}$ is the lowest. The regular excited
configurations, formed by the excitation of one electron from the $5d$ sub-
shell, are of the type $5p^{6}5d^{7}$_nl_ $(\emph{n}\geq 5,\emph{l}\geq 0)$.
Promotion of two or three electrons leads to the complex configurations such
as $5d^{6}6s^{2}$, $5d^{6}6p^{2}$, $5d^{6}6s6p$, and $5d^{5}6s^{2}6p$. These
configurations are incorporated in the theoretical calculations for better
accuracy.

The first spectral analysis which provided an insight into the energy level
structure of Au IV was performed by Joshi et al. (1991). They studied the
$5d^{8}$–$5d^{7}6p$ transition array in the wavelength region of 554–850 Å.
Wyart et al. (1994) provided an extended analysis of Au IV spectrum by
identifying about 700 lines of the $(5d^{8}+5d^{7}6s)$–$5d^{7}6p$ transition
array in the wavelength region of 554–2080 Å. They established 33 (out of 38)
energy levels of the $5d^{7}6s$ configuration and increased the known levels
of $5d^{7}6p$ from 64 to 95. Apart from these, the $4f$ and $5p$
photoabsorption spectra of Au IV have been studied in the wavelength region of
98 to 180 Å using a dual laser-plasma technique (Su et al., 2009). This work
is beyond the scope of our investigation, therefore, we did not include it in
this critical evaluation.

In this work, we have critically evaluated all the previously reported data on
the Au IV using the spectrum recorded on a 10.7-m normal incidence vacuum
spectrograph, and also by providing a theoretical support for our observations
within the pseudo-relativistic Hartree-Fock approach, and the effects of core-
polarization are accounted for computing the accurate transition rates for Au
IV spectrum. We aim to provide the wavelengths of observed lines (together
with their Ritz counterpart), the optimized energy levels with their
uncertainties, uniformly-scaled intensities, and transition rates for observed
and possibly observable lines of both allowed and forbidden types. The latter
types are intra- and inter-configurations transitions between the levels of
$5d^{8}$ and $5d^{7}6s$, however, may have implications in astrophysics, in
particular to interpret the visible and near-infrared parts of the kilonova
spectra associated with NSM event (Gillanders et al., 2021).

##  2 Experimental Details

The spectral plates used for this work were the same as those used for the
previous analysis of Au III by Zainab & Tauheed (2019). Nevertheless, the
necessary details regarding the spectrograms and its recording are provided
here for the completeness. The recording of the gold spectra, in the region of
500–2106 Å, was performed on a 10.7-m normal incidence vacuum spectrograph
(NIVS) at the National Institute of Standard and Technology (NIST, USA) using
sliding spark as the excitation source. The spectrograph was equipped with a
1200 lines per mm grating which had the first order reciprocal dispersion of
0.78 Å mm-1. The gold spectra were also recorded at the Antigonish laboratory
on a 3-m NIVS with reciprocal dispersion of 1.385 Å mm-1 using a triggered
spark source. The latter was used just for the purpose of ionization
separation. Kodak Short Wave Radiation (SWR) plates were used for recording of
the spectra. Several tracks of exposures were taken on each plate by varying
the experimental conditions, which were achieved by either adjusting the
capacitor’s charging potential or by inserting inductor coils in series with
the discharge circuit. The variation in line intensity at different discharge
settings allowed for a satisfactory ionization separation. The track with the
strongest Au IV lines was used to measure the wavelengths and the remaining
tracks on each plate were used to accomplish the ionization separation. The
relative positions of the spectral lines along with their relative visual-
intensities were measured on a Zeiss Abbe comparator at Aligarh Muslim
University, Aligarh. The calibration of the spectrograms were then carried out
using reference lines of C II–IV, Si II–IV, Al II–III, O II–V (Kramida et al.,
2022a) together with some Au II lines (Rosberg & Wyart, 1997). The general
estimate of wavelength uncertainty is due to the combined effect of the
statistical deviation of the line position measured on the comparator and the
systematic uncertainty of reference wavelengths used in the fitting. The final
wavelength uncertainty for sharp and unperturbed lines is estimated to be
better than 0.005 Å and the figure has been doubled for all perturbed lines.

The spectral lines’ intensities were visual estimates representing the
photographic emulsion blackening. To bring these intensities on a uniform
scale, intensity modelling was performed (see Section. 5).

##  3 Analysis of the spectrum

The first spectroscopic analysis of Au IV was carried out by Joshi et al.
(1991) using the spectra recorded on a 6.65-m NIVS at the Zeeman Laboratory
and on a 3-m NIVS at the Antigonish laboratory in the wavelength region of
554–850 Å. For both the cases, triggered spark was used as the excitation
source. Several exposures were recorded on Kodak SWR plates with different
experimental conditions. The relative positions of spectral lines were
measured on Cospinsca or Grant semiautomatic comparators and the line
intensity is reported on a scale of 1 to 99. The wavelength calibration was
done using the internal standards of carbon, oxygen, and silicon ions’ lines
and their measured wavelength uncertainty was 0.005 Å. On the basis of the
classification of 196 lines, 8 out of 9 levels of $5d^{8}$ and 64 out of 110
levels of $5d^{7}6p$ configuration were reported by them.

In the extended analysis of Au IV spectrum, Wyart et al. (1994) reported the
lines belonging to $5d^{7}6s$–$5d^{7}6p$ transition array in the region of
1020–1930 Å. The spectrograms were recorded on a 10.7-m NIVS of the National
Bureau of Standards (now known as NIST, USA) having 0.78 Å mm-1 as the
reciprocal dispersion. A sliding spark was used as the excitation source which
was operated at different experimental conditions to achieve ionization
separation. The spectrograms were measured on a semi-automatic comparator at
Observatoire de Paris-Meudon and were calibrated using the reference standards
of Cu (copper hollow cathode spectrum was recorded on the same plates), Si, C,
N and Al. The accuracy of this measurement was quoted $\pm$0.007 Å. Additional
gold plates, recorded by Joshi et al. (1991) on the same experimental setup in
the wavelength region of 554–2080 Å, were also supplemented to support the
analyses. In the $5d^{7}6s$–$5d^{7}6p$ transition array, a total of 657 lines
and between $5d^{8}$–$5d^{7}6p$ configurations 47 newly classified lines have
been reported by them. This lead to the establishment of 33 out of 38 energy
levels of $5d^{7}6s$ configuration and among $5d^{7}6p$ levels, two were
revised and 31 being newly established.

Our investigation started with the verification of the previously reported
data on Au IV. In total 139 energy levels belonging to the $5d^{8}$,
$5d^{7}6s$, and $5d^{7}6p$ configurations have been confirmed. A total of 981
observed lines classified to 1031 transitions were used to obtain the
optimized energy levels of Au IV spectrum. All classified lines of Au IV are
assembled in Table 1 with their observed wavelengths and uncertainties. The
optimized energy levels of Au IV are given in Table 2. The major findings of
our present analysis are summarized below:

One level of $5d^{7}6p$ configuration with $J$ = 2, reported earlier by Joshi
et al. (1991) at $\approx$ 188525 cm-1 is now revised to 188170.6 cm-1 with
the aid of five transitions. We are also successful in establishing the
missing ${}^{1}S_{0}$ level of the $5d^{8}$ configuration. This level was
already known in the Hg V (Wyart et al., 1993b), Tl VI (Raassen et al.,
1994a), Pb VII (Raassen et al., 1994b), and Bi VIII (Kildiyarova et al., 1995)
ions, thus it was possible to recalculate all the Slater parameters of this
configuration and enhance the accuracy of its predicted value along the iso-
electronic sequence. Therefore, after eliminating the previously classified
lines in the expected region, the level was established at 55277.8 cm-1 and is
supported by six Au IV transitions. This energy level value compares well with
55391 cm-1, which was predicted by Wyart et al. (1993a) based on the
orthogonal operator treatment. The determination of the $5d^{8}$ ${}^{1}S_{0}$
level resulted in new calculation parameters for the ground configuration (see
Section 6.1). Additionally, two new levels of $5d^{7}6p$ configuration with
$J$ = 0 were established at 140590.70 cm-1 and 149963.62 cm-1 on the basis of
four and three transitions, respectively. These observed lines were weak in
our spectrograms, but they exhibited a distinct Au IV character similar to
that of other previously classified Au IV lines that appeared in these
spectrograms.

Table 1: Classified Lines of Au IV

_I_ obs a | Char.a |  $\lambda_{obs}$ b | Unc.b,c | Lower Leveld | Upper Leveld |  $\lambda_{Ritz}$ b | Unc.b |  $\lambda_{prev}^{corr}$ e |  _A_ -value (in s-1) f | Acc.g | Line Ref.h | Comm.i
---|---|---|---|---|---|---|---|---|---|---|---|---
(arb. u.) |  | (Å) | (Å) |  |  | (Å) | (Å) | (Å) | HFR+CPOL | HFR |  |  |
|  |  |  | 5 _d_ 8 3 _F_ 4 | 5 _d_ 7(2 _Da_)6 _p_ 1 _F_ ${}^{\circ}_{3}$ | 524.6742 | 0.0008 |  | 2.51e+06 | 3.52e+06 | E |  |
|  |  |  | 5 _d_ 8 3 _F_ 4 | 5 _d_ 7(2 _F_)6 _p_ 1 _F_ ${}^{\circ}_{3}$ | 530.9707 | 0.0011 |  | 5.64e+05 | 5.31e+05 | E |  |
|  |  |  | 5 _d_ 8 3 _F_ 4 | 5 _d_ 7(2 _Db_)6 _p_ 3 _F_ ${}^{\circ}_{3}$ | 535.9620 | 0.0009 |  | 4.87e+05 | 4.32e+05 | E |  |
… | … | … | … | … | … | … | … | … | … | … | … | … | …
4900 |  | 608.188 | 0.005 | 5 _d_ 8 3 _P_ 2 | 5 _d_ 7(2 _G_)6 _p_ 1 _F_ ${}^{\circ}_{3}$ | 608.1802 | 0.0008 | 608.183 | 4.08e+07 | 5.88e+07 | D | TW,J91 | U
1800 | * | 608.883 | 0.016 | 5 _d_ 8 3 _F_ 4 | 5 _d_ 7(2 _G_)6 _p_ 3 _F_ ${}^{\circ}_{3}$ | 608.8920 | 0.0008 | 608.887 | 4.18e+07 | 3.49e+07 | D | TW,J91 |
1800 | * | 608.883 | 0.013 | 5 _d_ 8 3 _P_ 1 | 5 _d_ 7(2 _Da_)6 _p_ 3 _F_ ${}^{\circ}_{2}$ | 608.8844 | 0.0011 | 608.887 | 1.11e+08 | 1.40e+08 | D+ | TW,J91 |
940 |  | 610.140 | 0.005 | 5 _d_ 8 3 _F_ 3 | 5 _d_ 7(2 _P_)6 _p_ 3 _D_ ${}^{\circ}_{2}$ | 610.1429 | 0.0008 | 610.143 | 8.61e+07 | 4.78e+07 | D | TW,J91 |
… | … | … | … | … | … | … | … | … | … | … | … | … | …
650 |  | 1110.180 | 0.005 | 5 _d_ 7(2 _F_)6 _s_ 3 _F_ 2 | 5 _d_ 7(2 _H_)6 _p_ 3 _G_ ${}^{\circ}_{3}$ | 1110.1858 | 0.0022 |  | 6.38e+07 | 8.22e+07 | D+ | TW |
1500 |  | 1110.657 | 0.005 | 5 _d_ 7(2 _G_)6 _s_ 3 _G_ 4 | 5 _d_ 7(2 _G_)6 _p_ 1 _H_ ${}^{\circ}_{5}$ | 1110.6593 | 0.0016 | 1110.659 | 8.62e+07 | 8.77e+07 | D+ | TW,W94 | V
930 | d | 1110.872 | 0.010 | 5 _d_ 7(4 _P_)6 _s_ 5 _P_ 2 | 5 _d_ 7(2 _Db_)6 _p_ 3 _D_ ${}^{\circ}_{3}$ | 1110.8667 | 0.0013 | 1110.866 | 2.51e+08 | 2.76e+08 | D+ | TW,W94 |
930 | d | 1110.951 | 0.010 | 5 _d_ 7(2 _H_)6 _s_ 3 _H_ 6 | 5 _d_ 7(2 _H_)6 _p_ 3 _H_ ${}^{\circ}_{5}$ | 1110.9557 | 0.0024 | 1110.951 | 1.55e+08 | 1.42e+08 | D+ | TW,W94 |
… | … | … | … | … | … | … | … | … | … | … | … | … | …
480 | SA | 1510.878 | 0.005 | 5 _d_ 7(4 _F_)6 _s_ 3 _F_ 4 | 5 _d_ 7(4 _F_)6 _p_ 5 _G_ ${}^{\circ}_{4}$ | 1510.8796 | 0.0022 | 1510.880 | 1.31e+08 | 1.25e+08 | D+ | TW,W94 |
480 | d | 1511.011 | 0.010 | 5 _d_ 7(4 _F_)6 _s_ 5 _F_ 1 | 5 _d_ 7(4 _F_)6 _p_ 5 _F_ ${}^{\circ}_{2}$ | 1511.010 | 0.003 | 1511.005 | 8.54e+07 | 1.11e+08 | D+ | TW,W94 |
450 |  | 1511.442 | 0.005 | 5 _d_ 7(2 _P_)6 _s_ 3 _P_ 1 | 5 _d_ 7(2 _P_)6 _p_ 3 _D_ ${}^{\circ}_{1}$ | 1511.4414 | 0.0023 | 1511.443 | 9.90e+07 | 1.09e+08 | D+ | TW,W94 | U
… | … | … | … | … | … | … | … | … | … | … | … | … | …
89 |  | 1891.924 | 0.005 | 5 _d_ 7(2 _P_)6 _s_ 1 _P_ 1 | 5 _d_ 7(4 _F_)6 _p_ 5 _F_ ${}^{\circ}_{2}$ | 1891.930 | 0.003 | 1891.928 | 3.80e+06 | 5.58e+06 | D | TW,W94 | T
… | … | … | … | … | … | … | … | … | … | … | … | … | …
|  |  |  | 5 _d_ 7(2 _F_)6 _s_ 3 _F_ 3 | 5 _d_ 7(4 _F_)6 _p_ 5 _D_ ${}^{\circ}_{4}$ | 3624.831 | 0.013 |  | 2.42e+04 | 2.27e+04 | E |  |

Note. — (A few columns are omitted in this condensed sample, but their
footnotes (c, d, f) are fully retained for guidance regarding their types and
content.)

a Averaged relative observed intensities in arbitrary units are given on a
uniform scale corresponding to the Boltzmann populations in a plasma with an
effective excitation temperature of 5.5 eV, for our spectrum (see Section 5).
The intensity value is followed by the line character encoded as follows:
bl–blended by other lines; d–diffused; h–hazy; m–masked by other nearby lines;
q–asymmetric; s–shaded; SA–self-absorbed; SL–shoulder line of long wavelength
side; SS–shoulder line of short wavelength side; w–wide; ++–too intense than
expected; ?–questionable line; *–intensity shared by more than one lines.

b Observed and Ritz wavelengths are in vacuum for $\lambda$ $<$ 2000 Å and in
standard air outside this limit. Conversion between air and vacuum was made
with the five-parameter formula from Peck & Reeder (1972). Assigned
uncertainty of given observed wavelength or computed uncertainty of Ritz
wavelength are determined in the level optimization procedure.

c Observed wavenumber (in vacuum) and its uncertainty. These two columns are
omitted in this condensed table.

d Level designations and their energies from Table 2. Two columns for energies
are dropped from this condensed table.

e Previous observed wavelength, reported either by Joshi et al. (1991) or by
Wyart et al. (1994), was corrected using Ritz wavelength of this work (see
Section 4).

f Transition rates or _A_ -values, from HFR+CPOL and HFR calculations. The
quantity _$|$ CF$|$_min is the minimum of their absolute cancellation factors
(see Section 7). This column of _$|$ CF$|$_min is omitted in this condensed
table.

g Accuracy code of the _A_ -value is given in Table 4 (see Section 7.1).

h Line references: J91– Joshi et al. (1991); W94– Wyart et al. (1994); TW–This
work.

i Comments: T–the variation of individual line intensities used for intensity
averaging are within a factor of one; U–those vary within a factor of two;
V–those vary within a factor of three; W–those vary by more than a factor of
three but less than ten; X–the variation is more than a factor of ten, hence
it is excluded from the intensity averaging; Y–the line reported by previous
observer is a perturbed line, therefore, excluded from the intensity
averaging.

(This table is available in its entirety in machine-readable form.)

Table 2: Optimized Energy Levels of Au IV

=1in  Configurationa Terma _J_ Energy Unc.b Perc.c Perc2c Conf2c Perc3c Conf3c
NoLd $\Delta$E${}_{o-c}^{e}$ Comm.f (cm-1) (cm-1) (cm-1) 5 _d_ 8 3 _F_ 4 0.00
0.20 94 5 5 _d_ 8 1 _G_ … 39 131 5 _d_ 8 3 _P_ 2 6630.12 0.18 46 35 5 _d_ 8 1
_D_ 18 5 _d_ 8 3 _F_ 43 -63 5 _d_ 8 3 _F_ 3 12293.66 0.18 99 … … 40 41 5 _d_ 8
3 _F_ 2 18100.97 0.16 48 46 5 _d_ 8 3 _P_ … 48 -37 5 _d_ 8 3 _P_ 0 18185.2 0.4
82 16 5 _d_ 8 1 _S_ … 11 -161 5 _d_ 8 3 _P_ 1 21489.95 0.21 97 2 5 _d_ 7(2
_P_)6 _s_ 3 _P_ … 27 -9 5 _d_ 8 1 _G_ 4 25702.13 0.16 94 5 5 _d_ 8 3 _F_ … 31
33 5 _d_ 8 1 _D_ 2 30735.67 0.20 49 35 5 _d_ 8 3 _F_ 14 5 _d_ 8 3 _P_ 30 -5 5
_d_ 7(4 _F_)6 _s_ 5 _F_ 5 51296.97 0.15 86 13 5 _d_ 7(2 _G_)6 _s_ 3 _G_ … 12
-105 5 _d_ 8 1 _S_ 0 55277.8 0.3 83 15 5 _d_ 8 3 _P_ … 6 64 N … … … … … … … …
… … … … … 5 _d_ 7(4 _P_)6 _s_ 5 _P_ 3 68890.98 67 17 5 _d_ 7(4 _F_)6 _s_ 5 _F_
8 5 _d_ 7(4 _F_)6 _s_ 3 _F_ 30 39 B 5 _d_ 7(4 _P_)6 _s_ 5 _P_ 1 72968.57 0.09
47 24 5 _d_ 7(4 _F_)6 _s_ 5 _F_ 19 5 _d_ 7(2 _P_)6 _s_ 3 _P_ 21 133 5 _d_ 7(2
_G_)6 _s_ 3 _G_ 5 75093.20 0.10 59 23 5 _d_ 7(2 _H_)6 _s_ 3 _H_ 12 5 _d_ 7(4
_F_)6 _s_ 5 _F_ 18 -165 5 _d_ 7(4 _F_)6 _s_ 3 _F_ 3 75819.28 0.08 58 14 5 _d_
7(4 _P_)6 _s_ 5 _P_ 13 5 _d_ 7(2 _Db_)6 _s_ 3 _D_ 30 -30 … … … … … … … … … … …
… … 5 _d_ 7(2 _Da_)6 _s_ 1 _D_ 2 123610 200 75 7 5 _d_ 7(2 _Db_)6 _s_ 1 _D_ 5
5 _d_ 7(2 _F_)6 _s_ 3 _F_ 0 L 5 _d_ 7(4 _F_)6 _p_ 5 _D_ ∘ 4 120217.42 0.09 42
20 5 _d_ 7(4 _F_)6 _p_ 5 _F_ ∘ 13 5 _d_ 7(2 _G_)6 _p_ 3 _F_ ∘ 7 104 5 _d_ 7(4
_F_)6 _p_ 3 _G_ ∘ 5 122495.68 0.21 30 30 5 _d_ 7(4 _F_)6 _p_ 5 _F_ ∘ 21 5 _d_
7(4 _F_)6 _p_ 5 _G_ ∘ 5 359 5 _d_ 7(2 _P_)6 _p_ 3 _P_ ∘ 1 130380.25 0.10 23 12
5 _d_ 7(2 _Db_)6 _p_ 3 _D_ ∘ 10 5 _d_ 7(4 _P_)6 _p_ 5 _D_ ∘ 8 -145 … … … … … …
… … … … … … … 5 _d_ 7(2 _Da_)6 _p_ 1 _P_ ∘ 1 207500 400 50 20 5 _d_ 7(2 _Da_)6
_p_ 3 _D_ ∘ 6 5 _d_ 7(2 _Db_)6 _p_ 3 _P_ ∘ 0 L 5 _d_ 7(2 _Da_)6 _p_ 3 _D_ ∘ 3
207800 400 46 16 5 _d_ 7(2 _Db_)6 _p_ 3 _D_ ∘ 15 5 _d_ 7(2 _Da_)6 _p_ 1 _F_ ∘
0 L (This table is available in its entirety in machine-readable form.)

Note. —

a The level designations are in LS coupling scheme. Designations in
Configuration and Term may correspond to a component with second/third/fourth
largest percentage in the eigenvector and they are opted to uniquely define
the levels (see text).

b The quantity given in column Unc. is the uncertainty of separation from the
“base” level 5 _d_ 7(4 _P_)6 _s_ 5 _P_ 3 at 68890.98 cm-1 (see Section 4). To
estimate the uncertainties of excitation energies from the ground level, the
given values in column Unc. should be combined in quadrature with the
uncertainty of the ground level, 0.20 cm-1. All uncertainties are derived by
the LOPT code.

c The first leading percentage value refers to the configuration and term
given in the first two columns of the table. The 2nd, 3rd, 4th, and 5th
percentages refer to the configuration and term subsequent to them. The four
columns (for 4th and 5th percentages and their compositions) are omitted in
this condensed table.

d Number of observed lines determining the level in the level optimization
procedure. Zero for unobserved levels.

e Differences between energy observed and those calculated in the parametric
least-squares fitting (LSF) with Cowan’s code. Blank for unobserved levels.

f Comments: B–the base level for presentation of uncertainties; L–the level
position and its uncertainty are obtained in the parametric LSF calculations
with Cowan’s codes; N–new level; R–revised level.

##  4 OPTIMIZATION of ENERGY LEVELS

Figure 1: Comparison of wavelengths observed by Joshi et al. (1991) with those
of Ritz in this work. The dashed line represents a correction curve fitted
with a seventh order polynomial function (see text).

The least-squares level optimization procedure was done by using the computer
code LOPT (Kramida, 2011), which helps in obtaining the best fitted energy
level values for all observed lines. This process also checks the consistency
of the line classifications, by comparing the observed wavelengths with their
corresponding Ritz values. A thorough description of this method can be found
in several previous publications (Kramida, 2013a, b, c; Haris et al., 2014).
The optimization procedure was started by including only the previously
classified lines of Au IV which led to an initial estimate of the energy level
values and Ritz wavelengths of several possibly observable lines with their
uncertainties. These lines were searched out in our line list and the obtained
lines (about 130) along with their satisfactory character and intensities were
added to the optimization procedure. The entire process involves several
iterations of level optimization, consequently, the best optimized energy
values and uncertainties were obtained for 139 levels (see Table 2) with the
help of 981 distinct lines that are classified to 1031 transitions (see Table
1). To determine the final level uncertainties given in Table 2, the 5 _d_ 7(4
_P_)6 _s_ 5 _P_ 3 level at 68890.98 cm-1 was selected as a base level, because
this level has maximum number of accurately measured transitions.

Using these results, the final Ritz wavelengths ($\lambda_{Ritz}$) with their
estimated uncertainties were computed for all observed and several possibly
observable lines (see Table 1). These counterpart (i.e., $\lambda_{Ritz}$)
wavelengths are at least two-times (or more) accurate than the observed ones,
therefore, were served as reference lines to check internal consistencies of
previous measurements (Joshi et al., 1991; Wyart et al., 1994). The results of
these comparisons are shown in Figure 1 and 2. The suitable systematic
correction curves were made with the help of different polynomial fits (see
captions of Figure 1 and 2), and the corrected wavelengths of previous
measurements were provided in Table 1. The agreement between corrected and
Ritz wavelengths was found to be satisfactory within a standard deviation of
0.005 Å, which fairly agrees with their original claimed accuracy.

Figure 2: Comparison of wavelengths observed by Wyart et al. (1994) with those
of Ritz in this work. The dashed lines represent the correction curves – the
first ($\lambda$ $<$ 1000 Å) is fitted with a fourth order polynomial and the
second is made with a fifth order polynomial function (see text).

##  5 Reduction of Line Intensities

The line intensities play a vital role for the proper identification of the
observed lines. Generally, different observers use different scales to express
the relative line intensities. One of the widely used techniques to provide
the relative intensities is by the visual assessment of blackening of the
photographic emulsion. Besides, optical densitometers are also used for this
purpose. As the data under study were observed by several authors using
different excitation sources and recording equipments, there was a need to
convert the overall intensities to a uniform scale. This reduction was
achieved by using local thermodynamic equilibrium (LTE) approximation; the
detailed procedure of which has been explained in many laboratory spectrum
analyses (Kramida, 2013a, b, c; Haris et al., 2014). In this method, the
effective excitation temperature for any particular atom or ion is determined
using a simplified LTE model applied to the observation (line intensities).
This method requires accurate transition probabilities (g$A$-values) as well,
however, they are often provided from computations. Once the approximate
effective excitation temperature (_T_ exc) for the light source used has been
determined, the spectral response function(s) of the instrument (including the
detector) can easily be determined by comparing the observed and calculated
intensities. This function is subtracted from the observed intensities to
remove the effects of any spectral variations caused due to the instrument.
This leads to the reduction of corrected intensities and then to obtain a more
accurate value of  _T_ exc from the Boltzmann plot. Several iterations of this
procedure is performed until a reasonable convergence is reached. In the same
manner _T_ exc is derived for each sets of observations. Finally, all of them
were effectively reduced to a global uniform scale with a common  _T_ exc
obtained from one of the observations. If the same set of observed lines are
available from multiple sources, the modeled intensities for each of them is
averaged out.

The above mentioned procedure was followed for the intensities of Au IV lines
observed on our spectrograms, which were taken from seven different plates
recorded at different experimental conditions on the same instrument. It
should be noted that our originally recorded intensities are visual estimates
of photographic blackening of emulsion. The modeling of the intensities was
done using the weighted transition rates obtained from HFR+CPOL calculations.
The final _T_ exc for the light source used for the present study was derived
to be 5.5 eV. This temperature was chosen as the base to reduce the
intensities of other observations (Joshi et al., 1991; Wyart et al., 1994).

Joshi et al. (1991) measured the relative positions of the observed lines on a
Cospinsca or Grant semiautomatic comparator and reported the intensity on the
scale of 1 to 99. On the other hand, the intensities reported by Wyart et al.
(1994) were obtained mostly from a densitometer, which they traced for four
separate spectral plates. For a few set of lines the visual estimates were
also made. Wyart et al. (1994) mentioned that the comparisons of lines’
intensities were limited to a small span of wavelength range, and intensities
were not consistent for the entire range of observation. He also supplemented
the linelist with the gold plates recorded on the same experimental setup as
Joshi et al. (1991). To reduce these (Joshi et al., 1991; Wyart et al., 1994)
relative intensities into a common _T_ exc scale, we combined their
observations and a _T_ exc = 5.3 eV was obtained for the combined observation.
To compare (and to average) these line intensities with that of our
spectrograms, the reduced (corrected) intensities were further scaled with
respect to the common _T_ exc = 5.5 eV of our work. In the end, the modelled
line intensities for the commonly observed lines were compared, and an
averaging of them was made if they agree within a standard deviation of one
order of magnitude. Our final modelled line intensities with their line
characters (_I_ obs & Char.) are given in the first two columns of Table 1,
and the lines particularly excluded from the intensity averaging, marked with
‘X’ symbol, are given in the last column of the same table.

##  6 Theoretical Interpretation

To obtain theoretical support for our experimental findings, the theoretical
calculations for energy levels, wavelengths, and transition rates (_A_
-values) of Au IV was performed using Cowan’s codes (Cowan, 1981). This atomic
structure calculation code works on the formalism of the pseudo-relativistic
Hartree-Fock (HFR) method with the superposition of interacting
configurations. However, it has been shown recently (Quinet et al., 2006; Xu
et al., 2007) that inclusion of the core polarization effect (CPOL) is
significantly important to achieve the accurate theoretical radiative
lifetimes (or transition rates) for Os I isoelectronic sequence. This
motivated us to perform a new set of improved HFR+CPOL calculations.

To obtain the radiative lifetime data for the levels of $5d^{8}$ and
$5d^{7}6s$ configurations, in addition to HFR and HFR+CPOL calculations,
separate computations were also made with a fully-relativistic
multiconfiguration Dirac-Hartree-Fock (MCDHF) method (Grant, 2007; Froese
Fischer et al., 2016) implemented in the latest version of General
Relativistic Atomic Structure Program, namely GRASP2018 (Froese Fischer et
al., 2019).

Further details of these individual calculations are described in below sub-
sections. The results and discussion on the critical evaluation of transition
rate data produced by different theoretical methods are given in section 7.

###  6.1 The HFR Calculations

Our extensive HFR calculations contain all major interacting configurations
for both parities. The even parity set consists of $5d^{8}$, $5d^{7}ns$ (_n_ =
6–8), $5d^{7}nd$ (_n_ = 6–8), $5d^{6}6l^{2}$ (_l_ = $s$, $p$), $5d^{6}6s6d$,
and $5d^{6}6s7s$ configurations; whereas $5d^{7}np$ (_n_ = 6–8), $5d^{7}nf$
(_n_ = 5–7), $5d^{6}6snp$ (_n_ = 6, 7), and $5d^{5}6s^{2}6p$ configurations
were included in the odd parity system. The initial scaling for the average
energy $(E_{av})$ and spin-orbit interaction $(\zeta_{nl})$ parameters were
kept at 100% of the HFR values, while the radial wave integral $(F^{k})$,
exchange integral $(G^{k})$, and configuration interaction integral $(R^{k})$
were fixed at 75% of the HFR values. A least-squares parametric fitting (LSF)
was performed to minimize the differences between observed and theoretical
energy level values. The standard deviations of the LSF calculations for the
even and odd parity systems were found to be 92 cm-1 and 176 cm-1,
respectively. The fitted LSF parameters are shown in Table 3, and were further
used to compute the improved transition parameters.

Table 3: LSF parameters for Au IV

Configurationa | Slater Parametera | LSFa | Unc.b | Indexc | HFRa | LSF/HFRa | Commentsd
---|---|---|---|---|---|---|---
|  | (cm-1) | (cm-1) |  | (cm-1) |  |
5 _d_ 8 | Eav | 18247.6 | 37.0 |  | 19163.7 | 0.952 |
5 _d_ 8 | $F^{2}(5d,5d)$ | 59636.9 | 157.0 | 1 | 73337.2 | 0.813 |
5 _d_ 8 | $F^{4}(5d,5d)$ | 44803.0 | 275.0 | 2 | 48865.2 | 0.917 |
5 _d_ 8 | $\alpha(5d)$ | 17.2 | 4.0 | 3 | 0.0 |  |
5 _d_ 8 | $\beta(5d)$ | -437.9 | -74.0 | 7 | 0.0 |  |
5 _d_ 8 | $T(5d)$ | 0.0 |  |  | 0.0 |  | F
5 _d_ 8 | $\zeta(5d)$ | 5589.7 | 16.0 | 4 | 5769.1 | 0.969 |
5 _d_ 76 _s_ | $E_{av}$ | 85932.6 | 20.0 |  | 89638.1 | 0.959 |
… | … | … | … | … | … | … | …
… | $R^{k}$ |  |  |  |  | 0.750 | R
5 _d_ 76 _p_ | $E_{av}$ | 164844.4 | 21.0 |  | 166636.7 | 0.989 |
5 _d_ 76 _p_ | $F^{2}(5d,5d)$ | 60028.6 | 247.0 | 1 | 75500.9 | 0.795 |
5 _d_ 76 _p_ | $F^{4}(5d,5d)$ | 44375.0 | 473.0 | 2 | 50491.4 | 0.879 |
5 _d_ 76 _p_ | $\alpha(5d)$ | 21.9 | 4.0 | 3 | 0.0 |  |
… | … | … | … | … | … | … | …
… | $R^{k}$ |  |  |  |  | 0.750 | R

(This table is available in its entirety in machine-readable form.)

Note. — a Configurations involved in the calculations and their defining
Slater parameters with their Hartree-Fock (HFR) and/or least-squares-fitted
(LSF) value or their ratio. b Uncertainty of each parameter represents their
standard deviation. Blank for fixed values. c Parameters in each numbered
group were linked together with their ratio fixed at the HFR level. d
Comments: F–-The parameters are fixed at given LSF/HFR ratio; R-–All
configuration-interaction parameters _R_ k in both even and odd parity sets
are fixed at 75% of their HFR value.

###  6.2 The HFR+CPOL Calculations

The physical model used for the HFR+CPOL calculations is based on the
consideration of valence-valence correlations within a set of interacting
configurations including $5d^{8}$, $5d^{7}ns$ ($n$ = 6–8), $5d^{7}nd$ ($n$ =
6–8), $5d^{6}6s^{2}$, 5d66p2, 5d66d2, 5d66s6d, 5d66s7s and 5d7$n$p ($n$ =
6–8), 5d7$n$f ($n$ = 5–6), 5d66s$n$p ($n$ = 6–7), 5d66p6d, 5d${}^{6}6s5f$ for
even and odd parities, respectively. This list of configurations includes a
large amount of valence correlation outside of the W-like Au VI ionic core.
Therefore, we estimated the core-valence interactions by considering core-
polarization contributions with the dipole polarizability, $\alpha_{d}$, equal
to 3.62 a${}_{0}^{3}$ and a cut-off radius, $r_{c}$, equal to 1.40 a0. As no
data are available in the literature, the first parameter was deduced from the
extrapolation of $\alpha_{d}$-values published by Fraga et al. (1976) along
the tungsten isoelectronic sequence, from W I to Pt V. As for the cut-off
radius, it corresponds to the HFR average value $<$$r$$>$ for the outermost
core orbital (5d). The semi-empirical LSF approach performed using this
HFR+CPOL model gave similar results to those obtained in our HFR calculations
with standard deviations of 111 cm-1 and 173 cm-1 in even and odd parities,
respectively.

###  6.3 The MCDHF Calculations

The MCDHF calculations are based on two multireferences (MR) for even and odd
parities including the 5d8, 5d76s, 5d66s2 and 5d76p, 5d66s6p configurations,
respectively. The orbitals were optimized using all the energy levels from
each MR. Valence-valence (VV) correlations were estimated by considering
single and double (SD) excitations from the MR configurations to 7s, 7p, 7d
and 7f orbitals, giving rise to 143441 and 602493 configuration state
functions (CSFs) in the even and odd parities, respectively. In this step,
only the new orbitals were optimized, the other ones being kept to their
values obtained before. Then core-valence (CV) effects were taken into account
by considering SD excitations from the 4d, 4f, 5s, 5p core orbitals to the
valence orbitals characterizing the MR configurations. This led to 344673 CSFs
(even parity) and 623038 CSFs (odd parity). The electric dipole (E1)
transitions, allowing us to estimate the MCDHF radiative lifetimes of Au IV
levels, were computed by gathering the two parities while the transition
probabilities for forbidden lines (M1 and E2) were considered only within the
even parity.

##  7 Evaluation of Transition Rates

Figure 3: Energy level diagram for the known levels of Au IV. Fine structure
levels of the ground $5d^{8}$ configuration are shown along with their
selected forbidden (M1 and E2) transitions. The transitions within the levels
of $5d^{7}6s$ are not shown.

An energy level diagram for the known levels of Au IV is illustrated in Figure
3 along with its intra- and inter-configuration transitions. In terms of the
observations, only the allowed electric dipole E1-types of ($5d^{8}$ \+
$5d^{7}6s$)–$5d^{7}6p$ transitions are observed (see Table 1). The forbidden
M1-type (magnetic dipole) of radiations are dominated in the intra-
configuration transitions, for example, within the levels of $5d^{8}$ and
$5d^{7}6s$ configurations. However, in case of the $5d^{8}$–$5d^{7}6s$ inter-
configuration transitions the transition amplitudes are largely forbidden
E2-types (electric quadrupole).

For E1-types, the transitions rates (_A_ -values) were obtained from the HFR
and HFR+CPOL methods and their comparison are described in section 7.1. On the
other hand for forbidden M1- and E2- types the transition parameters including
_A_ -values were obtained from three different methods (namely: MCDHF, HFR,
and HFR+CPOL), and their comparisons are discussed in a separate section 7.2.

###  7.1 Allowed E1-Type Transitions

Figure 4: Comparison of line strengths (_S_ –values) computed within the
framework of the HFR and HFR+CPOL calculations for E1-types. For uncertainty
evaluations, the entire data was divided into three separate groups depending
on their _$|$ CF$|$_min-values (see text).

As discussed briefly above, inclusion of CPOL effects in HFR calculations
significantly improves the accuracy of transition rate data (or lifetime,
$\tau_{k}$ = 1/$\Sigma$_A_ ki data) for Os I and Ir II (Quinet et al., 2006;
Xu et al., 2007). These authors have shown that their computed lifetime data
from the HFR+CPOL calculations agree fairly well (within 30% and 20% for Os I
and Ir II, respectively) with the experimental lifetimes data (for 10
available levels of the 5 _d_ 76 _p_ configuration). No experimental lifetime
data is available for higher members of Os I sequence including Au IV
spectrum. Nonetheless, comparison of transition rates from different sources
is a prerequisite to estimate the uncertainty of transition rate data
(Kramida, 2013a; Haris et al., 2014). The computed lifetime data for the
levels of $5d^{7}6p$ from the HFR calculations are systematically (about 73 %)
lower to those of the HFR+CPOL ones. Therefore, the HFR lifetime data are
scaled to the HFR+CPOL level, and using the scaled lifetime data, the HFR
transition rates were re-calculated. For comparison, the transition rates are
first converted into their corresponding “line-strengths” (_S_ -values) using
the numerical expression, _S_ = _gA_ $\lambda^{3}$/2.0261269e+18, where line
strength _S_ (in atomic units, AU), weighted transition rate _gA_ (in s-1),
and wavelength $\lambda$ (in Å) are expressed in their customary units. The
logarithmic difference of two sets of $S$-values (HFR and HFR+CPOL) as a
function of _S_ HFR+CPOL is plotted, and is shown in Figure 4. It is evident
from Figure 4 that the uncertainty varies with the _S_ -values, however, apart
from the dependency on magnitude of the S-value it also depends on the
absolute value of the cancellation factor (Cowan, 1981). Both HFR and HFR+CPOL
calculations provide the _CF_ -factor, thus a minimum value, _$|$ CF$|$_min is
taken into account. Generally, the _S_ -values (or transition rates) with _$|$
CF$|$_ $<$ 0.10 are considered as unreliable (Kramida, 2013a), but we found
that the average deviation of _S_ -values with 0 $<$  _$|$ CF$|$_min $<$ 0.10
is about 62 % and those with _$|$ CF$|$_min = 0 deviate more than three orders
of magnitude. In fact the lines with _$|$ CF$|$_min $\geq$ 0.10 show least
deviation or they have the higher accuracy. The uncertainty evaluations are
made separately for three different cases of _$|$ CF$|$_min and the results
are summarized in column 2 of Table 4. It should be noted that these
uncertainties represent the statistical (Unc.stat) ones for the two data sets,
and for a more comprehensive uncertainty estimates, experimental lifetime data
and their agreement with the theoretical data are required. Since no
experimental lifetime data is available for Au IV, a conservative estimate of
additional (systematic) uncertainty of about 30% was adopted from the Os I and
Ir II lifetime data comparisons as discussed above. To derive the final total
uncertainties (Unc.tot) for _A_ -values, the systematic uncertainty is
combined in quadrature with Unc.stat, and their corresponding uncertainty
codes are provided in Table 1.

Table 4: Uncertainty Estimate and Code for Transition Rate of Allowed (E1) and
Forbidden (M1 + E2)-Types

Unc.stat for E1-type a |  | Unc.tot b
---|---|---
_S_ HFR+CPOL, (AU) | Unc.stat |  | Symbol | in _A_ -value | in log(_gf_)
- | - |  | C |  $\leq$25% |  $\leq$0.11
i) For _$|$ CF$|$_min $\geq$ 0.10
$\geq$2 | 10% |  | D+ |  $\leq$40% |  $\leq$0.18
$[$0.2, 2) | 17% |  | D+ |  $\leq$40% |  $\leq$0.18
ii) For _$|$ CF$|$_min $<$ 0.10
$[$0.2, 0.9) | 25% |  | D+ |  $\leq$40% |  $\leq$0.18
$[$0.02, 0.2) | 35% |  | D |  $\leq$50% |  $\leq$0.24
$[$0.002, 0.02) | 50% |  | E |  $>$50% |  $>$0.24
iii) For _$|$ CF$|$_min = 0
$<$0.002 | 300% |  | E |  $>$50% |  $>$0.24

Note. — a The statistical uncertainty (Unc.stat) is estimated from the
comparison of two (HFR and HFR+CPOL) datasets. b The total uncertainty
(Unc.tot) includes an additional 30% of systematic component, combined in
quadrature with the Unc.stat for all E1-type (see Section 7.1). For forbidden
(M1 + E2)-types the Unc.tot determined from the comparison of different
dataset (see Section 7.2).

###  7.2 Forbidden M1- and E2-Type Transitions

Figure 5: Comparison of line strengths (_S_ -values) computed within the
framework of the HFR and HFR+CPOL methods for the intra- and inter-
configuration transitions (see text). Figure 6: Logarithmic difference between
the line-strengths (_S_) from MCDHF and HFR+CPOL calculations plotted as a
function of _S_ MCDHF-values (see text).

In this section, a comparative evaluation of the _A_ -values for the forbidden
transitions, within the levels of $5d^{8}$ and $5d^{7}6s$ and those of
$5d^{8}$–$5d^{7}6s$, from three different computational approaches, _viz._
MCDHF, HFR, and HFR+CPOL has been presented. For the comparison purposes, the
initially obtained _A_ -values from these sources were first normalized or
rescaled with respect to the experimental transition energies, which are
computed from Table 2. These _A_ -values were also used to compute the
radiative lifetimes for the levels of $5d^{8}$ and $5d^{7}6s$ configurations,
and these lifetimes are given in Table 5.

Table 5: Radiative Lifetimes $\tau$ (in ms) for the Levels of $5d^{8}$ and
$5d^{7}6s$ in Au IV

Level a |  $\Delta$EO-M b | MCDHF c | HFR+CPOL c
---|---|---|---
| (cm-1) | $\tau^{v}$ | $\tau^{l}$ | $\tau$
5 _d_ 8 3 _F_ 4 | 0 | .. | .. | ..
5 _d_ 8 3 _P_ 2 | -1157 | 2284000 | 1136000 | 891000
5 _d_ 8 3 _F_ 3 | 810 | 21.00 | 21.00 | 21.27
5 _d_ 8 3 _F_ 2 | -307 | 38.1 | 37.9 | 37.9
5 _d_ 8 3 _P_ 0 | -2101 | 930000 | 12130 | 11430
5 _d_ 8 3 _P_ 1 | -1491 | 44.1 | 44.1 | 36.5
5 _d_ 8 1 _G_ 4 | -2330 | 45.8 | 46.1 | 34.4
5 _d_ 8 1 _D_ 2 | 391 | 10.57 | 10.54 | 9.12
5 _d_ 7(4 _F_)6 _s_ 5 _F_ 5 | 2426 | 65.2 | 117.8 | 105.8
5 _d_ 8 1 _S_ 0 | -2001 | 3.21 | 2.90 | 2.60
5 _d_ 7(4 _F_)6 _s_ 5 _F_ 4 | 2310 | 8.41 | 12.59 | 8.47
5 _d_ 7(4 _F_)6 _s_ 5 _F_ 3 | 2598 | 28.9 | 31.2 | 26.8
5 _d_ 7(4 _P_)6 _s_ 5 _P_ 2 | 1756 | 9.80 | 10.59 | 7.41
5 _d_ 7(4 _F_)6 _s_ 5 _F_ 1 | 1937 | 9.21 | 11.89 | 8.58
5 _d_ 7(4 _F_)6 _s_ 5 _F_ 2 | 1289 | 7.45 | 8.99 | 14.70
5 _d_ 7(4 _F_)6 _s_ 3 _F_ 4 | 1420 | 1.147 | 1.595 | 1.684
5 _d_ 7(4 _P_)6 _s_ 5 _P_ 3 | 1142 | 7.69 | 9.15 | 9.58
5 _d_ 7(4 _P_)6 _s_ 5 _P_ 1 | 1219 | 6.06 | 7.86 | 9.31
5 _d_ 7(2 _G_)6 _s_ 3 _G_ 5 | 754 | 1.812 | 2.456 | 2.211
5 _d_ 7(4 _F_)6 _s_ 3 _F_ 3 | 1301 | 1.116 | 1.443 | 1.304
5 _d_ 7(4 _F_)6 _s_ 3 _F_ 2 | 1094 | 1.142 | 1.502 | 1.373
5 _d_ 7(2 _G_)6 _s_ 3 _G_ 4 | 630 | 1.840 | 2.59 | 2.130
5 _d_ 7(2 _P_)6 _s_ 1 _P_ 1 | 640 | 1.139 | 1.404 | 1.315
5 _d_ 7(4 _P_)6 _s_ 3 _P_ 2 | 511 | 0.839 | 0.969 | 0.900
5 _d_ 7(2 _H_)6 _s_ 3 _H_ 6 | -536 | 1.394 | 2.097 | 1.779
5 _d_ 7(2 _P_)6 _s_ 3 _P_ 0 | 471 | 1.493 | 1.934 | 1.475
5 _d_ 7(2 _G_)6 _s_ 3 _G_ 3 | 919 | 2.207 | 2.92 | 2.84
5 _d_ 7(2 _H_)6 _s_ 3 _H_ 5 | -634 | 1.869 | 2.92 | 2.477
5 _d_ 7(2 _G_)6 _s_ 1 _G_ 4 | 5 | 1.196 | 1.675 | 1.482
5 _d_ 7(2 _Db_)6 _s_ 3 _D_ 3 | 1934 | 1.045 | 1.205 | 1.117
5 _d_ 7(2 _Db_)6 _s_ 3 _D_ 2 | 858 | 0.833 | 1.049 | 1.080
5 _d_ 7(4 _P_)6 _s_ 3 _P_ 1 | 1216 | 0.879 | 0.969 | 0.987
5 _d_ 7(2 _F_)6 _s_ 3 _F_ 2 | 845 | 1.036 | 1.164 | 1.560
5 _d_ 7(2 _P_)6 _s_ 3 _P_ 2 | -1311 | 1.807 | 2.352 | 1.142
5 _d_ 7(2 _F_)6 _s_ 3 _F_ 3 | -2262 | 1.250 | 1.566 | 1.242
5 _d_ 7(2 _P_)6 _s_ 3 _P_ 1 | 1190 | 1.216 | 1.432 | 1.399
5 _d_ 7(2 _H_)6 _s_ 3 _H_ 4 | 286 | 1.358 | 1.861 | 1.733
5 _d_ 7(2 _H_)6 _s_ 1 _H_ 5 | -273 | 0.870 | 1.250 | 1.095
5 _d_ 7(4 _P_)6 _s_ 3 _P_ 0 | 995 | 0.537 | 0.608 | 0.603
5 _d_ 7(2 _F_)6 _s_ 3 _F_ 4 | -926 | 1.205 | 1.538 | 1.181
5 _d_ 7(2 _Db_)6 _s_ 1 _D_ 2 | -531 | 0.780 | 0.915 | 0.788
5 _d_ 7(2 _Db_)6 _s_ 3 _D_ 1 | -482 | 0.846 | 0.996 | 0.836
5 _d_ 7(2 _F_)6 _s_ 1 _F_ 3 | -1945 | 0.661 | 0.787 | 0.739
5 _d_ 7(2 _Da_)6 _s_ 3 _D_ 1 | 250 | 0.678 | 0.661 | 0.566
5 _d_ 7(2 _Da_)6 _s_ 3 _D_ 2 | -162 | 0.638 | 0.647 | 0.546
5 _d_ 7(2 _Da_)6 _s_ 3 _D_ 3 | -2517 | 0.633 | 0.648 | 0.525
5 _d_ 7(2 _Da_)6 _s_ 1 _D_ 2 | -2292 | 0.425 | 0.432 | 0.374

Note. — a The levels are from Table 2. b Difference between the observed
energy level value and its corresponding MCDHF value in $cm^{-1}$. c The MCDHF
(in velocity and lengths forms) and HFR+CPOL radiative lifetimes (in
millisecond) for the levels were determined using the scaled _A_ -values. The
scaling were carried out with the help of transition energies computed from
Table 2 (see text).

The evaluations were started with the comparison of HFR and HFR+CPOL results
for M1- and E2- type of transitions which is shown in Figure 5. The error bars
in this figure represents the internal uncertainties of the _S_ -values
obtained from the HFR calculations, which has been evaluated using the Monte
Carlo technique (Kramida, 2014). A total of 20 trials were made to estimate
the uncertainties (of _A_ \- or _S_ -values) for 537 M1- and 777 E2- types of
transitions. About 835 transitions have their uncertainty within 3%, 238
transitions have 7%, 132 have 18%, 61 transitions have uncertainties varying
between 25% to 50%, and 48 transitions have more than 50% (half of them have 2
or 3 orders of magnitude deviation). In general, an excellent agreement
(within 0.33 dex) is observed for HFR and HFR+CPOL data sets:- as expected the
strong lines with _S_ (in AU) $\geq$ 1 agreed within 10% of uncertainty, 18%
for the lines with _S_ $\in$ [0.2, 1), 25% for _S_ $\in$ [0.02, 0.2), 40% for
_S_ $\in$ [0.0001, 0.02), and the remaining weak lines are deviated by more
than 50%.

However, in order to obtain more reliable estimates, the _S_ -values from HFR
and HFR+CPOL were further compared with the MCDHF ones. For M1-types of
transitions, the _S_ MCDHF-values agree within 0.79 dex and 0.68 dex for _S_
HFR and _S_ HFR+CPOL, respectively. In the case of E2-types, the _S_ MCDHF-
values are available in the length and velocity (Babushkin and Coulomb gauges,
respectively) forms. Comparison of these two forms reflects the internal
accuracy of the computation, which is generally given in terms of uncertainty
indicator $\delta$_T_ defined as, $\delta$_T_ = $|$_A_ l– _A_
${}^{v}|$/max(_A_ l, _A_ v), where _A_ l and _A_ v are the _A_ ki values
calculated in length and velocity gauges, respectively. Note that a similar
indicator, $\delta$_S_ , can also be computed from their corresponding _S_
-values. However, using $\delta$_T_ or $\delta$_S_ for computation of
uncertainty is normally discouraged, since the presence of ‘max’ term in the
denominator underestimates the uncertainty (Kramida et al., 2022b). Instead a
reliable uncertainty estimate can be obtained from the _dS_ comparisons, which
are made as a function of _S_ -values (see section 7.1). For the present case,
the global disagreement, between length and velocity forms, for 777 E2-type of
transitions is within 1.22 dex or three orders of magnitude. However, this
large deviation does not necessarily means the entire computational accuracy
is poorer, the stronger _S_ -values of a certain type of transitions still
have better agreement. As E2-types are dominant for inter-configurations
transitions, they ought to have better accuracy. This can be confirmed from
the gross deviation for the $5d^{8}$–$5d^{7}6s$ transitions, which is
$\approx$0.44 dex and $\approx$1.4 dex for the transitions within the levels
of $5d^{8}$ and $5d^{7}6s$ configurations. Both length and velocity forms
should produce comparably same results with reasonably accurate approximate
wavefunctions, yet the velocity forms are not a good choice for small
transition energies (Cowan, 1981). Therefore, in general, length form results
are considered to be more accurate than that of velocity form (Hibbert, 1974;
Froese Fischer, 2009), except in the case of Rydberg type of transitions, for
which velocity forms could be more appropriate (Papoulia et al., 2019).

For this reason we have chosen the length form for the final comparisons. The
agreement of _S_ MCDHF-values for E2-type transitions is $\approx$0.80 dex
with _S_ HFR as well as with _S_ HFR+CPOL-values. The comparison plots of M1-
and E2-types for HFR+CPOL and MCDHF calculations are shown in Figure 6, which
represent a fairly good agreement since their gross deviation was within 0.68
dex and 0.80 dex, respectively. For M1- type transitions, the strong lines
with _S_ (in AU) $\geq$ 2 agreed within 25% of uncertainty, 38% for the lines
with _S_ $\in$ [0.6, 2), 50% for _S_ $\in$ [0.1, 0.6), and the remaining weak
lines are deviated by more than 50%. Similarly for E2- transitions, lines with
_S_ $\geq$ 5 agreed within 23%, 40% for the lines with _S_ $\in$ [1, 5), 50%
for _S_ $\in$ [0.3, 1), and the rest of the weak lines are deviated by more
than 50%. The data on the transition rates (_A_ -values) of the M1- and E2-
components, obtained from MCDHF, HFR+CPOL, and HFR calculations, along with
their accuracy codes and absolute branching fractions are summarized in Table
6. The absolute branching fraction, $BF_{ki}^{abs}$ of a spectral line
originating from an upper level _k_ to a lower level _i_ is defined as
$BF_{ki}^{abs}$ = $\tau_{k}A_{ki}^{tot}$, where $A_{ki}^{tot}$ =
$A_{ki}^{M1}$+$A_{ki}^{E2}$, and is helpful for line identification and
confirmation. To derive the effective uncertainty for $A_{ki}^{tot}$ of a
spectral line its M1- and E2- component uncertainties can be directly weighted
on the basis of their relative branching factor. It should be noted that our
synthesized forbidden spectrum of Au IV falls in the broad wavelength range
809 Å–6.8 $\mu$m and its numerous lines are within the bandpass of the Near
Infrared Spectrograph (NIRSpec; 0.6 to 5 $\mu$m) and/or Mid-Infrared
Instrument (MIRI; 5 to 28 $\mu$m) of the JWST. However, only a few selected
strong lines of Au IV will be detected by JWST at its maximum resolution R =
3000, and all those strong lines were already predicted by Taghadomi et al.
(2022). Further, Taghadomi et al. reported transition parameters for 14
M1-type of lines between the levels of $5d^{8}$, which we accessed from their
opacity database (Stancil et al., 2021). However, our comparison shows that
their disagreement was about 200% with our MCDHF and HFR+CPOL and/or HFR
results. On the other hand, the agreement between our MCDHF and HFR+CPOL or
HFR values were within 20% for these lines. This indicates higher
computational accuracy for our results.

Finally, the lifetime data computed within the framework of HFR, HFR+CPOL and
MCDHF calculations (see Table 5) were compared. The very close agreement,
within 4%, between lifetimes from the HFR and HFR+CPOL methods should not be
overlooked. Nevertheless, the HFR+CPOL results are preferred because they are
more extensive than the other. In MCDHF framework, the lifetime data are
provided in both length and velocity forms. For the present case, their
disagreement is within 30% on average, excluding those of $5d^{8}$
${}^{3}P_{0}$ level. This indicates that the internal consistency between
length and velocity forms, even for strong branches of several transitions, is
not very reliable. Most of them are inter-configurations transitions
(E2-types) from the $5d^{7}6s$ configuration. Finally, lifetime data from the
HFR+CPOL are compared with those of the MCDHF. It was found that the average
deviation of $\tau_{HFR+CPOL}$ was 24% with respect to $\tau^{l}$ (length
form) and 32% with $\tau^{v}$ (velocity form). The radiative lifetime data for
the levels of $5d^{8}$ and $5d^{7}6s$ is presented in Table 5. For the
computed lifetime of the uppermost $5d^{7}6s$ ${}^{1}D_{2}$ level, at 123610
cm-1, its $A_{ki}^{E1}$ to two lower levels of $5d^{7}6p$ is not included.
These transitions are allowed but are of high-spin changing inter-combination
types, and hence they are very weak.

Table 6: Transition Rates for Forbidden M1 and E2 Transitions of Astrophysical
Interest in Au IV

=1in  $\lambda_{Ritz}$ a Unc.a Lower Levelb Upper Levelb _A_ (in s-1) for
M1-component c _A_ (in s-1) for E2-component c BFabs e Å Å MCDHF HFR+CPOL HFR
Acc. d MCDHF HFR+CPOL HFR Acc. d 809.0 1.3 5 _d_ 8 3 _F_ 4 5 _d_ 7(2 _Da_)6
_s_ 1 _D_ 2 1.83e+01 1.80e+01 2.14e+01 E 0.0079 841.5 1.4 5 _d_ 8 3 _F_ 4 5
_d_ 7(2 _Da_)6 _s_ 3 _D_ 3 2.50e-01 3.81e-02 5.17e-02 E 1.85e+02 1.40e+02
1.91e+02 D 0.1197 848.1 1.4 5 _d_ 8 3 _F_ 4 5 _d_ 7(2 _Da_)6 _s_ 3 _D_ 2
3.70e+01 2.30e+01 3.36e+01 E 0.0239 854.8 1.5 5 _d_ 8 3 _P_ 2 5 _d_ 7(2 _Da_)6
_s_ 1 _D_ 2 1.69e-01 1.42e-02 1.02e-02 E 2.31e+01 5.89e+00 1.07e+01 E 0.0100 …
… … … … … … … … … … … … 1659.480 0.004 5 _d_ 8 3 _F_ 2 5 _d_ 7(2 _G_)6 _s_ 3
_G_ 4 2.88e+01 4.22e+01 4.16e+01 D+ 0.0745 1664.022 0.005 5 _d_ 8 1 _G_ 4 5
_d_ 7(2 _G_)6 _s_ 1 _G_ 4 2.71e-01 6.05e-02 6.15e-02 E 1.23e+02 1.15e+02
1.15e+02 C 0.2073 1665.680 0.004 5 _d_ 8 3 _F_ 2 5 _d_ 7(4 _F_)6 _s_ 3 _F_ 2
7.08e-01 8.50e-02 1.12e-01 E 2.54e+01 2.38e+01 2.74e+01 D+ 0.0393 1668.021
0.010 5 _d_ 8 3 _P_ 0 5 _d_ 7(4 _F_)6 _s_ 3 _F_ 2 2.97e+01 5.38e+01 4.27e+01
D+ 0.0447 … … … … … … … … … … … … … 3222 21 5 _d_ 7(2 _P_)6 _s_ 3 _P_ 2 5 _d_
7(2 _Da_)6 _s_ 1 _D_ 2 4.76e+01 2.48e+01 1.79e+01 D 2.79e-04 4.04e-01 4.79e-01
E 0.0205 3228 21 5 _d_ 7(2 _F_)6 _s_ 3 _F_ 3 5 _d_ 7(2 _Da_)6 _s_ 1 _D_ 2
1.82e+01 1.78e+01 2.05e+01 D 5.25e-03 7.67e-02 1.36e-01 E 0.0079 3228.761
0.013 5 _d_ 7(4 _F_)6 _s_ 5 _F_ 4 5 _d_ 7(2 _Db_)6 _s_ 3 _D_ 3 5.47e+01
4.15e+01 4.09e+01 D 2.98e-02 2.61e-02 2.25e-02 E 0.0660 3252.61 0.03 5 _d_ 8 3
_F_ 4 5 _d_ 8 1 _D_ 2 3.06e-01 2.16e-01 2.18e-01 D 0.0032 … … … … … … … … … …
… … … 7455.92 0.13 5 _d_ 8 3 _F_ 3 5 _d_ 8 1 _G_ 4 1.76e+00 2.38e+00 2.37e+00
D 5.06e-06 1.02e-04 1.02e-04 E 0.0814 7467.85 0.06 5 _d_ 7(4 _F_)6 _s_ 5 _F_ 1
5 _d_ 7(4 _P_)6 _s_ 3 _P_ 2 6.98e+00 1.00e+01 9.56e+00 D 3.05e-03 2.79e-03
3.27e-03 D 0.0068 7467.93 0.04 5 _d_ 7(4 _F_)6 _s_ 3 _F_ 3 5 _d_ 7(2 _Db_)6
_s_ 3 _D_ 3 8.11e+00 9.29e+00 8.61e+00 D+ 3.40e-05 2.71e-05 1.37e-05 E 0.0098
7484.56 0.06 5 _d_ 7(2 _Db_)6 _s_ 3 _D_ 2 5 _d_ 7(2 _Db_)6 _s_ 3 _D_ 1
1.78e+01 1.60e+01 1.71e+01 D+ 2.81e-03 3.07e-03 3.20e-03 E 0.0177 … … … … … …
… … … … … … … 12755.91 0.17 5 _d_ 7(2 _P_)6 _s_ 3 _P_ 1 5 _d_ 7(2 _Db_)6 _s_ 3
_D_ 1 9.01e-01 7.97e-01 7.71e-01 D 3.25e-04 9.64e-04 7.92e-04 E 0.0009
12767.77 0.12 5 _d_ 7(2 _F_)6 _s_ 3 _F_ 3 5 _d_ 7(2 _F_)6 _s_ 3 _F_ 4 6.08e+00
4.99e+00 5.19e+00 C 7.37e-04 7.65e-04 6.28e-04 D+ 0.0094 12900 300 5 _d_ 7(4
_P_)6 _s_ 3 _P_ 1 5 _d_ 7(4 _P_)6 _s_ 3 _P_ 0 1.54e+01 1.46e+01 1.46e+01 D+
0.0094 13049.56 0.14 5 _d_ 7(4 _F_)6 _s_ 3 _F_ 2 5 _d_ 7(2 _G_)6 _s_ 1 _G_ 4
1.01e-04 5.93e-05 5.19e-05 D 0.0000 … … … … … … … … … … … … … 452590 180 5 _d_
7(2 _Db_)6 _s_ 3 _D_ 2 5 _d_ 7(4 _P_)6 _s_ 3 _P_ 1 2.22e-05 5.68e-05 5.98e-05
E 1.43e-11 1.57e-11 1.32e-11 D 0.0000 1187000 6000 5 _d_ 8 3 _F_ 2 5 _d_ 8 3
_P_ 0 6.66e-15 2.89e-14 0.0000 1607700 2000 5 _d_ 7(2 _P_)6 _s_ 1 _P_ 1 5 _d_
7(4 _P_)6 _s_ 3 _P_ 2 9.01e-08 6.30e-14 0.0000 1797300 2300 5 _d_ 7(2 _P_)6
_s_ 3 _P_ 2 5 _d_ 7(2 _F_)6 _s_ 3 _F_ 3 3.20e-06 1.32e-15 0.0000 (This table
is available in its entirety in machine-readable form.)

Note. —

a Ritz wavelength and its uncertainty. The wavelengths are in standard air for
$\lambda$ = (2000–20000) Å region and in vacuum outside this region.
Conversion between air and vacuum was made with the five-parameter formula of
Peck & Reeder (1972). Wavelength uncertainties are determined in the level
optimization procedure (see Section 4).

b Level designations and their energies from Table 2. Two columns for energies
are dropped from this condensed table.

c The scaled _A_ -values (in s-1) for M1- and E2- components from MCDHF,
HFR+CPOL, and HFR calculations. The scaling were carried out with the help of
transition energies computed from Table 2.

d Accuracy code of the _A_ -value is explained in Table 4.

e Absolute branching fraction for the line is calculated from the MCDHF-
values.

##  8 Transition Data of Au IV for the Calculation Opacity in Kilonova Spectra

As briefly mentioned in the introduction, Tanaka et al. (2020) and Taghadomi
et al. (2022) provided large scale atomic data for Au IV with specific
application to compute the opacity in the kilonova ejecta. On the other hand,
our results in Tables 1, 2, & 6 describe accurate Ritz wavelengths along with
their transition probabilities, optimized energy levels with their
uncertainties for $5d^{8}$, $5d^{7}6s$ and $5d^{7}6p$ configurations, and
accurately computed line parameters for several forbidden transitions for
levels of $5d^{8}$ and $5d^{7}6s$ configurations. The accurate atomic data are
important for abundance estimates of r-process elements in kilonova ejecta
(Vieira et al., 2023). In their HULLAC code calculations (Tanaka et al., 2020;
Kato et al., 2021) included a limited set of configurations; namely, $5d^{8}$,
$5d^{7}nl$($n\geq 7$, $l=s,p$), $5d^{7}6d$, and $5d^{6}6s^{2}$, however, they
generated about thirty thousand E1-type transitions for their possible 507
levels. Whereas Taghadomi et al. (2022) have performed the calculations using
two different versions of GRASP codes with varying set of configurations for
Os I isoelectronic sequence including Au IV. For Au IV spectrum, about seventy
thousand E1-type transitions were computed with A-values for 551 levels of
$5d^{8}$, $5d^{7}6s$, $5d^{7}6p$, $5d^{6}6s^{2}$, and $5d^{6}6s6p$
configurations. The GRASP2K calculations were found converging with smaller
set of configurations, and the comparison with experimental energy values was
found to be in reasonable agreement for levels of the ground $5d^{8}$
configuration only. Although among atomic structure codes the GRASP
calculations are considered to be more accurate, however, the accuracy of
those calculations is still a subject of debate for heavy-elements such as
gold with open $d$-shells, and large number of configurations sets are often
required to build the internal consistency of computed quantities, for
example, comparisons of transition probabilities in length and velocity forms.

To check the quality of these calculations, we have made a gross comparison
for the energy levels computed with the LSF of Cowan’s code calculations
described in Section 6.1 with those computed by Taghadomi et al. (2022). Their
data was accessed from the opacity database (Stancil et al., 2021). It has
been found that the fractional energy differences vary between 5% and 15%, and
the gross disagreement for A-values were found to be accurate within two-to-
three orders of magnitude for lines in the ($5d^{8}$+$5d^{7}6s$)–$5d^{7}6p$
transition array. Though the strong transitions with $S\geq 10$ agree within
125% have better agreement, and there were 500% for $S\in[4,10)$ but
deviations were more than three orders of magnitude for the remaining weak
lines. These large deviations even for strong lines could be due to poor
computation of the LS-composition vectors in the GRASP calculations. A similar
large deviations (200% for $S\geq 10$, 500% for $S\in[3,10)$, and more than
three orders of magnitudes for other weak lines) were also noticed for the
comparisons of HULLAC code results for Au IV by Tanaka et al. (2020),
therefore, we argue that our computed radiative parameters for Au IV are
expected to be more accurate than those by previous works (Tanaka et al.,
2020; Taghadomi et al., 2022) as we considered an extensive sets of almost all
interacting configurations in our calculations (see Table 3). This motivated
us to provide large scale data for computing the opacity of Au IV in the
kilonova ejecta. Nonetheless, from the HFR calculations described in Section
6.1, only selected set of configurations, $5d^{8}$, $5d^{7}$($6s+7s+6d$),
$5d^{6}6s^{2}$, $5d^{7}$($6p+7p+5f$), and $5d^{6}6s6p$, for which most of the
interacting configurations were accounted for has been considered for the
computation of radiative transition parameters. This resulted in computing the
radiative line parameters for about ninety five thousand E1-type transitions
between 1070 levels of the selected configuration set mentioned above. All
those data were supplemented by us (Zainab et al., 2023). It should be noted
that the LS-composition vector provided for the levels have little physical
meaning due to very high configuration mixing but they are kept in the
supplementary table (of energy levels) for bookkeeping purpose only.

##  9 Conclusion

A critically evaluated set of data for Au IV ion has been presented in the
wavelength region 500–2106 Å. Theoretical interpretation has been done using
Cowan’s suite of codes which works on the formalism of pseudo-relativistic
Hartree–Fock method. 981 spectral lines have been used to optimize 139 energy
levels of $5d^{8},5d^{7}6s$, and $5d^{7}6p$ configurations. All previously
reported levels have been confirmed except one $J$ = 2 level of $5d^{7}6p$,
which is revised now. Also, three new levels, including the only missing
${}^{1}S_{0}$ level of the ground configuration $5d^{8}$, have been
established. Uncertainties have been provided for all the observed and Ritz
wavelengths of the spectral transitions. Intensities of the observed lines
have been reduced to a common scale. The linelist of Au IV has also been
supplemented with Ritz wavelengths of about 830 possibly observable lines and
their _gA_ -values. Additionally, Ritz wavelengths and radiative parameters of
about 800 forbidden (M1- and E2-type) lines have also been provided. For
evaluation of the uncertainty of transition probability data, comparisons have
been made between the calculations of HFR, HFR+CPOL and MCDHF methods. The
overall agreement was found to be fairly well within the three sets of
computations. This enabled us to calculate the radiative lifetimes of $5d^{8}$
and $5d^{7}6s$ levels. Besides these, large scale atomic data with specific
application to compute the opacity of Au IV in the kilonova ejecta have been
supplemented in this work.

A. Tauheed would like to duly acknowledge Dr. Y. N. Joshi (late) for giving
the spectral plates of gold. The authors highly thankful to Dr. Alexander
Kramida of NIST, Gaithersburg, for providing the updated version of the Cowan
(1981) codes and for helpful discussions regrading various computational
problems. P. Quinet is Research Director of the Belgian National Fund for
Scientific Research (F.R.S.-FNRS) from which the financial support is very
appreciated. Part of the atomic calculations in Mons are supported by the
Consortium des Equipements de Calcul Intensif (CECI) funded by the
F.R.S.-FNRS.

## References

  * Abbott et al. (2017) Abbott, B. P., Abbott, R., Abbott, T. D., et al. 2017, ApJ, 848, L12, doi: 10.3847/2041-8213/aa91c9
  * Bartos et al. (2016) Bartos, I., Huard, T. L., & Márka, S. 2016, ApJ, 816, 61, doi: 10.3847/0004-637X/816/2/61
  * Bromley et al. (2020) Bromley, S. J., Johnson, C. A., Ennis, D. A., et al. 2020, ApJS, 250, 19, doi: 10.3847/1538-4365/abaa4d
  * Cowan (1981) Cowan, R. D. 1981, The Theory of Atomic Structure and Spectra (Berkeley, CA: University of California Press) and Cowan code package for Windows by A. Kramida, available from https://doi.org/10.18434/T4/1502500
  * Fontes et al. (2020) Fontes, C. J., Fryer, C. L., Hungerford, A. L., Wollaeger, R. T., & Korobkin, O. 2020, Monthly Notices of the Royal Astronomical Society, 493, 4143, doi: 10.1093/mnras/staa485
  * Fraga et al. (1976) Fraga, S., Karwoswski, J., & Saxena, K. 1976, Handbook of Atomic Data (Amsterdam: Elsevier)
  * Froese Fischer (2009) Froese Fischer, C. 2009, Physica Scripta Volume T, 134, 014019, doi: 10.1088/0031-8949/2009/T134/014019
  * Froese Fischer et al. (2019) Froese Fischer, C., Gaigalas, G., Jönsson, P., & Bieroń, J. 2019, Computer Physics Communications, 237, 184, doi: 10.1016/j.cpc.2018.10.032
  * Froese Fischer et al. (2016) Froese Fischer, C., Godefroid, M., Brage, T., Jönsson, P., & Gaigalas, G. 2016, Journal of Physics B: Atomic, Molecular and Optical Physics, 49, 182004, doi: 10.1088/0953-4075/49/18/182004
  * Gillanders et al. (2021) Gillanders, J. H., McCann, M., Sim, S. A., Smartt, S. J., & Ballance, C. P. 2021, Monthly Notices of the Royal Astronomical Society, 506, 3560, doi: 10.1093/mnras/stab1861
  * Grant (2007) Grant, I. P. 2007, Relativistic Quantum Theory of Atoms and Molecules: Theory and Computation (New York: Springer), doi: 10.1007/978-0-387-35069-1
  * Haris et al. (2014) Haris, K., Kramida, A., & Tauheed, A. 2014, Phys. Scr, 89, 115403, doi: 10.1088/0031-8949/89/11/115403
  * Hibbert (1974) Hibbert, A. 1974, Journal of Physics B: Atomic and Molecular Physics (1968-1987), 7, 1417
  * Joshi et al. (1991) Joshi, Y. N., Raassen, A. J. J., & van der Valk, A. A. 1991, Journal of the Optical Society of America B Optical Physics, 8, 1372, doi: 10.1364/JOSAB.8.001372
  * Kajino et al. (2019) Kajino, T., Aoki, W., Balantekin, A. B., et al. 2019, Progress in Particle and Nuclear Physics, 107, 109, doi: 10.1016/j.ppnp.2019.02.008
  * Kasen et al. (2017) Kasen, D., Metzger, B., Barnes, J., Quataert, E., & Ramirez-Ruiz, E. 2017, Nature, 551, 80, doi: 10.1038/nature24453
  * Kasliwal et al. (2022) Kasliwal, M. M., Kasen, D., Lau, R. M., et al. 2022, MNRAS, 510, L7, doi: 10.1093/mnrasl/slz007
  * Kato et al. (2021) Kato, D., Murakami, I., Tanaka, M., et al. 2021, Japan-Lithuania Opacity Database for Kilonova (2021), (Version 1.0). Available online: http://dpc.nifs.ac.jp/DB/Opacity-Database/ (accessed on March 15, 2023)
  * Kildiyarova et al. (1995) Kildiyarova, R. R., Joshi, Y. N., Lumsden, M. A., & Raassen, A. J. J. 1995, Canadian Journal of Physics, 73, 63, doi: 10.1139/p95-011
  * Kramida (2013a) Kramida, A. 2013a, Fusion Science and Technology, 63, 313, doi: 10.13182/FST13-A16437
  * Kramida (2013b) —. 2013b, Journal of research of the National Institute of Standards and Technology, 118, 52, doi: 10.6028/jres.118.004
  * Kramida (2013c) —. 2013c, Journal of research of the National Institute of Standards and Technology, 118, 168, doi: 10.6028/jres.118.009
  * Kramida (2014) Kramida, A. 2014, Atoms, 2, 86, doi: 10.3390/atoms2020086
  * Kramida et al. (2022a) Kramida, A., Ralchenko, Y., Reader, J., & NIST ASD Team. 2022a, NIST Atomic Spectra Database, Version 5.10 (Gaithersburg, MD: National Institute of Standards and Technology), available at http://physics.nist.gov/asd
  * Kramida et al. (2022b) Kramida, A., Ryabtsev, A. N., & Young, P. R. 2022b, ApJS, 258, 37, doi: 10.3847/1538-4365/ac3a7e
  * Kramida (2011) Kramida, A. E. 2011, Computer Physics Communications, 182, 419, doi: 10.1016/j.cpc.2010.09.019
  * Leckrone et al. (1993) Leckrone, D. S., Johansson, S., Wahlgren, G. M., & Adelman, S. J. 1993, Physica Scripta Volume T, 47, 149, doi: 10.1088/0031-8949/1993/T47/024
  * McCann et al. (2022) McCann, M., Bromley, S., Loch, S. D., & Ballance, C. P. 2022, Monthly Notices of the Royal Astronomical Society, 509, 4723, doi: 10.1093/mnras/stab3285
  * Papoulia et al. (2019) Papoulia, A., Ekman, J., Gaigalas, G., et al. 2019, Atoms, 7, 106, doi: 10.3390/atoms7040106
  * Peck & Reeder (1972) Peck, E. R., & Reeder, K. 1972, Journal of the Optical Society of America (1917-1983), 62, 958, doi: 10.1364/JOSA.62.000958
  * Quinet et al. (2006) Quinet, P., Palmeri, P., Biémont, É., et al. 2006, A&A, 448, 1207, doi: 10.1051/0004-6361:20053852
  * Raassen et al. (1994a) Raassen, A. J. J., Uylings, P. H. M., Joshi, Y. N., & Wyart, J. F. 1994a, Phys. Scr, 49, 682, doi: 10.1088/0031-8949/49/6/008
  * Raassen et al. (1994b) Raassen, A. J. J., Uylings, P. H. M., Joshi, Y. N., et al. 1994b, Phys. Scr, 49, 180, doi: 10.1088/0031-8949/49/2/008
  * Rosberg & Wyart (1997) Rosberg, M., & Wyart, J. F. 1997, Phys. Scr, 55, 690, doi: 10.1088/0031-8949/55/6/009
  * Stancil et al. (2021) Stancil, P. C., Zhao, L., Yang, B., & Osborn, A. 2021, Molecular Opacity Project Database at The University of Georgia, available at https://www.physast.uga.edu/ugamop/index1.html, (accessed on March 15, 2023)
  * Su et al. (2009) Su, M. G., Dong, C. Z., Murphy, N., & O’Sullivan, G. 2009, Phys. Rev. A, 79, 042507, doi: 10.1103/PhysRevA.79.042507
  * Taghadomi et al. (2022) Taghadomi, Z. S., Wan, Y., Flowers, A., et al. 2022, Atoms, 10, doi: 10.3390/atoms10030094
  * Tanaka et al. (2020) Tanaka, M., Kato, D., Gaigalas, G., & Kawaguchi, K. 2020, MNRAS, 496, 1369, doi: 10.1093/mnras/staa1576
  * Tanaka et al. (2018) Tanaka, M., Kato, D., Gaigalas, G., et al. 2018, The Astrophysical Journal, 852, 109, doi: 10.3847/1538-4357/aaa0cb
  * Vieira et al. (2023) Vieira, N., Ruan, J. J., Haggard, D., et al. 2023, ApJ, 944, 123, doi: 10.3847/1538-4357/acae72
  * Villar et al. (2018) Villar, V. A., Cowperthwaite, P. S., Berger, E., et al. 2018, ApJ, 862, L11, doi: 10.3847/2041-8213/aad281
  * Wahlgren (2011) Wahlgren, G. M. 2011, in 2010 NASA Laboratory Astrophysics Workshop, I11
  * Wahlgren et al. (1995) Wahlgren, G. M., Leckrone, D. S., Johansson, S. G., Rosberg, M., & Brage, T. 1995, ApJ, 444, 438, doi: 10.1086/175618
  * Wu et al. (2019) Wu, M.-R., Barnes, J., Martínez-Pinedo, G., & Metzger, B. D. 2019, Phys. Rev. Lett., 122, 062701, doi: 10.1103/PhysRevLett.122.062701
  * Wyart et al. (1994) Wyart, J. F., Joshi, Y. N., Raassen, A. J. J., Uylings, P. H. M., & Tchang-Brillet, L. 1994, Phys. Scr, 50, 672, doi: 10.1088/0031-8949/50/6/012
  * Wyart et al. (1993a) Wyart, J. F., Raassen, A. J. J., Uylings, P. H. M., & Joshi, Y. N. 1993a, Physica Scripta Volume T, 47, 59, doi: 10.1088/0031-8949/1993/T47/008
  * Wyart et al. (1993b) Wyart, J. F., Raassen, A. J. J., van het Hof, G. J., & Joshi, Y. N. 1993b, Phys. Scr, 47, 784, doi: 10.1088/0031-8949/47/6/016
  * Xu et al. (2007) Xu, H. L., Svanberg, S., Quinet, P., Palmeri, P., & Biémont, É. 2007, J. Quant. Spec. Radiat. Transf., 104, 52, doi: 10.1016/j.jqsrt.2006.08.010
  * Zainab et al. (2023) Zainab, A., K., H., Gamrath, S., Quinet, P., & A., T. 2023, Supplementary data for “Critically Evaluated Atomic Data for Au IV Spectrum”, Zenodo, doi: 10.5281/zenodo.7788722
  * Zainab & Tauheed (2019) Zainab, A., & Tauheed, A. 2019, J. Quant. Spec. Radiat. Transf., 237, 106614, doi: 10.1016/j.jqsrt.2019.106614