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Atoms 2018, 6(3), 47;

Extended Analysis of Ar III and Ar IV
Centro de Investigaciones Ópticas, M. B. Gonnet, P. O. Box 3, La Plata 1897, Argentina
Departamento de Materia Condensada, Escuela de Física, Universidad Nacional Autónoma de Honduras, Tegucigalpa 11101, Honduras
Author to whom correspondence should be addressed.
Received: 18 July 2018 / Accepted: 16 August 2018 / Published: 21 August 2018


A pulsed discharge light source was used to study the two and three times ionized argon (Ar II, Ar III) spectra in the 480–6218 Å region. A set of 129 transitions of Ar III and 112 transitions of Ar IV were classified for the first time. We extended the analysis of Ar III to five new energy levels belonging to 3s23p34d, 3s23p35s odd configurations. For Ar IV, 10 new energy levels of the 3s23p23d and 3s23p24p even and odd configurations, respectively, are presented. For the prediction of energy levels, line transitions, and transition probabilities, relativistic Hartree–Fock calculations were used.
atomic spectra; energy levels; capillary pulsed-discharge; relativistic Hartree–Fock calculations

1. Introduction

Spectral analysis of several ions of argon has implications in different fields. In astrophysics [1,2,3], argon spectral lines are important in determining the chemical abundance of elements and estimating radiative transfer through stellar plasmas. Argon plasma sources are also applied in various fields of industry and research [4,5,6,7].
A compilation of energy levels and observed spectral lines of all ionization stages of Ar was reported in [8]. Many of the papers published on the spectra of two and three times ionized argon (Ar III, Ar IV) are cited in this work [8]. The report by Hansen and Persson [9] that presented a revised and extended analysis of the optical spectrum of Ar III is noteworthy. They used hollow cathode and theta-pinch sources analyzing the 3s23p4, 3s3p5, 3p6, 3s23p34s, 3s23p34p, and 3s23p33d configurations. Improved energy levels in this ion resulting from the best wavelengths in the literature in the range between 508 Å and 4183 Å were presented by Kaufman and Whaling [10]. For Ar IV, Bredice et al. [11] reanalyzed the 3s23p3, 3s3p4, 3s23p2 (3d + 4s) configurations to obtain new energy levels and classify new transitions. A more recent paper [12] presented an analysis of beam-foil and beam-gas excited spectrum of argon observed in the wavelength region 2965–3090 Å. New transitions in the spectrum of Ar III and Ar IV were also identified.
In the last few decades [13,14,15,16,17,18], there has been intense research on determining and compiling the transition probabilities of ionized argon. In the work of Burger et al. [19], transition probabilities were presented for 38 Ar III and 14 Ar IV spectral lines from the wavelength interval 2400–3080 Å. These were compared to other papers reporting theoretical values [15,17]. In [15], Luna et al. used the Cowan code [20] carried out according to the relativistic Hartree–Fock (HF) approach.
To continue the study of the two and three times ionized argon spectra, a new spectral analysis of these ions is presented in this work. We used our experimental data of the argon spectrum covering the wavelength range 480–6218 Å for the visible ultraviolet (VUV) region. A set of 129 transitions of Ar III and 112 transitions of Ar IV were classified for the first time. Five new energy levels belonging to 3s23p34d, 3s23p35s odd configurations of Ar III and 10 new energy levels of the 3s23p23d and 3s23p24p even and odd configurations, respectively, of Ar IV are presented. Theoretical predictions of the configuration structure and transition probabilities for the spectral lines were obtained from the computer code developed by Cowan [20]. The energy matrix was calculated using energy parameters adjusted to fit the experimental energy levels.

2. Experimental Methods

The experimental data for argon were obtained at Centro de Investigaciones Opticas (CIOp). In order to excite the spectra, a capillary-pulsed discharge was used. It consisted of a Pyrex tube about 100 cm long, with an inner diameter of 0.5 cm. The electrodes, placed 80 cm apart, were made of tungsten and covered with indium. Gas excitation was produced by discharging a bank of low-inductance capacitors between 20 and 280 nF and charged up to 20 kV. To study the VUV region, one end of the tube was connected to a vacuum spectrograph and in this way a continuous flow of gas between the gas inlet and the spectrograph was established. Light emitted axially was recorded in the VUV and in the visible regions. In the VUV region, the light was analyzed using a 3 m normal incidence vacuum spectrograph with a concave diffraction grating with 1200 lines/mm and plate factor 2.77 Å/mm in the first diffraction order. To record the spectra, Ilford Q plates were used and known lines of carbon, nitrogen, oxygen, and different noble gas ions served as wavelength standards. The wavelength range above 2000 Å was observed using a diode array detector coupled to a 3.4 m Ebert plane-grating spectrograph with 600 lines/mm and a plate factor of 5 Å/mm in the first diffraction order. Photographic plates were used to record the spectra in the first, second, and third diffraction orders. Thorium lines from an electrodeless discharge were superimposed on the spectrograms and served as reference lines. To distinguish between different states of ionization, the gas pressure, discharge voltage, and number of discharges were varied. Wavelengths above 2000 Å were tabulated in air using the Edlén formula (Sections 1–4 in Reference [20]). The spectrograms were measured with a photoelectric semiautomatic Grant comparator, and the uncertainty in the determination of the wavelength of unperturbed lines was estimated to be ±0.02 Å in the VUV region and ±0.01 Å in the visible region. Energy level values derived from the observed lines were determined by means of an iterative procedure, which took into account the wave numbers of the lines, weighted by their estimated uncertainties. The uncertainty of the adjusted experimental energy level values was assumed to be lower than 2 cm−1.

3. Results and Discussion

In the present work, we used Cowan’s atomic structure package [20], with corrections to the code made by Kramida [21] due to an error in Cowan’s atomic structure theory, to calculate the solution for relativistic Hartree–Fock (HF) equations including configuration interaction for Ar III and Ar IV. We adjusted the values of energy parameters to the experimental energy levels of these ions by means of a least squares calculation. With the adjusted values, we calculated the energy and composition of the levels, as well as the weighted transition probability rate gA [15,20], where g is the statistical weight 2J + 1 of the upper level. We present a revised and extended analysis of 3s23p34d, 3s23p35s odd configurations for Ar III and of 3s23p23d and 3s23p24p even and odd configurations for Ar IV. The configuration sets used were 3s23p4, 3s23p3 (4p,5p,6p), 3s23p3 (4f,5f), 3s3p43d, 3p6, 3s23p23d2 and 3s3p5, 3s23p3 (3d,4d,5d,6d), 3s23p3 (4s,5s,6s,7s) for Ar III even and odd parities, respectively, and 3s23p3, 3s23p2 (4p,5p), 3p5, 3s3p33d, 3s23p24f, 3s23p3d2 and 3s3p4, 3s23p2 (3d,4d), 3s23p2 (4s,5s), 3s3p23d2, 3p43d for Ar IV odd and even parities, respectively.
Table 1 and Table 2 show the new and calculated energy level values for these ions with the percentage composition in LS notation. We report three new energy levels belonging to 3s23p34d and two to 3s23p35s configurations of Ar III, and in Ar IV five new energy levels for 3s23p23d and five for 3s23p24p configurations. The calculated energy level values were obtained by least squares fit [20]. Our calculations included all the energy levels experimentally known.
Table 3 and Table 4 show 23 and 53 new classified lines for Ar III and Ar IV, respectively, that were classified with the new levels presented in this work. We also present 106 and 59 new spectral lines for Ar III and Ar IV, respectively, corresponding to transitions with previously known levels. In these tables we also present gA transition probabilities to compare with the experimental intensity of the new observed lines. In the last columns of these tables we compare the values of gA with those of reference [16]. The observed differences could be due to the fact that weighted values of the energy parameters were used in our work and the calculations presented in reference [16] are ab initio, therefore the composition percentages of the experimental levels are different; besides, the set of configurations used is not exactly the same and there are effects of cancellation factors in our calculations (Sections 14 and 15 in Reference [20]).
The least squares calculation results are shown in Table 5, Table 6, Table 7 and Table 8 for Ar III and Ar IV. In Table 5 and Table 6, we show the radial parameters for the even and odd parity configurations of Ar III. In this calculation we also included the illegal-k effective-operator parameters Fk (i,j) and Gk (i,j) (Section 16-7 in Reference [20]). In the case of 3s23p33d configuration for the odd parity, we set free the G2 (3p, 3d) parameter (there is no HF value for this parameter). The fitted value is in agreement with that published in [10]. In these tables, all the adjusted parameters that were set free are in good agreement with the scaled HF values. The parameter α was left free in the calculation and then fixed to its optimized value. The strong configuration interactions for the even parity (Table 5) between 3s23p4–3s3p43d and 3s23p4–3p6 configurations were optimized and fixed at 90%, 85%, and 70% of their HF values, respectively. For the odd parity (Table 6), the interaction integrals between 3s3p5–3s23p33d and 3s23p33d–3s23p34d configurations were set free in the calculation. In the energy adjustment of Ar III, the standard deviation was 101 and 339 cm−1 for the even and odd parities, respectively.
In Table 7 and Table 8, we show the radial parameters for the odd and even parity configurations of Ar IV. The adjusted parameters in these tables are in accordance with the scaled HF values. The parameter α was left free in the calculation and then fixed to its optimized value, except for the 3s23p24s configuration, which was left fixed at the value of zero. The configuration interactions were set to 85% of their HF values. These values are omitted in Table 7 and Table 8. For the even configurations, the integral of interaction between 3s3p4 and 3s23p23d is significant, as it was seen in reference [11]. The standard deviation was 266 and 242 cm−1 for the odd and even parities, respectively.
It should be mentioned that the accuracy in our calculations of the fitted values of the previously known energy levels are given according to the standard deviation for each of the parities in Ar III and Ar IV.

4. Conclusions

In this work we studied the Ar III and Ar IV spectra covering the wavelength range 480–6218 Å for the visible ultraviolet region using a pulsed electrical discharge. A set of 129 transitions of Ar III and 112 transitions of Ar IV were classified. Five new energy levels belonging to 3s23p34d, 3s23p35s and 10 new energy levels of 3s23p23d, 3s23p24p for Ar III and Ar IV, respectively, were presented. Relativistic Hartree–Fock calculations were used. We considered optimized values of the energy parameters using least squares technique where we adjusted the theoretical parameter values to fit the experimental levels.

Author Contributions

Investigation, Writing-Original Draft Preparation, Conceptualization and Atomic calculation, M.R.; Software, R.E.M.C.; Formal Analysis, M.G.; Methodology and Investigation, J.R.A.


This research received no external funding.


This research was supported by the Consejo Nacional de Investigaciones Científicas y Técnicas, Argentina. The Comision de Investigaciones Científicas de la Provıncia de Buenos Aires (CIC), where M. Raineri is a researcher, is also gratefully acknowledged.

Conflicts of Interest

The authors declare no conflict of interest.


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Table 1. New Ar III energy levels.
Table 1. New Ar III energy levels.
ConfigurationTermJExp Level (cm−1)Fitted a (cm−1)Composition b
3s23p3 (2D°) 4d10267,275.7267,24498
3s23p3 (2P°) 4d13286,381.9286,37578 3s23p3 (2P°) 4d1F° + 8 3s23p3 (2D°) 5d1
3s23p3 (2P°) 4d11292,090.9292,12263 3s23p3 (2P°) 4d1P° + 18 3s23p3 (2D°) 5d1
3s23p3 (2D°) 5s12272,655.2272,63657 3s23p3 (2D°) 5s1D° + 34 3s23p3 (2D°) 4d1
3s23p3 (2P°) 5s11286,878.2286,84597
a Calculated energy level values obtained using the fitted energy parameters. b Percentages below 5% have been omitted.
Table 2. New Ar IV energy levels.
Table 2. New Ar IV energy levels.
ConfigurationTermJExp Level (cm−1)Fitted a (cm−1)Composition b
3s23p2 (1D) 3d2F5/2185,795.6185,87046 3s23p2 (1D) 3d 2F + 39 3s23p2 (3P) 3d 2F
3s23p2 (1D) 3d2F7/2186,451.8186,59144 3s23p2 (1D) 3d 2F + 31 3s23p2 (3P) 3d 2F
3s23p2 (1D) 3d2P1/2245,175.2245,28757 3s23p2 (1D) 3d2P + 21 3s23p2 (3P) 3d 2P
3s23p2 (1S) 3d2D5/2261,761.1261,94658 3s23p2 (1S) 3d 2D + 30 3s23p2 (3P) 3d 2D
3s23p2 (1S) 3d2D3/2262,626.1262,73555 3s23p2 (1S) 3d 2D + 31 3s23p2 (3P) 3d 2D
3s23p2 (3P) 4p21/2282,726.0282,59698
3s23p2 (1D)4p21/2311,018.3310,97387 3s23p2 (1D) 4p2P° + 10 3s23p2 (3P) 4p2
3s23p2 (1D)4p23/2311,276.3311,20176 3s23p2 (1D) 4p2P° + 123s23p2 (3P) 4p2
3s23p2 (1S)4p21/2327,113.4327,12696
3s23p2 (1S)4p23/2327,388.9327,33396
a Calculated energy level values obtained using the fitted energy parameters. b Percentages below 5% have been omitted.
Table 3. New classified lines of Ar III.
Table 3. New classified lines of Ar III.
Rel. Int.Observed Wavelength Vac (Å)Wavenumber (cm−1) σobsLower Level Conf. Term, JUpper Level Conf. Term, JgA (s−1)gA (s−1) Reference [16]
3764.09130,8753s23p41D23s23p3 (4S°) 3d514.12 × 1042.20 × 105
4790.77126,4593s3p5323s23p3 (2P°) 4p3D21.74 × 1073.22 × 107
8797.48125,3953s3p5323s23p3 (2P°) 4p3S11.77 × 1084.35 × 108
6797.75125,3533s3p5313s23p3 (2P°) 4p3D11.96 × 1073.64 × 107
7803.88124,3973s3p5313s23p3 (2P°) 4p3S11.60 × 1083.95 × 108
2807.32123,8673s3p5303s23p3 (2P°) 4p3S16.66 × 1073.52 × 107
1817.90122,2643s3p5323s23p3 (2D°) 4p1D21.18 × 106
2855.01116,9583s3p5313s23p3 (2D°) 4p3P08.33 × 1072.18 × 108
6855.94116,8313s3p5313s23p3 (2D°) 4p3P13.96 × 1071.21 × 108
3887.30112,7023s3p5323s23p3 (2D°) 4p3F31.25 × 1079.22 × 106
7896.02111,6053s3p5323s23p3 (2D°) 4p3D35.62 × 1071.78 × 108
3896.37111,5613s3p5313s23p3 (2D°) 4p3F22.82 × 106
6906.18110,3533s3p5313s23p3 (2D°) 4p3D22.65 × 1079.18 × 107
2910.22109,8643s3p5323s23p3 (2D°) 4p1P18.82 × 103
21019.5998,0793s23p3 (4S°) 3d313s23p3 (2P°) 4p1S01.13 × 106
61048.6795,359 *3s23p3 (4S°) 3d523s23p3 (2D°) 4p3D21.85 × 105
61048.6795,359 *3s23p3 (4S°) 3d533s23p3 (2D°) 4p3D29.23 × 103
31143.6287,4423s23p3 (4S°) 3d333s23p3 (2P°) 4p1D23.14 × 105
81151.1586,8703s23p3 (4S°) 3d513s23p3 (2D°) 4p3P02.96 × 104
31152.9286,7363s23p3 (4S°) 3d523s23p3 (2D°) 4p3P17.69 × 104
41156.6386,4583s23p3 (4S°) 3d513s23p3 (2D°) 4p3P26.57 × 104
11225.2781,6153s23p3 (4S°) 3d523s23p3 (2D°) 4p3F35.61 × 104
61226.5281,5323s23p41S03s3p5312.33 × 105
21227.8881,4413s23p3 (4S°) 4p5P13s23p3 (2P°) 5s322.80 × 105
11231.1381,2263s23p3 (4S°) 4p5P23s23p3 (2P°) 5s312.36 × 103
91232.5281,1353s3p5113s23p3 (2D°) 4p3D19.26 × 107
11246.0780,2523s23p3 (4S°) 3d533s23p3 (2D°) 4p3D29.23 × 103
11287.2277,6873s23p3 (4S°) 4p3P13s23p3 (2P°) 5s115.26 × 105
41294.8477,2323s23p3 (4S0) 4p3P23s23p3 (2P°) 4d133.74 × 105
91308.2576,4383s23p3 (2D°) 3d323s23p3 (2P°) 4p3S19.63 × 105
21382.7172,3223s23p3 (4S°) 4p3P23s23p3 (2P°) 4d331.03 × 105
61461.3868,4283s23p3 (2D°) 4p1P13s23p3 (2P°) 4d111.90 × 108
11478.8767,6193s23p3 (4S°) 4p5P13s23p3 (2D°) 5s323.02 × 103
11479.3367,5983s23p3 (4S°) 4p5P23s23p3 (2D°) 5s331.19 × 105
11498.2166,7463s23p3 (4S°) 3d323s23p3 (2D°) 4p1P11.56 × 107
71498.3866,7393s23p3 (4S°) 3d323s23p3 (2D°) 4p1P18.52 × 107
11501.7766,5883s23p3 (2P°) 3d313s23p3 (2P°) 4p1S01.92 × 103
31517.1565,9133s23p3 (4S°) 4s523s23p3 (2P°) 4p3D34.39 × 106
11551.7164,4453s23p3 (4S°) 4p5P13s23p3 (2D°) 4d322.90 × 105
21565.0763,8953s23p3 (4S°) 4s313s23p3 (2P°) 4p3P22.47 × 1073.17 × 107
21583.5463,1503s23p3 (2D°) 4p1P13s23p3 (2P°) 5s113.88 × 107
11584.7463,1023s23p3 (4S°) 4p3P23s23p3 (2D°) 5s331.63 × 106
21621.9161,6563s23p3 (2D°) 4p3D13s23p3 (2P°) 5s116.94 × 106
31641.8560,9073s23p3 (2D°) 3d103s23p3 (2D°) 4p1P11.96 × 108
11646.5060,7353s23p3 (2D°) 4p3D23s23p3 (2P°) 5s312.50 × 107
21654.1260,4553s23p3 (2D°) 4p1P13s23p3 (2P°) 4d312.16 × 104
21657.3960,3363s23p3 (2D0) 4p3P03s23p3(2P°) 4d117.81 × 105
21670.1059,8773s23p3 (2D0) 4p3F33s23p3 (2P°) 4d133.57 × 104
31674.0959,7343s23p3 (2D0) 4p3F43s23p3 (2P°) 4d134.57 × 104
11756.0556,9463s23p3 (2D°) 4p3D13s23p3 (2P°) 4d323.39 × 106
11758.8956,8543s23p3 (2D°) 4p3D23s23p3 (2P°) 4d314.34 × 103
21784.8656,0263s23p3 (2D0) 4p1D23s23p3(2P°) 4d1P016.97 × 105
11818.1555,0013s23p3 (2P°) 3d313s23p3 (2P°) 4p3P13.07 × 1074.91 × 107
21821.2654,9073s23p3 (2P°) 3d323s23p3 (2P°) 4p3P22.59 × 1083.19 × 108
21833.4554,5423s23p3 (2D°) 4p3P23s23p3 (2P°) 5s311.12 × 107
11877.3453,2673s23p3 (2D°) 3d343s23p3 (2D°) 4p3D31.39 × 1083.84 × 107
11885.0553,0493s23p3 (2D°) 3d333s23p3 (2D°) 4p3D24.94 × 1071.79 × 107
31925.4051,9393s23p3(2P°) 4p3D13s23p3 (2P°) 4d111.54 × 107
11967.8050,8183s23p3 (2D°) 4p1D23s23p3 (2P°) 5s1P013.98 × 107
Observed Wavelength Air (Å)
62041.248,9913s23p3 (2D0) 4p1P13s23p3 (2D°) 5s121.67 × 109
12339.2342,736.03s23p3 (2P°) 4p3P13s23p3 (2P°) 5s311.73 × 108
22351.8042,5213s23p3 (2P°) 4p1D23s23p3 (2P°) 5s111.30 × 109
52378.8242,024.73s23p3 (2P°) 4p1D23s23p3 (2P°) 4d135.30 × 109
22394.8541,743.63s23p3 (2P°) 4p3D23s23p3 (2P°) 4d311.46 × 106
42572.9238,854.73s23p3 (2P°) 4p3P13s23p3 (2P°) 4d311.24 × 108
12628.2638,036.63s23p3 (2P°) 4p3P23s23p3 (2P°) 4d325.33 × 106
12710.0936,888.23s23p3 (4S°) 4p3P23s23p3 (4S°)4d531.39 × 106
22710.3636,884.53s23p3 (2P°) 4p1S03s23p3 (2P°) 4d114.38 × 108
92767.3936,124.53s23p3 (2D°) 4p1D23s23p3 (2D°) 5s321.42 × 107
32771.9236,065.43s23p3 (2D°) 4p1D23s23p3 (2D°) 5s311.58 × 106
42804.3635,648.33s23p3 (2D°) 4p3P13s23p3 (2D°)4d101.51 × 106
42891.4634,574.53s23p3 (2P°) 4s323s23p3 (2P°) 4p1P12.61 × 107
23037.2532,914.93s23p3 (2D°) 4p1D23s23p3 (2P°) 4d312.00 × 106
93048.4732,793.83s23p3 (2P°) 3d313s23p3 (2P°) 4p1D27.18 × 106
13075.7032,503.5 *3s23p3 (2P°) 4p3S13s23p3 (2D°)4d3P006.26 × 104
13075.7032,503.5 *3s23p3 (2P°) 4p3D13s23p3 (2D°) 5s126.94 × 105
33089.0332,363.23s23p3 (2P°) 4p3D33s23p3 (2D°) 5s124.64 × 103
23120.4132,037.83s23p3 (2P°) 4p3D13s23p3 (2D°)5s3D025.91 × 106
43132.1331,917.93s23p3 (2P°) 4p3D13s23p3 (2D°)4d316.40 × 105
13137.8231,860.03s23p3 (2P°)3d313s23p3 (2P°) 4p3P21.12 × 1061.04 × 107
63140.3031,834.93s23p3 (2P°) 4p3D23s23p3 (2D°) 4d121.30 × 107
73199.0831,250.03s23p3 (2P°) 4p3D23s23p3 (2D°) 4d321.04 × 105
63245.5830,802.33s23p3 (2P°) 3d323s23p3 (2P°) 4p1P14.11 × 1071.58 × 107
23290.3730,383.03s23p3 (2P°) 4p1P13s23p3 (2D°) 5s321.33 × 107
83300.9530,285.63s23p3 (2P°) 4p1P13s23p3 (2D°) 4d124.58 × 107
83352.4929,820.03s23p3 (2P°) 4p3S13s23p3 (2D°) 4d322.00 × 106
23356.4729,784.73s23p3 (2P°) 4p3S13s23p3 (2D°)4d315.91 × 105
23373.3529,635.63s23p3 (2P°)3d123s23p3 (4S°) 4p3P21.34 × 102
73387.8529,508.83s23p3 (2P°) 4p3P13s23p3 (2D°) 5s121.14 × 106
23420.1229,230.43s23p3 (2P°) 4p3P23s23p3 (2D°) 5s127.43 × 105
43442.1829,043.03s23p3 (2P°) 4p3P13s23p3 (2D°) 5s321.59 × 107
13445.7929,012.63s23p3 (2P°) 4p1S03s23p3 (2P°) 4d311.81 × 106
33449.3228,982.93s23p3 (2P°) 4p3P13s23p3 (2D°) 5s318.36 × 106
23453.6128,946.93s23p3 (2P°) 4p3P13s23p3 (2D°) 4d122.18 × 107
53456.4828,922.93s23p3 (2P°) 4p3P13s23p3 (2D°) 4d312.61 × 107
23463.8128,861.73s23p3 (2P°) 4p3D13s23p3 (2D°) 4d325.00 × 106
63467.9828,827.0 *3s23p3 (2P°) 4p3D13s23p3 (2D°) 4d311.83 × 107
63467.9828,827.0 *3s23p3 (2P°) 4p3P23s23p3 (2D°) 5s334.58 × 107
73482.1528,709.73s23p3 (2P°)4p3D33s23p3 (2D°) 4d335.48 × 107
63490.1228,644.13s23p3 (2P°) 4p3P23s23p3 (2D°) 4d312.71 × 107
23501.5728,550.53s23p3 (2P°) 4p3P13s23p3 (2D°) 4d308.20 × 106
33504.5428,526.33s23p3 (2P°) 4p3P13s23p3 (2D°) 4d317.90 × 105
13524.8628,361.83s23p3 (2P°) 4p3P13s23p3 (2D°) 4d323.55 × 106
73532.9228,297.13s23p3 (2P°) 4p1D23s23p3 (2D°) 5s126.12 × 107
63546.5228,188.63s23p3 (2P°) 3d323s23p3 (2P°) 4p3S11.13 × 107
73557.6828,100.23s23p3 (4S°) 4p3P23s23p3 (2P°) 3d111.27 × 104
83559.9428,082.3 *3s23p3 (2P°) 4p3P23s23p3 (2D°) 4d326.00 × 106
83559.9428,082.3 *3s23p3 (2P°) 4p3S13s23p3 (2D°)4d106.15 × 105
13604.6027,734.43s23p3 (2P°) 4p1D23s23p3 (2D°) 4d121.72 × 107
33618.2827,629.63s23p3 (2P°) 3d313s23p3 (2P°) 4p3S13.69 × 106
83632.1327,524.23s23p3 (2P°)4p3D23s23p3 (2D°) 4d337.87 × 105
23674.6327,205.93s23p3 (2P°)4p1P13s23p3 (2D°) 4d322.00 × 104
23787.0626,398.23s23p3 (2P°) 4p1D23s23p3 (2D°) 4d112.28 × 107
23908.7825,576.23s23p3 (2P°) 4p3P23s23p3 (2D°) 4d331.22 × 106
53978.7225,126.63s23p3 (2P°) 3d123s23p3 (4S°) 4p5P24.49 × 102
33989.3525,059.73s23p3 (2P°) 3d323s23p3 (2D°) 4p1D22.21 × 106
33998.7725,000.63s23p3 (2P°)4s113s23p3 (2D°) 4p1D25.83 × 1069.23 × 106
44012.3124,916.33s23p3 (2D°) 4p1P13s23p3 (2D°) 4d325.69 × 104
74143.3824,128.13s23p3 (2P°) 4p3P13s23p3 (2D°) 4d105.46 × 106
14520.8722,113.43s23p3 (2D°)3d323s23p3 (2D°) 4p1D21.47 × 106
64553.6921,954.13s23p3 (2D°)3d313s23p3 (4S°) 4p3P15.49 × 1061.68 × 108
74693.0621,302.13s23p3 (2D°)3d323s23p3 (4S°) 4p3P11.33 × 1074.83 × 108
15587.8017,891.23s23p3 (4S°)4s313s23p3 (4S°) 4p5P14.62 × 105
95869.9617,031.23s23p3 (2P°)3d333s23p3 (2D°) 4p1F31.21 × 106
95976.6216,727.23s23p3 (2P°)3d123s23p3 (2D°) 4p1D23.59 × 107
96054.4316,512.33s23p3 (2D°) 4p1D23s23p3 (4S°) 5s314.23 × 103
76167.0516,210.63s23p3 (2D°) 4p1D23s23p3 (4S°) 4d313.17 × 104
86187.8416,156.33s23p3 (2D°)3d113s23p3 (2D°)4p1D21.14 × 107
36217.6515,940.43s23p3 (2D°) 3d333s23p3 (4S) 4p5P24.48 × 104
* Double classification.
Table 4. New classified lines of Ar IV.
Table 4. New classified lines of Ar IV.
Rel. Int.Observed Wavelength Vac (Å)Wavenumber (cm−1) σobsLower Level Conf. Term, JUpper Level Conf. Term, JgA (s−1)gA (s-1) Reference [16]
1480.61208,0683s3p44P1/23s23p2 (1S) 4p21/22.30 × 104
4491.01203,6623s23p323/23s23p2 (3P) 3d2D3/25.87 × 109
3499.48200,2083s23p323/23s23p2 (3P) 3d4P3/24.41 × 107
2500.75199,7003s23p323/23s23p2 (3P) 3d4P5/21.97 × 107
5501.09199,5653s23p325/23s23p2 (3P) 3d4P5/21.53 × 108
1520.90191,9753s3p44P1/23s23p2 (1D) 4p21/25.91 × 103
7536.08186,5393s23p325/23s23p2 (1D) 3d2G7/24.11 × 1072.48 × 107
2564.06177,2863s3p44P3/23s23p2 (3P) 4p21/25.73 × 105
3596.65167,6023s23p323/23s23p2 (3P) 3d4D1/29.99 × 1066.18 × 106
2599.11166,9123s3p44P1/23s23p2 (3P) 4p41/23.00 × 1071.05 × 107
3604.76165,3553s3p42D3/23s23p2 (1D) 4p23/27.34 × 108
2605.06165,2733s3p42D5/23s23p2 (1D) 4p23/28.37 × 108
2627.10159,4643s23p325/23s23p2 (3P) 3d4F3/23.00 × 105
6632.95157,9903s3p42D5/23s23p2 (1D) 4p27/23.95 × 108
2686.52145,6623s3p42D5/23s23p2 (3P) 4p25/21.43 × 1066.31 × 107
2694.89143,9073s3p42D3/23s23p2 (3P) 4p45/21.05 × 105
2695.27143,8303s23p2 (3P)3d2P1/23s23p2 (1D) 4p23/26.60 × 107
2698.33143,1993s3p42D3/23s23p2 (3P) 4p41/24.33 × 105
2716.50139,5673s23p2 (3P)3d4D5/23s23p2 (1S) 4p23/21.62 × 104
7773.31129,3143s23p2 (3P)3d2P3/23s23p2 (3P) 4p21/22.53 × 1083.82 × 108
8779.07128,3583s23p2 (3P)3d2P1/23s23p2 (3P) 4p23/22.96 × 1084.56 × 108
1806.55123,9853s23p2 (3P)3d4D1/23s23p2 (1D) 4p23/26.66 × 105
7844.39118,4293s23p2 (3P)3d4D3/23s23p2 (1D) 4p2Do5/22.74 × 106
3847.68117,9693s3p42S1/23s23p2 (3P) 4p23/21.78 × 1061.98 × 107
1848.39117,8703s23p2 (1D) 3d2F5/23s23p2 (1D) 4p25/21.01 × 109
2850.80117,5373s23p2 (1D) 3d2F7/23s23p2 (1D) 4p27/21.20 × 109
2853.14117,2143s23p2 (1D) 3d2F7/23s23p2 (1D) 4p25/21.17 × 108
3859.34116,3683s23p2 (3P) 3d2P3/23s23p2 (3P) 4p21/21.04 × 1091.21 × 109
3860.82116,1683s23p2 (3P) 3d4D5/23s23p2 (1D) 4p27/26.59 × 106
3863.24115,8433s23p2 (3P) 3d4D5/23s23p2 (1D) 4p25/25.20 × 107
1903.25110,7113s23p2 (3P) 3d4F5/23s23p2 (3P) 4p43/23.94 × 104
9922.68108,3803s23p2 (3P) 3d4D1/23s23p2 (3P) 4p21/23.80 × 106
2945.05105,8143s23p2 (3P) 3d4P3/23s23p2 (1S) 4p21/25.74 × 105
1953.37104,8913s3p42S1/23s23p2 (3P) 4p21/22.79 × 106
1957.32104,4573s23p2 (1D) 3d2F5/23s23p2 (3P) 4p23/23.01 × 1092.53 × 109
6958.34104,3473s23p2 (3P) 3d4D3/23s23p2 (3P) 4p43/22.57 × 1077.19 × 107
6959.10104,2643s23p2 (3P) 3d4D3/23s23p2 (3P) 4p25/29.61 × 1062.01 × 107
5962.27103,9213s23p2 (3P) 3d4D5/23s23p2 (3P) 4p43/24.76 × 1074.93 × 107
2982.76101,7543s23p2 (1D) 3d2F5/23s23p2 (3P) 4p47/21.19 × 1078.94 × 107
7986.07101,4133s23p2 (3P) 3d4D5/23s23p2 (3P) 4p43/22.15 × 1092.07 × 109
1987.70101,2453s23p2 (3P) 3d2D5/23s23p2 (1S) 4p23/21.05 × 109
1989.12101,1003s23p2 (1D) 3d2F7/23s23p2 (3P) 4p47/24.13 × 1083.11 × 108
2990.57100,9523s23p2 (1D) 3d2F5/23s23p2 (3P) 4p45/23.03 × 1072.48 × 108
1997.06100,2953s23p2 (1D) 3d2F7/23s23p2 (3P) 4p45/28.36 × 1074.77 × 107
21019.7398,0653s23p2 (1D) 3d2G7/23s23p2 (1D) 4p2Do5/22.07 × 107
11114.6089,7183s23p2 (3P) 3d4P3/23s23p2 (1D) 4p21/28.89 × 105
41118.7089,3903s23p2 (3P) 3d4P1/23s23p2 (1D) 4p21/21.26 × 105
11127.1988,7163s23p2 (1D) 3d2D5/23s23p2 (1S) 4p23/27.89 × 107
11132.0088,3393s23p2 (1D) 3d2D3/23s23p2 (1S) 4p23/28.98 × 106
11135.5688,0623s3p42P3/23s23p2 (1D) 4p21/22.95 × 107
11135.5688,0623s23p2 (1D) 3d2D3/23s23p2 (1S) 4p21/22.34 × 107
11146.0287,2593s3p42P1/23s23p2 (1D) 4p23/25.06 × 107
21217.8882,1153s23p2 (1D) 3d2P1/23s23p2 (1S) 4p23/22.70 × 107
51218.5282,0673s23p2 (1D) 3d2G7/23s23p2 (3P) 4p45/23.34 × 105
61232.3781,1453s23p2 (3P) 3d2D3/23s23p2 (1D) 4p2Do3/21.23 × 107
51233.4781,0723s23p2 (3P) 3d2D3/23s23p2 (1D) 4p2Do5/21.71 × 107
51254.8779,6903s23p2 (1D) 3d2G9/23s23p2 (3P) 4p47/22.68 × 105
71254.9779,6833s23p2 (3P) 3d2D5/23s23p2 (1D) 4p2Do5/24.47 × 107
41307.4176,4873s23p2 (3P)4s4P3/23s23p2 (1S) 4p23/21.05 × 105
21312.1176,2133s23p2 (3P)4s4P3/23s23p2 (1S) 4p21/21.00 × 105
11333.0675,0153s23p2 (3P) 3d4P5/23s23p2 (3P) 4p23/24.31 × 106
71372.7572,8473s3p42P3/23s23p2 (3P) 4p23/28.47 × 1073.83 × 107
11377.3572,6033s23p2 (1D) 3d2D5/23s23p2 (1D) 4p23/23.15 × 108
21407.9471,0263s23p2(3P) 4s2P1/23s23p2 (1S) 4p21/22.21 × 107
81410.8970,8773s23p2 (3P) 3d4P5/23s23p2 (3P) 4p25/23.09 × 1073.61 × 107
71421.2470,3613s23p2 (3P) 3d4P3/23s23p2 (3P) 4p25/21.62 × 1072.10 × 107
11433.2869,7703s23p2 (3P) 4s2P3/23s23p2 (1S) 4p21/21.26 × 107
41439.5869,4653s23p2 (3P) 3d4P5/23s23p2 (3P) 4p23/21.20 × 1072.83 × 107
21453.7468,7883s3p42P3/23s23p2 (3P) 4p43/27.27 × 1061.88 × 107
71487.5167,2263s23p2 (1D) 3d2D5/23s23p2 (1D) 4p2Do3/25.18 × 107
51489.1067,1553s23p2 (1D) 3d2D5/23s23p2 (1D) 4p2Do5/21.19 × 109
31494.5966,9083s23p2 (3P) 3d2D3/23s23p2 (3P) 4p25/22.47 × 107
71497.6066,7743s23p2 (1D) 3d2D3/23s23p2 (1D) 4p2Do5/21.04 × 108
21512.8766,1013s23p2 (1D) 3d2P1/23s23p2 (1D) 4p23/22.96 × 107
21538.6364,9933s23p2 (1D) 3d2D5/23s23p2 (1D) 4p25/21.58 × 107
11636.6961,0993s23p2 (3P) 3d4P1/23s23p2 (3P) 4p21/22.48 × 1038.40 × 106
11646.8460,7223s23p2 (1D) 3d2P1/23s23p2 (1D) 4p23/22.32 × 107
11795.8555,6843s23p2 (3P) 4s4P1/23s23p2 (1D) 4p2Do3/21.11 × 107
21887.0152,9923s23p2 (1D) 3d2D5/23s23p2 (3P) 4p25/27.60 × 1073.22 × 107
11953.1251,2003s23p2 (1D) 3d2D3/23s23p2 (3P) 4p23/24.88 × 1072.45 × 107
11975.1050,6303s23p2 (1D) 3d2P1/23s23p2 (3P) 4p23/21.18 × 1071.29 × 107
21980.4150,4953s23p2 (1D) 3d2P1/23s23p2 (3P) 4p21/21.51 × 1061.83 × 106
Observed Wavelength Air (Å)
32311.0543,257.13s23p2(1D) 4s2D3/23s23p2 (1D) 4p21/28.16 × 108
12319.8243,093.63s23p2 (3P) 3d2F7/23s23p2 (3P) 4p45/22.00 × 107
62385.6341,904.13s23p2 (1S) 3d2D5/23s23p2 (1D) 4p25/24.40 × 106
12435.9141,040.03s23p2 (1S) 3d2D3/23s23p2 (1D) 4p25/23.48 × 107
42451.4240,780.33s23p2 (1D) 3d2P1/23s23p2 (3P) 4p41/29.44 × 103
32906.1334,400.03s23p2 (3P) 4s2P3/23s23p2 (3P) 4p43/24.97 × 105
42936.8534,040.13s23p2 (1S) 3d2D5/23s23p2 (3P) 4p23/27.71 × 1076.40 × 108
33013.4533,174.93s23p2 (1S) 3d2D3/23s23p2 (3P) 4p23/28.83 × 1069.85 × 107
83025.4433,043.43s23p2 (1S) 3d2D3/23s23p2 (3P) 4p21/23.77 × 1073.57 × 108
23074.8632,512.43s23p2 (3P) 4s4P1/23s23p2 (3P) 4p21/23.05 × 106
33141.2531,825.23s23p2 (3P) 4s4P3/23s23p2 (3P) 4p21/25.81 × 1064.22 × 106
43143.8931,778.33s23p2 (3P) 4s2P3/23s23p2 (3P) 4p41/24.74 × 106
13317.2930,136.43s23p2 (3P) 4s2P1/23s23p2 (3P) 4p43/21.02 × 106
43399.8829,404.43s23p2 (3P) 4s2P3/23s23p2 (3P) 4p45/21.83 × 106
23561.5728,069.53s23p2 (1S) 3d2D5/23s23p2 (3P) 4p45/21.33 × 106
43618.6127,627.03s23p2 (1S) 3d2D3/23s23p2 (3P) 4p23/21.23 × 1076.96 × 107
13639.0927,471.63s23p2 (1S) 3d2D5/23s23p2 (3P) 4p43/21.29 × 105
23674.9327,203.73s23p2 (1S) 3d2D3/23s23p2 (3P) 4p45/25.55 × 104
13752.7926,639.23s23p2 (3P) 4s2P1/23s23p2 (3P) 4p21/21.07 × 1086.94 × 107
24000.6424,988.93s23p2 (1S) 3d2D5/23s23p2 (3P) 4p45/21.73 × 103
94168.1423,984.83s23p2(1D) 4s2D3/23s23p2 (3P) 4p43/27.90 × 102
84178.8123,923.53s23p2(1D) 4s2D5/23s23p2 (3P) 4p25/29.64 × 1078.11 × 107
64182.4123,902.93s23p2(1D) 4s2D3/23s23p2 (3P) 4p25/21.01 × 108
64044.8522,511.93s23p2(1D) 4s2D5/23s23p2 (3P) 4p23/26.02 × 106
34285.0123,330.63s23p2 (1S) 3d2D3/23s23p2 (3P) 4p41/21.19 × 104
84444.9622,491.13s23p2 (1D) 4s2D3/23s23p2 (3P) 4p23/24.58 × 1073.85 × 107
64525.4622,091.03s23p2 (1D) 4s2D5/23s23p2 (3P) 4p45/23.52 × 106
34529.6422,070.63s23p2 (1D) 4s2D3/23s23p2 (3P) 4p45/24.37 × 105
44655.5921,473.53s23p2 (1D) 4s2D3/23s23p2 (3P) 4p43/27.00 × 105
24680.0821,361.23s23p2 (1D) 4s2D3/23s23p2 (3P) 4p4½5.39 × 103
* Double classification.
Table 5. Energy parameters (cm−1) for the studied even parity configurations of Ar III. HF, Hartree–Fock.
Table 5. Energy parameters (cm−1) for the studied even parity configurations of Ar III. HF, Hartree–Fock.
ConfigurationParameterHF ValueFitted ValueFitt/HF a
3s23p4Eav 22,421 ± 52
F2 (3p, 3p)68,55857,745 ± 2030.84
α 69 (FIX)
ζ3p10051096 ± 981.09
3s23p34pEav219,988227,971 ± 201.04
F2 (3p, 3p)72,04056,805 ± 1170.79
α 100 (FIX)
ζ3p11141659 ± 1421.49
ζ4p150143 (FIX)0.95
F2 (3p, 4p)14,69414,240 ± 2140.97
G0 (3p, 4p)39793343 ± 220.84
G2 (3p, 4p)45563441 ± 1180.75
Configuration Interaction (CI) Integrals
3s23p4–3s3p43dR1 (3s3p, 3p3d)80,05372,047 (FIX)0.90
3s23p4–3s3p43dR1 (3s3p, 3d 3p)59,37550,469 (FIX)0.85
3s23p4–3p6R1 (3s3s, 3p3p)94,23865,967 (FIX)0.70
a Parameters omitted from this table: direct and exchange integrals and spin-orbit ζ parameters set to 85% and 95% of their HF values, respectively; CI integrals were set to 85% of their HF values. The standard deviation for the energy adjustment was 101 cm−1.
Table 6. Energy parameters (cm−1) for the studied odd parity configurations of Ar III.
Table 6. Energy parameters (cm−1) for the studied odd parity configurations of Ar III.
ConfigurationParameterHF ValueFitted ValueFitt/HF a
3s3p5Eav147,157150,084 ± 3981.02
ζ3p10081008 ± 3991.00
G1 (3s, 3p)94,42277,710 ± 21550.82
3s23p33dEav173,498181,366 ± 1451.04
F2 (3p, 3p)69,68054,348 ± 4810.78
α 248 (FIX)
ζ3p10461176 ± 2071.12
ζ3d2524 (FIX)0.95
F2 (3p, 3d)54,65449,263 ± 5970.90
G1 (3p, 3d)68,21657,194 ± 6260.84
G2 (3p, 3d) 5394 ± 463
G3 (3p, 3d)40,86632,109 ± 6010.78
3s23p34sEav189,895197,135 ± 1221.04
F2 (3p, 3p)71,61954,250 ± 5610.76
α 240 (FIX)
ζ3p11041049 (FIX)0.95
G1 (3p, 4s)57354923 ± 2840.86
3s23p34dEav261,115268,449 ± 1221.03
F2 (3p, 3p)71,95457,693 ± 4830.80
α 119 (FIX)
ζ3p11091949 ± 4151.76
ζ4d66 (FIX)1.00
F2 (3p, 4d)11,48610,068 ± 13750.88
G1 (3p, 4d)89057143 ± 6010.80
G3 (3p, 4d)59825085 (FIX)0.85
3s23p35sEav264,555272,420 ± 1141.03
F2 (3p, 3p)72,13657,347 ± 6310.79
α 86 (FIX)
ζ3p11171299 ± 2971.16
G1 (3p, 5s)17141467 ± 2990.85
Configuration Interaction Integrals
3s3p5–3s23p33dR1 (3p3p, 3s3d) 78,62561,091 ± 6050.78
3s23p33d–3s23p34dR2 (3p3d, 3p4d) 16,76512,132 ± 10460.72
3s23p33d–3s23p34dR1 (3p3d, 4d 3p)23,11624,234 ± 11421.05
3s23p33d–3s23p34dR3 (3p3d, 4d 3p)14,59418,936 ± 23101.30
a Parameters omitted from this table: direct and exchange integrals, and spin-orbit ζ parameters set to 85% and 95% of their HFR values, respectively; CI integrals were set to 85% of their HFR values. The standard deviation for the energy adjustment was 339 cm−1.
Table 7. Energy parameters (cm−1) for the studied odd parity configurations of Ar IV.
Table 7. Energy parameters (cm−1) for the studied odd parity configurations of Ar IV.
ConfigurationParameterHF ValueFitted ValueFitt/HF a
3s23p3Eav 27,428± 135
F2 (3p, 3p)72,35266,464 ± 7750.92
α −281 (FIX)
ζ3p11231292 ± 2531.15
3s23p24pEav285,513297,973 ± 641.04
F2 (3p, 3p)75,48561,386 ± 3800.81
α 74 (FIX)
ζ3p12351045 ± 1940.85
F2 (3p, 4p)19,06815940 ± 4070.84
G0 (3p, 4p)53964064 ± 910.75
G2 (3p, 4p)61864272 ± 4040.69
a Parameters omitted from this table: direct and exchange integrals, and spin-orbit ζ parameters set to 85% and 95% of their HF values, respectively; CI integrals were set to 85% of their HF values. The standard deviation for the energy adjustment was 266 cm−1.
Table 8. Energy parameters (cm−1) for the studied even parity configurations of Ar IV.
Table 8. Energy parameters (cm−1) for the studied even parity configurations of Ar IV.
ConfigurationParameterHF valueFitted ValueFitt/HF a
3s3p4Eav151,175176,374 ± 1341.17
F2 (3p, 3p)72,20263,402 ± 5740.88
α −490 (FIX)
ζ3p11241154 ± 2621.03
G1 (3s, 3p)98,56987,487 ± 3270.89
3s23p23dEav196,615220,619 ± 741.12
F2 (3p, 3p)73,02375,396 ± 17811.03
α −774 (FIX)
ζ3p11531371 ± 1481.19
ζ3d3836 (FIX)0.95
F2 (3p, 3d)63,29554,769 ± 6450.86
G1 (3p, 3d)79,28068,405 ± 2340.86
G3 (3p, 3d)48,28530,970 ± 8050.64
3s23p24sEav248,237260,502 ± 1041.05
F2 (3p, 3p)75,07360,250 ± 9230.80
α 0 (FIX)
ζ3p12241299 ± 2061.06
G1 (3p, 4s)69795956 ± 2260.85
a Parameters omitted from this table: direct and exchange integrals, and spin-orbit ζ parameters set to 85% and 95% of their HF values, respectively; CI integrals were set to 85% of their HF values. The standard deviation for the energy adjustment was 242 cm−1.

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