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Article

New Transition and Energy Levels of Three-Times Ionized Krypton (Kr IV)

by
M. Raineri
1,*,
M. Gallardo
1,
J. Reyna Almandos
1,
A. G. Trigueiros
2 and
C. J. B. Pagan
3
1
Centro de Investigaciones Ópticas (CIOp), M.B. Gonnet, La Plata P.O. Box 3 (1897), Argentina
2
Institute of Physics “Gleb Wataghin”, University of Campinas (UNICAMP), Campinas 13083-970, SP, Brazil
3
School of Electrical and Computer Engineering, University of Campinas (UNICAMP), Campinas 13083-970, SP, Brazil
*
Author to whom correspondence should be addressed.
Atoms 2021, 9(3), 48; https://doi.org/10.3390/atoms9030048
Submission received: 29 June 2021 / Revised: 15 July 2021 / Accepted: 19 July 2021 / Published: 23 July 2021
(This article belongs to the Section Atomic, Molecular and Nuclear Spectroscopy and Collisions)
Versions Notes

Abstract

:
A capillary pulsed-discharge and a theta-pinch were used to record Kr spectra in the region of 330–4800 Å. A set of 168 transitions of these spectra were classified for the first time. We extended the analysis to twenty-five new energy levels belonging to 3s23p24d, 3s23p25d even configurations. We calculated weighted transition probabilities (gA) for all of the experimentally observed lines and lifetimes for new energy levels using a relativistic Hartree–Fock method, including core-polarization effects.

1. Introduction

Krypton that has been three-times ionized, Kr IV, belongs to the arsenic isoelectronic sequence. The most recent and complete compilation of the observed energy levels and transitions of the Kr IV ion was reported by Saloman [1]; that work used the extended analysis of our group (Reyna Almandos et al. [2]) for all but two Kr IV levels, 208,920 and 231,940 cm−1, which they took from Sugar and Musgrove [3]. The observed spectral lines of Kr IV were published by Saloman [1] from six sources: Boyce [4], Irwin et al. [5], Livingston [6], Fawcett and Bromage [7], Persson and Pettersson [8], and Bredice et al. [9]. The spectra of ions along the sequence of As I have been studied over many years [2] (references cited therein). These data and other recently published data on the arsenic isoelectronic sequence, for example, Rb V [10] and Y VII [11], were reported by NIST [12]. Reliable values of oscillator strengths, transition probabilities, and radiative lifetimes of energy levels are essential for the study of the ionized noble gases in Kr IV [9]; also, for astrophysical applications, for example, calculating Kr IV-VII oscillator strengths to consider radiative and collisional bound–bound transitions in detail in the non-LTE stellar–atmosphere models for the analysis of Kr lines that are exhibited in high resolution and high S/N ultraviolet (UV) observations of the hot white dwarf RE0503289 [13]. Recently energies and transition parameters have been reported for triply ionized Kr IV, Xe IV, and Rn IV using the general-purpose relativistic atomic structure package based on a fully relativistic multiconfiguration Dirac–Fock method [14]. In this article, we present an extension of the analysis of Kr IV from reference [2], including five energy levels of the configuration 3s23p24d and twenty levels of the 3s23p25d configuration. We interpreted this study using Hartree–Fock relativistic (HFR) calculations and parametric fits. We used the Cowan package [15] considering core polarization (CP) effects [16], which is the distortion of the internal cloud by the electric field of the outer electron orbital. For these energy levels, lifetimes were calculated using electron correlation effects. A set of 168 spectral lines of the Kr IV spectrum were classified for the first time; weighted transition probabilities (gA) were also reported for these transitions considering the CP effects.

2. Experiment

Krypton spectra covering the region from 330 to 4800 Å obtained from two different light sources (a capillary-pulsed discharge and a theta-pinch) were used. The discharge tube was built at Centro de Investigaciones Opticas (CIOp) in La Plata to study highly ionized gases [17], and the theta-pinch, used several years ago by A.G.T. and J.R.A. at the Lund Institute of Technology, Sweden, is described in Ref. [18]. Other experimental devices are detailed in reference [19]. A 3-m normal incidence vacuum spectrograph with a concave diffraction grating of 1200 lines/mm and a plate factor of 2.77 Å/mm in the first order was used in both experiments below 2000 Å. C, N, O, and available lines of krypton were recorded as internal standard lines. A wavelength range above 2000 Å was recorded in La Plata on a 3.4-m Ebert plane-grating spectrograph, with a plate factor of 5 Å/mm in the first diffraction order. The lines observed in this interval were measured by polynomial interpolation using reference lines from a thorium 232Th lamp, whose wavelengths were determined interferometrically [20]. The uncertainty in the wavelength values for lines that are not classified as w,d, or ul in Table 1 is ±0.01 Å in the measurements from Lund and ±0.01 Å and ±0.02 Å in the measurements from La Plata for the visible and the vacuum ultraviolet (VUV) regions, respectively. The intensity figures are visual estimates of photographic density and are only on a uniform scale within the limited wavelength ranges. To distinguish among different stages of ionization, we studied the behavior of the spectral line intensity as a function of pressure and discharge voltage. We used the LOPT [21] program to recalculate the energy levels from the observed wavelengths. In this adjustment, we considered the previously known lines [12] and included the new ones. The conversion between the air and vacuum wavelength used as the refraction index of the air was derived from the five-parameter formula given by E.R. Peck and K. Reeder [22].

3. Spectral Analysis and Theoretical Interpretation

To help in the spectral analysis, we calculated the level structures, the energy level lifetimes (τ), and weighted transition probabilities (gA) with the Hartree–Fock Cowan’s package [15] corrected by Kramida [23,24] and downloaded from the NIST website [25]. The programs that we used were modified as described by Pagan et al. [16] to include core polarization effects [26,27,28]. These methods demand knowledge of the polarizability and core cut radius. In this case, for Kr IV, a dipole polarizability αd = 0.20 a03 and a cut off radius rc = 0.55 a0 were taken from references [13,29], corresponding to a Kr8+ closed shell ionic core of the type 1s22s22p63s23p63d10, while the latter value was chosen as the mean value of ‹r› for the outer most core orbital (3d), as calculated by the HFR approach. We adjusted the values of the energy parameters to the experimental energy levels of this ion using a least squares calculation. With the adjusted values, we calculated the energy and composition of the levels as well as the gA and lifetimes of the energy levels [9,15]. The set of configurations for both of the parities used in our calculation was 4s24p3 + 4s24p25p + 4s24p26p + 4s24p24f + 4s24p25f + 4s24p26f + 4s4p34d + 4s4p35d + 4s4p36d + 4s4p35s + 4s4p36s + 4s24p4d2 + 4s24p4f2 + 4p5 + 4p44f (odd parity) and 4s4p4 + 4s24p24d + 4s24p25d + 4s24p26d + 4s24p25s + 4s24p26s + 4s24p27s + 4s4p34f + 4s4p35f + 4s4p36f + 4s4p35p + 4s4p36p + 4p44d + 4p45s + 4s4p24d2 (even parity). Intravalence correlations were considered in this calculation compared to previous work [2,9], where fewer configurations were taken into account. The introduction of the Rydberg series CI reduced the discrepancy between the observed and calculated levels values. Table 2 shows the new experimental and fitted energy level level values obtained by the least-squares fit with the percentage composition in LS notation. We extended the analysis of reference [2], presenting five and twenty new energy levels for the 4s24p24d and 4s24p25d configurations respectively. Additionally, the lifetimes of the energy levels calculated with HFR were reported by taking the fitted energy parameters and HFR + CP effects into account, as shown in the last two columns of this table. Table 1 shows 168 new classified lines of Kr IV that were classified using the new levels presented in this work, where the intensities of the lines given in the table were based on visual estimates of plate blackening. This table also reports the Ritz wavelength and its difference to observed values, calculated with the LOPT program [21]. The classification of the lower and the upper levels is presented. With the exception of transitions involving J = 9/2, it can be seen from this table that more than four spectral lines determine each experimental level. For example, in the best case, the level 4s24p2(3P)5d 2D3/2 in 303,713.2 cm−1 is determined by 17 transitions. The gA values in this table are from HFR and HFR + CP calculations, made with energy parameters adjusted by least-squares fitting. The label “*” in the last column refers to lines with cancellation factors [9] less than 0.05, as this fact may reflect errors in the estimation of gA values [15]. The least-squares calculation results are shown in Table 3 for even parity. The average energies (Eav) for the observed energy levels, the spin-orbit integrals (ζnl), and the single-configuration Slater integrals (Fk,Gk) were adjusted, keeping them free in the calculation except for the G1(4p,5s) of the 4s24p25s configuration, which was fixed at 85% at its HF value. The αd values for the 4s24p25d, 4s24p25s and 4s24p26s configurations were also fixed in the calculation. The configuration interactions 4s4p4-4s24p24d (R1(4p4p,4s4d)) and 4s4p4-4s24p25d (R1(4p4p,4s5d)) were kept free, but the CI integrals omitted in this table were set to 85% of their HFR values, and the direct and exchange integral, and spin- orbit ζ parameters were set to 85% and 95% of their HFR values. The standard deviation for the energy adjustment was 266 cm−1.

4. Conclusions

We studied the Kr IV spectrum covering the wavelength range 330–4800 Å using a capillary-pulsed discharge and a theta-pinch. We extended the analysis of this ion, including five energy levels of the configuration 3s23p24d and twenty levels of the 3s23p25d configuration. A total of 168 spectral lines were classified for the first time. Atomic HFR and HFR + CP calculation to determine weighted transition rates (gA) for all experimentally observed lines and lifetimes for new energy levels were used.

Author Contributions

Formal analysis, M.R., M.G., J.R.A. and C.J.B.P.; Investigation, M.R., M.G., J.R.A., A.G.T. and C.J.B.P.; Methodology, A.G.T.; Software, M.R. and C.J.B.P.; Supervision, J.R.A.; Writing—original draft, M.R. All authors have read and agreed to the published version of the manuscript.

Funding

This research was supported by the Consejo Nacional de Investigaciones Científicas y Tecnicas (CONICET), Argentina, and by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), Brazil, Finance Code 001. The support from the Comision de Investigaciones Científicas de la Província de Buenos Aires (CIC), where M.R. and J.R.A. are researchers, is gratefully acknowledged.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

All new data used in this study is contained within the article. Data from other sources are cited in the references.

Acknowledgments

We are very grateful to Fausto Bredice, who helped us in the preliminary discussions.

Conflicts of Interest

The authors declare no conflict of interest.

References

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Table
Table 1. New classified lines of Kr IV.
Table 1. New classified lines of Kr IV.
Int.λobsλRitzλobs–λRitzσobsLower Level Upper LevelgAgA(CP)
Vac(Å)(Å)(Å)cm−1Conf.TermJ Conf.TermJs−1s−1
3333.33333.3060.023300,0034s24p34S3/2–4s24p2(3P)5d2P1/23.24 × 1083.21 × 108
1333.52333.542−0.022299,8324s24p34S3/2–4s24p2(3P)5d4P1/27.53 × 1094.49 × 109
1337.00337.024−0.025296,7364s24p34S3/2–4s24p2(3P)5d4D3/23.11 × 1092.21 × 109
1338.21338.2140.000295,6744s24p32D3/2–4s24p2(1D)5d2P1/22.63 × 1091.56 × 109
1338.21338.223−0.010295,6744s24p32D5/2–4s24p2(1D)5d2P3/28.16 × 1088.64 × 108 *
1338.91338.9010.009295,0644s24p34S3/2–4s24p2(3P)5d4P5/21.38 × 10109.02 × 109
1339.52339.542−0.020294,5334s24p32D3/2–4s24p2(1D)5d2F5/28.31 × 1095.99 × 109
1339.52339.5240.000294,5334s24p32D5/2–4s24p2(1D)5d2D5/24.71 × 1092.37 × 109 *
2341.44341.470−0.030292,8774s24p32D5/2–4s24p2(1D)5d2F5/21.43 × 10101.08 × 1010
1343.26343.282−0.023291,3244s24p32D5/2–4s24p2(1D)5d2F7/21.43 × 10109.50 × 109
1350.88350.8600.020284,9984s24p32D5/2–4s24p2(3P)5d2D3/21.30 × 1091.11 × 109
1351.09351.116−0.027284,8274s24p32D5/2–4s24p2(3P)5d2D5/27.36 × 1094.28 × 109
1355.88355.925−0.045280,9944s24p32P3/2–4s24p2(1D)5d2P3/26.25 × 1097.53 × 109
1357.54357.555−0.015279,6894s24p32D3/2–4s24p2(3P)5d4D3/23.11 × 1092.06 × 109
1359.53359.5230.007278,1414s24p32P3/2–4s24p2(1D)5d2F5/22.99 × 1082.79 × 107 *
3359.65359.668−0.018278,0484s24p32D3/2–4s24p2(3P)5d4P5/22.50 × 1081.69 × 108 *
5364.15364.156−0.007274,6124s24p32D3/2–4s24p2(3P)5d4F5/21.51 × 1099.84 × 108
1366.37366.375−0.006272,9484s24p32D5/2–4s24p2(3P)5d4F5/21.09 × 1087.71 × 107
1366.74366.758−0.019272,6734s24p32P1/2–4s24p2(3P)5d2D3/21.08 × 10108.05 × 109
1369.93369.947−0.017270,3214s24p32P3/2–4s24p2(3P)5d2D3/23.50 × 1092.08 × 109
11370.22370.232−0.012270,1104s24p32P3/2–4s24p2(3P)5d2D5/27.95 × 1095.37 × 109
1372.09372.0830.007268,7524s24p32P1/2–4s24p2(3P)5d4P1/24.13 × 1083.95 × 108
1379.78379.782−0.002263,3104s24p32P3/2–4s24p2(3P)5d4D3/27.38 × 1085.14 × 108 *
2480.62480.656−0.036208,0654s24p32D3/2–4s24p2(1D)4d2S1/25.29 × 1095.66 × 109
3484.77484.7550.015206,2834s24p32D3/2–4s24p2(3P)4d2P1/22.21 × 1091.35 × 109
5494.15494.1430.007202,3684s24p34S3/2–4s24p2(3P)4d4P3/21.46 × 10111.32 × 1011
8515.35515.382−0.032194,0434s24p32P1/2–4s24p2(1D)4d2S1/26.27 × 1085.79 × 107
3520.10520.0970.003192,2714s24p32P1/2–4s24p2(3P)4d2P1/25.91 × 10105.67 × 1010
7521.70521.7000.000191,6814s24p32P3/2–4s24p2(1D)4d2S1/25.82 × 10105.35 × 1010
9544.44544.453−0.013183,6754s24p32D5/2–4s24p2(3P)4d4P3/21.30 × 1091.28 × 109
7557.75557.757−0.010179,2924s24p32D5/2–4s24p2(1D)4d2G7/21.85 × 1091.74 × 109
3591.83591.836−0.010168,9674s24p32P3/2–4s24p2(3P)4d4P3/23.46 × 1082.84 × 108 *
1d1140.741140.768−0.02887,6624s24p2(3P)5p2D3/2–4s24p2(1S)5d2D3/21.37 × 1081.41 × 108
71148.171148.196−0.02687,0954s24p2(3P)5p4P5/2–4s24p2(1S)5d2D3/22.79 × 1062.67 × 106 *
101177.211177.216−0.00684,9474s24p2(3P)5p4S3/2–4s24p2(1S)5d2D3/21.62 × 1071.97 × 107 *
91214.301214.2880.01282,3524s24p2(3P)5p2D5/2–4s24p2(1S)5d2D3/29.48 × 1068.93 × 106 *
91228.721228.723−0.00381,3854s24p2(3P)5p2P3/2–4s24p2(1S)5d2D3/25.88 × 1061.34 × 107 *
101237.021237.030−0.01080,8394s24p2(3P)5p2D5/2–4s24p2(1S)5d2D5/21.09 × 1081.52 × 108
71239.721239.738−0.01880,6634s24p2(3P)5p2P1/2–4s24p2(1S)5d2D3/22.01 × 1074.27 × 107 *
91252.011252.014−0.00479,8724s24p2(3P)5p2P3/2–4s24p2(1S)5d2D5/28.27 × 1071.89 × 108 *
91257.301257.309−0.01079,5354s24p2(3P)5p2S1/2–4s24p2(1D)5d2P3/24.62 × 1066.83 × 106 *
12w1334.041334.0350.00574,9604s24p2(3P)5p4D3/2–4s24p2(1D)5d2D5/28.59 × 1066.72 × 106 *
91366.051366.054−0.00473,2044s24p2(1D)5p2D3/2–4s24p2(1S)5d2D3/21.10 × 1071.95 × 107 *
111371.721371.6960.02472,9014s24p2(1D)5p2F5/2–4s24p2(1S)5d2D5/29.20 × 1063.05 × 106 *
2d1373.711373.7050.00572,7964s24p2(1D)5p2D5/2–4s24p2(1S)5d2D3/28.33 × 1068.31 × 106 *
81397.901397.910−0.01071,5364s24p2(1D)5p2F7/2–4s24p2(1S)5d2D5/21.70 × 1062.94 × 106
131402.881402.882−0.00271,2824s24p2(1D)5p2D5/2–4s24p2(1S)5d2D5/25.62 × 1077.45 × 107 *
101416.881416.894−0.01470,5784s24p2(3P)5p4D5/2–4s24p2(1D)5d2G7/25.35 × 1063.00 × 106 *
1d1422.291422.2810.00970,3094s24p2(3P)5p4D5/2–4s24p2(1D)5d2F5/21.83 × 1071.65 × 107 *
3d1430.681430.6780.00069,8974s24p2(3P)5p4P5/2–4s24p2(1D)5d2P3/21.08 × 1081.36 × 108
31441.731441.6950.03569,3614s24p2(3P)5p4S3/2–4s24p2(1D)5d2S1/23.16 × 1062.11 × 106 *
101446.371446.3420.02869,1394s24p2(3P)5p4P1/2–4s24p2(1D)5d2P1/22.48 × 1051.28 × 106 *
91451.641451.672−0.03268,8884s24p2(3P)5p2S1/2–4s24p2(3P)5d2D3/22.88 × 1072.13 × 107 *
101454.251454.264−0.01068,7644s24p2(3P)5p4D5/2–4s24p2(1D)5d2F7/21.69 × 1066.99 × 105 *
101454.251454.2490.00068,7644s24p2(3P)5p4P5/2–4s24p2(1D)5d2D5/25.61 × 1085.58 × 108
101461.991462.007−0.01768,4004s24p2(1D)5p2P1/2–4s24p2(1S)5d2D3/24.55 × 1071.81 × 107 *
2d1484.231484.2290.00167,3754s24p2(3P)5p4D7/2–4s24p2(1D)5d2G7/21.17 × 1051.85 × 104 *
91484.741484.7210.01967,3524s24p2(3P)5p4P5/2–4s24p2(1D)5d2G7/21.36 × 1076.87 × 106 *
81489.841489.8320.00867,1214s24p2(3P)5p4D7/2–4s24p2(1D)5d2G9/21.36 × 1042.58 × 105 *
101490.171490.1420.02867,1064s24p2(3P)5p4D7/2–4s24p2(1D)5d2F5/21.19 × 1052.77 × 105 *
91490.641490.6380.00267,0854s24p2(3P)5p4P5/2–4s24p2(1D)5d2F5/21.59 × 1082.12 × 108 *
71519.701519.712−0.01265,8024s24p2(3P)5p2P3/2–4s24p2(1D)5d2S1/22.18 × 1082.43 × 108
10w1525.271525.287−0.01765,5624s24p2(3P)5p4D7/2–4s24p2(1D)5d2F7/21.40 × 1071.60 × 107 *
2d1527.991528.009−0.01965,4454s24p2(3P)5p4D3/2–4s24p2(3P)5d2D3/27.96 × 1069.46 × 106 *
101532.861532.885−0.02065,2374s24p2(3P)5p4D3/2–4s24p2(3P)5d2D5/29.49 × 1061.49 × 107 *
101533.841533.8340.00665,1964s24p2(3P)5p2S1/2–4s24p2(3P)5d2P1/26.85 × 1087.06 × 108
41536.581536.598−0.01865,0804s24p2(3P)5p2P1/2–4s24p2(1D)5d2S1/21.16 × 1081.17 × 108
7d1538.821538.828−0.00864,9854s24p2(3P)5p2S1/2–4s24p2(3P)5d4P1/29.25 × 1054.51 × 106 *
2d1557.861557.897−0.03764,1914s24p2(3P)5p2P3/2–4s24p2(1D)5d2P3/27.24 × 1071.80 × 108 *
81561.931561.9220.01064,0234s24p2(3P)5p2D5/2–4s24p2(1D)5d2D5/25.38 × 1087.16 × 108
101575.661575.6460.01063,4654s24p2(3P)5p2P1/2–4s24p2(1D)5d2P3/21.06 × 1081.89 × 108
51597.091597.128−0.03862,6144s24p2(3P)5p2D5/2–4s24p2(1D)5d2G7/25.93 × 1074.68 × 107 *
4d1599.141599.143−0.00362,5344s24p2(3P)5p2P3/2–4s24p2(1D)5d2P1/25.22 × 1052.00 × 106 *
20w1600.721600.7100.01062,4724s24p2(3P)5p4D5/2–4s24p2(3P)5d2D3/26.90 × 1067.53 × 106 *
81603.991603.9770.01362,3444s24p2(3P)5p2D5/2–4s24p2(1D)5d2F5/23.28 × 1084.76 × 108
91615.201615.216−0.01661,9124s24p2(3P)5p4P3/2–4s24p2(3P)5d2D3/23.29 × 1083.49 × 108
91615.881615.8690.01061,8864s24p2(3P)5p2S1/2–4s24p2(3P)5d4D3/26.34 × 1086.13 × 108
2d1617.861617.8500.01061,8104s24p2(3P)5p2P1/2–4s24p2(1D)5d2P1/27.68 × 1078.58 × 107
7d1620.631620.665−0.03561,7044s24p2(3P)5p4P3/2–4s24p2(3P)5d2D5/21.00 × 1064.66 × 106 *
3d1629.271629.2600.01061,3774s24p2(3P)5p2P3/2–4s24p2(1D)5d2F5/28.66 × 1071.02 × 108 *
101644.781644.7700.01060,7984s24p2(3P)5p2D5/2–4s24p2(1D)5d2F7/28.72 × 1063.17 × 106 *
101670.791670.798−0.00859,8524s24p2(1D)4d2G9/2–4s24p2(1D)5p2F7/23.44 × 1093.74 × 109
91671.801671.816−0.01659,8164s24p2(3P)5p2D3/2–4s24p2(3P)5d2D3/26.59 × 1086.75 × 108
91687.231687.2270.00059,2694s24p2(3P)5p4D1/2–4s24p2(3P)5d4D3/27.19 × 1086.97 × 108
21687.801687.818−0.01859,2494s24p2(3P)5p4P5/2–4s24p2(3P)5d2D3/27.34 × 1078.58 × 107
2d1690.541690.5350.00559,1534s24p2(1D)4d2G7/2–4s24p2(1D)5p2F5/22.08 × 1091.92 × 109
51711.031711.0180.01058,4444s24p2(3P)5p4D3/2–4s24p2(3P)5d4D3/27.21 × 1077.75 × 107 *
91717.591717.5870.00358,2214s24p2(3P)5p4P3/2–4s24p2(3P)5d2P1/22.09 × 1082.12 × 108
81720.661720.679−0.01958,1174s24p2(3P)5p4D5/2–4s24p2(3P)5d4D5/21.75 × 1081.80 × 108 *
61735.481735.503−0.02357,6214s24p2(1D)5p2D3/2–4s24p2(1D)5d2S1/24.37 × 1084.03 × 108
101751.251751.279−0.02957,1024s24p2(3P)5p4S3/2–4s24p2(3P)5d2D3/29.20 × 1079.09 × 107
91771.271771.2690.00156,4574s24p2(3P)5p4P1/2–4s24p2(3P)5d2P1/25.48 × 1085.27 × 108
2d1777.921777.932−0.01256,2454s24p2(3P)5p4P1/2–4s24p2(3P)5d4P1/24.51 × 1075.85 × 107
81781.731781.731−0.00156,1254s24p2(3P)5p2D3/2–4s24p2(3P)5d2P1/23.67 × 1082.87 × 108
1d1788.471788.473−0.00355,9144s24p2(3P)5p2D3/2–4s24p2(3P)5d4P1/22.21 × 1081.67 × 108
41820.981821.005−0.02554,9154s24p2(3P)5p4D7/2–4s24p2(3P)5d4D5/28.76 × 1088.68 × 108
2d1821.121821.1170.00054,9114s24p2(3P)5p4P3/2–4s24p2(3P)5d4D3/25.58 × 1085.63 × 108
91821.721821.746−0.02654,8934s24p2(3P)5p4P5/2–4s24p2(3P)5d4D5/22.49 × 1092.46 × 109
81828.941828.955−0.02054,6764s24p2(1D)5p2F5/2–4s24p2(1D)5d2G7/26.35 × 1086.39 × 108
2d1834.591834.602−0.01254,5084s24p2(3P)5p2D5/2–4s24p2(3P)5d2D3/21.21 × 1081.43 × 108
101835.991835.9830.00754,4664s24p2(1D)5p2D5/2–4s24p2(1D)5d2D5/24.95 × 1074.61 × 106 *
101837.931837.942−0.01254,4094s24p2(1D)5p2F5/2–4s24p2(1D)5d2F5/21.94 × 1082.32 × 108 *
61839.861839.867−0.00754,3524s24p2(1D)5p2D3/2–4s24p2(1D)5d2P1/29.20 × 1089.35 × 108
101841.661841.6350.02554,2994s24p2(3P)5p2D5/2–4s24p2(3P)5d2D5/21.09 × 1097.22 × 108
2d1856.661856.6390.02153,8604s24p2(1D)5p2D3/2–4s24p2(1D)5d2D3/23.39 × 1093.26 × 109
101867.741867.753−0.01353,5414s24p2(3P)5p2P3/2–4s24p2(3P)5d2D3/28.85 × 1088.23 × 108
101870.791870.801−0.01153,4534s24p2(1D)5p2D5/2–4s24p2(1D)5d2D3/24.20 × 1084.37 × 108
21872.271872.2690.00153,4114s24p2(3P)5p4S3/2–4s24p2(3P)5d2P1/22.83 × 1062.39 × 107 *
121873.531873.546−0.01653,3754s24p2(3P)5p4D3/2–4s24p2(3P)5d4F5/27.41 × 1097.38 × 109
111875.041875.043−0.00353,3324s24p2(3P)5p2P3/2–4s24p2(3P)5d2D5/25.46 × 1095.68 × 109
51875.891875.8580.03253,3084s24p2(1D)5p2F7/2–4s24p2(1D)5d2G7/21.49 × 1091.97 × 109
121879.711879.714−0.00453,2004s24p2(3P)5p4S3/2–4s24p2(3P)5d4P1/22.27 × 1092.25 × 109
111879.851879.8470.00353,1964s24p2(1D)5p2D3/2–4s24p2(1D)5d2F5/23.31 × 1093.12 × 109
101881.591881.5800.01053,1464s24p2(3P)5p4P1/2–4s24p2(3P)5d4D3/21.88 × 1091.91 × 109
121884.811884.817−0.00753,0564s24p2(1D)5p2F7/2–4s24p2(1D)5d2G9/21.12 × 10101.38 × 1010
121884.821884.8210.00053,0554s24p2(1D)5p2D5/2–4s24p2(1D)5d2G7/28.86 × 1098.78 × 109
101885.311885.312−0.00253,0424s24p2(1D)5p2F7/2–4s24p2(1D)5d2F5/21.37 × 1082.51 × 108
111891.711891.7030.00752,8624s24p2(1D)5p2F5/2–4s24p2(1D)5d2F7/29.39 × 1099.42 × 109
111893.311893.323−0.01352,8184s24p2(3P)5p2P1/2–4s24p2(3P)5d2D3/22.34 × 1092.45 × 109
101893.391893.3900.00052,8154s24p2(3P)5p2D3/2–4s24p2(3P)5d4D3/26.37 × 1086.42 × 108
111894.381894.3670.01352,7884s24p2(1D)5p2D5/2–4s24p2(1D)5d2F5/23.75 × 1093.88 × 109
111895.871895.898−0.02852,7464s24p2(3P)5p4S3/2–4s24p2(3P)5d4D5/23.07 × 1093.04 × 109
101897.701897.6870.01352,6954s24p2(3P)5p4D7/2–4s24p2(3P)5d4F9/21.32 × 10101.32 × 1010
15w1901.491901.4540.03652,5904s24p2(1S)5p2P3/2–4s24p2(1S)5d2D3/25.81 × 1081.95 × 107 *
101941.931941.9230.00751,4954s24p2(1D)5p2F7/2–4s24p2(1D)5d2F7/21.15 × 1091.32 × 109
51951.531951.531−0.00151,2424s24p2(1D)5p2D5/2–4s24p2(1D)5d2F7/22.13 × 1072.77 × 107 *
50w1954.141954.181−0.04151,1734s24p2(3P)5p2D3/2–4s24p2(3P)5d4P5/21.56 × 1086.14 × 108
101975.251975.2090.04150,6264s24p2(3P)5p4D7/2–4s24p2(3P)5d4P5/21.78 × 1061.43 × 106 *
121979.081979.125−0.04550,5284s24p2(1D)5p2P3/2–4s24p2(1D)5d2S1/29.50 × 1081.12 × 109
71984.011984.034−0.02450,4034s24p2(3P)5p4D5/2–4s24p2(3P)5d4F5/22.12 × 1082.26 × 108 *
111993.921993.936−0.01650,1524s24p2(3P)5p2D5/2–4s24p2(3P)5d4D5/21.33 × 1091.35 × 109
61995.931995.958−0.02850,1024s24p2(3P)5p4S3/2–4s24p2(3P)5d4D3/21.42 × 1053.26 × 105 *
λobsλRitzλobs− λRitz
Air(Å)Air (Å)Air (Å)
32013.932013.9070.02349,638.14s24p2(3P)5p2P3/2–4s24p2(3P)5d4P1/26.75 × 1066.90 × 106
9ul2017.632017.6220.01049,547.14s24p2(1D)5p2P1/2–4s24p2(1D)5d2P1/21.18 × 1091.17 × 109
32034.882034.879−0.00349,127.34s24p2(3P)5p2P1/2–4s24p2(3P)5d2P1/24.00 × 1084.67 × 108
92037.852037.8180.02749,055.74s24p2(1D)5p2P1/2–4s24p2(1D)5d2D3/26.09 × 1086.31 × 108
22043.672043.680−0.00648,915.84s24p2(3P)5p2P1/2–4s24p2(3P)5d4P1/28.84 × 1071.07 × 108
1d2060.142060.0890.05248,524.84s24p2(3P)4d4P3/2–4s24p2(3P)5p2P1/25.21 × 1051.14 × 106 *
72092.172092.188−0.02047,782.24s24p2(1D)5p2P3/2–4s24p2(1D)5d2D5/22.59 × 1092.87 × 109
72093.742093.783−0.04847,746.44s24p2(3P)5p2D3/2–4s24p2(3P)5d4F5/21.66 × 1071.92 × 107 *
22104.272104.2470.02647,507.34s24p2(3P)5p2D5/2–4s24p2(3P)5d4D3/24.52 × 1074.15 × 107 *
42115.322115.331−0.01047,259.24s24p2(1D)5p2P3/2–4s24p2(1D)5d2P1/21.49 × 1081.27 × 108
102148.012147.9950.02046,540.04s24p2(3P)5p2P3/2–4s24p2(3P)5d4D3/25.56 × 1085.62 × 108
1d2150.952150.963−0.01046,476.44s24p2(1D)4d2G7/2–4s24p2(3P)5p4P5/22.44 × 1072.09 × 107
82152.002151.9970.00646,453.74s24p2(1D)4d2G7/2–4s24p2(3P)5p4D7/21.24 × 1051.06 × 105 *
72156.202156.204−0.00246,363.34s24p2(1D)5p2F5/2–4s24p2(3P)5d2D5/24.15 × 1094.36 × 109
52181.912181.8980.01045,817.14s24p2(3P)5p2P1/2–4s24p2(3P)5d4D3/22.27 × 1082.05 × 108
1d2183.422183.4120.00545,785.44s24p2(1D)4d2G9/2–4s24p2(3P)5p4D7/21.53 × 1071.32 × 107 *
52214.122214.132−0.01245,150.64s24p2(1D)5p2D3/2–4s24p2(3P)5d2D5/22.14 × 1082.49 × 108
1d2221.752221.7210.02844,995.64s24p2(1D)5p2F7/2–4s24p2(3P)5d2D5/24.23 × 1067.72 × 106 *
2d2223.962223.963−0.00544,950.94s24p2(1D)5p2D5/2–4s24p2(3P)5d2D3/24.78 × 1075.69 × 107
202259.702259.5890.11144,240.04s24p2(3P)4d4P3/2–4s24p2(3P)5p4S3/22.98 × 1082.72 × 108
42399.162399.164−0.00441,668.64s24p2(1D)5p2D3/2–4s24p2(3P)5d2P1/21.28 × 1081.06 × 108
92465.052465.098−0.04440,554.84s24p2(1D)5p2P1/2–4s24p2(3P)5d2D3/23.90 × 1083.86 × 108
12587.912587.912−0.00238,629.64s24p2(1D)5p2F7/2–4s24p2(3P)5d4F9/28.88 × 1062.78 × 106 *
42612.552612.5250.02538,265.34s24p2(1D)5p2P3/2–4s24p2(3P)5d2D3/27.81 × 1076.89 × 107
52701.332701.3220.00837,007.84s24p2(1S)5p2P3/2–4s24p2(1D)5d2S1/22.92 × 1041.75 × 107 *
12824.422824.4180.00235,395.04s24p2(1S)5p2P3/2–4s24p2(1D)5d2P3/22.93 × 1079.48 × 107
12897.562897.578−0.01834,501.64s24p2(1D)5p2F5/2–4s24p2(3P)5d4F5/24.34 × 1064.21 × 106
52948.132948.1180.01233,909.84s24p2(1D)5p2P3/2–4s24p2(3P)5d4D5/22.54 × 1061.91 × 106 *
12979.382979.384−0.00433,554.24s24p2(1D)5p2P1/2–4s24p2(3P)5d4D3/21.01 × 1078.11 × 106 *
13006.773006.775−0.00533,248.54s24p2(1S)5p2P3/2–4s24p2(1D)5d2D3/21.08 × 1078.76 × 106
23068.133068.139−0.00932,583.64s24p2(1S)5p2P3/2–4s24p2(1D)5d2F5/22.60 × 1055.35 × 106 *
43626.083626.113−0.03327,570.14s24p2(3P)4d2P1/2–4s24p2(3P)5p2P1/22.16 × 1071.47 × 107
23723.813723.7800.03026,846.54s24p2(3P)4d2P1/2–4s24p2(3P)5p2P3/23.17 × 1073.37 × 107
33816.343816.3230.01726,195.64s24p2(1D)5p2P3/2–4s24p2(3P)5d4F5/21.72 × 1051.63 × 105 *
63873.253873.2490.00125,810.84s24p2(1D)4d2S1/2–4s24p2(3P)5p2P1/21.74 × 1072.30 × 107
14039.874039.8700.00224,746.24s24p2(1S)5p2P3/2–4s24p2(3P)5d2D3/21.64 × 1061.95 × 105 *
w: this line appeared wider than the others in our experiment; d: the line contour does not appear very clearly on our plate, increasing the error in the measurement; and ul is shaded to longer wavelengths. * Refers to lines with a cancellation factor less than 0.05.
Table
Table 2. New Kr IV energy levels.
Table 2. New Kr IV energy levels.
ConfigurationTermJObseved Levels
(cm−1)		Fitted a
(cm−1)		Composition bLifetimes
(ns)
HFRHFR + CP
4s24p2(1D)4d2G7/2197,989.6198,019954.3134.586
4s24p2(1D)4d2G9/2198,657.9198,83695∞ c∞ c
4s24p2(3P)4d4P3/2202,370.6202,48864 4s24p2(3P)4d4P + 15 4s24p2(3P)5s4P0.0270.030
4s24p2(3P)4d2P1/2223,326.7223,28643 4s24p2(1D)4d2P + 17 4s24p2(3P)4d2P + 17 4s24p2(1D)4d2S0.0320.034
4s24p2(1D)4d2S1/2225,085.8225,56535 4s24p2(1D)4d2S + 18 4s24p2(1S)5s2S + 12 4s4p4(1S)2S0.0310.034
4s24p2(3P)5d4F5/2291,643.9291,61353 4s24p2(3P)5d4F + 24 4s24p2(3P)5d4D + 6 4s24p2(3P)5d4P0.4110.487
4s24p2(3P)5d4P5/2295,071.0295,05438 4s24p2(3P)5d4P + 37 4s24p2(3P)5d4F + 15 4s24p2(3P)5d4D0.2510.324
4s24p2(3P)5d4D3/2296,713.9296,70834 4s24p2(3P)5d2P + 30 4s24p2(3P)5d4D + 20 4s24p2(3P)5d4P0.2500.317
4s24p2(3P)5d4F9/2297,139.1297,23592 4s24p2(3P)5d4F + 64 s24p2(1D)5d2G0.6440.672
4s24p2(3P)5d4D5/2299,358.1299,23855 4s24p2(3P)5d4D + 28 4s24p2(3P)5d4P + 6 4s24p2(1D)5d2D0.2650.341
4s24p2(3P)5d4P1/2299,812.3299,736810.1770.248
4s24p2(3P)5d2P1/2300,023.8300,10663 4s24p2(3P)5d2P + 13 4s24p2(3P)5d4D + 13 4s24p2(3P)6s2P0.2690.314
4s24p2(3P)5d2D5/2303,505.7303,48377 4s24p2(3P)5d2D + 12 4s24p2(1D)5d2F0.1660.222
4s24p2(3P)5d2D3/2303,713.8303,52377 4s24p2(3P)5d2D + 54 s24p2(1D)5d2D0.1820.228
4s24p2(1D)5d2F7/2310,004.9310,01660 4s24p2(1D)5d2F + 32 4s24p2(1D)5d2G0.2960.369
4s24p2(1D)5d2F5/2311,551.1311,45537 4s24p2(1D)5d2F + 33 4s24p2(1D)5d2D + 7 4s24p2(3P)6d2F0.1830.228
4s24p2(1D)5d2G9/2311,565.1311,27794 4s24p2(1D)5d2G + 6 4s24p2(3P)5d4F0.6290.657
4s24p2(1D)5d2G7/2311,818.5312,03857 4s24p2(1D)5d2G + 21 4s24p2(1D)5d2F + 14 4s24p2(3P)5d2F0.2750.320
4s24p2(1D)5d2D3/2312,216.1312,118820.1650.219
4s24p2(1D)5d2P1/2312,707.1313,106910.2540.326
4s24p2(1D)5d2D5/2313,229.8313,11249 4s24p2(1D)5d2D + 15 4s24p2(1D)5d2F + 10 4s24p2(3P)5d2D0.1860.220
4s24p2(1D)5d2P3/2314,362.6313,98648 4s24p2(1D)5d2P + 26 5s5p3(4S)5p4P0.3050.266
4s24p2(1D)5d2S1/2315,975.5316,13672 4s24p2(1D)5d2S + 6 5s5p3(4S)5p4P0.2240.255
4s24p2(1S)5d2D5/2330,044.9330,45282 4s24p2(1S)5d2D + 8 4s24p2(3P)6d2D0.2250.334
4s24p2(1S)5d2D3/2331,558.9331,14174 4s24p2(1S)5d2D + 8 4s24p2(3P)6d2D0.1730.271
a Calculated energy level values obtained using the fitted energy parameters. b Percentages below 5% have been omitted. c Lifetime is infinite for electric dipole (E1) transitions.
Table
Table 3. Energy parameters (cm−1) for the studied even parity configurations of Kr IV.
Table 3. Energy parameters (cm−1) for the studied even parity configurations of Kr IV.
ConfigurationParameterH-F ValueFitted ValueFitt/H-F a
4s4p4Eav139,218167,777 ± 2921.20
F2(4p,4p)63,17857,606 ± 8330.91
α −135 ± 75
ζ4p41904151 ± 3080.99
G1(4s,4p)85,05571,598 ± 4640.84
4s24p24dEav178,106206,020 ± 9241.16
F2(4p,4p)64,22551,349 ± 9240.80
α 127 ± 45
ζ4p43734649 ± 1471.06
ζ4d208198(FIX)0.95
F2(4p,4d)46,83041,477 ± 7340.88
G1(4p,4d)55,58546,768 ± 2770.84
G3(4p,4d)34,13228,337 ± 7240.83
4s24p25dEav285,175304,785 ± 751.07
F2(4p,4p)65,62350,322 ± 4770.77
α 40(FIX)
ζ4p45684827 ± 1521.06
ζ5d6865(FIX)0.95
F2(4p,5d)12,90710,007 ± 5280.77
G1(4p,5d)94877048 ± 3510.74
G3(4p,5d)64834164 ± 5900.64
4s24p25sEav195,483218,447 ± 1681.12
F2(4p,4p)65,13251,051 ± 14550.78
α 0(FIX)
ζ3p45213059 ± 2870.67
G1(4p,5s)65965607(FIX)0.85
4s24p26sEav289,383309,075 ± 1211.07
F2(4p,4p)65,68652,182 ± 14770.79
α 0(FIX)
ζ3p45864417 ± 2320.96
G1(4p,6s)20231390 ± 3680.69
Configuration Interaction Integrals
4s4p4–4s24p24dR1(4p4p,4s4d)66,56857,280 ± 3810.86
4s4p4–4s24p25dR1(4p4p,4s5d)27,41223,228 ± 24280.85
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 266 cm−1.
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Raineri, M.; Gallardo, M.; Reyna Almandos, J.; Trigueiros, A.G.; Pagan, C.J.B. New Transition and Energy Levels of Three-Times Ionized Krypton (Kr IV). Atoms 2021, 9, 48. https://doi.org/10.3390/atoms9030048

AMA Style

Raineri M, Gallardo M, Reyna Almandos J, Trigueiros AG, Pagan CJB. New Transition and Energy Levels of Three-Times Ionized Krypton (Kr IV). Atoms. 2021; 9(3):48. https://doi.org/10.3390/atoms9030048

Chicago/Turabian Style

Raineri, M., M. Gallardo, J. Reyna Almandos, A. G. Trigueiros, and C. J. B. Pagan. 2021. "New Transition and Energy Levels of Three-Times Ionized Krypton (Kr IV)" Atoms 9, no. 3: 48. https://doi.org/10.3390/atoms9030048

APA Style

Raineri, M., Gallardo, M., Reyna Almandos, J., Trigueiros, A. G., & Pagan, C. J. B. (2021). New Transition and Energy Levels of Three-Times Ionized Krypton (Kr IV). Atoms, 9(3), 48. https://doi.org/10.3390/atoms9030048

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