New Energy Levels and Transitions of 5s25p2 (6d+7s) Configurations in Xe IV

Jorge Reyna Almandos; Mónica Raineri; Cesar J. B. Pagan; Mario Gallardo

doi:10.3390/atoms7040108

,

and

¹

Centro de Investigaciones Opticas (CIOp), CC 3, 1897, Gonnet, 1900 La Plata, Argentina

²

School of Electrical and Computer Engineering, University of Campinas (UNICAMP), 13083-970 Campinas, SP, Brazil

^*

Author to whom correspondence should be addressed.

Atoms2019, 7(4), 108;https://doi.org/10.3390/atoms7040108

This article belongs to the Special Issue 13th International Colloquium on Atomic Spectra and Oscillator Strengths for Astrophysical and Laboratory Plasmas

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Abstract

Three-times ionized xenon Xe IV spectrum in the 1070–6400 Å region was analyzed using a pulsed discharge light source. A set of 163 transitions was classified for the first time, and 36 new energy levels belonging to the 5s²5p²6d and 5s²5p²7s even configurations were determined. The relativistic Hartree–Fock method, including core-polarization effects, were used. In these calculations, the electrostatic parameters were optimized by a least-square procedure in order to improve the adjustment to experimental energy levels. We also present a calculation based on a relativistic multiconfigurational Dirac–Fock approach.

Keywords:

atomic databases and related topics; astrophysical and laboratory plasmas: atomic data needs; atomic lifetime and oscillator strength determination

1. Introduction

There is great interest in spectroscopy data of Xenon due to their applications in collision physics, astrophysics, and laser physics. Various atomic parameters, such as energy levels, oscillator strengths, transition probabilities, and radiative lifetimes, have many important astrophysical applications. Transition probabilities are needed for calculating the energy transport through the star in model atmospheres [1] and for direct analysis of stellar chemical compositions [2]. Xenon was observed in chemically peculiar stars [3] and planetary nebulae [4]. The spectrum analysis of planetary nebula NGC7027 by Péquignot and Baluteau [5] has stimulated the calculation of transition probabilities for some forbidden lines of astrophysical interest [6]. The Xe VI and Xe VII lines were observed in the ultraviolet spectrum of the hot DO-type white dwarf RE 0503-289 [7,8]. In particular, the Xe IV spectrum was detected in the spectrum of NGC 7027 together with a variety of ionic species, providing a unique opportunity to study the chemical composition of the nebula at a level normally unachievable in another emission line nebulae [9,10].

Saloman [11] published a revised compilation of energy levels and observed spectral lines of all ionization stages of Xe, referring to studies published to date [12,13,14,15,16]. Light sources include direct-current hollow cathode discharge, theta-pinch discharge, and pulsed capillary discharge. Most of the information is from two studies: Tauheed et al. [13] classified 114 Xe IV lines in VUV using a modified triggered spark initiated by a xenon gas blast as spectral source, and Gallardo et al. [14], who analyzed the 5s²5p²6p, 5s²5p²4f, 5s5p⁴, 5s²5p²5d, and 5s²5p²6s configurations, providing the wavelengths for 618 classified lines in their list, using a capillary discharge as light source.

More recently the study by Raineri et al. [15] reported the weighted oscillator strengths and cancellation factor (CF), calculated from fitted values of the energy parameters of all 769 dipole electric lines belonging to the Xe IV spectrum reported in the compilation [11], including 49 new classified lines. Hartree–Fock relativistic (HFR) calculations and parametric fits were used. In addition, the results presented in their study were compared to those from Bertuccelli et al. [16].

In order to proceed withthe study of the threetimes ionized xenon spectrum, a new spectral analysis of this ion is presented in this paper. New 36 energy levels for 5s²5p² (6d+7s) configurations and 163 new transitions in the 1070–6400 Å region are reported. The relativistic Hartree–Fock method based on the code of Cowan [17] was used. The energy matrix was calculated using energy parameters adjusted to fit the experimental energy levels. Core polarization effects were taken into account in our calculations [18]. We also present a multiconfigurational relativistic approach for the Dirac equation (MCDF), by using the general relativistic atomic structure package (GRASP) [19].

2. Experimental Methods

The spectral source used in this study is based on the pulsed discharge tube built at the Centro de Investigaciones Opticas to study highly ionized noble gases [20]. It consists of a Pyrex tube of about 100 cm with inner diameter of 0.5 cm. The electrodes, placed 80 cm apart, are made of tungsten covered with indium to avoid the impurities coming from the electrodes. The gas excitation was produced by discharging a bank of low-inductance capacitors ranging from 20 to 280 nF, charged with voltages up to 20 kV. The VUV region of the spectrum was recorded using a 3m normal incidence spectrograph equipped with 1200 lines/mm concave diffraction grating and with a plate factor of 2.77 Å/mm in the first diffraction order. Internal wavelength standards are from C, N, O, and known lines of xenon. The wavelength range above 2000 Å was recorded using 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. Thorium lines from an electrodeless discharge were superimposed on the spectrograms and served as reference lines. A photoelectric semiautomatic Grant comparator was used to measure the spectrograms. The uncertainty of the wavelength values of lines was estimated to be correct to ±0.01Å above 2000 Å and ±0.02 Å in the VUV region.

3. Results and Discussion

In this study, we used the modified version of Cowan’s atomic calculation package [17], described in our paper [18], for the inclusion of the polarization potentials as a modification in the Hartree–Fock equations. In addition, we considered the corrections of the reduced matrix element used in our previous papers [21], which is the same modification used by Quinet et al. [22] to correct transition matrix elements when including CP and core penetration effects. These methods demand knowledge on the polarizability andcore cut-off radius. The value of α_d for Xe IV core, that is, for Xe 8+ is given by Koch [23] in 0.81130 a₀³ and the rc value in 1.16 a₀, defines the boundaries of the atomic core.

We adjusted the values of energy parameters to the experimental energy levels of the Xe IV through a least-squares calculation. With the adjusted values, we calculated the composition of the 5s²5p² (6d+7s) energy levels presented in Table 1, where we included lifetimes calculated using HFR and HFR+CP with adjusted energy parameters (here named HFRa and HFR+CPa, respectively) and using multiconfigurational Dirac Fock (MCDF). The MCDF approach was carried out with the extended average level assuming a uniform charge distribution in the nucleus, with a xenon atomic weight of 131.3. The values presented in this work for lifetimes in the MCDF calculation are in Babushkin gauge since this one, in the non-relativistic limits (length), has been found to be the most stable value in many situations, in the sense that it converges smoothly as more correlation is included [24].

Table 1. Energy levels, composition, and lifetimes of Xe IV.

In the analysis of spectroscopic data, we take into account isoelectronic trends, Ritz combinations, least-squares adjustment, and relative line intensities in order to identify 36 energy levels belonging to 5s²5p²(6d+7s) configurations for the first time.

As for the isoelectronic sequence calculations used to produce the plots for observed minus calculated (“obs.-calc.”) trends along the six first elements of the Sb sequence, we used the configurations 5s²5p³, 5s²5p²4f, 5s²5p²6p, 5s5p³6s, 5s5p³7s, 5s5p³5d, 5s5p³ 6d, 5p⁵ for odd parity and 5s5p⁴, 5s²5p²5d, 5s5p³5f, 5s²5p²5g, 5s²5p²6s, 5s²5p²6d, 5s²5p²7s for even parity. The calculations included core polarization effects (HFR+CP), with the values of α_d and rc taken from Table 2.

Table 2. Values for polarizability α_d and cut-off radius r_c, used in antimony isoelectronic sequence calculations (HFR+CP). Here,

a_{0}

is the Bohr radius.

It must be noted that we implemented the modifications suggested by Kramida [25,26] to correct an error in Cowan’s package in order to perform the calculations presented here.

Data for isoelectronic analysis are from NIST [27] for Sb I, Te II, I III and from Sharman, Tauheed, and Rahimullah for Ba VI [28]. Our analysis is synthesized in Figure 1, Figure 2 and Figure 3. Surely the LS coupling scheme is not the most appropriate to describe the 6d and 7s configurations, which we concluded after glancing over configuration purities; intermediate couplings provide better descriptions for these levels. We observed a strong eigenvector mixing for all elements studied. However, most of the isoelectronic data available for comparisons are described in the LS scheme, and that was the reason why we chose it.

Figure 1. Isoelectronic trend for the multiplet (³P) ⁴F energy levels of the 5s²5p² 6d configuration.

Figure 2. Isoelectronic trend for the multiplet (³P) ⁴P energy levels of the 5s²5p² 6d configuration.

Figure 3. Isoelectronic trend for the multiplet (³P) ⁴P energy levels of the 5s²5p² 7s configuration.

There is no absolute scale for experimental intensity and therefore we only test its proportionality with the theoretical intensity. We do not include corrections due to the variation of plate reflectivity as a function of wavelength—there is no precise model for this. Our criterion for statistical correlation is to obtain a positive value as close as possible to the unit. Therefore, having a good statistical correlation supports our analysis, but it is just one of the analysis criteria.

The formula

I \propto σ g A

from Cowan’s book [17], page 403, tells us that line intensity is proportional to wavenumber

σ

and weighted transition probability. We analyzed the statistical correlation of the logarithm related to this quantity with the experimental line intensities, which is a visual estimate of the plate blackening (hence the logarithm), obtaining 0.20 for the array

6 p - 6 d,

0.32 for

6 p - 7 s,

and 0.34 for

4 f - 6 d

. These values were acquired by the HFR+CPa calculation, which is close to HFRa and much better thanab initioHFR and HFR+CP calculations. We also performed a MCDF calculation for gA values. Its agreement with the experimental line intensity shows a poor correlation when compared with HFRa and HFR+CPa for

l o g (σ g A)

, that is, 0.06 for the

6 p - 6 d

line array, 0.14 for

6 p - 7 s

, and 0.18 for

4 f - 6 d .

It is important to note that our MCDF calculations were performed using a non-current version of the GRASP code where more configurations could not be included. By using a newer version of Grasp codes it would be possible to expand the number of configurations to get better results, which could be more competitive to HFRa and HFR + CPa methods

To understand thesignificance of these values, we compared our values of gA with the experimental values that are in the paper by Bertuccelli et al. [16]. Similarly to them, only 25% of our gA values (HFR+CPa) are within the experimental error. However, a statistical correlation of 0.94 indicates that our values are very linearly proportional to their experiment. When considering the same lines of [16], but substituting their experimental gA values by our estimates for line intensity, correlation with HFR+CPa

l o g (σ g A)

results in 0.33 for the

6 s - 6 p

line array, 0.48 for

5 d - 6 p

, and 0.50 for

5 d - 4 f .

Therefore, we can conclude that the calculated

σ

gA values support our line classification with reasonable agreement.

It is important to note that in this spectral analysis all new levels but two are classified on the basis of two or more lines. The level ⁴F_5/2 is a classification attempt based on the only possible line in our spectrograms at 1801.53 Å, a transition with 4f:⁴G_5/2, the strongest spontaneous emission from this level. However, this value does not fit the isoelectronic “obs.-calc.” curve. We remove this problem by switching the positions of levels 6d:⁴P_5/2 and 6d:⁴F_5/2 for Xe IV in the isoelectronic analysis. An intense mixing for 6d:⁴P_5/2, ⁴D_5/2, and ⁴F_5/2 makes the components for the eigenvectors exchange their intensity along with the four first elements, and our choice grouped the energy of the respective multiplets.

Due to similar reasons, we also switched ⁴D_5/2 and ⁴P_5/2 energy levels for Te III and I III in the respective isoelectronic sequences.

The other level that only has one observed transition is (¹S)6d: ²D_3/2 that we confirm by our isoelectronic analysis and considering the good agreement in the least squares fit calculation.

There is not much data available for isoelectronic analysis. The lack of information on Cesium and the composition mixing makes level designation a challenge. However, the isoelectronic sequences agree reasonably well with our designations.

Table 3 shows 163 Xe IV lines classified for the first time for transitions involving 5s²5p²(6d+7s) energy levels. We also calculated the weighted transition probability rate gA, where g is the statistical weight 2J+1 of the upper level. We presented gA values obtained from the four methods studied: With and without optimized parameters obtained from least-squares calculations, and with and without core polarization effects for wavefunctions and reduced matrix elements calculations.In these methods, we used the same configuration sets as in [15], that is, 5s²5p³, 5²5p² (4f+6p), 5s 5p³5d, 5p⁵ and 5s5p⁴, 5s²5p² (6s+7s+5d+6d) configurations for odd and even parities, respectively.

Table 3. Transitions and weighted transition rates for Xe IV.

Table 4 shows the result of least squares adjustment for even parity levels, where 6d and 7s configurations are included. All single configuration parameters, the R^k integrals for 5s5p⁴-5s²5p²6s, 5s5p⁴-5s²5p²5d, 5s²5p²6s-5s²5p² 5d interactions, and the R¹(5p,5d;6d,5p)of the 5s²5p² 5d-5s²5p²6d interaction were left free during the final calculation. The rest of the configuration interaction integrals remained fixed at 85% of their Hartree–Fock values. We found a standard deviation of 138 cm⁻¹ for this adjustment.

Table 4. Least-squares parameters for even parity of Xe IV. Standard deviation is 138 cm⁻¹.

4. Conclusions

In this study we extended the knowledge of the Xe IV spectrum to the 5s²5p²7s and 5s²5p² 6d configuration, from a set of 163 new line classifications. To produce this new information, we used a set of different analysis tools, including calculations from three models (HFR, HFR+CP, and MCDF), least-squares adjustment, line intensity comparisons, and isoelectronic analysis, which makes us very confident in our results.

Author Contributions

All authors contributed equally to this work.

Funding

This research received no external funding.

Acknowledgments

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 authors thank Espaço da Escrita–Pró-Reitoria de Pesquisa–UNICAMP-for the language services provided. Support of the Comision de Investigaciones Científicas de la Província de Buenos Aires (CIC), where M.R. is a researcher, is also gratefully acknowledged.

Conflicts of Interest

The authors declare no conflicts of interest.

References

Gustafsson, B. The future of stellar spectroscopy and its dependence on YOU. Phys. Scr. 1991, 34, 14–19. [Google Scholar] [CrossRef]
Biémont, E.; Blagoev, K.; Campos, J.; Mayo, R.; Malcheva, G.; Ortíz, M.; Quinet, P. Radiative parameters for some transitions in Cu(II) and Ag(II) spectrum. Spectrosc. Relat. Phenom. 2005, 144, 27–28. [Google Scholar] [CrossRef]
Cowley, C.R.; Hubrig, S.; Palmeri, P.; Quinet, P.; Biémont, É.; Wahlgren, G.M.; Schütz, O.; González, J.F. HD 65949: Rosetta stone or red herring. Mon. Not. R. Astron. Soc. 2010, 405, 1271–1284. [Google Scholar] [CrossRef]
Otsuka, M.; Tajitsu, A. Chemical abundances in the extremely carbon-rich and xenon-rich halo planetary nebula H4-1. Astrophys. J. 2013, 778, 146. [Google Scholar] [CrossRef]
Péquignot, D.; Baluteau, J.-P. The identification of krypton, xenon, and other elements of rows 4, 5 and 6 of the periodic table in the planetary nebula NGC 7027. Astron. Astrophys. 1994, 283, 593–625. [Google Scholar]
Biémont, E.; Hansen, J.E.; Quinet, P.; Zeippen, C.J. Forbidden transitions of astrophysical interest in the 5pk (k=1–5) configurations. Astron. Astrophys. Suppl. Ser. 1995, 111, 333–346. [Google Scholar]
Werner, K.; Rauch, T.; Ringat, E.; Kruk, J.W. First detection of krypton and xenon in a white dwarf. Astrophys. J. 2012, 753, L7. [Google Scholar] [CrossRef]
Rauch, T.; Hoyer, D.; Quinet, P.; Gallardo, M.; Raineri, M. The Xe VI ultraviolet spectrum and the xenon abundance in the hot do-type white dwarf RE 0503−289. Astron. Astrophys. 2015, 577, A88. [Google Scholar] [CrossRef]
Zhang, Y.; Liu, X.-W.; Luo, S.-G.; Péquignot, D.; Barlow, M.J. Integrated spectrum of the planetary nebula NGC 7027. Astron. Astrophys. 2005, 442, 249–262. [Google Scholar] [CrossRef]
Zhang, Y.; Williams, R.; Pellegrini, E.; Cavagnolo, K.; Baldwin, J.A.; Sharpee, B.; Phillips, M.; Liu, X.-W. Abundances of s-process elements in planetary nebulae: Br, Kr &Xe in Planetary Nebulae in Our Galaxy and Beyond. Proc. IAU Symp. 2006, 234, 549–550. [Google Scholar] [CrossRef]
Saloman, E.B. Energy levels and observed spectral lines of xenon, Xe I through Xe LIV. J. Phys. Chem. Ref. Data 2004, 33, 765–921. [Google Scholar] [CrossRef]
Gallardo, M.; ReynaAlmandos, J.G. XenonLines in the Range from 2000 Å to 7000 Å; Serie “Monografias Cientificas” No. 1; Centro de Investigaciones Opticas: LaPlata, Argentina, 1981.
Tauheed, A.; Joshi, Y.N.; Pinnington, E.H. Revised and extended analysis of the 5s²5p³, 5s5p⁴, 5s²5p²5d and 5s²5p²6s configurations of trebly ionized xenon (Xe IV). Phys. Scr. 1993, 47, 555–560. [Google Scholar] [CrossRef]
Gallardo, M.; Raineri, M.; Reyna Almandos, J.G.; Di Rocco, H.O.; Bertuccelli, D.; Trigueiros, A.G. 5s25p2(6p + 4f) configurations in triply ionized xenon (Xe IV). Phys. Scr. 1995, 51, 737–751. [Google Scholar] [CrossRef]
Raineri, M.; Lagorio, C.; Padilla, S.; Gallardo, M.; Reyna Almandos, J. Weighted oscillator strengths for the Xe IV spectrum. At. Data Nucl. Data Tables 2008, 94, 140–159. [Google Scholar] [CrossRef]
Bertuccelli, G.; Di Rocco, H.O.; Iriarte, D.I.; Pomarico, J.A. Experimental Determination of Transition Probabilities of Xe IV; Comparison with Semiempirical Calculations. Phys. Scr. 2000, 62, 277–281. [Google Scholar] [CrossRef]
Cowan, R.D. The Theory of Atomic Structure and Spectra; University of California Press: Berkeley, CA, USA, 1981. [Google Scholar]
Pagan, C.J.B.; Raineri, M.; Gallardo, M.; Reyna Almandos, J. Spectral Analysis and New Visible and Ultraviolet Lines of ArV. Astron. Astrophys. Suppl. Ser. 2019, 242, 24. [Google Scholar] [CrossRef]
Dyal, K.G.; Grant, I.; Johnson, C.T.; Parpia, F.A.; Plummer, E.P. GRASP: A general-purpose relativistic atomic structure program. Comput. Phys. Commun. 1989, 55, 425–456. [Google Scholar] [CrossRef]
Reyna Almandos, J.; Bredice, F.; Raineri, M.; Gallardo, M. Spectral analysis of ionized noble gases and implications for astronomy and laser studies. Phys. Scr. 2009, T134, 014018. [Google Scholar] [CrossRef]
Raineri, M.; Gallardo, M.; Pagan, C.J.B.; Trigueiros, A.G.; ReynaAlmandos, J. Lifetimes and transition probabilities in KrV. J. Quant. Spectrosc. Radiat. Transf. 2012, 113, 1612–1627. [Google Scholar] [CrossRef]
Quinet, P.; Palmeri, P.; Biémont, E.; McCurdy, M.M.; Rieger, G.; Pinnington, E.H.; Wickliffe, M.E.; Lawler, J.E. Experimental and theoretical radiative lifetimes, branching fractions and oscillator strengths in Lu II. Mon. Not. R. Astron. Soc. 1999, 307, 934–940. [Google Scholar] [CrossRef]
Koch, V.; Andrae, D. Static Electric DipolePolarizabilities for Isoelectronic Sequences. Int. J. Quantum Chem. 2011, 111, 891–903. [Google Scholar] [CrossRef]
Grant, I. Relativistic Quantum Theory of Atoms and Molecules: Theory and Computation; Springer: Oxford, UK, 2007. [Google Scholar]
Kramida, A. Configuration interactions of class 11: Na error in Cowan’s atomic structure theory. Comput. Phys.Commun. 2017, 215, 47–48. [Google Scholar] [CrossRef]
Kramida, A. Corrigendum to “Configuration interactions of class 11: Na error in Cowan’s atomic structure theory”. Comput. Phys. Commun. 2018, 232, 266–267. [Google Scholar] [CrossRef]
NIST Standard Reference Database 78. Version 5.6. Available online: https://www.nist.gov/pml/atomic-spectra-database (accessed on 31 October 2018).
Sharman, M.K.; Tauheed, A.; Rahimullah, K. Spectral analysis of 5s²5p² (6p+6d+7s) configurations of Ba VI. J. Quant. Spectrosc. Radiat. Transf. 2014, 142, 37–48. [Google Scholar] [CrossRef]

Figure 1. Isoelectronic trend for the multiplet (³P) ⁴F energy levels of the 5s²5p² 6d configuration.

Figure 2. Isoelectronic trend for the multiplet (³P) ⁴P energy levels of the 5s²5p² 6d configuration.

Figure 3. Isoelectronic trend for the multiplet (³P) ⁴P energy levels of the 5s²5p² 7s configuration.

Table 1. Energy levels, composition, and lifetimes of Xe IV.

Designation		Energy (cm⁻¹)		Composition	Lifetime(ns)
		Exp.	Fitted		HFRa	HFR	MCDF Babushkin
						+CPa	MCDF Babushkin
5s²5p²(³P)7s	⁴P_1/2	239,145	239,126	68.8%⁴P + 22.5% 5s²5p²(³P)7s ²P + 8.1% 5s²5p²(¹S)7s ²S	0.304	0.297	0.364
	⁴P_3/2	246,689	246,769	84.5%⁴P + 9.2% 5s²5p²(³P)7s ²P + 3.3% 5s²5p²(³P)6d ⁴D	0.324	0.322	0.414
	²P_1/2	247,583	247,559	66.7%²P + 23.2% 5s²5p²(³P)7s ⁴P + 3.8% 5s²5p²(³P)6d ²P	0.247	0.232	0.298
	⁴P_5/2	251,851	251,784	74.6%⁴P + 22.9% 5s²5p²(¹D)7s ²D	0.355	0.357	0.553
	²P_3/2	252,943	252,992	62.5%²P + 25.1% 5s²5p²(¹D)7s ²D + 6.7% 5s²5p²(³P)7s ⁴P	0.190	0.190	0.287
5s²5p²(¹D)7s	²D_5/2	266,331	266,382	60.5%²D + 17.1% 5s²5p²(³P)7s ⁴P + 9.6% 5s²5p²(¹D)6d ²D	0.239	0.257	0.287
	²D_3/2	266,623	266,574	68.9%²D + 22.7% 5s²5p²(³P)7s ²P + 3.6% 5s²5p²(³P)7s ⁴P	0.221	0.228	0.176
5s²5p²(¹S)7s	²S_1/2	283,512	283,519	91.3%²S + 5.2% 5s²5p²(³P)7s ⁴P + 2.9% 5s²5p²(³P)7s ²P	0.318	0.302	0.454
5s²5p²(³P)6d	⁴F_3/2	234,291	234,304	58%⁴F + 15% 5s²5p²(³P)6d ⁴D + 10% 5s²5p²(³P)6d ²P	0.519	0.563	0.507
	⁴F_5/2	235,660	235,710	35.1%⁴F + 15.3% 5s²5p²(³P)6d ⁴P + 28.5% 5s²5p²(³P)6d ⁴D	0.369	0.427	0.337
	²P_3/2	241,896	241,998	31.2%²P + 33.3% 5s²5p²(³P)6d ⁴F + 22.7% 5s²5p²(³P)6d ⁴D	0.380	0.416	0.230
	⁴F_7/2	242,080	242,086	63.1%⁴F + 30.5% 5s²5p²(³P)6d ⁴D + 5.4% 5s²5p²(³P)6d ²F	0.744	0.796	0.679
	⁴D_1/2	242,541	242,397	80.7%⁴D + 12.6% 5s²5p²(³P)6d ²P + 5.5% 5s²5p²(³P)6d ⁴P	0.527	0.570	0.481
	⁴P_5/2	242,534	242,571	28.3%⁴P + 54.8% 5s²5p²(³P)6d ⁴F + 5.1% 5s²5p²(³P)6d ⁴D	0.338	0.389	0.302
	⁴D_3/2	244,577	244,535	30.2%⁴D + 35.1% 5s²5p²(³P)6d ²P + 14.7% 5s²5p²(³P)6d ⁴P	0.299	0.330	0.314
	²F_5/2	244,722	244,609	65.4%²F + 19.4% 5s²5p²(³P)6d ⁴P + 9.9% 5s²5p²(¹D)6d ²F	0.277	0.326	0.223
	⁴D_7/2	246,494	246,470	36.2%⁴D + 26.4% 5s²5p²(³P)6d ⁴F + 18.9% 5s²5p²(¹D)6d ²F	0.760	0.804	0.793
	⁴F_9/2	246,662	246,625	80.2%⁴F + 19.6% 5s²5p²(¹D)6d ²G	0.845	0.891	0.818
	⁴D_5/2	248,027	248,123	49.6%⁴D + 24.6% 5s²5p²(³P)6d ⁴P + 16% 5s²5p²(¹D)6d ²D	0.281	0.325	0.234
	⁴P_3/2	248,565	248,623	57.2%⁴P + 19.7% 5s²5p²(³P)6d ⁴D + 12.7% 5s²5p²(¹D)6d ²P	0.259	0.313	0.205
	⁴P_1/2	249,115	249,043	75.8%⁴P + 11.7% 5s²5p²(¹D)6d ²S + 4.9% 5s²5p²(¹D)6d ²P	0.197	0.235	0.159
	²P_1/2	250,691	250,595	69.6%²P + 10.3% 5s²5p²(³P)6d ⁴D + 6.6% 5s²5p²(³P)7s ²P	0.213	0.244	0.165
	²F_7/2	251,073	251,083	55.5%²F + 22.9% 5s²5p²(¹D)6d ²G + 17% 5s²5p²(³P)6d ⁴D	0.221	0.267	0.176
	²D_5/2	251,211	251,204	61.9%²D + 25% 5s²5p²(¹D)6d ²F + 7.9% 5s²5p²(¹D)6d ²D	0.203	0.251	0.144
	²D_3/2	251,890	251,977	59.7%²D + 14.1% 5s²5p²(¹D)6d ²D + 8.3% 5s²5p²(¹D)6d ²P	0.249	0.295	0.148
5s²5p²(¹D)6d	²F_7/2	260,362	260,428	58.7%²F + 20.5% 5s²5p²(¹D)6d ²G + 14.1% 5s²5p²(³P)6d ⁴D	0.546	0.614	0.527
	²G_9/2	261,548	261,656	80.3%²G + 19.6% 5s²5p²(³P)6d ⁴F	0.839	0.906	0.862
	²D_5/2	262,379	262,321	44.1%²D + 30.4% 5s²5p²(¹D)6d ²F + 10% 5s²5p²(³P)6d ⁴D	0.196	0.230	0.155
	²D_3/2	262,438	262,480	69.4%²D + 7.5% 5s²5p²(¹D)6d ²P + 6.9% 5s²5p²(³P)6d ⁴D	0.206	0.234	0.171
	²P_1/2	262,937	262,904	85.4%²P + 4.6% 5s²5p²(³P)6d ²P + 4.3% 5s²5p²(³P)6d ⁴D	0.323	0.395	0.286
	²G_7/2	262,860	262,969	48.4%²G + 22.2% 5s²5p²(³P)6d ²F + 19.3% 5s²5p²(¹D)6d ²F	0.234	0.293	0.175
	²F_5/2	265,205	265,171	24.4%²F + 22.1% 5s²5p²(³P)6d ²D + 20.3% 5s²5p²(¹D)6d ²D	0.216	0.253	0.157
	²P_3/2	265,501	265,400	64.9%²P + 9.7% 5s²5p²(³P)6d ²P + 7.4% 5s²5p²(³P)6d ²D	0.278	0.334	0.346
	²S_1/2	265,930	265,908	81.3%²S + 11.4% 5s²5p²(³P)6d ⁴P + 4.6% 5s²5p²(³P)6d ²P	0.198	0.226	0.171
5s²5p²(¹S)6d	²D_5/2	280,142	279,777	91.2%²D + 2.8% 5s²5p²(³P)6d ²F + 2.3% 5s²5p²(³P)6d ⁴D	0.361	0.421	0.316
	²D_3/2	279,799	280,132	89.4%²D + 4.3% 5s²5p²(³P)6d ²D + 2.8% 5s²5p²(³P)6d ⁴F	0.244	0.293	0.211

Table 2. Values for polarizability α_d and cut-off radius r_c, used in antimony isoelectronic sequence calculations (HFR+CP). Here,

a_{0}

is the Bohr radius.

Table 2. Values for polarizability α_d and cut-off radius r_c, used in antimony isoelectronic sequence calculations (HFR+CP). Here,

a_{0}

is the Bohr radius.

Ion	α_d (a₀³)	r_c (a₀)
Sb I	1.61620	1.33000
Te II	1.25140	1.27000
I III	0.99660	1.21000
Xe IV	0.81130	1.16000
Cs V	0.67210	1.11000
Ba VI	0.56500	1.07000

Table 3. Transitions and weighted transition rates for Xe IV.

Int	λ (Å)	Energy (cm⁻¹)		Designation		Weighted Transition Rates—gA (s⁻¹)
		Lower	Upper	Lower	Upper	Adjusted
		Level	Level	Level	Level	HFRa	HFR+CPa	HFR+CP
1	1078.51	190,793	283,512	5s²5p²(³P)6p ⁴D_3/2	5s²5p²(¹S)7s ²S_1/2	6.623 × 10⁶	3.771 × 10⁶	9.474 × 10⁴
3	1115.44	193,861	283,512	5s²5p²(³P)6p ²S_1/2	5s²5p²(¹S)7s ²S_1/2	8.542 × 10⁴	8.067 × 10⁴	2.572 × 10⁵
2	1139.89	195,785	283,512	5s²5p²(³P)4f ⁴D_3/2	5s²5p²(¹S)7s ²S_1/2	2.395 × 10⁴	2.750 × 10³	2.061 × 10⁵
2	1151.31	196,655	283,512	5s²5p²(³P)4f ⁴D_1/2	5s²5p²(¹S)7s ²S_1/2	9.396 × 10³	6.026 × 10³	4.447 × 10⁴
2	1212.39	201,028	283,512	5s²5p²(³P)6p ⁴S_3/2	5s²5p²(¹S)7s ²S_1/2	1.932 × 10⁴	5.698 × 10⁴	7.434 × 10⁶
2	1240.09	182,219	262,860	5s²5p²(³P)4f ⁴G_7/2	5s²5p²(¹D)6d ²G_7/2	1.210 × 10⁶	9.729 × 10⁵	9.768 × 10⁵
2	1259.87	204,140	283,512	5s²5p²(³P)6p ⁴P_3/2	5s²5p²(¹S)7s ²S_1/2	7.200 × 10⁶	6.818 × 10⁶	2.361 × 10⁵
1	1291.10	206,061	283,512	5s²5p²(³P)6p ²P_3/2	5s²5p²(¹S)7s ²S_1/2	1.288 × 10⁷	1.543 × 10⁷	1.891 × 10⁷
2	1326.93	189,842	265,205	5s²5p²(³P)4f ⁴D_7/2	5s²5p²(¹D)6d ²F_5/2	3.168 × 10⁷	2.181 × 10⁷	2.609 × 10⁷
2	1340.56	205,205	279,799	5s²5p²(¹D)4f ²F_5/2	5s²5p²(¹S)6d²D_3/2	7.092 × 10⁶	1.296 × 10⁶	1.155 × 10⁷
1	1357.65	188,721	262,379	5s²5p²(³P)4f ²D_5/2	5s²5p²(¹D)6d ²D_5/2	4.998 × 10⁶	4.123 × 10⁶	3.280 × 10⁶
2	1386.74	188,252	260,362	5s²5p²(³P)4f ⁴G_9/2	5s²5p²(¹D)6d ²F_7/2	1.755 × 10⁶	1.789 × 10⁶	1.046 × 10⁶
1	1394.58	189,842	261,548	5s²5p²(³P)4f ⁴D_7/2	5s²5p²(¹D)6d ²G_9/2	3.174 × 10³	7.428 × 10³	7.100 × 10³
1	1419.25	191,978	262,438	5s²5p²(³P)4f ⁴D_5/2	5s²5p²(¹D)6d ²D_3/2	5.438 × 10⁵	2.925 × 10⁵	2.289 × 10⁵
1	1420.42	191,978	262,379	5s²5p²(³P)4f ⁴D_5/2	5s²5p²(¹D)6d ²D_5/2	4.326 × 10⁶	3.840 × 10⁶	7.217 × 10⁶
1	1430.66	196,725	266,623	5s²5p²(³P)6p ²D_3/2	5s²5p²(¹D)7s ²D_3/2	1.565 × 10⁷	9.181 × 10⁶	3.609 × 10⁷
1	1434.39	195,785	265,501	5s²5p²(³P)4f ⁴D_3/2	5s²5p²(¹D)6d ²P_3/2	5.789 × 10⁶	3.652 × 10⁶	2.398 × 10⁵
1	1477.52	198,943	266,623	5s²5p²(³P)6p ⁴D_5/2	5s²5p²(¹D)7s ²D_3/2	1.049 × 10⁶	2.225 × 10⁵	3.155 × 10⁶
1	1496.21	186,109	252,943	5s²5p²(³P)6p ⁴D_1/2	5s²5p²(³P)7s ²P_3/2	2.673 × 10⁷	3.318 × 10⁷	1.700 × 10⁷
2	1507.08	196,506	262,860	5s²5p²(³P)4f ⁴F_5/2	5s²5p²(¹D)6d ²G_7/2	1.549 × 10⁴	5.596 × 10⁵	9.001 × 10⁶
1	1521.44	200,899	266,623	5s²5p²(³P)6p ⁴P_1/2	5s²5p²(¹D)7s ²D_3/2	2.177 × 10⁵	1.502 × 10⁴	1.926 × 10⁵
9	1551.78	182,219	246,662	5s²5p²(³P)4f ⁴G_7/2	5s²5p²(³P)6d⁴F_9/2	1.587 × 10⁷	1.008 × 10⁷	9.882 × 10⁶
4	1552.22	180,152	244,577	5s²5p²(³P)4f ⁴G_5/2	5s²5p²(³P)6d⁴D_3/2	8.606 × 10⁵	2.951 × 10⁵	2.936 × 10⁷
7	1573.83	187,533	251,073	5s²5p²(³P)4f ²G_7/2	5s²5p²(³P)6d²F_7/2	1.203 × 10⁷	7.570 × 10⁶	4.904 × 10⁶
7	1615.28	201,028	262,937	5s²5p²(³P)6p ⁴S_3/2	5s²5p²(¹D)6d ²P_1/2	6.055 × 10⁷	4.595 × 10⁷	5.730 × 10⁶
6	1618.41	204,140	265,930	5s²5p²(³P)6p ⁴P_3/2	5s²5p²(¹D)6d ²S_1/2	1.484 × 10⁷	2.801 × 10⁶	8.778 × 10⁵
1	1626.69	186,109	247,583	5s²5p²(³P)6p ⁴D_1/2	5s²5p²(³P)7s ²P_1/2	2.319 × 10⁷	2.526 × 10⁷	2.055 × 10⁷
3	1645.20	202,076	262,860	5s²5p²(³P)4f ⁴F_9/2	5s²5p²(¹D)6d ²G_7/2	6.376 × 10⁷	4.843 × 10⁷	1.556 × 10⁸
5	1650.75	186,109	246,689	5s²5p²(³P)6p ⁴D_1/2	5s²5p²(³P)7s ⁴P_3/2	1.606 × 10⁶	1.586 × 10⁶	2.029 × 10⁶
7	1658.00	182,219	242,534	5s²5p²(³P)4f ⁴G_7/2	5s²5p²(³P)6d⁴F_5/2	3.389 × 10⁷	2.586 × 10⁷	3.940 × 10⁸
2	1665.77	191,858	251,890	5s²5p²(³P)4f ⁴F_3/2	5s²5p²(³P)6d²D_3/2	2.043 × 10⁷	2.421 × 10⁷	7.476 × 10⁵
4	1666.86	191,858	251,851	5s²5p²(³P)4f ⁴F_3/2	5s²5p²(³P)7s ⁴P_5/2	1.451 × 10⁶	7.145 × 10⁴	1.065 × 10⁵
5	1670.08	200,486	260,362	5s²5p²(³P)6p ²D_5/2	5s²5p²(¹D)6d ²F_7/2	1.713 × 10⁷	1.995 × 10⁷	7.747 × 10⁷
6	1670.33	206,061	265,930	5s²5p²(³P)6p ²P_3/2	5s²5p²(¹D)6d ²S_1/2	1.361 × 10⁸	1.050 × 10⁸	1.881 × 10⁸
3	1670.60	182,219	242,080	5s²5p²(³P)4f ⁴G_7/2	5s²5p²(³P)6d⁴F_7/2	1.019 × 10⁷	7.394 × 10⁶	1.384 × 10⁷
3	1678.74	207,057	266,623	5s²5p²(³P)6p ⁴P_5/2	5s²5p²(¹D)7s ²D_3/2	1.362 × 10⁸	8.177 × 10⁷	6.031 × 10⁶
5	1681.48	202,076	261,548	5s²5p²(³P)4f ⁴F_9/2	5s²5p²(¹D)6d ²G_9/2	5.905 × 10⁷	4.145 × 10⁷	2.013 × 10⁷
7	1686.18	188,721	248,027	5s²5p²(³P)4f ²D_5/2	5s²5p²(³P)6d⁴D_5/2	3.718 × 10⁶	2.399 × 10⁶	3.658 × 10⁶
4	1691.19	187,533	246,662	5s²5p²(³P)4f ²G_7/2	5s²5p²(³P)6d⁴F_9/2	1.109 × 10⁷	8.797 × 10⁶	2.209 × 10⁷
4	1692.52	193,861	252,943	5s²5p²(³P)6p ²S_1/2	5s²5p²(³P)7s ²P_3/2	6.667 × 10⁷	7.498 × 10⁷	2.117 × 10⁷
6	1694.50	224,498	283,512	5s²5p²(¹D)6p ²P_3/2	5s²5p²(¹S)7s ²S_1/2	3.004 × 10⁶	1.175 × 10⁷	3.405 × 10⁵
7	1709.63	206,713	265,205	5s²5p²(¹D)4f ²G_7/2	5s²5p²(¹D)6d ²F_5/2	1.281 × 10⁷	1.748 × 10⁶	2.737 × 10⁷
6	1710.31	186,109	244,577	5s²5p²(³P)6p ⁴D_1/2	5s²5p²(³P)6d⁴D_3/2	9.124 × 10⁷	1.199 × 10⁸	1.594 × 10⁸
2	1712.04	188,252	246,662	5s²5p²(³P)4f ⁴G_9/2	5s²5p²(³P)6d⁴F_9/2	3.385 × 10⁷	2.261 × 10⁷	2.546 × 10⁷
4	1730.94	188,721	246,494	5s²5p²(³P)4f ²D_5/2	5s²5p²(³P)6d⁴D_7/2	1.525 × 10⁶	8.100 × 10⁴	1.367 × 10⁶
4	1730.94	190,793	248,565	5s²5p²(³P)6p ⁴D_3/2	5s²5p²(³P)6d⁴P_3/2	2.244 × 10⁶	7.523 × 10⁶	2.589 × 10⁶
6	1734.81	205,217	262,860	5s²5p²(¹D)4f ²F_7/2	5s²5p²(¹D)6d ²G_7/2	3.324 × 10⁷	2.371 × 10⁷	6.740 × 10⁷
5	1747.19	190,793	248,027	5s²5p²(³P)6p ⁴D_3/2	5s²5p²(³P)6d⁴D_5/2	5.268 × 10⁶	7.486 × 10⁶	2.265 × 10⁴
4	1749.08	205,205	262,379	5s²5p²(¹D)4f ²F_5/2	5s²5p²(¹D)6d ²D_5/2	8.193 × 10⁷	4.709 × 10⁷	4.908 × 10⁸
4	1749.39	205,217	262.,379	5s²5p²(¹D)4f ²F_7/2	5s²5p²(¹D)6d ²D_5/2	1.931 × 10⁸	9.089 × 10⁷	1.992 × 10⁸
4	1759.59	193,861	250,691	5s²5p²(³P)6p ²S_1/2	5s²5p²(³P)6d²P_1/2	1.497 × 10⁸	1.798 × 10⁸	1.994 × 10⁸
4	1765.15	189,842	246,494	5s²5p²(³P)4f ⁴D_7/2	5s²5p²(³P)6d⁴D_7/2	1.249 × 10⁷	9.511 × 10⁶	2.037 × 10⁷
6	1765.42	206,216	262,860	5s²5p²(¹D)4f ²H_9/2	5s²5p²(¹D)6d ²G_7/2	1.762 × 10⁷	1.752 × 10⁷	5.048 × 10⁵
3	1778.77	196,725	252,943	5s²5p²(³P)6p ²D_3/2	5s²5p²(³P)7s ²P_3/2	9.427 × 10⁷	8.509 × 10⁷	4.613 × 10⁸
4	1780.72	209,344	265,501	5s²5p²(³P)6p ²P_1/2	5s²5p²(¹D)6d ²P_3/2	1.806 × 10⁸	2.079 × 10⁸	4.567 × 10⁸
4	1781.04	206,713	262,860	5s²5p²(¹D)4f ²G_7/2	5s²5p²(¹D)6d ²G_7/2	1.404 × 10⁷	1.256 × 10⁷	5.619 × 10⁶
4	1782.39	195,785	251,890	5s²5p²(³P)4f ⁴D_3/2	5s²5p²(³P)6d²D_3/2	1.465 × 10⁸	1.280 × 10⁸	3.935 × 10⁷
3	1784.18	191,978	248,027	5s²5p²(³P)4f ⁴D_5/2	5s²5p²(³P)6d⁴D_5/2	1.175 × 10⁷	6.655 × 10⁶	1.529 × 10⁷
4	1789.02	190,793	246,689	5s²5p²(³P)6p ⁴D_3/2	5s²5p²(³P)7s ⁴P_3/2	1.186 × 10⁸	9.404 × 10⁷	1.597 × 10⁸
4	1797.14	224,498	280,142	5s²5p²(¹D)6p ²P_3/2	5s²5p²(¹S)6d²D_5/2	5.493 × 10⁷	1.126 × 10⁸	1.487 × 10⁷
4	1800.99	196,325	251,851	5s²5p²(³P)4f ⁴F_7/2	5s²5p²(³P)7s ⁴P_5/2	2.801 × 10⁶	7.025 × 10⁵	3.792 × 10⁵
7	1801.53	180,152	235,660	5s²5p²(³P)4f ⁴G_5/2	5s²5p²(³P)6d⁴P_5/2	2.977 × 10⁷	2.086 × 10⁷	8.452 × 10⁶
6	1807.29	206,216	261,548	5s²5p²(¹D)4f ²H_9/2	5s²5p²(¹D)6d ²G_9/2	3.229 × 10⁷	2.550 × 10⁷	2.172 × 10⁷
6	1813.02	205,205	260,362	5s²5p²(¹D)4f ²F_5/2	5s²5p²(¹D)6d ²F_7/2	2.235 × 10⁷	3.081 × 10⁷	2.006 × 10⁷
3	1813.39	205,217	260,362	5s²5p²(¹D)4f ²F_7/2	5s²5p²(¹D)6d ²F_7/2	1.362 × 10⁸	1.150 × 10⁸	1.140 × 10⁸
4	1813.95	196,725	251,851	5s²5p²(³P)6p ²D_3/2	5s²5p²(³P)7s ⁴P_5/2	1.231 × 10⁸	9.434 × 10⁷	3.600 × 10⁴
1	1821.29	195,785	250,691	5s²5p²(³P)4f ⁴D_3/2	5s²5p²(³P)6d²P_1/2	2.749 × 10⁷	2.287 × 10⁷	5.120 × 10⁶
8	1822.13	189,842	244,722	5s²5p²(³P)4f ⁴D_7/2	5s²5p²(³P)6d²F_5/2	4.321 × 10⁸	3.081 × 10⁸	3.510 × 10⁸
3	1823.68	206,713	261,548	5s²5p²(¹D)4f ²G_7/2	5s²5p²(¹D)6d ²G_9/2	1.275 × 10⁸	1.092 × 10⁸	3.008 × 10⁸
5	1833.29	187,533	242,080	5s²5p²(³P)4f ²G_7/2	5s²5p²(³P)6d⁴F_7/2	5.893 × 10⁷	4.396 × 10⁷	5.539 × 10⁷
3	1853.01	196,725	250,691	5s²5p²(³P)6p ²D_3/2	5s²5p²(³P)6d²P_1/2	2.641 × 10⁶	8.155 × 10⁵	6.555 × 10⁷
5	1854.27	190,793	244,722	5s²5p²(³P)6p ⁴D_3/2	5s²5p²(³P)6d²F_5/2	5.464 × 10⁵	1.286 × 10⁶	3.530 × 10⁶
4	1858.13	208,621	262,438	5s²5p²(³P)4f ²F_5/2	5s²5p²(¹D)6d ²D_3/2	1.071 × 10⁸	9.091 × 10⁷	2.376 × 10⁷
3	1863.98	206,713	260,362	5s²5p²(¹D)4f ²G_7/2	5s²5p²(¹D)6d ²F_7/2	1.796 × 10⁴	1.370 × 10⁶	2.856 × 10⁷
2	1874.10	188,721	242,080	5s²5p²(³P)4f ²D_5/2	5s²5p²(³P)6d⁴F_7/2	7.040 × 10⁶	7.698 × 10⁶	1.683 × 10⁷
5	1883.46	209,344	262,438	5s²5p²(³P)6p ²P_1/2	5s²5p²(¹D)6d ²D_3/2	4.162 × 10⁷	3.800 × 10⁷	7.917 × 10⁷
6	1890.04	198,943	251,851	5s²5p²(³P)6p ⁴D_5/2	5s²5p²(³P)7s ⁴P_5/2	4.565 × 10⁸	3.836 × 10⁸	2.559 × 10⁶
3	1894.62	195,785	248,565	5s²5p²(³P)4f ⁴D_3/2	5s²5p²(³P)6d⁴P_3/2	9.841 × 10⁶	6.703 × 10⁶	2.840 × 10⁸
7	1897.88	189,842	242,534	5s²5p²(³P)4f ⁴D_7/2	5s²5p²(³P)6d⁴F_5/2	4.812 × 10⁷	2.681 × 10⁷	1.772 × 10⁶
5	1901.17	191,978	244,577	5s²5p²(³P)4f ⁴D_5/2	5s²5p²(³P)6d⁴D_3/2	2.501 × 10⁸	1.785 × 10⁸	1.428 × 10⁴
4	1905.07	199,397	251,890	5s²5p²(³P)4f ²D_3/2	5s²5p²(³P)6d²D_3/2	5.527 × 10⁷	5.888 × 10⁷	2.821 × 10⁷
7	1906.20	196,655	249,115	5s²5p²(³P)4f ⁴D_1/2	5s²5p²(³P)6d⁴P_1/2	9.874 × 10⁷	7.103 × 10⁷	6.996 × 10⁷
6	1913.18	198,943	251,211	5s²5p²(³P)6p ⁴D_5/2	5s²5p²(³P)6d²D_5/2	2.215 × 10⁸	1.343 × 10⁸	8.697 × 10⁶
8	1914.28	189,842	242,080	5s²5p²(³P)4f ⁴D_7/2	5s²5p²(³P)6d⁴F_7/2	3.153 × 10⁷	2.053 × 10⁷	1.020 × 10⁷
4	1918.27	198,943	251,073	5s²5p²(³P)6p ⁴D_5/2	5s²5p²(³P)6d²F_7/2	3.502 × 10⁸	2.137 × 10⁸	1.380 × 10⁷
5	1929.04	196,725	248,565	5s²5p²(³P)6p ²D_3/2	5s²5p²(³P)6d⁴P_3/2	3.905 × 10⁸	2.829 × 10⁸	8.032 × 10⁶
2	1930.57	195,785	247,583	5s²5p²(³P)4f ⁴D_3/2	5s²5p²(³P)7s ²P_1/2	1.205 × 10⁸	1.336 × 10⁸	5.103 × 10⁸
4	1960.89	215,626	266,623	5s²5p²(¹D)6p ²F_5/2	5s²5p²(¹D)7s ²D_3/2	1.521 × 10⁹	1.359 × 10⁹	9.246 × 10⁸
6	1961.19	200,899	251,890	5s²5p²(³P)6p ⁴P_1/2	5s²5p²(³P)6d²D_3/2	1.312 × 10⁷	1.068 × 10⁷	3.950 × 10⁷
4	1966.19	196,725	247,583	5s²5p²(³P)6p ²D_3/2	5s²5p²(³P)7s ²P_1/2	5.960 × 10⁸	5.444 × 10⁸	4.223 × 10⁸
2	1967.55	201,028	251,851	5s²5p²(³P)6p ⁴S_3/2	5s²5p²(³P)7s ⁴P_5/2	7.882 × 10⁷	1.314 × 10⁸	1.316 × 10⁹
7	1972.35	232,811	283,512	5s²5p²(¹S)6p ²P_1/2	5s²5p²(¹S)7s ²S_1/2	8.420 × 10⁸	7.097 × 10⁸	7.885 × 10⁸
2	1973.04	191,858	242,541	5s²5p²(³P)4f ⁴F_3/2	5s²5p²(³P)6d⁴D_1/2	1.839 × 10⁸	1.453 × 10⁸	1.563 × 10⁸
2	1976.77	200,486	251,073	5s²5p²(³P)6p ²D_5/2	5s²5p²(³P)6d²F_7/2	1.277 × 10⁹	1.374 × 10⁹	2.637 × 10⁸
5	1980.87	216,141	266,623	5s²5p²(¹D)6p ²D_3/2	5s²5p²(¹D)7s ²D_3/2	2.008 × 10⁸	2.357 × 10⁸	8.700 × 10⁷
5	2007.72	200,899	250,691	5s²5p²(³P)6p ⁴P_1/2	5s²5p²(³P)6d²P_1/2	1.785 × 10⁸	1.802 × 10⁸	2.370 × 10⁸
2	2010.79	199,397	249,115	5s²5p²(³P)4f ²D_3/2	5s²5p²(³P)6d⁴P_1/2	1.249 × 10⁷	4.943 × 10⁶	4.035 × 10⁷
8	2014.59	198,943	248,565	5s²5p²(³P)6p ⁴D_5/2	5s²5p²(³P)6d⁴P_3/2	3.953 × 10⁷	1.658 × 10⁷	7.665 × 10⁷
1	2016.33	215,626	265,205	5s²5p²(¹D)6p ²F_5/2	5s²5p²(¹D)6d ²F_5/2	8.577 × 10⁸	4.038 × 10⁸	6.030 × 10⁸
3	2022.77	216,911	266,331	5s²5p²(¹D)6p ²D_5/2	5s²5p²(¹D)7s ²D_5/2	5.091 × 10⁸	3.580 × 10⁸	5.529 × 10⁸
4	2025.24	216,141	265,501	5s²5p²(¹D)6p ²D_3/2	5s²5p²(¹D)6d ²P_3/2	9.701 × 10⁷	4.608 × 10⁷	3.323 × 10⁷
2	2033.21	199,397	248,565	5s²5p²(³P)4f ²D_3/2	5s²5p²(³P)6d⁴P_3/2	2.115 × 10⁵	1.036 × 10⁶	2.923 × 10⁷
1	2036.36	217,240	266,331	5s²5p²(¹D)6p ²F_7/2	5s²5p²(¹D)7s ²D_5/2	2.256 × 10⁹	1.670 × 10⁹	1.307 × 10⁹
1	2036.71	198,943	248,027	5s²5p²(³P)6p ⁴D_5/2	5s²5p²(³P)6d⁴D_5/2	6.800 × 10⁸	5.262 × 10⁸	4.763 × 10⁷
1	2048.41	204,140	252,943	5s²5p²(³P)6p ⁴P_3/2	5s²5p²(³P)7s ²P_3/2	1.331 × 10⁶	2.474 × 10⁶	4.866 × 10⁷
2	2071.42	202,951	251,211	5s²5p²(³P)6p ⁴D_7/2	5s²5p²(³P)6d²D_5/2	3.115 × 10⁷	2.743 × 10⁷	1.306 × 10⁸
5	2071.80	196,325	244,577	5s²5p²(³P)4f ⁴F_7/2	5s²5p²(³P)6d⁴D_3/2	1.306 × 10⁸	1.306 × 10⁸	1.306 × 10⁸
7	2073.30	196,506	244,722	5s²5p²(³P)4f ⁴F_5/2	5s²5p²(³P)6d²F_5/2	2.372 × 10⁷	1.778 × 10⁷	7.477 × 10⁷
7	2073.30	200,899	249,115	5s²5p²(³P)6p ⁴P_1/2	5s²5p²(³P)6d⁴P_1/2	8.505 × 10⁷	7.698 × 10⁷	7.506 × 10⁷
3	2074.74	186,109	234,291	5s²5p²(³P)6p ⁴D_1/2	5s²5p²(³P)6d⁴F_3/2	4.587 × 10⁹	4.423 × 10⁹	4.385 × 10⁹
3	2077.37	202,951	251,073	5s²5p²(³P)6p ⁴D_7/2	5s²5p²(³P)6d²F_7/2	3.747 × 10⁸	3.835 × 10⁸	5.358 × 10⁸
3	2078.87	201,028	249,115	5s²5p²(³P)6p ⁴S_3/2	5s²5p²(³P)6d⁴P_1/2	8.110 × 10⁷	1.455 × 10⁸	2.137 × 10⁹
9	2079.23	200,486	248,565	5s²5p²(³P)6p ²D_5/2	5s²5p²(³P)6d⁴P_3/2	1.066 × 10⁹	1.029 × 10⁹	1.502 × 10⁷
3	2081.10	193,861	241,896	5s²5p²(³P)6p ²S_1/2	5s²5p²(³P)6d²P_3/2	2.500 × 10⁹	2.376 × 10⁹	9.586 × 10⁸
2	2093.75	198,943	246,689	5s²5p²(³P)6p ⁴D_5/2	5s²5p²(³P)7s ⁴P_3/2	1.854 × 10⁹	1.981 × 10⁹	2.738 × 10⁸
2	2094.11	205,205	252,943	5s²5p²(¹D)4f ²F_5/2	5s²5p²(³P)7s ²P_3/2	3.332 × 10⁷	3.297 × 10⁷	3.947 × 10⁸
6	2102.94	201,028	248,565	5s²5p²(³P)6p ⁴S_3/2	5s²5p²(³P)6d⁴P_3/2	9.059 × 10⁷	1.802 × 10⁸	2.927 × 10⁹
2	2136.22	216,141	262,937	5s²5p²(¹D)6p ²D_3/2	5s²5p²(¹D)6d ²P_1/2	8.568 × 10⁸	8.495 × 10⁸	6.086 × 10⁸
2	2147.31	201,028	247,583	5s²5p²(³P)6p ⁴S_3/2	5s²5p²(³P)7s ²P_1/2	5.096 × 10⁸	5.571 × 10⁸	5.606 × 10⁵
4	2149.87	219,002	265,501	5s²5p²(¹D)4f ²D_5/2	5s²5p²(¹D)6d ²P_3/2	1.852 × 10⁸	1.390 × 10⁸	3.914 × 10⁷
2	2183.24	206,061	251,851	5s²5p²(³P)6p ²P_3/2	5s²5p²(³P)7s ⁴P_5/2	2.778 × 10⁷	7.787 × 10⁶	1.668 × 10⁸
2	2183.24	200,899	246,689	5s²5p²(³P)6p ⁴P_1/2	5s²5p²(³P)7s ⁴P_3/2	6.598 × 10⁸	6.667 × 10⁸	1.009 × 10⁹
3	2207.67	193,861	239,145	5s²5p²(³P)6p ²S_1/2	5s²5p²(³P)7s ⁴P_1/2	4.086 × 10⁶	6.405 × 10⁶	7.185 × 10⁶
1	2214.68	217,240	262,379	5s²5p²(¹D)6p ²F_7/2	5s²5p²(¹D)6d ²D_5/2	1.526 × 10⁸	9.614 × 10⁷	2.354 × 10⁸
1	2239.94	206,061	250,691	5s²5p²(³P)6p ²P_3/2	5s²5p²(³P)6d²P_1/2	2.758 × 10⁸	2.702 × 10⁸	3.217 × 10⁸
1	2242.39	235,561	280,142	5s²5p²(¹S)6p ²P_3/2	5s²5p²(¹S)6d²D_5/2	6.465 × 10⁹	6.274 × 10	6.193 × 10⁹
5	2295.89	202,951	246,494	5s²5p²(³P)6p ⁴D_7/2	5s²5p²(³P)6d⁴D_7/2	2.371 × 10⁹	2.357 × 10⁹	2.815 × 10⁹
1	2298.23	190,793	234,291	5s²5p²(³P)6p ⁴D_3/2	5s²5p²(³P)6d⁴F_3/2	4.862 × 10⁸	4.099 × 10⁸	5.482 × 10⁸
1	2317.55	199,397	242,534	5s²5p²(³P)4f ²D_3/2	5s²5p²(³P)6d⁴F_5/2	3.469 × 10⁸	4.846 × 10⁸	1.949 × 10⁵
3	2407.63	206,061	247,583	5s²5p²(³P)6p ²P_3/2	5s²5p²(³P)7s ²P_1/2	1.076 × 10⁸	9.367 × 10⁷	7.285 × 10⁷
6	2408.41	207,057	248,565	5s²5p²(³P)6p ⁴P_5/2	5s²5p²(³P)6d⁴P_3/2	2.324 × 10⁸	2.041 × 10⁸	1.291 × 10⁹
2	2472.25	204,140	244,577	5s²5p²(³P)6p ⁴P_3/2	5s²5p²(³P)6d⁴D_3/2	2.832 × 10⁷	5.368 × 10⁷	1.035 × 10⁸
3	2498.99	202,076	242,080	5s²5p²(³P)4f ⁴F_9/2	5s²5p²(³P)6d⁴F_7/2	6.998 × 10⁶	4.645 × 10⁶	9.367 × 10⁵
3	2502.73	208,621	248,565	5s²5p²(³P)4f ²F_5/2	5s²5p²(³P)6d⁴P_3/2	4.929 × 10⁷	7.502 × 10⁷	5.397 × 10⁵
1	2595.56	206,061	244,577	5s²5p²(³P)6p ²P_3/2	5s²5p²(³P)6d⁴D_3/2	4.640 × 10⁸	4.162 × 10⁸	4.734 × 10⁷
1	2596.23	195,785	234,291	5s²5p²(³P)4f ⁴D_3/2	5s²5p²(³P)6d⁴F_3/2	6.854 × 10⁶	4.678 × 10⁶	1.515 × 10⁶
1	2603.52	204,140	242,541	5s²5p²(³P)6p ⁴P_3/2	5s²5p²(³P)6d⁴D_1/2	1.003 × 10⁷	1.586 × 10⁷	4.086 × 10⁷
2	2622.74	201,028	239,.145	5s²5p²(³P)6p ⁴S_3/2	5s²5p²(³P)7s ⁴P_1/2	1.124 × 10⁷	6.599 × 10⁶	5.223 × 10⁶
1	2789.76	206,.061	241,896	5s²5p²(³P)6p ²P_3/2	5s²5p²(³P)6d²P_3/2	4.024 × 10⁷	3.675 × 10⁷	3.847 × 10⁸
1	2855.73	204,140	239,145	5s²5p²(³P)6p ⁴P_3/2	5s²5p²(³P)7s ⁴P_1/2	3.366 × 10⁶	1.750 × 10⁶	2.920 × 10⁷
4	3021.77	206,061	239,145	5s²5p²(³P)6p ²P_3/2	5s²5p²(³P)7s ⁴P_1/2	4.846 × 10⁶	5.063 × 10⁶	5.461 × 10⁶
1	3031.95	216,141	249,115	5s²5p²(¹D)6p ²D_3/2	5s²5p²(³P)6d⁴P_1/2	3.455 × 10⁶	1.022 × 10⁶	7.316 × 10⁴
1	3083.27	216,141	248,565	5s²5p²(¹D)6p ²D_3/2	5s²5p²(³P)6d⁴P_3/2	5.342 × 10⁶	1.452 × 10⁶	2.771 × 10⁵
1	3117.20	219,002	251,073	5s²5p²(¹D)4f ²D_5/2	5s²5p²(³P)6d²F_7/2	7.948 × 10⁷	5.664 × 10⁷	4.145 × 10⁶
4	3143.02	220,082	251,890	5s²5p²(¹D)6p ²P_1/2	5s²5p²(³P)6d²D_3/2	3.672 × 10⁷	4.216 × 10⁶	7.089 × 10⁷
3	3214.51	220,790	251,890	5s²5p²(¹D)4f ²P_1/2	5s²5p²(³P)6d²D_3/2	9.984 × 10⁶	4.387 × 10⁷	2.031 × 10⁶
3	3238.65	215,626	246,494	5s²5p²(¹D)6p ²F_5/2	5s²5p²(³P)6d⁴D_7/2	1.314 × 10⁵	2.120 × 10⁵	1.061 × 10⁶
1	3241.45	213,736	244,577	5s²5p²(¹D)4f ²D_3/2	5s²5p²(³P)6d⁴D_3/2	4.030 × 10⁶	4.550 × 10⁶	1.601 × 10⁵
1	3247.11	217,240	248,027	5s²5p²(¹D)6p ²F_7/2	5s²5p²(³P)6d⁴D_5/2	2.611 × 10⁶	1.551 × 10⁶	2.332 × 10⁵
1	3248.98	235,561	266,331	5s²5p²(¹S)6p ²P_3/2	5s²5p²(¹D)7s ²D_5/2	2.561 × 10⁶	5.870 × 10⁶	1.354 × 10⁶
2	3515.63	216,141	244,577	5s²5p²(¹D)6p ²D_3/2	5s²5p²(³P)6d⁴D_3/2	1.258 × 10⁴	8.724 × 10¹	1.223 × 10⁵
2	3550.01	213,736	241,896	5s²5p²(¹D)4f ²D_3/2	5s²5p²(³P)6d²P_3/2	7.120 × 10⁵	5.240 × 10⁵	1.064 × 10⁶
2	3594.60	216,911	244,722	5s²5p²(¹D)6p ²D_5/2	5s²5p²(³P)6d²F_5/2	8.503 × 10⁵	1.321 × 10⁶	4.517 × 10⁶
1	3636.34	219,002	246,494	5s²5p²(¹D)4f ²D_5/2	5s²5p²(³P)6d⁴D_7/2	6.194 × 10⁶	3.751 × 10⁶	1.249 × 10⁶
1	3637.66	217,240	244,722	5s²5p²(¹D)6p ²F_7/2	5s²5p²(³P)6d²F_5/2	4.573 × 10⁵	2.214 × 10⁵	1.336 × 10⁶
3	3654.96	224,498	251,851	5s²5p²(¹D)6p ²P_3/2	5s²5p²(³P)7s ⁴P_5/2	3.333 × 10⁵	9.256 × 10⁴	3.850 × 10⁴
2	3715.25	215,626	242,534	5s²5p²(¹D)6p ²F_5/2	5s²5p²(³P)6d⁴F_5/2	1.159 × 10⁵	1.184 × 10⁴	4.643 × 10⁵
2	3901.70	216,911	242,534	5s²5p²(¹D)6p ²D_5/2	5s²5p²(³P)6d⁴F_5/2	2.684 × 10⁵	2.945 × 10⁵	3.263 × 10⁴
4	4061.12	224,498	249,115	5s²5p²(¹D)6p ²P_3/2	5s²5p²(³P)6d⁴P_1/2	9.721 × 10⁵	4.089 × 10⁵	7.330 × 10⁴
3	4248.40	219,002	242,534	5s²5p²(¹D)4f ²D_5/2	5s²5p²(³P)6d⁴F_5/2	2.127 × 10⁴	6.785 × 10⁴	2.765 × 10²
2	4470.40	219,717	242,080	5s²5p²(³P)4f ²F_7/2	5s²5p²(³P)6d⁴F_7/2	8.612 × 10⁵	9.968 × 10⁵	1.711 × 10⁴
1	4366.60	219,002	241,896	5s²5p²(¹D)4f ²D_5/2	5s²5p²(³P)6d²P_3/2	4.677 × 10⁵	3.493 × 10⁵	2.294 × 10⁵
1	4505.10	224,498	246,689	5s²5p²(¹D)6p ²P_3/2	5s²5p²(³P)7s ⁴P_3/2	6.198 × 10²	2.209 × 10⁴	4.401 × 10⁴
2	4582.85	220,082	241,896	5s²5p²(¹D)6p ²P_1/2	5s²5p²(³P)6d²P_3/2	5.479 × 10⁵	5.230 × 10⁵	5.416 × 10⁴
1	5240.06	232,811	251,890	5s²5p²(¹S)6p ²P_1/2	5s²5p²(³P)6d²D_3/2	1.262 × 10⁶	1.642 × 10⁶	2.573 × 10⁵
4	6348.69	228,975	244,722	5s²5p²(¹S)4f ²F_7/2	5s²5p²(³P)6d²F_5/2	9.962 × 10³	9.580 × 10³	3.369 × 10³

Table 4. Least-squares parameters for even parity of Xe IV. Standard deviation is 138 cm⁻¹.

Configuration	Parameter	HFR (cm⁻¹)		HFRa./HFR ^a
		HFR	HFRa
5s5p⁴	E_av(5s5p⁴)	145,275	132,757	−12,519
	F²(5p,5p)	53,464	46,502	87%
	α	0	−402
	ζ_5p	8246	8600	104%
	G¹(5s,5p)	70,216	48,430	69%

5s²5p²6s	E_av (5s²5p²6s)	187,245	176,036	−11,209
	F²(5p,5p)	54,783	43,692	80%
	α	0	−55
	ζ_5p	8859	8945	101%
	G¹(5p,6s)	5898	4379	74%
5s²5p²7s	E_av (5s²5p²7s)	267,957	257,041	−10,916
	F²(5p,5p)	55,283	47,384	86%
	ζ_5p	8999	8556	95%
	G¹(5p,7s)	1801	1633	91%
5s²5p²5d	E_av (5s²5p²5d)	170,438	158,790	−11,648
	F²(5p,5p)	54,191	42,089	78%

	α	0	−123
	ζ_5p	8593	8754	102%
	ζ_5d	478	695	145%
	F²(5p,5d)	39,705	32,721	82%
	G¹(5p,5d)	44,921	32,124	72%
	G³(5p,5d)	28,247	20,111	71%
5s²5p²6d	E_av (5s²5p²6d)	264,034	253,060	−10,975
	F²(5p,5p)	55,267	47,585	86%
	ζ_5p	8972	8449	94%
	ζ_6d	161	153	95%
	F²(5p,6d)	11,723	10,009	85%
	G¹(5p,6d)	7747	6753	87%
	G³(5p,6d)	5444	5575	102%
5s5p⁴-5s²5p²6s	R¹(5p,5p;5s,6s)	−1237	−851	69%
5s5p⁴-5s²5p²7s	R¹(5p,5p;5s,7s)	−1351	−1148	85%
5s5p⁴-5s²5p²5d	R¹(5p,5p;5s,5d)	53,926	37,094	69%
5s5p⁴-5s²5p²6d	R¹(5p,5p;5s,6d)	22,435	19,069	85%
5s²5p²6s-5s²5p²7s	R¹(5p,6s;7s,5p)	3120	2652	85%
5s²5p²6s-5s²5p²5d	R²(5p,6s;5p,5d)	−12,799	−10,336	81%
	R¹(5p,6s;5d,5p)	−5075	−4098	81%
5s²5p²6s-5s²5p²6d	R²(5p,6s;5p,6d)	4779	4062	85%
	R¹(5p,6s;6d,5p)	85	73	85%
5s²5p²7s-5s²5p²5d	R²(5p,7s;5p,5d)	−6519	−5541	85%
	R¹(5p,7s;5d,5p)	−3294	−2800	85%
5s²5p²7s-5s²5p²6d	R²(5p,7s;5p,6d)	−3058	−2599	85%
	R¹(5p,7s;6d,5p)	−391	−333	85%
5s²5p²5d-5s²5p²6d	R²(5p,5d;5p,6d)	12,162	10,338	85%
	R¹(5p,5d;6d,5p)	17,415	13,061	75%
	R³(5p,5d;6d,5p)	11,432	9717	85%

^a Ratio HFRa to HFR for each case, except for average energies, where values are the difference of HFRa minus HFR for each case.

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

New Energy Levels and Transitions of 5s²5p² (6d+7s) Configurations in Xe IV

Abstract

1. Introduction

2. Experimental Methods

3. Results and Discussion

4. Conclusions

Author Contributions

Funding

Acknowledgments

Conflicts of Interest

References

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