# Measurements and identifications of extreme ultraviolet spectra of highly-
charged Sm and Er

Y.A. Podpaly, J.D. Gillaspy, J. Reader, Yu. Ralchenko  National Institute of
Standards and Technology, Gaithersburg, MD 20899, USA<EMAIL_ADDRESS>
###### Abstract

We report spectroscopic measurements of highly charged samarium and erbium
performed at the National Institute of Standards and Technology (NIST)
Electron Beam Ion Trap (EBIT). These measurements are in the extreme
ultraviolet (EUV) range, and span electron beam energies from 0.98 keV to 3.00
keV. We observed 71 lines from Kr-like Sm26+ to Ni-like Sm34+, connecting 83
energy levels, and 64 lines from Rb-like Er32+ to Ni-like Er40+, connecting 78
energy levels. Of these lines, 64 in Sm and 60 in Er are new. Line
identifications are performed using collisional-radiative modeling of the EBIT
plasma. All spectral lines are assigned individual uncertainties, most in the
$\sim$0.001 nm range. Energy levels are derived from the wavelength
measurements.

##  1 Introduction

Spectroscopy of rare earth elements has recently become a subject of active
research due to the possible use of gadolinium and terbium as next generation
light sources for extreme ultraviolet (EUV) lithography [1, 2]. There are also
few available data about transitions of highly charged ions in the
lanthanides, which makes this an important area for additional study.

In the NIST Atomic Spectra Database [3], erbium and samarium transitions are
available primarily for Sm I and II and Er I, II, and III. Fewer data are
available for more highly ionized ions. Some transitions have been measured on
Electron Beam Ion Traps (EBITs) in the EUV and X-ray regimes [4, 5, 6, 7].
Much of the available data have been generated from laser produced plasmas [8,
9, 10, 11, 12, 13, 14, 15, 16]. Highly charged samarium has also been observed
in tokamak plasmas [17, 18, 19]. In highly charged erbium, likewise, there are
limited available data, including that generated by EBITs [4, 20, 21], laser
plasmas [10, 11, 12, 22], and tokamaks [17, 18, 23].

In this paper, we report Er and Sm n=4-n=4 transitions in the EUV, continuing
on our previous studies of Gd [1] and Dy [24]. A full list of identifications,
wavelengths, and wavelength uncertainties is generated, and we calculate
energy levels with uncertainties for these ions as well. The intent of this
research is to expand the number of measured transitions among the rare earth
elements near those of interest for EUV light sources and provide a systematic
accounting of uncertainties for transitions and energy levels.

##  2 Experiment

This work was performed at the NIST EBIT [25]. Sm spectra were studied at
twelve electron beam energies between 0.98 keV and 2.2 keV, and Er spectra
were studied at twelve beam energies between 1.3 keV and 3.0 keV. These
energies are sufficient to produce ions between approximately Rb-like and Ni-
like ionization stages [3]. Beam currents varied between 15 mA and 86 mA.
Plasma confinement was achieved, as usual, through the electrostatic trapping
via the electron beam, two drift tubes (at 500 V and 220 V), and a 2.8 T axial
magnetic field. Er and Sm were injected into the trap by using a multi-cathode
Metal Vapor Vacuum Arc (MeVVA) [26]. The trap was emptied and new ions were
injected from the MeVVA every 10 seconds. Elements used for calibration were
introduced by the MeVVA, by the gas injection system (described in [27]), or
were present as intrinsic impurities.

Spectra were recorded with a spectrometer designed for use in the EUV [28].
The spectrometer is a flat-field variable-line spacing type grating
spectrometer. Data were collected with a 2048 pixel$\times$512 pixel (13.5
$\mu$m x 13.5 $\mu$m pixel dimensions) liquid-nitrogen-cooled charge coupled
device (CCD). Spectra were taken as ten one-minute exposures, and a cosmic ray
filtering program was used to automatically remove data that were outside of
five Poisson standard deviations of the signal, effectively removing the
majority of the cosmic rays and aberrant electronic noise. The spectral range
for Sm measurements covered approximately 4 nm to 20 nm, and for Er
approximately 3 nm to 17 nm.

Calibration of the samarium spectra was accomplished using twelve lines from
Ne4+ through Ne7+, one line of Fe23+, one line of Fe22+, and one line of
Ba26+. Spectra of neon were taken at 2 keV and 4 keV, iron was taken at 4 keV,
and barium, which is an intrinsic impurity, was taken at 5.8 keV. Calibration
of the erbium spectra was performed using twelve lines from Ne4+ through Ne7+,
four lines from Xe43+ and Xe42+, one line from Ba45+, one line from O4+, and
one line from O5+. Spectra of neon were taken at 2 keV and 4 keV, xenon and
barium at 5.8 keV, and oxygen at 1.8 keV. All lines were fit with unweighted
Gaussian profiles, and uncertainties were generated for each calibration
point. Third order calibration polynomials relating wavelength to detector
channel number were calculated, and confidence intervals were generated from
which calibration uncertainties were derived. By setting the requirement that
the calibration polynomial fit had $\chi^{2}\\!\approx\\!n-N$, where $n$ is
the number of calibration points and $N$ is the degrees of freedom of the
calibration curve [29], the systematic uncertainty was estimated. For
samarium, the systematic uncertainty was found to be 0.00055 nm; for erbium,
the systematic uncertainty was found to be 0.0010 nm.

Spectra were recorded at a variety of energies; typical results are shown in
figures 1 and 2. The intensities of the experimental spectra are given in the
analog-to-digital units (ADU) of the CCD. Lines were fit with unweighted
Gaussians, and statistical, systematic, and calibration confidence interval
uncertainties were added in quadrature for each line to generate a total
uncertainty.

Figure 1: Samarium experimental results at five beam energies. Select lines
are labeled by their isoelectronic sequence. Figure 2: Erbium experimental
results at five beam energies. Select lines are labeled by their isoelectronic
sequence.

##  3 Collisional-Radiative Modeling

The measured spectra were analyzed with the collisional-radiative (CR)
modeling that has been extensively described elsewhere (see, e.g., [30, 31,
32]), and therefore only the most relevant features will be described below.
The line intensities for Er and Sm were calculated with the non-Maxwellian CR
code NOMAD [33] utilizing atomic data generated with the Flexible Atomic Code
(FAC) [34]. The level energies, radiative transition probabilities (allowed
and forbidden), and electron-impact cross sections (excitation, deexcitation,
ionization, and radiative recombination) were calculated for 8575 and 8570
levels in Sr-like to Ni-like ions of Er and Sm, respectively. The level
energies were improved using an extended calculation taking into account all
possible excitations within the n=4 complex, as described in [31]. The
energies of the $3d^{9}4l$ levels in Ni-like ions were taken from a more
accurate relativistic many-body perturbation theory (RMBPT) calculation of
[35]. The rate of charge exchange between highly-charged ions and neutral
atoms in the trap was included as the only free parameter, aside from a small
shift in electron beam energy due to space charge as discussed below. A
typical calculation of an EBIT spectrum would include 6-7 ionization stages
since ions with ionization potentials larger than the beam energy are very
weakly populated. The calculated bound-bound spectra were then Gaussian-
broadened and convolved with the calculated efficiency curve of the EUV
spectrometer.

Figure 3: Comparison of the experimental spectrum of erbium with the
theoretical spectrum.

Examples of agreement between theoretical and experimental spectra of Er are
presented in figures 3 and 4. The agreement between theory and experiment for
the Sm spectra is practically the same. The second order spectra are shown by
the shifted dotted lines. Starting with figure 3, one can see that our CR
modeling explains intensities and positions of all strong spectral lines. Note
that the theoretical beam energy is lower than the nominal experimental
energy; this is due to the space charge effects that are common in EBITs.
Although for some lines there is a small shift in wavelength between theory
and experiment, a very good match of line intensities allows us to
unambiguously identify all prominent lines in the spectrum. For instance, the
main groups of spectral lines near 8 nm and 15 nm are found to be due to the
$4s_{1/2}$-$4p_{3/2}$ and $4s_{1/2}$-$4p_{1/2}$, respectively, in Cu-, Zn-,
and Ga-like ions of Er.

The theoretical spectrum in Fig. 4 is also seen to agree well with the
measured spectrum. The contributions from different ions are shown by
different colors, while the total theoretical spectrum is marked by a black
solid line. For this energy, the calculated ion populations are the following:
[Kr]:[Br]:[As]:[Se]:[Ge] = 0.015:0.106:0.372:0.439:0.066 (see the inset in
Fig. 4), and the remaining population ($<$ 1%) is in the lower ions.
Accordingly, the most prominent lines are due to transitions in As-like (blue)
and Ge-like (orange) ions. Although a simple visual comparison allows us to
identify practically all experimental lines, additional assistance in
identification is provided by comparison of the intensity of the lines at the
various beam energies. A similar $E_{beam}$-dependence of line intensities
from a particular ionization stage is especially helpful in identification of
blended lines.

Figure 4: Comparison of the experimental spectrum of erbium with the
theoretical spectrum. The inset shows the calculated ionization distribution
at 1.54 keV. Contributions from different ionization stages are shown in
different colors in the theoretical spectrum.

##  4 Results

Results of our measurements are shown in tables LABEL:t:full_results_sm and
LABEL:t:full_results_er. Wavelengths calculated by FAC are presented as well.
All uncertainties for wavelengths are reported as one standard deviation. The
table also presents previous measurements of several spectral lines. If a line
has significant blending with another line the letter ‘b’ is appended to the
wavelength. For samarium, 71 lines were measured, with 64 of them new lines.
For erbium, 64 lines were measured, with 60 of them new lines. In the erbium
data, some the of the Br-like lines were measured from their second orders and
these wavelengths are marked with ‘(*2)’.

The level identifications are given in standard notations for relativistic
configurations (e.g, $4p_{+}$ for $4p_{j=l+1/2}$ and $4d_{-}$ for
$4d_{j=l-1/2}$). As is customary for the FAC calculations, the electron pairs
with total zero momentum are omitted. Since only the largest component of a
wavefunction is presented, this may result in non-unique labels for some
levels. For instance, levels 7 and 9 in As-like Sm are both shown in table
LABEL:t:full_results_sm as belonging to the term $4d_{-}$ of configuration
$4p^{2}4d$. The calculations show that level 7 is composed of 45.7% of
$4p^{2}4d$ $4d_{-}$, 45.3% of $4s4p^{4}$ $(4s_{+},(4p_{+}^{2})_{2})$, and 3.3%
of $4s4p^{4}$ $((4s_{+},4p_{-})_{1},(4p_{+}^{3})_{3/2})$, while for level 9
the same relativistic terms have contributions of 49.9%, 34.2% and 5.3%,
respectively. Such strong mixing is not uncommon in highly-charged N-shell
ions.

The energy levels for samarium and erbium are reported in tables
LABEL:t:full_results_sm_energy and LABEL:t:full_results_er_energy. The
conversion factor from eV to cm-1 was 1 eV = 8065.544219(18) cm-1 [36]. The
first energy level, ground level, is taken to have zero energy. In some cases,
groups of levels are not connected to the ground level by measured radiative
transitions, and therefore the energy of a reference level is taken from FAC
or, in the case of Ni-like ions, from Ref. [35]. These levels are marked in
our tables with the symbol $+$ followed by a letter. For those levels, the
reported results are given as the weighted mean ($\propto 1/\sigma^{2}$) of
the possible derivations. Since none of the derived levels have uncertainties
less than 20 cm-1, the results are all rounded to 10 cm-1, unless they are
from calculations.

For some lines, their identifications were validated by using the Ritz
combination principle. For instance, the 8.2227 nm spectral line in Ga-like Er
that corresponds to the transition between the ground state (level 1) and
level 6, is blended by a strong line in the Ge-like ion, and therefore
additional confirmation of its wavelength would be helpful. The ground state
and the first excited level in this ion are both connected to levels 6 and 7,
all four lines having been measured in the present experiment. The energy
differences between the two lowest levels calculated from two pairs of
measured wavelengths agree within approximately 0.1%, thereby confirming our
identifications for all those lines, including the 1–6 transition. Similar
analysis was performed for transitions in the Ni-like ions of Sm and Er.

For the spectral range analyzed here, there exist only a handful of other
measurements for Sm and Er. Our wavelengths for Ni-like Sm agree very well
with the low-resolution measurements from laser-produced plasmas [9]. The
high-resolution measurements for Cu-like Sm and Er [10, 14] also agree with
our results within experimental uncertainties. Similar level of agreement is
observed for other measurements in Zn-like ions [11, 12]. This provides
additional confidence in our measured wavelengths and identifications of
spectral lines from other ions of Sm and Er for which no measured lines are
known.

For most cases, the FAC wavelengths deviate from the measured values to within
a fraction of per cent. The only exception is the transitions in Ni-like Sm
that connect level 35 with quantum numbers $3d^{9}4d$
(($3d^{3}_{-}$)3/2,$4d_{-}$)0 with levels 9 and 12. For this J=0 level the
difference between theory and experiment reaches 1.6% for calculations that
include double core excitations from n=3 into n=4 (value in table
LABEL:t:full_results_sm_energy) and 4% for single 3–4 excitations. The RMBPT
results of Ref. [35] do not contain J=0 levels and there is no other recent
theoretical work addressing the energy of this particular level. We would like
to point out that our measured 9–35 and 12–35 wavelengths can provide an
interesting test for advanced atomic structure theories.

##  5 Conclusions

We report the results of EUV measurements of highly charged ions of samarium
and erbium in an EBIT. One hundred and thirty-five lines are measured with
individual uncertainties calculated for each line. From these transitions, a
total of 161 energy levels were derived and uncertainties were assigned to
each value. Overall, the agreement between theory and experiment is excellent
with respect to the intensities of the lines and very good for the
wavelengths. Our line identifications agree very well with the already known
data for Ni-, Cu-, and Zn-like ions.

##  6 Acknowledgments

The authors would like to thank J. Smiga for assistance with calibration of
the erbium spectra. This work was funded in part by the Office of Fusion
Energy Sciences of the U.S. Department of Energy. Y.P. is supported by a
postdoctoral appointment with the National Institute of Standards and
Technology National Research Council Research Associateship Program.

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Table 1: Wavelengths (nm) of highly charged samarium. The numbers in parentheses are the wavelength uncertainties in units of the last significant digit. The numbers in square brackets in column “FAC” are the ordinal numbers for the lower and upper levels. b-blended line.  Stage | Lower Level | Upper Level | Wavelength | FAC | Prev. Exp.
---|---|---|---|---|---
| Conf. | State | Conf. | State |  |  |
34+ [Ni] | $3d^{9}4p$ | $((3d_{-}^{3})_{3/2},4p_{-})_{1}$ | $3d^{9}4d$ | $((3d_{-}^{3})_{3/2},4d_{-})_{0}$ | 6.8494(7) | 6.7384 [9-35] |  6.85(2)a
34+ [Ni] | $3d^{9}4p$ | $((3d_{+}^{5})_{5/2},4p_{+})_{1}$ | $3d^{9}4d$ | $((3d_{-}^{3})_{3/2},4d_{-})_{0}$ | 7.3563(8) | 7.2344 [12-35] |  7.36(2)a
34+ [Ni] | $3d^{9}4p$ | $((3d_{+})^{5}_{5/2},4p_{+})_{4}$ | $3d^{9}4d$ | $((3d_{+}^{5})_{5/2},4d_{+})_{5}$ | 10.4908(11) | 10.4800 [10-23] |
34+ [Ni] | $3d^{9}4s$ | $((3d_{+}^{5})_{5/2},4s_{+})_{3}$ | $3d^{9}4p$ | $((3d_{+}^{5})_{5/2},4p_{-})_{3}$ | 17.6366(17) | 17.5836 [2-7] |
34+ [Ni] | $3d^{9}4s$ | $((3d_{+}^{5})_{5/2},4s_{+})_{3}$ | $3d^{9}4p$ | $((3d_{+}^{5})_{5/2},4p_{-})_{2}$ | 17.8926(14) | 17.8722 [2-6] |
34+ [Ni] | $3d^{9}4s$ | $((3d_{+}^{5})_{5/2},4s_{+})_{2}$ | $3d^{9}4p$ | $((3d_{+}^{5})_{5/2},4p_{-})_{3}$ | 17.9864(16) | 17.9661 [3-7] |
34+ [Ni] | $3d^{9}4s$ | $((3d_{-}^{3})_{3/2},4s_{+})_{2}$ | $3d^{9}4p$ | $((3d_{-}^{3})_{3/2},4p_{-})_{2}$ | 18.1084(20) | 18.0985 [5-8] |
34+ [Ni] | $3d^{9}4s$ | $((3d_{+}^{5})_{5/2},4s_{+})_{2}$ | $3d^{9}4p$ | $((3d_{+}^{5})_{5/2},4p_{-})_{2}$ | 18.2491(16) | 18.2674 [3-6] |
33+ [Cu] | $4p$ | $4p_{-}$ | $4d$ | $4d_{-}$ | 8.2176(7)b | 8.2193 [2-4] |  8.2206(15)b
|  |  |  |  |  |  |  8.2155(15)c
33+ [Cu] | $4d$ | $4d_{+}$ | $4f$ | $4f_{+}$ | 10.2238(7) | 10.2183 [5-7] |  10.2249(15)b
|  |  |  |  |  |  |  10.2223(15)c
33+ [Cu] | $4p$ | $4p_{+}$ | $4d$ | $4d_{+}$ | 10.3555(7) | 10.3588 [3-5] |  10.3571(15)b
|  |  |  |  |  |  |  10.3551(15)c
33+ [Cu] | $4s$ | $4s_{+}$ | $4p$ | $4p_{+}$ | 11.3516(7) | 11.1969 [1-3] |  11.3509(15)b
|  |  |  |  |  |  |  11.3504(15)c
33+ [Cu] | $4s$ | $4s_{+}$ | $4p$ | $4p_{-}$ | 17.7416(13) | 17.3523 [1-2] |  17.7450d
32+ [Zn] | $4s4d$ | $(4s_{+},4d_{+})_{2}$ | $4s4f$ | $(4s_{+},4f_{+})_{3}$ | 9.9127(7) | 9.8855 [14-30] |
32+ [Zn] | $4s4p$ | $(4s_{+},4p_{+})_{1}$ | $4s4d$ | $(4s_{+},4d_{+})_{2}$ | 10.0851(7) | 10.0602 [5-14] |
32+ [Zn] | $4s^{2}$ | $(4s_{+}^{2})_{0}$ | $4s4p$ | $(4s_{+},4p_{+})_{1}$ | 10.9125(6) | 10.8361 [1-5] |  10.911(2)e
|  |  |  |  |  |  |  10.9101(10)f
32+ [Zn] | $4s4p$ | $(4s_{+},4p_{-})_{1}$ | $4p^{2}$ | $(4p_{-},4p_{+})_{2}$ | 11.2465(8) | 11.2393 [3-8] |
32+ [Zn] | $4s^{2}$ | $(4s_{+}^{2})_{0}$ | $4s4p$ | $(4s_{+},4p_{-})_{1}$ | 18.8153(19) | 18.658 [1-3] |
31+ [Ga] | $4p$ | $4p_{-}$ | $4d$ | $4d_{-}$ | 7.7461(8) | 7.7150 [1-11] |
31+ [Ga] | $4p$ | $4p_{-}$ | $4s4p_{2}$ | $(4s_{+},(4p_{+}^{2})_{2})_{3/2}$ | 8.2146(7) | 8.1951 [1-9] |
31+ [Ga] | $4p$ | $4p_{+}$ | $4d$ | $4d_{-}$ | 10.1294(7) | 10.0619[2-11] |
31+ [Ga] | $4p$ | $4p_{-}$ | $4s4p^{2}$ | $(4s_{+},(4p_{+}^{2})_{2})_{5/2}$ | 10.8203(7) | 10.7701 [1-7] |
31+ [Ga] | $4p$ | $4p_{+}$ | $4s4p^{2}$ | $(4s_{+},(4p_{+})_{2})_{3/2}$ | 10.9448(20)b | 10.8942 [2-9] |
31+ [Ga] | $4p$ | $4p_{-}$ | $4s4p^{2}$ | $((4s_{+},4p_{-})_{1},4p_{+})_{1/2}$ | 11.1279(7) | 11.1055 [1-6] |
31+ [Ga] | $4p$ | $4p_{+}$ | $4s4p^{2}$ | $((4s_{+},4p_{-})_{1},4p_{+})_{1/2}$ | 16.8114(11) | 16.7187 [2-6] |
31+ [Ga] | $4p$ | $4p_{-}$ | $4s4p^{2}$ | $4s_{+}$ | 18.3603(16) | 18.3159 [1-3] |
31+ [Ga] | $4p$ | $4p_{+}$ | $4s4p^{2}$ | $((4s_{+},4p_{-})_{1},4p_{+})_{5/2}$ | 19.1476(22) | 19.1158 [2-5] |
30+ [Ge] | $4p^{2}$ | $(4p_{-}^{2})_{0}$ | $4p4d$ | $(4p_{-},4d_{-})_{1}$ | 7.7020(7) | 7.6492 [1-16] |
30+ [Ge] | $4p^{2}$ | $(4p_{-},4p_{+})_{2}$ | $4p4d$ | $(4p_{+},4d_{-})_{3}$ | 7.9406(7) | 7.8988 [3-23] |
30+ [Ge] | $4p^{2}$ | $(4p_{-}^{2})_{0}$ | $4s4p^{3}$ | $((4s_{+},4p_{-})_{1},(4p_{+}^{2})_{0})_{1}$ | 8.1809(10) | 8.135 [1-13] |
30+ [Ge] | $4p^{2}$ | $(4p_{-},4p_{+})_{1}$ | $4p4d$ | $(4p_{-},4d_{-})_{1}$ | 9.6994(7)b | 9.6032 [2-16] |
30+ [Ge] | $4p^{2}$ | $(4p_{-},4p_{+})_{2}$ | $4p4d$ | $(4p_{-},4d_{+})_{3}$ | 9.9701(7) | 9.9429 [3-15] |
30+ [Ge] | $4s4p^{3}$ | $(4s_{+},4p_{+})_{1}$ | $4s4p^{2}4d$ | $(4s_{+},4d_{+})_{2}$ | 10.0424(7) | 10.0244 [7-33] |
30+ [Ge] | $4p^{2}$ | $(4p_{-},4p_{+})_{2}$ | $4s4d$ | $(4p_{-},4d_{-})_{2}$ | 10.6728(9) | 10.6342 [3-14] |
30+ [Ge] | $4p^{2}$ | $(4p_{-},4p_{+})_{2}$ | $4s4p^{3}$ | $((4s_{+},4p_{-})_{1},(4p_{+}^{2})_{0})_{1}$ | 10.7648(8) | 10.6784 [3-13] |
30+ [Ge] | $4p^{2}$ | $(4p_{-},4p_{+})_{1}$ | $4p4p^{3}$ | $((4s_{+},4p_{-})_{1},(4p_{+}^{2})_{2})_{1}$ | 10.9423(7)b | 10.8984 [2-12] |
30+ [Ge] | $4p^{2}$ | $(4p_{-}^{2})_{0}$ | $4s4p^{3}$ | $(4s_{+},4p_{+})_{1}$ | 11.1501(7) | 11.1261 [1-7] |
30+ [Ge] | $4p^{2}$ | $(4p_{-},4p_{+})_{2}$ | $4p4d$ | $(4p_{-},4d_{-})_{2}$ | 11.7114(8) | 11.7236 [3-10] |
30+ [Ge] | $4p^{2}$ | $(4p_{-},4p_{+})_{2}$ | $4s4p^{3}$ | $((4s_{+},4p_{-})_{1},(4p_{+}^{2})_{2})_{3}$ | 12.3270(11) | 12.3630 [3-9] |
30+ [Ge] | $4p^{2}$ | $(4p_{-},4p_{+})_{2}$ | $4s4p^{3}$ | $(4s_{+},4p_{+})_{1}$ | 16.5715(9) | 16.5015 [3-7] |
29+ [As] | $4p^{3}$ | $4p_{+}$ | $4p^{2}4d$ | $((4p_{-},4p_{+})_{2},4d_{-})_{1/2}$ | 7.6812(7)b | 7.6310 [1-24] |
29+ [As] | $4p^{3}$ | $4p_{+}$ | $4p^{2}4d$ | $((4p_{-},4p_{+})_{2},4d_{+})_{5/2}$ | 7.6812(7)b | 7.6372 [1-23] |
29+ [As] | $4p^{3}$ | $4p_{+}$ | $4p^{2}4d$ | $((4p_{-},4p_{+})_{2},4d_{-})_{3/2}$ | 7.8640(8) | 7.8150 [1-22] |
29+ [As] | $4p^{3}$ | $4p_{+}$ | $4p^{2}4d$ | $((4p_{-},4p_{+})_{1},4d_{+})_{5/2}$ | 7.9127(8) | 7.8810 [1-21] |
29+ [As] | $4p^{3}$ | $(4p_{-},(4p_{+}^{2})_{2})_{3/2}$ | $4p^{2}4d$ | $((4p_{-},4p_{+})_{2},4d_{+})_{5/2}$ | 9.0907(8) | 8.9946 [2-28] |
29+ [As] | $4p^{3}$ | $4p_{+}$ | $4p^{2}4d$ | $4d_{+}$ | 9.9388(8) | 9.9104[1-10] |
29+ [As] | $4p^{3}$ | $4p_{+}$ | $4p^{2}4d$ | $4d_{-}$ | 10.5983(7) | 10.5592[1-9] |
29+ [As] | $4p^{3}$ | $4p_{+}$ | $4p^{2}4d$ | $4d_{-}$ | 11.5407(7) | 11.5409[1-7] |
29+ [As] | $4p^{3}$ | $4p_{+}$ | $4s4p^{4}$ | $(4s_{+},(4p_{+}^{2})_{2})_{5/2}$ | 12.5081(7) | 12.5409 [1-6] |
29+ [As] | $4p^{3}$ | $(4p_{-},(4p_{+}^{2})_{2})_{5/2}$ | $4p^{2}4d$ | $4d_{-}$ | 17.3265(12) | 17.3085 [3-7] |
29+ [As] | $4p^{3}$ | $(4p_{-},(4p_{+}^{2})_{0})_{1/2}$ | $4s4p^{4}$ | $(4s_{+},(4p_{+}^{2})_{0})_{1/2}$ | 17.6760(14) | 17.6538 [4-8] |
29+ [As] | $4p^{3}$ | $(4p_{-},(4p_{+}^{2})_{2})_{3/2}$ | $4s4p^{4}$ | $(4s_{+},(4p_{+}^{2})_{2})_{5/2}$ | 18.4066(17) | 18.4182 [2-6] |
29+ [As] | $4p^{3}$ | $(4p_{-},(4p_{+}^{2})_{2})_{5/2}$ | $4s4p^{4}$ | $(4s_{+},(4p_{+}^{2})_{2})_{5/2}$ | 19.6006(24) | 19.6597 [3-6] |
28+ [Se] | $4p^{4}$ | $(4p_{+}^{2})_{2}$ | $4p^{3}4d$ | $((4p_{-},(4p_{+}^{2})_{2})_{3/2},4d_{-})_{3}$ | 7.7090(7) | 7.6446 [1-32] |
28+ [Se] | $4p^{4}$ | $(4p_{+}^{2})_{2}$ | $4p^{3}4d$ | $((4p_{-},(4p_{+}^{2})_{2})_{5/2},4d_{-})_{2}$ | 7.7800(7) | 7.7198 [1-29] |
28+ [Se] | $4p^{4}$ | $(4p_{+}^{2})_{2}$ | $4p^{3}4d$ | $(4p_{+},4d_{+})_{3}$ | 9.6502(7)b | 9.6084 [1-14] |
28+ [Se] | $4p^{4}$ | $(4p_{+}^{2})_{0}$ | $4p^{3}4d$ | $(4p_{+},4d_{+})_{1}$ | 9.8209(13) | 9.7842 [2-15] |
28+ [Se] | $4p^{4}$ | $(4p_{+}^{2})_{2}$ | $4p^{3}4d$ | $(4p_{+},4d_{+})_{2}$ | 9.9790(8) | 9.9450 [1-13] |
28+ [Se] | $4p^{3}4d$ | $((4p_{+}^{3})_{3/2},4d_{+})_{4}$ | $4s4p^{4}4d$ | $((4s_{+},(4p_{+}^{2})_{0})_{1/2},4d_{+})_{3}$ | 10.4393(7) | 10.4893 [12-65] |
28+ [Se] | $4p^{4}$ | $(4p_{+}^{2})_{2}$ | $4p^{3}4d$ | $(4p_{+},4d_{-})_{3}$ | 10.9516(9) | 10.9310 [1-10] |
28+ [Se] | $4p^{4}$ | $(4p_{+}^{2})_{2}$ | $4p^{3}4d$ | $(4p_{+},4d_{-})_{1}$ | 11.5467(11) | 11.5440 [1-7] |
28+ [Se] | $4p^{4}$ | $(4p_{+}^{2})_{2}$ | $4s4p^{5}$ | $(4s_{+},(4p_{+})_{3/2})_{2}$ | 12.1372(8) | 12.1546 [1-6] |
27+ [Br] | $4p^{5}$ | $(4p_{+}^{3})_{3/2}$ | $4p^{4}4d$ | $((4p_{-},(4p_{+}^{3})_{3/2})_{2},4d_{-})_{5/2}$ | 7.6242(7) | 7.5549 [1-27] |
27+ [Br] | $4p^{5}$ | $(4p_{+}^{3})_{3/2}$ | $4p^{4}4d$ | $(4p_{-},(4p_{+}^{3})_{2},4d_{-})_{1/2}$ | 7.7321(12) | 7.6606 [1-25] |
27+ [Br] | $4p^{5}$ | $(4p_{+}^{3})_{3/2}$ | $4p^{4}4d$ | $((4p_{+}^{2})_{2},4d_{+}{{}_{5/2}})_{5/2}$ | 9.5321(7) | 9.4986 [1-14] |
27+ [Br] | $4p^{5}$ | $(4p_{+}^{3})_{3/2}$ | $4s$ | $4s_{+}$ | 9.6479(7)b | 9.6142 [1-13] |
27+ [Br] | $4p^{5}$ | $(4p_{+}^{3})_{3/2}$ | $4p^{4}4d$ | $((4p_{+}^{2})_{0},4d_{+}{{}_{5/2}})_{5/2}$ | 9.8126(9) | 9.7848 [1-12] |
27+ [Br] | $4p^{5}$ | $(4p_{+}^{3})_{3/2}$ | $4p^{4}4d$ | $((4p_{+}^{2})_{2},4d_{+}{{}_{5/2}})_{1/2}$ | 9.9000(7) | 9.8682 [1-11] |
26+ [Kr] | $4p^{6}$ | $(4p_{+}^{4})_{0}$ | $4p^{5}4d$ | $(4p_{-},4d_{-})_{1}$ | 7.5901(7) | 7.4940 [1-13] |
26+ [Kr] | $4p^{6}$ | $(4p_{+}^{4})_{0}$ | $4p^{5}4d$ | $((4p_{+}^{3})_{3/2},4d_{+})_{1}$ | 9.4330(7) | 9.3654 [1-9] |
26+ [Kr] | $4p^{6}$ | $(4p_{+}^{4})_{0}$ | $4p^{5}4d$ | $((4p_{+}^{3})_{3/2},4d_{-})_{1}$ | 11.2694(9) | 11.2303 [1-3] |
a \- [9], b \- [10], c -[14], d \- [19], e \- [11], f -[12]

Table 2: Wavelengths (nm) of highly charged erbium. The numbers in parentheses are the wavelength uncertainties in units of the last significant digit. The numbers in square brackets in column “FAC” are the ordinal numbers for the lower and upper levels. b-blended line. (*2)-wavelength derived from second order measurement.  Stage | Lower Level | Upper Level | Wavelength | FAC | Prev. Exp. |
---|---|---|---|---|---|---
| Conf. | State | Conf. | State |  |  |  |
40+ [Ni] | $3d^{9}4p$ | $((3d_{+}^{5})_{5/2},4p_{+})_{4}$ | $3d^{9}4d$ | $((3d_{+}^{5})_{5/2},4d_{+})_{5}$ | 8.7119(12) | 8.7307 [10-23] |  |
40+ [Ni] | $3d^{9}4s$ | $((3d_{+}^{5})_{5/2},4s_{+})_{3}$ | $3d^{9}4p$ | $((3d_{+}^{5})_{5/2},4p_{-})_{3}$ | 14.8490(14) | 14.8038 [2-7] |  |
40+ [Ni] | $3d^{9}4s$ | $((3d_{+}^{5})_{5/2},4s_{+})_{3}$ | $3d^{9}4p$ | $((3d_{+}^{5})_{5/2},4p_{-})_{2}$ | 15.0340(12) | 15.0153 [2-6] |  |
40+ [Ni] | $3d^{9}4s$ | $((3d_{+}^{5})_{5/2},4s_{+})_{2}$ | $3d^{9}4p$ | $((3d_{+}^{5})_{5/2},4p_{-})_{3}$ | 15.1355(13) | 15.1163 [3-7] |  |
40+ [Ni] | $3d^{9}4s$ | $((3d_{-}^{3})_{3/2},4s_{+})_{2}$ | $3d^{9}4p$ | $((3d_{-}^{3})_{3/2},4p_{-})_{2}$ | 15.2200(12) | 15.2079 [5-8] |  |
40+ [Ni] | $3d^{9}4s$ | $((3d_{+}^{5})_{5/2},4s_{+})_{2}$ | $3d^{9}4p$ | $((3d_{+}^{5})_{5/2},4p_{-})_{2}$ | 15.3297(12) | 15.3369 [3-6] |  |
39+ [Cu] | $4p$ | $4p_{-}$ | 4d | $4d_{-}$ | 6.3391(14) | 6.3379 [2-4] |  6.3403(15)a |
39+ [Cu] | $4s$ | $4s_{+}$ | $4p$ | $4p_{+}$ | 8.3796(12) | 8.3654 [1-3] |  8.3813(15)a |
39+ [Cu] | $4p$ | $4p_{+}$ | $4d$ | $4d_{+}$ | 8.5733(12) | 8.5712 [3-5] |  8.5760(15)a |
39+ [Cu] | $4s$ | $4s_{+}$ | $4p$ | $4p_{-}$ | 14.8817(13) | 14.8305 [1-2] |  |
38+ [Zn] | $4s4p$ | $(4s_{+},4p_{-})_{1}$ | $4s4d$ | $(4s_{+},4d_{-})_{2}$ | 6.2733(12) | 6.2686 [3-10] |  |
38+ [Zn] | $4s^{2}$ | $(4s_{+}^{2})_{0}$ | $4s4p$ | $(4s_{+},4p_{+})_{1}$ | 8.1312(12) | 8.0900 [1-5] |  8.131(2)b |
38+ [Zn] | $4s4p$ | $(4s_{+},4p_{+})_{1}$ | $4s4d$ | $(4s_{+},4d_{+})_{2}$ | 8.1732(21) | 8.1548 [5-14] |  |
38+ [Zn] | $4s^{2}$ | $(4s_{+}^{2})_{0}$ | $4s4p$ | $(4s_{+},4p_{-})_{1}$ | 15.6499(12) | 15.5430 [1-3] |  |
37+ [Ga] | $4p$ | $4p_{-}$ | $4d$ | $4d_{-}$ | 6.1755(12) | 6.1626 [1-9] |  |
37+ [Ga] | $4p$ | $4p_{-}$ | $4s4p^{2}$ | $((4s_{+},4p_{-})_{1},4p_{+})_{1/2}$ | 8.0777(14) | 8.0497 [1-7] |  |
37+ [Ga] | $4p$ | $4p_{-}$ | $4s4p^{2}$ | $((4s_{+},4p_{-})_{1},4p_{+})_{3/2}$ | 8.2227(12)b | 8.2109 [1-6] |  |
37+ [Ga] | $4p$ | $4p_{-}$ | $4s4p^{2}$ | $((4s_{+},4p_{-})_{0},4p_{+})_{3/2}$ | 9.3102(12) | 9.3281 [1-4] |  |
37+ [Ga] | $4p$ | $4p_{+}$ | $4s4p^{2}$ | $((4s_{+},4p_{-})_{2},4p_{+})_{1/2}$ | 13.5942(13) | 13.4904 [2-7] |  |
37+ [Ga] | $4p$ | $4p_{+}$ | $4s4p^{2}$ | $((4s_{+},4p_{-})_{1},4p_{+})_{3/2}$ | 14.0226(13) | 13.9493 [2-6] |  |
37+ [Ga] | $4p$ | $4p_{-}$ | $4s4p^{2}$ | $4s_{+}$ | 15.1604(12) | 15.1163 [1-3] |  |
37+ [Ga] | $4p$ | $4p_{+}$ | $4s4p^{2}$ | $((4s_{+},4p_{-})_{1},4p_{+})_{5/2}$ | 15.8957(13) | 15.8643 [2-5] |  |
36+ [Ge] | $4p^{2}$ | $(4p_{-}^{2})_{0}$ | $4p4d$ | $(4p_{-},4d_{-})_{1}$ | 6.1041(12) | 6.0786 [1-11] |  |
36+ [Ge] | $4p^{2}$ | $(4p_{-}^{2})_{0}$ | $4s4p^{3}$ | $(4s_{+},4p_{+})_{1}$ | 8.2214(12)b | 8.2014 [1-7] |  |
36+ [Ge] | $4p^{2}$ | $(4p_{-},4p_{+})_{2}$ | $4s4p^{3}$ | $(4s_{+},4p_{+})_{1}$ | 13.7334(12) | 13.6693 [3-7] |  |
35+ [As] | $4p^{3}$ | $4p_{+}$ | $4p^{2}4d$ | $((4p_{-},4p_{+})_{2},4d_{-})_{3/2}$ | 6.0497(13) | 6.0137 [1-21] |  |
35+ [As] | $4p^{3}$ | $4p_{+}$ | $4p^{2}4d$ | $((4p_{-},4p_{+})_{1},4d_{-})_{5/2}$ | 6.0727(23) | 6.0435 [1-20] |  |
35+ [As] | $4p^{3}$ | $(4p_{-},(4p_{+})_{0})_{1/2}$ | $4p^{2}4d$ | $((4p_{-},4p_{+})_{1},4d_{+})_{7/2}$ | 8.8392(13) | 8.8433 [3-17] |  |
35+ [As] | $4p^{3}$ | $(4p_{-},(4p_{+}^{2})_{2})_{3/2}$ | $4s4p^{4}$ | $(4s_{+},(4p_{+}^{2})_{2})_{5/2}$ | 15.4209(13) | 15.4358 [2-7] |  |
35+ [As] | $4p^{3}$ | $(4p_{-},(4p_{+}^{2})_{2})_{5/2}$ | $4s4p^{4}$ | $(4s_{+},(4p_{+}^{2})_{2})_{5/2}$ | 16.3966(13) | 16.4483 [3-7] |  |
35+ [As] | $4p^{3}$ | $(4p_{-},(4p_{+}^{2})_{2})_{5/2}$ | $4p^{2}4d$ | $4d_{-}$ | 17.1697(15) | 17.1498 [3-6] |  |
34+ [Se] | $4p^{4}$ | $(4p_{+}^{2})_{2}$ | $4p^{3}4d$ | $((4p_{-},(4p_{+}^{2})_{2})_{3/2},4d_{-})_{3}$ | 5.9929(18) | 5.9580 [1-30] |  |
34+ [Se] | $4p^{4}$ | $(4p_{+}^{2})_{2}$ | $4p^{3}4d$ | $((4p_{-},(4p_{+}^{2})_{2})_{5/2},4d_{-})_{2}$ | 6.0230(22) | 5.9797 [1-29] |  |
34+ [Se] | $4p^{4}$ | $(4p_{+}^{2})_{2}$ | $4p^{3}4d$ | $(4p_{+},4d_{+})_{3}$ | 7.8933(12) | 7.8593 [1-14] |  |
34+ [Se] | $4p^{4}$ | $(4p_{+}^{2})_{0}$ | $4p^{3}4d$ | $(4p_{+},4d_{+})_{1}$ | 7.9546(12) | 7.9199 [2-15] |  |
34+ [Se] | $4p^{4}$ | $(4p_{+}^{2})_{2}$ | $4p^{3}4d$ | $(4p_{+},4d_{+})_{2}$ | 8.0042(12) | 7.9737 [1-13] |  |
34+ [Se] | $4p^{4}$ | $(4p_{+}^{2})_{2}$ | $4p^{3}4d$ | $(4p_{+},4d_{-})_{3}$ | 9.1787(15) | 9.169 [1-9] |  |
33+ [Br] | $4p^{5}$ | $(4p_{+}^{3})_{3/2}$ | $4p^{4}4d$ | $((4p_{-},(4p_{+}^{3})_{3/2})_{2},4d_{-})_{5/2}$ | 5.9479(6)(*2) | 5.9049 [1-26] |  |
33+ [Br] | $4p^{5}$ | $(4p_{+}^{3})_{3/2}$ | $4p^{4}4d$ | $((4p_{-},(4p_{+}^{3})_{3/2})_{2},4d_{-})_{3/2}$ | 5.9789(7)b(*2) | 5.9390 [1-25] |  |
33+ [Br] | $4p^{5}$ | $(4p_{+}^{3})_{3/2}$ | $4p^{4}4d$ | $((4p_{-},(4p_{+}^{3})_{3/2})_{2},4d_{-})_{1/2}$ | 5.9789(7)b(*2) | 5.9443 [1-24] |  |
33+ [Br] | $4p^{5}$ | $(4p_{+}^{3})_{3/2}$ | $4p^{4}4d$ | $((4p_{+}^{2})_{2},4d_{+})_{5/2}$ | 7.7630(12) | 7.7217 [1-14] |  |
33+ [Br] | $4p^{5}$ | $(4p_{+}^{3})_{3/2}$ | $4s$ | $4s_{+}$ | 7.8578(10) | 7.8181[1-13] |  |
33+ [Br] | $4p^{5}$ | $(4p_{+}^{3})_{3/2}$ | $4p^{4}4d$ | $((4p_{+}^{2})_{2},4d_{+})_{3/2}$ | 7.8717(13) | 7.8352 [1-12] |  |
33+ [Br] | $4p^{5}$ | $(4p_{+}^{3})_{3/2}$ | $4p^{4}4d$ | $((4p_{+}^{2})_{2},4d_{+})_{1/2}$ | 9.2830(14) | 9.2630 [1-6] |  |
33+ [Br] | $4p^{5}$ | $(4p_{+}^{3})_{3/2}$ | $4p^{4}4d$ | $((4p_{+}^{2})_{2},4d_{-})_{5/2}$ | 9.4626(47) | 9.4519 [1-5] |  |
33+ [Br] | $4p^{5}$ | $(4p_{+}^{3})_{3/2}$ | $4p^{4}4d$ | $((4p_{+}^{2})_{2},4d_{-})_{3/2}$ | 9.5823(12) | 9.5710 [1-3] |  |
32+ [Kr] | $4p^{6}$ | $(4p_{+}^{4})_{0}$ | $4p^{5}4d$ | $(4p_{-},4d_{-})_{1}$ | 5.9356(13) | 5.8792 [1-13] |  |
32+ [Kr] | $4p^{6}$ | $(4p_{+}^{4})_{0}$ | $4p^{5}4d$ | $((4p_{+}^{3})_{3/2},4d_{+})_{1}$ | 7.6746(12) | 7.6221 [1-9] |  |
32+ [Kr] | $4p^{6}$ | $(4p_{+}^{4})_{0}$ | $4p^{5}4d$ | $((4p_{+}^{3})_{3/2},4d_{-})_{1}$ | 9.4129(12) | 9.3900 [1-3] |  |
31+ [Rb] | $4d$ | $4d_{-}$ | $4p^{5}4d^{2}$ | $(4p_{-},(4d_{-}^{2})_{2})_{3/2}$ | 5.8139(13) | 5.7583 [1-45] |  |
31+ [Rb] | $4d$ | $4d_{-}$ | $4p^{5}4d^{2}$ | $(4p_{-},(4d_{-}^{2})_{0})_{1/2}$ | 5.9709(18) | 5.9212 [1-40] |  |
31+ [Rb] | $4d$ | $4d_{-}$ | $4p^{5}4d^{2}$ | $(4p_{-},(4d_{-}^{2})_{2})_{5/2}$ | 6.2905(12) | 6.2377 [1-34] |  |
31+ [Rb] | $4d$ | $4d_{-}$ | $4f$ | $4f_{-}$ | 6.9150(11) | 6.8765[1-32] |  |
31+ [Rb] | $4d$ | $4d_{-}$ | $4p^{5}4d^{2}$ | $(((4p_{+}^{3})_{3/2},4d_{-})_{3},4d_{+})_{1/2}$ | 7.4543(12) | 7.3946 [1-28] |  |
31+ [Rb] | $4d$ | $4d_{-}$ | $4p^{5}4d^{2}$ | $(((4p_{+})_{3/2},4d_{-})_{3},4d_{+})_{3/2}$ | 7.8144(12) | 7.7673 [1-25] |  |
31+ [Rb] | $4d$ | $4d_{-}$ | $4p^{5}4d^{2}$ | $((4p_{+}^{3})_{3/2},(4d_{+}^{2})_{4})_{5/2}$ | 7.9633(13)b | 7.9128 [1-21] |  |
31+ [Rb] | $4d$ | $4d_{-}$ | $4p^{5}4d^{2}$ | $((4p_{+}^{3})_{3/2},(4d_{+}^{2})_{2})_{5/2}$ | 7.9633(13)b | 7.9255 [1-22] |  |
31+ [Rb] | $4d$ | $4d_{-}$ | $4p^{5}4d^{2}$ | $(((4p_{+}^{3})_{3/2},4d_{-})_{3},4d_{+})_{5/2}$ | 8.2514(12) | 8.2165 [1-17] |  |
31+ [Rb] | $4d$ | $4d_{-}$ | $4p^{5}4d^{2}$ | $(((4p_{+}^{3})_{3/2},4d_{-})_{1},4d_{+})_{3/2}$ | 8.6289(12) | 8.6045 [1-11] |  |
31+ [Rb] | $4d$ | $4d_{-}$ | $4p^{5}4d^{2}$ | $((4p_{+}^{3})_{3/2},(4d_{-}^{2})_{0})_{3/2}$ | 8.8905(13) | 8.8592 [1-8] |  |
31+ [Rb] | $4d$ | $4d_{+}$ | $4p^{5}4d^{2}$ | $(((4p_{+}^{3})_{3/2},4d_{-})_{2},4d_{+})_{7/2}$ | 8.9963(12) | 8.9544 [2-16] |  |
31+ [Rb] | $4d$ | $4d_{+}$ | $4p^{5}4d^{2}$ | $(((4p_{3}^{3})_{3/2},4d_{-})_{3},4d_{+})_{7/2}$ | 9.2249(12) | 9.1879 [2-14] |  |
31+ [Rb] | $4d$ | $4d_{-}$ | $4p^{5}4d^{2}$ | $(((4p_{+}^{3})_{3/2},(4d_{-}^{2})_{2})_{5/2}$ | 9.3670(13) | 9.3340 [1-5] |  |
31+ [Rb] | $4d$ | $4d_{+}$ | $4p^{5}4d^{2}$ | $((4p_{+}^{3})_{3/2},(4d_{-}^{2})_{2})_{7/2}$ | 10.1342(12) | 10.0913 [2-6] |  |
a \- [10], b \- [12], |

Table 3: Energy levels of highly charged samarium. RMBPT -relativistic many body perturbation theory [35], FAC - flexible atomic code [34], $\dagger$-weighted average from two transitions, $\dagger\dagger$-weighted average from three transitions  Stage and | Configuration | State | Level number | Energy |  | Unc.
---|---|---|---|---|---|---
sequence |  |  | (FAC) |  (cm-1) |  |  (cm-1)
34+ [Ni] | $3d^{10}$ | $(3d_{+}^{6})_{0}$ | 1 | 0 |  | 0
34+ [Ni] | $3d^{9}4s$ | $((3d_{+}^{5})_{5/2},4s_{+})_{3}$ | 2 | 7 522 190 | +x | RMBPT
34+ [Ni] | $3d^{9}4s$ | $((3d_{+}^{5})_{5/2},4s_{+})_{2}$ | 3 | 7 533 150 | +x |  50$\dagger$
34+ [Ni] | $3d^{9}4s$ | $((3d_{-}^{3})_{3/2},4s_{+})_{2}$ | 5 | 7 752 539 | +y | RMBPT
34+ [Ni] | $3d^{9}4p$ | $((3d_{+}^{5})_{5/2},4p_{-})_{2}$ | 6 | 8 081 080 | +x | 40
34+ [Ni] | $3d^{9}4p$ | $((3d_{+}^{5})_{5/2},4p_{-})_{3}$ | 7 | 8 089 190 | +x | 50
34+ [Ni] | $3d^{9}4p$ | $((3d_{-}^{3})_{3/2},4p_{-})_{2}$ | 8 | 8 304 770 | +y | 60
34+ [Ni] | $3d^{9}4p$ | $((3d_{-}^{3})_{3/2},4p_{-})_{1}$ | 9 | 8 322 930 | +z | RMBPT
34+ [Ni] | $3d^{9}4p$ | $((3d_{+}^{5})_{5/2},4p_{+})_{4}$ | 10 | 8 404 586 | +a | FAC
34+ [Ni] | $3d^{9}4p$ | $((3d_{+}^{5})_{5/2},4p_{+})_{1}$ | 12 | 8 423 520 | +z | 200
34+ [Ni] | $3d^{9}4d$ | $((3d_{+}^{5})_{5/2},4d_{+})_{5}$ | 23 | 9 357 800 | +a | 100
34+ [Ni] | $3d^{9}4d$ | $((3d_{-}^{3})_{3/2},4d_{-})_{0}$ | 35 | 9 782 910 | +z | 150
33+ [Cu] | $4s$ | $4s_{+}$ | 1 | 0 |  | 0
33+ [Cu] | $4p$ | $4p_{-}$ | 2 | 563 650 |  | 40
33+ [Cu] | $4p$ | $4p_{+}$ | 3 | 880 940 |  | 50
33+ [Cu] | $4d$ | $4d_{-}$ | 4 | 1 780 550 |  | 110
33+ [Cu] | $4d$ | $4d_{+}$ | 5 | 1 846 610 |  | 80
33+ [Cu] | $4f$ | $4f_{+}$ | 7 | 2 824 720 |  | 110
32+ [Zn] | $4s^{2}$ | $(4s_{+}^{2})_{0}$ | 1 | 0 |  | 0
32+ [Zn] | $4s4p$ | $(4s_{+},4p_{-})_{1}$ | 3 | 531 480 |  | 50
32+ [Zn] | $4s4p$ | $(4s_{+},4p_{+})_{1}$ | 5 | 916 380 |  | 50
32+ [Zn] | $4p^{2}$ | $(4p_{-},4p_{-})_{2}$ | 8 | 1 420 650 |  | 80
32+ [Zn] | $4s4d$ | $(4s_{+},4d_{+})_{2}$ | 14 | 1 907 940 |  | 90
32+ [Zn] | $4s4f$ | $(4s_{+},4f_{+})_{3}$ | 30 | 2 916 740 |  | 110
31+ [Ga] | $4p$ | $4p_{-}$ | 1 | 0 |  | 0
31+ [Ga] | $4p$ | $4p_{+}$ | 2 | 303 790 |  |  50$\dagger\dagger$
31+ [Ga] | $4s4p^{2}$ | $4s_{+}$ | 3 | 544 650 |  | 50
31+ [Ga] | $4s4p^{2}$ | $((4s_{+},4p_{-})_{1},4p_{+})_{5/2}$ | 5 | 826 040 |  | 80
31+ [Ga] | $4s4p^{2}$ | $((4s_{+},4p_{-})_{1},4p_{+})_{3/2}$ | 6 | 898 640 |  | 50
31+ [Ga] | $4s4p^{2}$ | $((4s_{+},4p_{-})_{1},4p_{+})_{1/2}$ | 7 | 924 190 |  | 60
31+ [Ga] | $4s4p^{2}$ | $(4s_{+},(4p_{+}^{2})_{2})_{3/2}$ | 9 | 1 217 350 |  | 100
31+ [Ga] | $4d$ | $4d_{-}$ | 11 | 1 290 970 |  | 130
30+ [Ge] | $4p^{2}$ | $(4p_{-}^{2})_{0}$ | 1 | 0 |  | 0
30+ [Ge] | $4p^{2}$ | $(4p_{-},4p_{+})_{1}$ | 2 | 267 370 |  | 140
30+ [Ge] | $4p^{2}$ | $(4p_{-},4p_{+})_{2}$ | 3 | 293 400 |  |  60$\dagger$
30+ [Ge] | $4s4p^{3}$ | $(4s_{+},4p_{+})_{1}$ | 7 | 896 850 |  | 50
30+ [Ge] | $4s4p^{3}$ | $((4s_{+},4p_{-})_{1},(4p_{+}^{2})_{2})_{3}$ | 9 | 1 104 630 |  | 90
30+ [Ge] | $4p4d$ | $(4p_{-},4d_{-})_{2}$ | 10 | 1 147 270 |  | 80
30+ [Ge] | $4p4p^{3}$ | $((4s_{+},4p_{-})_{1},(4p_{+}^{2})_{2})_{1}$ | 12 | 1 181 260 |  | 160
30+ [Ge] | $4s4p^{3}$ | $((4s_{+},4p_{-})_{1},(4p_{+}^{2})_{0})_{1}$ | 13 | 1 222 350 |  | 160
30+ [Ge] | $4p4d$ | $(4p_{-},4d_{+})_{2}$ | 14 | 1 230 370 |  | 100
30+ [Ge] | $4p4d$ | $(4p_{-},4d_{+})_{3}$ | 15 | 1 296 400 |  | 90
30+ [Ge] | $4p4d$ | $(4p_{-},4d_{-})_{1}$ | 16 | 1 298 360 |  | 120
30+ [Ge] | $4p4d$ | $(4p_{+},4d_{-})_{3}$ | 23 | 1 552 740 |  | 130
30+ [Ge] | $4s4p^{2}4d$ | $(4s_{+},4d_{+})_{2}$ | 33 | 1 892 630 |  | 900
29+ [As] | $4p^{3}$ | $(4p_{+}^{3})_{3/2}$ | 1 | 0 |  | 0
29+ [As] | $4p^{3}$ | $(4p_{-},(4p_{+}^{2})_{2})_{3/2}$ | 2 | 256 210 |  | 70
29+ [As] | $4p^{3}$ | $(4p_{-},(4p_{+}^{2})_{2})_{5/2}$ | 3 | 289 330 |  |  50$\dagger$
29+ [As] | $4p^{3}$ | $(4p_{-},(4p_{+}^{2})_{0})_{1/2}$ | 4 | 331 860 | +x | FAC
29+ [As] | $4s4p^{4}$ | $(4s_{+},(4p_{+}^{2})_{2})_{5/2}$ | 6 | 799 490 |  | 50
29+ [As] | $4p^{2}4d$ | $4d_{-}$ | 7 | 866 500 |  | 50
29+ [As] | $4s4p^{3}$ | $(4s_{+},(4p_{+}^{2})_{0})_{1/2}$ | 8 | 897 600 | +x | 50
29+ [As] | $4p^{2}4d$ | $4d_{-}$ | 9 | 943 540 |  | 60
29+ [As] | $4p^{2}4d$ | $4d_{+}$ | 10 | 1 006 160 |  | 100
29+ [As] | $4p^{2}4d$ | $((4p_{-},4p_{+})_{1},4d_{+})_{5/2}$ | 21 | 1 263 780 |  | 120
29+ [As] | $4p^{2}4d$ | $((4p_{-},4p_{+})_{2},4d_{-})_{3/2}$ | 22 | 1 271 620 |  | 120
29+ [As] | $4p^{2}4d$ | $((4p_{-},4p_{+})_{2},4d_{+})_{5/2}$ | 23 | 1 301 880b |  | 120
29+ [As] | $4p^{2}4d$ | $((4p_{-},4p_{+})_{2},4d_{-})_{1/2}$ | 24 | 1 301 880b |  | 120
29+ [As] | $4p^{2}4d$ | $((4p_{-},(4p_{+})_{2}),4d_{+})_{5/2}$ | 28 | 1 356 240 |  | 120
28+ [Se] | $4p^{4}$ | $(4p_{+}^{2})_{2}$ | 1 | 0 |  | 0
28+ [Se] | $4p^{4}$ | $(4p_{+}^{2})_{0}$ | 2 | 53 669 | +x | FAC
28+ [Se] | $4s4p^{5}$ | $(4s_{+},(4p_{+}^{3})_{3/2})_{2}$ | 6 | 823 910 |  | 50
28+ [Se] | $4p^{3}4d$ | $(4p_{+},4d_{-})_{1}$ | 7 | 866 050 |  | 80
28+ [Se] | $4p^{3}4d$ | $(4p_{+},4d_{-})_{3}$ | 10 | 913 110 |  | 70
28+ [Se] | $4p^{3}4d$ | $(4p_{+},4d_{+})_{4}$ | 12 | 964 703 | +y | FAC
28+ [Se] | $4p^{3}4d$ | $(4p_{+},4d_{+})_{2}$ | 13 | 1 002 100 |  | 80
28+ [Se] | $4p^{3}4d$ | $(4p_{+},4d_{+})_{3}$ | 14 | 1 036 250 |  | 70
28+ [Se] | $4p^{3}4d$ | $(4p_{+},4d_{+})_{1}$ | 15 | 1 071 900 | +x | 130
28+ [Se] | $4p^{3}4d$ | $((4p_{-},(4p_{+}^{2})_{2})_{5/2},4d_{-})_{2}$ | 29 | 1 285 350 |  | 120
28+ [Se] | $4p^{3}4d$ | $((4p_{-},(4p_{+}^{2})_{2})_{3/2},4d_{-})_{3}$ | 32 | 1 297 190 |  | 130
28+ [Se] | $4s4p^{4}4d$ | $((4s_{+},(4p_{+}^{2})_{0})_{1/2},4d_{+})_{3}$ | 65 | 1 922 620 | +y | 70
27+ [Br] | $4p^{5}$ | $(4p_{+}^{3})_{3/2}$ | 1 | 0 |  | 0
27+ [Br] | $4p^{4}4d$ | $((4p_{+}^{2})_{2},4d_{+})_{1/2}$ | 11 | 1 010 100 |  | 70
27+ [Br] | $4p^{4}4d$ | $((4p_{+}^{2})_{0},4d_{+})_{5/2}$ | 12 | 1 019 100 |  | 100
27+ [Br] | $4s$ | $4s_{+}$ | 13 | 1 036 490 |  | 70
27+ [Br] | $4p^{4}4d$ | $((4p_{+}^{2})_{2},4d_{+})_{5/2}$ | 14 | 1 049 090 |  | 80
27+ [Br] | $4p^{4}4d$ | $((4p_{-},(4p_{+}^{3})_{3/2})_{2},4d_{-})_{1/2}$ | 25 | 1 293 300 |  | 200
27+ [Br] | $4p^{4}4d$ | $((4p_{-},(4p_{+}^{3})_{3/2})_{2},4d_{-})_{5/2}$ | 27 | 1 311 620 |  | 120
26+ [Kr] | $4p^{6}$ | $(4p_{+}^{4})_{0}$ | 1 | 0 |  | 0
26+ [Kr] | $4p^{5}4d$ | $((4p_{+}^{3})_{3/2},4d_{-})_{1}$ | 3 | 887 360 |  | 70
26+ [Kr] | $4p^{5}4d$ | $((4p_{+}^{3})_{3/2},4d_{+})_{1}$ | 9 | 1 060 100 |  | 80
26+ [Kr] | $4p^{5}4d$ | $(4p_{-},4d_{-})_{1}$ | 13 | 1 317 500 |  | 120

Table 4: Energy levels of highly charged erbium. RMBPT -relativistic many-body perturbation theory [35], FAC - flexible atomic code [34], $\dagger$-weighted average from two transitions  Stage and | Configuration | State | Level number | Energy |  | Unc.
---|---|---|---|---|---|---
sequence |  |  | (FAC) |  (cm-1) |  |  (cm-1)
40+ [Ni] | $3d^{10}$ | $(3d_{+}^{6})_{0}$ | 1 | 0 |  | 0
40+ [Ni] | $3d^{9}4s$ | $((3d_{+}^{5})_{5/2},4s_{+})_{3}$ | 2 | 9 931 473 | +x | RMBPT
40+ [Ni] | $3d^{9}4s$ | $((3d_{+}^{5})_{5/2},4s_{+})_{2}$ | 3 | 9 944 260 | +x |  60$\dagger$
40+ [Ni] | $3d^{9}4s$ | $((3d_{-}^{3})_{3/2},4s_{+})_{2}$ | 5 | 10 294 420 | +y | RMBPT
40+ [Ni] | $3d^{9}4p$ | $((3d_{+}^{5})_{5/2},4p_{-})_{2}$ | 6 | 10 596 630 | +x | 60
40+ [Ni] | $3d^{9}4p$ | $((3d_{+}^{5})_{5/2},4p_{-})_{3}$ | 7 | 10 604 920 | +x | 70
40+ [Ni] | $3d^{9}4p$ | $((3d_{-}^{3})_{3/2},4p_{-})_{2}$ | 8 | 10 951 450 | +y | 50
40+ [Ni] | $3d^{9}4p$ | $((3d_{+}^{5})_{5/2},4p_{+})_{4}$ | 10 | 11 127 857 | +z | FAC
40+ [Ni] | $3d^{9}4d$ | $((3d_{+}^{5})_{5/2},4d_{+})_{5}$ | 23 | 12 275 710 | +z | 160
39+ [Cu] | $4s$ | $4s_{+}$ | 1 | 0 |  | 0
39+ [Cu] | $4p$ | $4p_{-}$ | 2 | 671 970 |  | 60
39+ [Cu] | $4p$ | $4p_{+}$ | 3 | 1 193 370 |  | 170
39+ [Cu] | $4d$ | $4d_{-}$ | 4 | 2 249 480 |  | 360
39+ [Cu] | $4d$ | $4d_{+}$ | 5 | 2 359 780 |  | 230
38+ [Zn] | $4s^{2}$ | $(4s_{+}^{2})_{0}$ | 1 | 0 |  | 0
38+ [Zn] | $4s4p$ | $(4s_{+},4p_{-})_{1}$ | 3 | 638 980 |  | 50
38+ [Zn] | $4s4p$ | $(4s_{+},4p_{+})_{1}$ | 5 | 1 229 820 |  | 180
38+ [Zn] | $4s4d$ | $(4s_{+},4d_{-})_{2}$ | 10 | 2 233 040 |  | 310
38+ [Zn] | $4s4d$ | $4s_{+},4d_{+})_{2}$ | 14 | 2 453 320 |  | 370
37+ [Ga] | $4p$ | $4p_{-}$ | 1 | 0 |  | 0
37+ [Ga] | $4p$ | $4p_{+}$ | 2 | 502 760 |  |  140$\dagger$
37+ [Ga] | $4s4p^{2}$ | $4s_{+}$ | 3 | 659 610 |  | 50
37+ [Ga] | $4s4p^{2}$ | $((4s_{+},4p_{-})_{0},4p_{+})_{3/2}$ | 4 | 1 074 090 |  | 140
37+ [Ga] | $4s4p^{2}$ | $((4s_{+},4p_{-})_{1},4p_{+})_{5/2}$ | 5 | 1 131 460 |  | 240
37+ [Ga] | $4s4p^{2}$ | $((4s_{+},4p_{-})_{1},4p_{+})_{3/2}$ | 6 | 1 216 140 |  | 170
37+ [Ga] | $4s4p^{2}$ | $((4s_{+},4p_{-})_{1},4p_{+})_{1/2}$ | 7 | 1 237 970 |  | 220
37+ [Ga] | $4d$ | $4d_{-}$ | 9 | 1 619 300 |  | 320
36+ [Ge] | $4p^{2}$ | $(4p_{-}^{2})_{0}$ | 1 | 0 |  | 0
36+ [Ge] | $4p^{2}$ | $(4p_{-},4p_{+})_{2}$ | 3 | 488 190 |  | 190
36+ [Ge] | $4s4p^{3}$ | $(4s_{+},4p_{+)_{1}}$ | 7 | 1 216 340 |  | 180
36+ [Ge] | $4p4d$ | $(4p_{-},4d_{-})_{1}$ | 11 | 1 638 250 |  | 330
35+ [As] | $4p^{3}$ | $(4p_{+}^{3})_{3/2}$ | 1 | 0 |  | 0
35+ [As] | $4p^{3}$ | $(4p_{-},(4p_{+}^{2})_{2})_{3/2}$ | 2 | 440 827 | +x | FAC
35+ [As] | $4p^{3}$ | $(4p_{-},(4p_{+}^{2})_{2})_{5/2}$ | 3 | 479 420 | +x | 70
35+ [As] | $4p^{2}4d$ | $4d_{-}$ | 6 | 1 061 840 | +x | 90
35+ [As] | $4s4p^{4}$ | $(4s_{+},(4p_{+}^{2})_{2})_{5/2}$ | 7 | 1 089 300 | +x | 50
35+ [As] | $4p^{2}4d$ | $((4p_{-},4p_{+})_{1},4d_{+})_{7/2}$ | 17 | 1 610 740 | +x | 170
35+ [As] | $4p^{2}4d$ | $((4p_{-},4p_{+})_{1},4d_{-})_{5/2}$ | 20 | 1 646 720 |  | 310
35+ [As] | $4p^{2}4d$ | $((4p_{-},4p_{+})_{2},4d_{-})_{3/2}$ | 21 | 1 652 980 |  | 370
34+ [Se] | $4p^{4}$ | $(4p_{+}^{4})_{2}$ | 1 | 0 |  | 0
34+ [Se] | $4p^{4}$ | $(4p_{+}^{2})_{0}$ | 2 | 63 215 | +x | FAC
34+ [Se] | $4p^{3}4d$ | $(4p_{+},4d_{-})_{3}$ | 9 | 1 089 480 |  | 180
34+ [Se] | $4p^{3}4d$ | $(4p_{+},4d_{+})_{2}$ | 13 | 1 249 340 |  | 180
34+ [Se] | $4p^{3}4d$ | $(4p_{+},4d_{+})_{3}$ | 14 | 1 266 900 |  | 190
34+ [Se] | $4p^{3}4d$ | $(4p_{+},4d_{+})_{1}$ | 15 | 1 320 360 | +x | 190
34+ [Se] | $4p^{3}4d$ | $((4p_{-},(4p_{+}^{2})_{2})_{5/2},4d_{-})_{2}$ | 29 | 1 660 300 |  | 590
34+ [Se] | $4p^{3}4d$ | $((4p_{-},(4p_{+}^{2})_{2})_{3/2})_{3}$ | 30 | 1 668 630 |  | 490
33+ [Br] | $4p^{5}$ | $(4p_{+}^{3})_{3/2}$ | 1 | 0 |  | 0
33+ [Br] | $4p^{4}4d$ | $((4p_{+}^{2})_{2},4d_{-})_{3/2}$ | 3 | 1 043 590 |  | 130
33+ [Br] | $4p^{4}4d$ | $((4p_{+}^{2})_{2},4d_{-})_{5/2}$ | 5 | 1 056 800 |  | 530
33+ [Br] | $4p^{4}4d$ | $((4p_{+}^{2})_{2},4d_{-})_{7/2}$ | 6 | 1 077 240 |  | 160
33+ [Br] | $4p^{4}4d$ | $((4p_{+}^{2})_{2},4d_{+})_{3/2}$ | 12 | 1 270 380 |  | 210
33+ [Br] | $4s$ | $4s_{+}$ | 13 | 1 272 610 |  | 160
33+ [Br] | $4p^{4}4d$ | $((4p_{+}^{2})_{2},4d_{+})_{5/2}$ | 14 | 1 288 160 |  | 190
33+ [Br] | $4p^{4}4d$ | $((4p_{-},(4p_{+}^{3})_{3/2})_{2},4d_{-})_{1/2}$ | 24 | 1 672 540 |  | 190
33+ [Br] | $4p^{4}4d$ | $((4p_{-},(4p_{+}^{3})_{3/2})_{2},4d_{-})_{3/2}$ | 25 | 1 672 540 |  | 190
33+ [Br] | $4p^{4}4d$ | $((4p_{-},(4p_{+}^{3})_{3/2})_{2},4d_{-})_{5/2}$ | 26 | 1 681 280 |  | 170
32+ [Kr] | $4p^{6}$ | $(4p_{+}^{4})_{0}$ | 1 | 0 |  | 0
32+ [Kr] | $4p^{5}4d$ | $((4p_{+}^{3})_{3/2},4d_{-})_{1}$ | 3 | 1 062 370 |  | 130
32+ [Kr] | $4p^{5}4d$ | $((4p_{+}^{3})_{3/2},4d_{+})_{1}$ | 9 | 1 303 010 |  | 200
32+ [Kr] | $4p^{5}4d$ | $(4p_{-},4d_{-})_{1}$ | 13 | 1 684 740 |  | 380
31+ [Rb] | $4d$ | $4d_{-}$ | 1 | 0 |  | 0
31+ [Rb] | $4d$ | $4d_{+}$ | 2 | 95 819 | +x | FAC
31+ [Rb] | $4p^{5}4d^{2}$ | $((4p_{+}^{3})_{3/2},(4d_{-}^{2})_{2})_{5/2}$ | 5 | 1 067 570 |  | 150
31+ [Rb] | $4p^{5}4d^{2}$ | $((4p_{+}^{3})_{3/2},(4d_{-}^{2})_{2})_{7/2}$ | 6 | 1 082 580 | +x | 120
31+ [Rb] | $4p^{5}4d^{2}$ | $((4p_{+}^{3})_{3/2},(4d_{-}^{0})_{2})_{3/2}$ | 8 | 1 124 800 |  | 170
31+ [Rb] | $4p^{5}4d^{2}$ | $(((4p_{+}^{3})_{3/2},4d_{-})_{1},4d_{+})_{3/2}$ | 11 | 1 158 890 |  | 160
31+ [Rb] | $4p^{5}4d^{2}$ | $(((4p_{+}^{3})_{3/2},4d_{-})_{3},4d_{+})_{7/2}$ | 14 | 1 179 840 | +x | 140
31+ [Rb] | $4p^{5}4d^{2}$ | $(((4p_{+}^{3})_{3/2},4d_{-})_{2},4d_{+})_{7/2}$ | 16 | 1 207 390 | +x | 150
31+ [Rb] | $4p^{5}4d^{2}$ | $(((4p_{+}^{3})_{3/2},4d_{-})_{3},4d_{+})_{5/2}$ | 17 | 1 211 910 |  | 180
31+ [Rb] | $4p^{5}4d^{2}$ | $((4p_{+}^{3})_{3/2},(4d_{+}^{2})_{4})_{5/2}$ | 21 | 1 255 770 |  | 200
31+ [Rb] | $4p^{5}4d^{2}$ | $((4p_{+}^{3})_{3/2},(4d_{+}^{2})_{4})_{5/2}$ | 22 | 1 255 770 |  | 200
31+ [Rb] | $4p^{5}4d^{2}$ | $(((4p_{+}^{3})_{3/2},4d_{-})_{3},4d_{+})_{3/2}$ | 25 | 1 279 690 |  | 190
31+ [Rb] | $4p^{5}4d^{2}$ | $(((4p_{+}^{3})_{3/2},4d_{-})_{3},4d_{+})_{1/2}$ | 28 | 1 341 500 |  | 210
31+ [Rb] | $4f$ | $4f_{-}$ | 32 | 1 446 140 |  | 240
31+ [Rb] | $4p^{5}4d^{2}$ | $(4p_{-},(4d_{-}^{2})_{2})_{5/2}$ | 34 | 1 589 690 |  | 300
31+ [Rb] | $4p^{5}4d^{2}$ | $(4p_{-},(4d_{-}^{2})_{0})_{1/2}$ | 40 | 1 674 780 |  | 510
31+ [Rb] | $4p^{5}4d^{2}$ | $(4p_{-},(4d_{+}^{2})_{2})_{5/2}$ | 45 | 1 720 010 |  | 400