This is the accepted manuscript made available via CHORUS. The article has been
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Visible transitions in Ag-like and Cd-like lanthanide ions
Shunichi Murata, Takayuki Nakajima, Marianna S. Safronova, Ulyana I. Safronova, andNobuyuki Nakamura
Phys. Rev. A 96, 062506 — Published 15 December 2017
DOI: 10.1103/PhysRevA.96.062506

Visible transitions in Ag-like and Cd-like lanthanide ions
Shunichi Murata,1 Takayuki Nakajima,1 Marianna S. Safronova,2, 3 Ulyana I. Safronova,4 and Nobuyuki Nakamura1
1

Institute for Laser Science, The University of Electro-Communications, Tokyo 182-8585, Japan
2
University of Delaware, Newark, Delaware 19716, USA
3
Joint Quantum Institute, NIST and the University of Maryland, Maryland 20742, USA
4
University of Nevada, Reno, Nevada 89557, USA(Dated: November 30, 2017)

We present visible spectra of Ag-like (4d10 4f ) and Cd-like (4d10 4f 2 ) ions of Ho (atomic number
Z = 67), Er (68), and Tm (69) observed with a compact electron beam ion trap. For Ag-like ions,prominent emission corresponding to the M1 transitions between the ground state fine structure
splitting 4f5/2 –4f7/2 is identified. For Cd-like ions, several M1 transitions in the ground state
configuration are identified. The transition wavelength and the transition probability are calculatedwith the relativistic many-body perturbation theory and the relativistic CI + all-order approach.
Comparisons between the experiments and the calculations show good agreement.

I.

INTRODUCTION

Visible transitions in highly charged heavy ions are ofinterest for many applications. For example, transitions
in highly charged W ions are in strong demand for the
stable operation of the large scale fusion reactor ITER
under construction. Since W is the material of the plasma
facing wall of ITER, sputtered W ions are considered tobe the main impurity in the ITER plasma [1]. Thus it
is important to diagnose and control the W influx andcharge evolution through spectroscopic diagnostics of W
ions. Although all the wavelength ranges, including shortwavelength ranges such as EUV and x-rays, are important for the diagnostics, transitions in the visible range
are especially important due to the advantage that a variety of common optical components, such as mirrors,
lenses, and fiber optics, can be applied. Optical transitions in highly charged ions (HCIs) have been proposed
for a new type of an optical clock that has a significantly
enhanced sensitivity to the fine-structure constant variation due to the strong relativistic effects [2]. The variation of fundamental constants arises in many theories
beyond the Standard Model of particle physics [3] and ishinted by the astrophysical observations [4]. Recently, it
was suggested that dark matter may lead to oscillationsof fundamental constants [5] or transient effects [5] that
may be potentially detectable with such clocks [6]. It isalso an advantage that the wavefunction of the electrontightly bound in a highly charged ion is less sensitive tothe perturbation such as external fields. A detailed assessment of systematic effects in optical clocks based on
HCI was carried out in [7, 8], reaching the conclusionthat the next order of magnitude improvement in the accuracy of frequency standards to 10−19 uncertainty may
also be achievable.
HCI with open 4f shell are particularly important forthese applications. For example, in the diagnostics of the
ITER plasma, it has been pointed out that the diagnostics and control of the edge plasma are extremely important for the steady state operation of high-temperatureplasmas [9, 10]. The impurity in the edge region will

be dominated by W ions with charge states below Aglike (4d10 4f ) [11]; thus the spectroscopic diagnostics of
4f open shell W ions plays a key role in the operationof ITER. For the application to an atomic clock, 4f –5stransitions in medium atomic number (Z) ions are potential candidates for a clock transition because they can fallin the optical range due to their nearly degenerate energy
levels [2]. For example, Ag-like (4d10 4f or 4d10 5s) to Snlike (5s2 4f 2 or 5s2 5p2 ) lanthanide (Ce, Pr, Nd, and Sm)
ions have been proposed by Safronova et al. [12], andI-like Ho (4d10 4f 6 5s) has been proposed by Dzuba et al.
[8]
In order to meet these demands, visible transitions in
4f open shell mid-Z ions have been extensively studied
recently both experimentally and theoretically. For example, visible spectra of W ions have been extensively
studied with electron beam ion traps (EBITs) [13, 14].
Theoretical analysis for identifying those experimental
spectra has also been performed [15, 16]. For the visible
transitions useful for an atomic clock, theoretical studies[2, 8, 12] have taken a lead role, and several experimental efforts [17, 18] to identify the proposed transitions
have followed the theoretical studies. In spite of such efforts, complex fine structure levels arising from the 4f
open shell often hamper the detailed understandings ofthe experimental spectra. Indeed, identification of the
Ho14+ lines observed with a compact EBIT has not yet
been achieved due to its complex structure arising fromthe 4d10 4f 6 5s and 4d10 4f 5 5s2 configurations [17]. Theoretically, precision calculations even of simpler systems
with 3-4 electrons in the valence 4f shell are very challenging, with a very few available experiential benchmarks.
No precision method currently exists to accurately treat
ions with the mid-filled 4f shell.
In this paper, we study the simplest 4f open shell systems, i.e. Ag-like (4d10 4f ) and Cd-like (4d10 4f 2 ) configurations, as the first step towards systematic understanding of complex 4f open shell systems. Z dependence also
provides important information; thus we study three lanthanide ions with Z = 67 (Ho), 68 (Er), and 69 (Tm).
We present visible spectra of these ions obtained using acompact EBIT. We also evaluate the atomic properties of2these ions using the relativistic many-body perturbation
theory (RMBPT) code and the CI+all-order (SD) approach. The level energies, transition wavelengths, andtransition rates are evaluated. For Ag-like ions, the finestructure splitting between 4f7/2 and 4f5/2 is experimentally determined from the direct measurement of the M1
transition between the fine structure levels, and compared with the results obtained by RMBPT, as well as
the existing experimental and theoretical values. For Cdlike ions, we compare the energy levels evaluated by the
CI+all-order (SD) approach. with results obtained by
the RMBPT code. Experimental transition wavelengths
in several Cd-like lines are compared with the results obtained by the CI+all-order (SD) approach.

II.

EXPERIMENTS

The present experiments were performed using a compact EBIT, called CoBIT. Detailed description of CoBIT
is given in Ref. [19]. Briefly, it consists of an electron
gun, a drift tube (DT), an electron collector, and a highcritical-temperature superconducting magnet. The DT is
composed of three successive cylindrical electrodes thatact as an ion trap by applying a positive trapping potential (typically 30 V) at both ends (DT1 and 3) with respect to the middle electrode (DT2). The electron beamemitted from the electron gun is accelerated towards theDT while it is compressed by the axial magnetic field(typically 0.08 T) produced by the magnet surrounding
the DT. The space charge potential of the compressedhigh-density electron beam acts as a radial trap in combination with the axial magnetic field. Highly charged
ions are produced through the successive ionization of
the trapped ions. The lanthanide element of interest was
introduced with an effusion cell [20]. The temperature of
the cell was 900 - 950 ◦ C.
The setup for observing visible spectra was essentiallythe same as that used in our previous studies, wherethe visible emission lines of tungsten ions were observed[14, 21, 22]. Briefly, the emission from the trapped lanthanide ions was focused by a convex lens on the entrance slit of a commercial Czerny-Turner type of visible
spectrometer (Jobin Yvon HR-320) with a focal lengthof 320 mm. For survey observations, a 300 gr/mm
grating blazed at 500 nm was used, whereas for wavelength determination, a high resolution 1200 gr/mm grating blazed at 400 nm was used. The diffracted light
was detected with either a liquid-nitrogen-cooled backilluminated CCD (Princeton Instruments Spec-10:400B
LN) operated at -115 ◦ C or a Peltier-cooled back illuminated CCD (Andor iDus 416) operated at -70 ◦ C. The
wavelength scale was calibrated using emission lines fromseveral standard lamps placed outside CoBIT. The uncertainty in the experimentally determined wavelength
was estimated from reproducibility to be about 0.06 nm.
The electron beam energy determines the maximum
charge state which can be produced in the trap according

TABLE I. Ionization energy of the ions of interest in eV [23].
For example, “In→Cd” represents the ionization energy of the
In-like ion.
element
Ho
Er
Tm

Sn→In
400
443
488

In→Cd
439
483
529

Cd→Ag
478
524
571

Ag→Pd
519
566
615

to the ionization energy listed in Table I. For example,
for Ho, when the electron energy is below 439 eV, themaximum charge state is In-like and Cd-like can not be
produced. In other words, the emission line from Cdlike Ho can be observed only when the electron energy
exceeds 439 eV. Thus the charge state of the ion thatshould be assigned to each observed line can be determined by observing the electron energy dependence.

III.

CALCULATIONSThe energy levels of Ag-like Ho20+ , Er21+ , and Tm22+
have been obtained using the second-order RMBPT
method, described in Ref. [24], where the second andthird order many-body calculations of energies and matrix elements were carried out for ions of the Ag-like sequence. In Ref. [24], second and third-order corrections
to energies and dipole matrix elements were included forneutral Ag and for ions with Z < 60, and second-ordercorrections were included for Z > 60. The effect of thirdorder is small for the M1 transitions in HCI.
The CI+all-order (SD) approach described in Ref. [16]was applied in this study for calculating the energies,
wavelengths, and transition rates of low-lying levels in
Cd-like Ho19+ , Er20+ , and Tm21+ ions. Table II showsthe energies for all the fine structure levels of 4f 2 configuration. The values obtained with the RMBPT code
are also listed in the table for comparison. The smallest(0.20-0.35%) difference for energies evaluated by CI+allorder and RMBPT codes is for the energies for the 1G4level. The largest (1.46-1.47%) difference for energies
evaluated by CI+all-order and RMBPT codes is for theenergies for the 3H5 level.
Figure 1 shows the energy levels of Cd-like Er obtainedby the CI+all-order code. The energy level structure for
Cd-like Ho and Tm is practically the same as that for
Cd-like Er, i.e. the level ordering is not changed in thisZ region except for the order between 3H5 and 3F2 (seeTable II).

IV.

RESULTS AND DISCUSSION

Figure 2 shows the electron energy dependence of survey spectra of Ho. According to the ionization energy
values (Table I), In-like Ho can not be produced with anelectron energy of below 400 eV; thus the spectrum ob-

3
TABLE II. Energies in cm−1 for the lowest levels in Cd-like Ho, Er, and Tm ions evaluated by the RMBPT and CI+all-ordermethods.

3

H4
H5
3
F2
3
F3
1
G4
3
H6
3
F4
1
D2
3
P0
3
P1
1
I6
3
P2
1
S0

Cd-like Ho
RMBPTCI+allCd-like Er
RMBPTCI+allCd-like Tm
RMBPT

0
11001
12439
20362
20872
21288
34539
44630
51158
55386
56444
62787
120738

0
11164
12642
20626
20945
21581
34714
44850
51511
55823
55863
63270
120395

0
12591
13256
22417
22887
24210
38361
47795
54085
59060
60316
67713
128181

0
12779
13411
22662
22933
24535
38543
47910
54274
59387
59702
68120
127515

0
14356
13983
24565
24980
27407
42449
50868
56731
62638
64302
72752
135190

0
14540
14191
24843
25060
27729
42663
51096
57082
63086
63732
73246
13482410

4−1Energy (10 cm )3

CI+allIntensity (arb. units)

Level

l
h

0
0

1

m

n

k

j

510eV
470eV
430eV

q
o

2
3
4
5
Angular momentum J

395eV

6

FIG. 1. Fine structure levels of the 4f 2 ground state configuration in Cd-like Er calculated with the CI+all-order code.
The solid arrows represent the transitions observed in thepresent experiment. The labels on the arrows are listed inTable IV.

tained at 395 eV should not contain any lines from In-like
Ho. When the electron energy was increased to 430 eV,
i.e. above the threshold energy for producing In-like Ho,
the lines indicated by arrows appeared; thus they can be
assigned to In-like Ho. Similarly, the lines indicated by
the arrows in the 470 eV spectra can be assigned to Cdlike Ho because they appeared when the electron energy
exceeded the threshold energy for producing Cd-like Ho.
The line at around 740 nm also appeared at an electronenergy of 470 eV similarly with the Cd-like lines. However, when the energy was further increased, the line at
740 nm kept increasing and became most prominent at
510 eV whereas the lines assigned to Cd-like decreased
and almost disappeared at 510 eV. Thus we have assigned
the prominent line at 740 nm to Ag-like Ho. The wavelength is consistent with the 2F7/2 -2F5/2 fine structure

550

600

650
700
Wavelegth (nm)750

FIG. 2. Electron beam energy dependence of visible spectraof Ho ions.

splitting value 13500 cm−1 derived from the interpolationof the experimentally determined fine structure splittingof other elements [25]. We thus believe that the present
assignment, but have no idea at present why the Ag-likeline was observed below the threshold energy. Appearance of a line below the threshold has often been observedin spectroscopy with an EBIT [26, 27]. For example, in
our previous study [26], a Rh-like Ba11+ line was observed below the threshold energy. It can be understoodby considering the ionization from the 4d9 5s metastablestate of Ba10+ as discussed in Ref. [26]. However, it is unlikely in the present case because there is no metastablestate in the electronic excited states of the Cd-like system. The energy dependence of the Er and Tm spectra
was also studied and the charge state was assigned to theobserved lines similarly to the Ho spectra.
Figure 3 shows spectra of Ho, Er, and Tm obtained at
the electron energies where the dominance of the Ag-likeline was confirmed (510, 560, and 600 eV, respectively).

4
j
l

h

m n
21+

Tm
560 eV

22+Tm
600 eV20+

Er510 eV21+

Er
560 eV19+

Ho
490 eV20+

Ho
510 eV

600
700
Wavelength (nm)FIG. 3. Visible spectra of Ag-like Ho20+ , Er21+ , and Tm22+ .
The prominent line indicated by the arrows in each spectrum
is the 2F7/2 -2F5/2 transition. The vertical bars connected by
the solid line represent the theoretical wavelength calculatedwith RMBPT. Note that the intensity can not be compared.

The line indicated by the arrow in each spectrum correspond to the M1 transitions between the ground statefine structure splitting 4f5/2 –4f7/2 .The vertical bars connected with a solid line represent the theoretical wavelength obtained in the present RMBPT calculations. As
seen in the figure, the theoretical values are in good agreement with the experimental ones although there can befound a slight shift between them. The transition was
also observed with a high resolution 1200 gr/mm grating
for wavelength determination. The fine structure splitting energies derived from the experimental wavelengths
are listed in Table III together with the available experimental and theoretical values. The multi-configuration
Dirac-Fock (MCDF) values [15] were obtained by extensive relativistic configuration interaction calculations
using the GRASP2K package. The active space techniques have been employed to extend the configuration
expansion systematically. The electron correlation effects, Breit interaction and quantum electrodynamics effects to the atomic state wavefunctions and the corresponding energies had been taken into account. Multiconfiguration Dirac-Hartree-Fock (MCDHF) method was
also employed in Ref. [28]. The work in Ref. [29] used relativistic perturbation theory with a zero-approximation
model potential (RPTMP). As seen in the table, the theoretical values are in good agreement with the present
experimental values.
It is noted that the experimental values by Zhao [30]and Sugar [25] were not directly measured, but determined from the experimental values for other Z. Thus
the present result is the first direct determination of thefine structure levels. As seen in the table, the present experimental values agree with existing experimental andtheoretical values.
Figure 4 shows spectra of Ho, Er, and Tm obtained at
the electron energies where the dominance of the Cd-like

400

500
600
Wavelength (nm)700

FIG. 4. Visible spectra of Cd-like Ho, Er, and Tm. Thelines assigned to Cd-like from the energy dependence measurements are indicated by the arrows. The other lines are
originated from other charge states or impurity ions. Notethat the intensity can not be compared. The vertical bars
connected by the solid line represent the CI+all-order wavelengths for five prominent lines.

line was confirmed (490, 510, and 560 eV, respectively).
The lines indicated by the arrows represent the transitions assigned to Cd-like from the energy dependence.
The vertical bars connected with a solid line represent
the theoretical wavelengths for the five prominent lines
obtained in the present RMBPT calculations. The transition wavelengths obtained in high resolution measurements are listed in Table IV together with the theoretical wavelengths and transition rates obtained with the
CI+all-order approximation. The M1 and E2 transition
rates were evaluated based on Eqs. 1 and 2 in Ref. [16].
It was demonstrated in Ref. [16] that M1 transition rates
are larger by factor of 10 - 100 than E2 contributions. As
a result, we present in Table IV,the M1 transition rate
for 20 transitions in Ho19+ , Er20+ , and Tm21+ ions. The
gAr values are charged from 10 s−1 up 1000 s−1 . The
theoretical wavelengths obtained by our CI+all-order calculation are in good agreement with experimental results
as confirmed in Fig. 4 and Table IV. Unfortunately, thepresent experimental results can not be used to evaluate
the theoretical transition probabilities because the line
intensity observed in the low-density EBIT plasma does
not reflect the gA value. The transition probabilities,
which are crucial for the envisaged studies, are expected
to be measured by observing radiative decay lifetime in
the magnetic trapping mode [31].
According to the energy diagram shown in Fig. 1, thesum of the transition energies of m and k should beequal to that of n and j. Although the line k is rather
weak, it was assigned in the high resolution spectrumfor Ho and Er. The sum of the observed transition energies (converted to the vacuum values) is confirmed to
be 34495 cm−1 for Ho and 38311 cm−1 for Er, for bothm+k and n+j. This confirms the reliability of the present
assignment.

5
TABLE III. Fine structure splitting 4f5/2 –4f7/2 in Ag-like Ho, Er, and Tm (cm−1 ).
element(Z)Ho (67)
Er (68)
Tm (69)

exp
Zhaoa
13392
15239
17271

present
13487(2)15297(2)17258(2)Sugarb
13500

RMBPT
13573
15383
17341

MCDF[15]
13140
14926
16871

theory
RPTMP[29]
13486
15371
17695

MCDHF[28]
13509
15320
17280

a Z-scaled value derived from the experimental fine structure splitting for several elements between Z = 62 and 74 [25, 30].
b Linearly interpolated value derived from the experimental fine structure splitting for other Z [25].

TABLE IV. Wavelength (nm in air) and transition rates for the lowest levels in Cd-like Ho, Er, and Tm ions evaluated by the
CI+all-order method.

Label
a
b
c
d
e
f
g
h
i
j
k
l
m
n
o
p
q
r
s
t

Term
3

Cd-like Howavelength
exp.
theory3

F2 − P2
H5 − 1I6
3
F2 − 3P1
3
F3 − 3P2
3
H6 − 1I6
3
H4 − 3F4
3
F2 − 1D2
3
F3 − 1D2
3
H5 − 3F4
3
H4 − 1G4
3
H4 − 3F3
1
D2 − 3P2
3
F3 − 3F4
1
G4 − 3F4
3
H4 − 3H5
1
D2 − 3P1
3
H5 − 3H63
H5 − 1G4
3
F2 − 3F3
3
P1 − 3P2
3

410.82479.88485.98546.83718.00731.77

198.6
220.0
232.8
235.6
284.4
289.4
310.6
411.9
424.7
479.0
491.0
550.6
705.2
731.5
908.8
929.5
971.8
1012.81261.81350.8gAr
6.65[0]4.61[2]
1.06[1]1.02[2]2.96[2]
4.79[1]
2.29[2]
1.67[2]
7.79[1]1.45[2]
7.19[0]2.19[2]
2.53[2]
2.11[2]
3.54[2]
1.82[1]
3.09[2]
1.55[1]
8.19[1]2.10[1]

Cd-like Er
wavelength
exp.
theory394.21438.21442.34498.29636.35645.07791.26860.89

183.6
209.5
218.3
220.7
276.9
260.6
289.4
393.9
387.9
436.8
446.0
501.9
627.0
646.1
794.0
887.5
860.4
971.0
1091.31155.4gAr
9.80[0]6.55[2]
1.59[1]1.50[2]
3.91[2]
6.11[1]
3.16[2]2.10[2]
1.05[2]
2.09[2]
1.08[1]
3.09[2]
3.67[2]
3.08[2]
5.27[2]
2.27[1]
4.43[2]
1.94[1]
1.26[2]
3.28[1]

Cd-like Tm
wavelength
exp.
theory379.25400.91454.50566.67571.74694.68766.68

170.1
200.2
205.5
207.5
271.0
235.5
271.0
380.1
355.9
400.2
407.0
456.8
559.0
572.3
696.4
849.4
766.0
941.0
944.7
988.5

gAr
1.38[1]
9.26[2]
2.39[1]
2.18[2]
5.12[2]
7.61[1]
4.34[2]
2.59[2]
1.41[2]
2.99[2]
1.61[1]
4.36[2]
5.27[2]
4.45[2]
7.75[2]2.81[1]
6.25[2]2.35[1]
1.91[2]
5.09[1]ACKNOWLEDGMENT

This work was mainly supported by JSPS KAKENHI
Grant Number JP16H04028. NN thanks Prof. H.
Tanuma (TMU) for lending the CCD used in the visible spectroscopy. MSS acknowledges the support of the
NSF grant PHY-1620687 (USA).

[1] C. H. Skinner, Can. J. Phys. 86, 285 (2008).
[2] J. C. Berengut, V. A. Dzuba, and V. V. Flambaum,
Phys. Rev. Lett. 105, 120801 (2010).
[3] J.-P. Uzan, Living Reviews in Relativity 14, 2 (2011).
[4] J. K. Webb, J. A. King, M. T. Murphy, V. V. Flambaum,
R. F. Carswell, and M. B. Bainbridge, Phys. Rev. Lett.
107, 191101 (2011).
[5] A. Arvanitaki, J. Huang, and K. Van Tilburg, Phys.
Rev. D 91, 015015 (2015).

[6] A. Derevianko and M. Pospelov, Nature Phys. 10, 933(2014).
[7] A. Derevianko, V. A. Dzuba, and V. V. Flambaum,
Phys. Rev. Lett. 109, 180801 (2012).
[8] V. A. Dzuba, V. V. Flambaum, and H. Katori, Phys.
Rev. A 91, 022119 (2015).
[9] M. Mita, H. A. Sakaue, D. Kato, I. Murakami, and
N. Nakamura, Atoms 5, 13 (2017).
[10] J. Clementson, T. Lennartsson, and P. Beiersdorfer,
Atoms 3, 407 (2015).

6[11] C. Biedermann, R. Radtke, R. Seidel, and T. Putterich,
Phys. Scr. 2009, 014026 (2009).
[12] M. S. Safronova, V. A. Dzuba, V. V. Flambaum, U. I.
Safronova, S. G. Porsev, and M. G. Kozlov, Phys. Rev.
Lett. 113, 030801 (2014).
[13] M. L. Qiu, W. X. Li, Z. Z. Zhao, Y. Yang, J. Xiao,
T. Brage, R. Hutton, and Y. Zou, J. Phys. B 48, 144029(2015).
[14] A. Komatsu, J. Sakoda, N. Nakamura, H. A. Sakaue, X.B. Din, D. Kato, I. Murakami, and F. Koike, Phys. Scr.
T144, 014012 (2011).
[15] X.-B. Ding, F. Koike, I. Murakami, D. Kato, H. A.
Sakaue, C.-Z. Dong, and N. Nakamura, J. Phys. B 45,
035003 (2012).
[16] U. I. Safronova, M. S. Safronova, and N. Nakamura,Phys. Rev. A 95, 042510 (2017).
[17] T. Nakajima, K. Okada, M. Wada, V. A. Dzuba, M. S.
Safronova, U. I. Safronova, N. Ohmae, H. Katori, and
N. Nakamura, Nucl. Instrum. and Methods B , in press(2017).
[18] A. Windberger,
J. R. Crespo López-Urrutia,
H. Bekker, N. S. Oreshkina, J. C. Berengut, V. Bock,
A. Borschevsky, V. A. Dzuba, E. Eliav, Z. Harman,
U. Kaldor, S. Kaul, U. I. Safronova, V. V. Flambaum,
C. H. Keitel, P. O. Schmidt, J. Ullrich, and O. O.
Versolato, Phys. Rev. Lett. 114, 150801 (2015).
[19] N. Nakamura, H. Kikuchi, H. A. Sakaue, and T. Watanabe, Rev. Sci. Instrum. 79, 063104 (2008).

[20] C. Yamada, K. Nagata, N. Nakamura, S. Ohtani, S. Takahashi, T. Tobiyama, M. Tona, M. Sakurai, A. P. Kavanagh, and F. J. Currell, Rev. Sci. Instrum. 77, 066110(2006).
[21] A. Komatsu, J. Sakoda, M. Minoshima, H. A. Sakaue, X.B. Ding, D. Kato, I. Murakami, F. Koike, and N. Nakamura, Plasma Fusion Res. 7, 1201158 (2012).
[22] Y. Kobayashi, K. Kubota, K. Omote, A. Komatsu,
J. Sakoda, M. Minoshima, D. Kato, J. Li, H. A. Sakaue,
I. Murakami, et al., Physical Review A 92, 022510 (2015).
[23] J. H. Scofield, LLNL Internal Report (1986).
[24] U. I. Safronova, I. M. Savukov, M. S. Safronova, andW. R. Johnson, Phys. Rev. A 68, 062505 (2003).
[25] J. Sugar and V. Kaufman, Phys. Scr. 24, 742 (1981).
[26] J. Sakoda, A. Komatsu, H. Kikuchi, and N. Nakamura,Phys. Scr. T144, 014011 (2011).
[27] A. Windberger, F. Torretti, A. Borschevsky, A. Ryabtsev, S. Dobrodey, H. Bekker, E. Eliav, U. Kaldor,
W. Ubachs, R. Hoekstra, J. R. Crespo López-Urrutia,
and O. O. Versolato, Phys. Rev. A 94, 012506 (2016).
[28] J. Grumer, R. Zhao, T. Brage, W. Li, S. Huldt, R. Hutton, and Y. Zou, Phys. Rev. A 89, 062511 (2014).
[29] E. Ivanova, At. Data Nucl. Data Tables 95, 786 (2009).
[30] R. Zhao, J. Grumer, W. Li, J. Xiao, T. Brage, S. Huldt,
R. Hutton, and Y. Zou, J. Phys. B 47, 185004 (2014).
[31] E. Träbert, “Handbook for highly charged ion spectroscopic research,” (CRC Press, Boca Raton) Chap. 10, p.
207.