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Atoms 2017, 5(3), 24; doi:10.3390/atoms5030024

Article
Spectrum of Singly Charged Uranium (U II) : Theoretical Interpretation of Energy Levels, Partition Function and Classified Ultraviolet Lines
Ali Meftah 1,2, Mourad Sabri 1, Jean-François Wyart 2,3 and Wan-Ü Lydia Tchang-Brillet 2,4,*
1
Laboratoire de Physique et Chimie Quantique, Université Mouloud Mammeri, BP 17 RP, 15000 Tizi-Ouzou, Algeria
2
LERMA, Observatoire de Paris, PSL Research University, CNRS, F-92195 Meudon, France
3
Laboratoire Aimé Cotton, CNRS UMR9188, Université Paris-Sud, ENS Cachan, Université Paris-Saclay, Bâtiment 505, F-91405 Orsay Cedex, France
4
Sorbonne Université, UPMC Université Paris 06, LERMA, F-75005 Paris, France
*
Correspondence: Tel.: +33-145-077-576
Academic Editor: Joseph Reader
Received: 23 March 2017 / Accepted: 16 June 2017 / Published: 26 June 2017

Abstract

:
In an attempt to improve U II analysis, the lowest configurations of both parities have been interpreted by means of the Racah-Slater parametric method, using Cowan codes. In the odd parity, including the ground state, 253 levels of the interacting configurations 5 f 3 7 s 2 + 5 f 3 6 d 7 s + 5 f 3 6 d 2 + 5 f 4 7 p + 5 f 5 are interpreted by 24 free parameters and 64 constrained ones, with a root mean square (rms) deviation of 60 cm 1 . In the even parity, the four known configurations 5 f 4 7 s , 5 f 4 6 d , 5 f 2 6 d 2 7 s , 5 f 2 6 d 7 s 2 and the unknown 5 f 2 6 d 3 form a basis for interpreting 125 levels with a rms deviation of 84 cm 1 . Due to perturbations, the theoretical description of the higher configurations 5 f 3 7 s 7 p + 5 f 3 6 d 7 p remains unsatisfactory. The known and predicted levels of U II are used for a determination of the partition function. The parametric study led us to a re-investigation of high resolution ultraviolet spectrum of uranium recorded at the Meudon Observatory in the late eighties, of which the analysis was unachieved. In the course of the present study, a number of 451 lines of U II has been classified in the region 2344–2955 Å. One new level has been established as 5 f 3 6 d 7 p ( 4 I ) 6 K ( J = 5.5 ) at 39113.98 ± 0.1 cm 1 .
Keywords:
uranium; actinide ions; emission spectrum; energy levels; energy parameters; partition function

1. Introduction

The spectroscopy of uranium is of interest in many respects. Being the element with the highest atomic number (Z = 92) naturally available, the nuclear decay of 238 U provides a tool for the evaluation of the age of the Universe [1]. In the astrophysical plasma models, the ionized uranium (U II) transition at 3859.572 Å ( 5 f 3 6 d 7 s 6 L 11 / 2 5 f 3 6 d 7 p 6 M 13 / 2 ) is used for the diagnostics. Not only are specific radiative data for this transition needed, but so are partition functions that depend on energy levels relative to the ground level 5 f 3 7 s 2 4 I 9 / 2 . Therefore a comprehensive picture of the level scheme in ionized uranium is desired. For U II, as for other complex spectra of heavy elements, the interpretation of the observed emission lines does not allow a complete determination of the energy level scheme. Nevertheless, by application of the Racah-Slater parametric method, the energy parameters adjusted against known experimental energy values E e x p should lead to improved predictions of energies E t h for the levels left undetermined. The relevance of the methods that were used with success in lower-Z elements [2] was confirmed in the cases of several higher-Z elements, including thorium [3,4], despite the fact that the non-relativistic perturbative model was primarily unsatisfactory for these heavy systems. Due to the limited computer capacities in the early times, the previous calculations on U II [5,6] had to neglect configuration interaction (CI) effects or to use truncated bases of configurations. Therefore, the necessary limitation of core configurations 5 f 3 and 5 f 4 to their lowest L S terms impaired the calculated energies and wave functions for the 5 f 3 l l and 5 f 4 l levels, consequence of the large spin-orbit interactions and the intermediate coupling conditions.
The critical compilation of energy levels and spectra of actinides published in 1992 by Blaise and Wyart [3] provided preliminary tables of energy levels of both parities in U II. The compilation of U II was based on emission data from Steinhaus et al. [7] and on new FTS measurements by Palmer et al. [8]. In particular, energy values of the lowest levels of configurations involving 5 f , 6 d , 7 s , 7 p electrons were reported, thus updating the previous estimates by Brewer [9]. The list of experimental energy levels in U II was further extended by Blaise et al. [6]. Although the earlier calculations [5,6] usefully supported the search for energy levels, it is worth taking advantage of the present possibilities of Cowan codes [10,11] implemented on modern computers for improving the interpretation of the level scheme in U II, and more generally in actinides. This is the main purpose of the present work.
On the experimental side, a set of uranium emission spectra in the ultraviolet range (1000–3000 Å) recorded in the late eighties at the Meudon Observatory was available at the beginning of the present work. The original aim of these recordings, involving one of the present authors (JFW), was to support the critical compilation of the U III spectrum in Blaise and Wyart [3] by supplementing the Fourier Transform measurements [12] in the range (2000 Å– 4 μ ) with data in the shorter wavelength range. However the spectrograms had been only partly measured and had never been completely analyzed, leaving most of the experimental material unpublished. Only improvements for U III were reported in an EGAS conference [13] and in the compilation [3]. The analysis of the unknown spectrum of U IV was also planned but never initiated. With the recent publication of IR data on uranium [14], these unused ultraviolet data represent an opportunity for a new step in a comprehensive description of ionized uranium emission spectra.

2. Available Experimental Data

The available experimental spectra in the wavelength range 1000–3000 Å were emitted by a vacuum triggered spark source with uranium electrode and recorded on photographic plates using the high-resolution 10.7 m normal incidence vacuum ultraviolet spectrograph of the Meudon Observatory. The spectrograph is equipped with a 3600 lines/mm holographic concave grating, leading to a linear dispersion of 0.26 Å/mm on the plates. At the time of the experiment, only partial measurement of the plates was carried out on a semi-automatic comparator (microdensitometer). Wavelength calibration was insured by external reference lines in a superimposed spectrum from a iron Penning discharge source. In addition to U III lines, the spectrograms contain known lines from U V [15] and U VI [16], and a number of unidentified lines. Among the last ones, many likely belong to the unknown U IV spectrum. Although the discharge conditions were favorable for producing more than doubly charged ions, many sharp lines were present at the long wavelength end, which we presumed to belong to U II. In the present work, more complete measurements have been resumed for the wavelength range 2250–2955 Å, by digitizing the spectral plates using a flatbed scanner. The plates were scanned simultaneously with a precision ruler with markings every 1 mm, allowing interpolation between markings for correction of possible distortions, as described in [17]. Then the positions of lines were determined by superimposing two symmetrical profiles of the line displayed by a “homemade” software that mimics the rotating prism set-up of the comparator [18]. For wavelength calibration, internal standards were preferred. These were chosen among the U III wavelengths from Fourier Transform Spectrometry (FTS) [12] and the U II Ritz wavelengths calculated from level energies determined by FTS [6]. For the wavelength range shorter than 2350 Å, some U V wavelengths [15] were used. The uncertainty of the wavelength measurements varies between ± 0.001 and ± 0.003 Å.
Figure 1 shows a section of the triggered spark spectrum between 2863–2875Å. The shape of the lines, from relatively sharp (for U II) to hazy (for U IV) may be attributed to Doppler broadening as higher charged ions are produced in hotter part of the sparks. Identified U II lines are numbered. The numbers and corresponding wavelengths can be found in Table 9.

3. Theoretical Interpretation of the Energy Levels

Figure 2 shows a diagram of U II configurations of both parities included in the present study. The energy levels spread as predicted by ab initio calculations in the Relativistic Hartree-Fock mode (Cf text below).
We started our work from the energy values tabulated in the final publication on U II [6]. Table 1 recalls the account of various observables available in [6] used for checking the validity of theoretical calculations. The lowest levels of configurations with 5 f , 6 d , 7 s and 7 p electrons, as determined in [6], may be supplemented by predictions for unknown configurations given in [3] according to Brewer’s work [9]. This guided our choice of the bases of interacting electronic configurations.

3.1. Odd Parity Levels

The present work benefited from the similarities between lanthanides and actinides elements. In the periodic table of elements, neodymium occupies the same position in the lanthanide row as does uranium in the actinide row. Similarities between the two spectra do exist, although configurations built on the 5 f 3 core are much lower relative to the core 5 f 4 in U II than are those built on 4 f 3 relative to 4 f 4 in Nd II.
In Nd II, the basis set of overlapping odd configurations 4 f 3 5 d 6 s + 4 f 3 5 d 2 + 4 f 3 6 s 2 + 4 f 4 6 p + 4 f 5 was adopted for the parametric interpretation of 596 energy levels of these configurations [19,20] by means of the Cowan’s codes [10,11]. It had been proven to be adequate by a root mean square (rms) deviation as small as 53 cm 1 . Since in U II the corresponding configurations (with principal quantum numbers increased by one) are also the lowest ones in the parity, we used the same basis set for resuming the calculation of odd parity levels, including the lowest odd parity levels listed in [6]. However, in the case of U II, the 5 f 5 configuration is unknown but is involved by electrostatic interaction with the 5 f 3 6 d 2 configuration. The next higher unknown configuration 5 f 2 6 d 7 s 7 p was not included in the basis. Since its lowest level is expected at 38000 ± 5000 cm 1 above the ground state, according to Brewer’s estimates [9], it should not overlap the other odd levels included in the calculation, although CI repulsion effects could be present.
In the first step of the calculation, the R C N and R C N 2 codes were used in the Relativistic Hartree-Fock ( H F R ) mode. The electrostatic and spin-orbit radial integrals were then scaled with factors obtained as averages from earlier actinide calculations [4] and helped for generating the set of parameters for the first diagonalization by the R C G code. Appropriate corrections on the average energy E a v parameters were made for establishing a fair correspondence between calculated and experimental energies and Landé factors [6] for the low levels of f 3 d s , f 3 d 2 and f 3 s 2 . Then the iterative Least Squares Fit (LSF) of the energy parameters was performed by means of the R C E code, minimizing the rms deviation Δ E = i ( E i e x p E i t h ) 2 / ( N i N p ) , where N i and N p are respectively the number of experimental energies and the number of free parameters, with a few dozens of experimental energies to start. Constraints on the parameters were applied for preventing uncontrolled divergence problems. Step by step, the number of levels in the fit was increased up to 253 with a final r m s deviation of 60 cm 1 . Final values for 22 free parameters and 64 constrained ones are reported in Table 2. The electrostatic and spin-orbit integrals are listed with their fitted values and their H F R values from which the scaling factors S F ( P ) = P f i t / P H F R are derived. In addition to the explicit CI effects, second order CI effects of distant configurations have been taken into account by using effective parameters. These are α , β and γ for the 5 f n core configurations and Slater forbidden parameters for 5 f n n l (enabled by a specific option of the R C G code). Their initial values were chosen semi-empirically by comparison with earlier works [4].
The comparison of experimental and calculated levels is given in Table 3, which is ordered by increasing theoretical energies E t h . One may notice that leading L S components of eigenfunctions often represent a small part of the total wave functions. As an example, the eigenfunction of the level at E e x p = 8379.697 cm 1 has three leading components representing respectively only 14, 11 and 10 percent of the total wavefunction. However, the calculation seems correct, as shown by the small deviations for both energies and Landé factors: E e x p –E t h = 22 cm 1 and g e x p – g t h = 0.002. At higher energies, in the bulk of calculated levels, it occurs that leading L S components become as small as 3% only. Considering that the configuration sharing is more meaningful than tiny term components, we have summed the squared amplitudes in the wave functions separately for the 5 configurations. The dominant configuration and its percentage are respectively reported in the last two columns of the table.
Below 20,000 cm 1 , it was possible to establish a reliable correspondence between experimental and theoretical energies for the LSF procedure, which was generally supported by agreement between g t h and g e x p Landé factors, when availabie [6]. However, a few exceptions have been observed. As an example, the two J = 7.5 levels at 8394.362 and 8521.922 cm 1 were previously [6] assigned respectively as f 3 d 2 6 M 15 / 2 and f 3 d s 6 K 15 / 2 , based on the empirical identification of Landé factors and isotope shifts. In the present work, the initial HFR step predicted these two levels in an inverted order of energies at respectively 8536 and 8438 cm 1 , with strongly mixed eigenfunctions. Furthermore, the LSF following this inverted order led to smaller deviations, although physically unsatisfactory. Therefore this order has been adopted in Table 3. Above 20,000 cm 1 Landé factors are missing for a majority of levels and the quantum number J is reported as ambiguous for some of them. Since the correspondence between calculated and experimental energies becomes uncertain as energy increases, identifications above 25,726 cm 1 are not reported here.
At an intermediate step of the parametric fitting, the previously assigned J value, J = 11 / 2 , of the level E e x p = 13,695.737 cm 1 raised questions. It was found that on one hand, no other level with J = 11 / 2 was predicted between the two experimental levels at 13,270.612 and 13,961.850 cm 1 , and on the other hand, one J = 9 / 2 level was missing between E e x p = 13,450.490 and 14,265.976 cm 1 . The possibility for correcting the J-value for E e x p = 13,695.737 was thus examined. Indeed, while a J = 11 / 2 attribution can be justified by only one unique transition with a J = 13 / 2 even level, a J = 9 / 2 value is supported by 16 lines of [7] and by two unidentified lines from the infrared line list of [14] that fit transitions with J = 7 / 2 even levels. Table 4 collects the transitions supporting the present assignation of a J = 9 / 2 for this level. Similar ambiguity for some other levels led us to be cautious and to avoid inclusion of too many E e x p values in the LSF fitting process with no other reason but a small Δ E value.

3.2. Even Parity Levels

Similarly to the odd parity study, the R C N and R C N 2 codes were used in the Relativistic Hartree-Fock ( H F R ) mode. Considering the large CI interaction integrals within the group 5 f 2 ( 6 d + 7 s ) 3 , the previously undetermined configuration 5 f 2 6 d 3 was added to the four lowest configurations 5 f 4 7 s , 5 f 4 6 d , 5 f 2 6 d 2 7 s , 5 f 2 6 d 7 s 2 . Appropriate scaling of Slater and spin-orbit integrals and corrections on the average energy parameters were applied for preparing the initial input data of the R C G code and of the LSF in the R C E code. In the final cycle of optimization, 125 levels and 22 free parameters led to a rms deviation of 84 cm 1 , i.e., which is less satisfactory than in the odd parity. One of these levels, given at E e x p = 22917.453 cm 1 without any label in [6] has been identified as the lowest level of the 5 f 2 6 d 3 configuration, slightly above the error bars of Brewer’s predictions [9]. It is seen that the scaling factors of fitted parameters reported in Table 5 are not very different from those obtained in the opposite parity (Table 2). With regard to the unachieved status of the parametric interpretation in the even parity, only the dominant configuration and the first component of the eigenfunctions are given in Table 6, together with the energies and Landé factors calculated in the final LSF.
Attempts to interpret 5 f 3 7 s 7 p + 5 f 3 6 d 7 p with the same method of parametric fitting could not go beyond the optimization of the average energy E a v and spin-orbit ζ 5 f parameters. In Table 7 energy parameters adopted for 5 f 3 7 s 7 p + 5 f 3 6 d 7 p are reported and they lead to the calculated energies in Table 8. The empirical attribution of E e x p levels to configurations derived from isotope shifts and transition intensities in [6] are not fully supported by the present calculations. There were more 5 f 3 7 s 7 p labels in Table 2 of [6] than predicted from the present work (Cf Table 8). The quantitative evaluation of the C I effects within the whole group 5 f 4 ( 7 s + 6 d ) + 5 f 2 ( 6 d + 7 s ) 3 + 5 f 3 7 s 7 p + 5 f 3 6 d 7 p has been attempted but has failed.

3.3. Partition Function

To get an idea of how semi-empirical parametric calculations could influence the value of the partition function Q ( T ) = i ( 2 J i + 1 ) e x p ( E i / k B T ) ( k B : Boltzmann constant), we made an estimation of the partition function of U II for a typical stellar temperature. The temperature chosen is 4825 K ( k B T = 3353.54 cm 1 ), which is the temperature quoted by Cayrel et al. [1] for a metal-poor star showing the U II line at 3859.57 Å in its spectrum.
Since experimental levels are incompletely determined, a partition function calculated with only known experimental energies would be underestimated. Therefore we calculated the partition function with all the available experimental energies supplemented by the final least squares fitted energies when experimental ones are missing. In the expression of the partition function we included all the levels below 46 000 cm 1 of both parities. The result is : Q e x p / L S F ( T ) = 122.99, which is the best value possible in the present case. When the partition function is calculated with the same number of levels, but with all the fitted energies, the result is: Q L S F (T) = 120.99, which agrees with Q e x p / L S F ( T ) within 2%. When ab initio HFR energy values are used, we have Q H F R (T) = 89.19, which is 26% smaller. Consequently, in absence of complete experimental level energies, the energies calculated from fitted parameters provide a realistic estimation of the partition function.

3.4. Transition Probabilities

The parametric calculations provide gA values for transition probabilities (g: upper level statistical weight; A: Einstein coefficient of spontaneous emission) between calculated levels. Extensive comparison with experimental transition probabilities is not possible because of the scarcity of measurements. Furthermore, because of the strongly mixed wave functions, weak transitions are sensitive to small changes of energy parameters and may not be reliable for comparison. Nevertheless, it is interesting to consider the line at 3859.6 Å, which is strong and used as cosmochronometer [1]. Chen and Borzileri [21] measured the gA value for this line and found 2.8 × 10 8 s 1 , to be compared with previous measurement 1.1 × 10 8 s 1 by Corliss [22]. Nilsson et al. [23] derived branching ratios from relative intensities measured in FTS spectra and combined with radiative lifetime of the upper level at 26191 cm 1 to find a g l f value of 0.856 for the oscillator strength weighted by the lower level degeneracy. The corresponding gA value (Equation (1) of [23]) is 3.8 × 10 8 s 1 in agreement with the value of 3.5 × 10 8 s 1 calculated by Kurucz [24]. Our calculations lead to gA = 1.53 × 10 9 s 1 , four times larger, but they confirm the order of magnitude. However, the parametric study for the high even levels of 5 f 3 7 s 7 p + 5 f 3 6 d 7 p is still unachieved, since treated without all the interacting even configurations. Its results should be taken with caution.

4. Classified Lines of U II in the Ultraviolet

On our spectrograms described in Section 2, some lines were relatively sharp and were likely emitted by singly charged uranium ions. For identification of U II lines, we searched experimental wave numbers matching the Ritz wave numbers calculated from the energy differences of known U II energy levels reported in [6], even when the level was not assigned with quantum numbers. The maximum uncertainty of the wavelength measurements is estimated to be ± 0.003 Å . Thus the corresponding uncertainty on wave numbers should be less than ± 0.05 cm 1 . To take into account any possible perturbations in the spark spectrum, we chose a tolerance of ± 0.1 cm 1 for a criterion of identification. Indeed, according to [14], the level energies in [6], therefore the Ritz wave numbers, have negligible uncertainties of about ± 0.01 cm 1 . Table 9 lists the 451 lines between 2344 and 2955 Å identified as U II transitions, with calculated Ritz wavelengths, experimental wavelengths, deviations exp-Ritz and line intensities, together with the corresponding upper and lower levels. One line has triple identification and 24 lines have double identification. These concern mostly lines with two deviations of opposite signs. Otherwise, the line with the smallest deviation is retained. No gA values were available here for confirmation of identifications since the even levels involved in these transitions have only experimental energy values but no quantum numbers assigned except the J values.
Search of new levels of 5 f 3 6 d 7 p close to the predicted energies of Table 8 was attempted using the possible U II lines left unidentified. Unfortunately, only one chain of transitions supported by calculated transition probabilities could be found leading to a level 5 f 3 6 d 7 p ( 4 I ) 6 K with J = 5.5 at 39113.98 ± 0.1 cm 1 . Table 10 lists the six transitions that establish this level.

5. Conclusions

The lowest energy levels of the singly ionized uranium are interpreted following the Racah-Slater parametric method by means of Cowan codes. In the odd parity, the number of interpreted levels is about ten times larger than the number of free parameters. The relatively small rms deviation of the energies and the deviations between g L t h and g L e x p Landé factors for many levels show that the present model is robust. Some experimental level energies, although supported by the high accuracy of the observed FTS wave numbers, could not be attributed unambiguously to a theoretical level energy. The limitations of the present theoretical description are even more obvious in the even parity with larger rms deviations on the energies for both groups of configurations studied. After 70 years of investigations, the spectrum of U II still deserves further experimental studies for removing uncertain interpretations. The main difficulties are due to the ambiguities on the J values of levels, the determination of which would need a more complete study of Zeeman effect. Furthermore, the description of the strongly mixed CI wave functions could only be confirmed by the value of the Landé factor. By remembering the sentence Levels without known g values are less certain because of the possibilities of fortuitous coincidences written in [6], we do consider that the present calculations are satisfactory in spite the uninterpreted levels. A theoretical interpretation of the core configurations 5 f 4 and 5 f 3 ( 6 d + 7 s ) of U III is presently under way for a better knowledge of appropriate scaling factors of the H F R radial integrals to be used in U II. An estimate of the partition function shows that level energies from parametric fit are preferable for its calculation. On the experimental side, a list of 451 ultraviolet spectral lines from high resolution vacuum spark spectra identified as U II transitions is reported, as well as six other transitions establishing a new energy level in the even parity configuration 5 f 3 6 d 7 p .

Acknowledgments

The photographic spectrograms were recorded between 1986 and 1988 with technical assistance of Françoise Launay and Maurice Benharrous. Christophe Blaess is acknowledged for digitizing the spectrograms. The financial support of the French CNRS – PNPS national program is acknowledged. This work is part of the Plas@Par LabEx project managed by the ANR (ANR-11-IDEX-0004-02). AM and MS wish to acknowledge supports from Université Mouloud Mammeri, Tizi-Ouzou, Algeria and from the project CNEPRU D00520110032, Algeria.

Author Contributions

These authors contributed equally to this work.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Section of a vacuum triggered spark spectrum (2863–2875 Å). Downward arrows: the U II lines identified in the present work, their numbers and corresponding wavelengths can be found in Table 9; Upward arrows: U III lines from [12]; x: Unidentified lines, likely from U IV. The superimposed iron spectrum is visible above the uranium spectrum but not used in the present work.
Figure 1. Section of a vacuum triggered spark spectrum (2863–2875 Å). Downward arrows: the U II lines identified in the present work, their numbers and corresponding wavelengths can be found in Table 9; Upward arrows: U III lines from [12]; x: Unidentified lines, likely from U IV. The superimposed iron spectrum is visible above the uranium spectrum but not used in the present work.
Atoms 05 00024 g001
Figure 2. Energy levels of U II belonging to the configurations included in the present study as predicted by ab initio HFR calculations. (a) Odd parity configurations. (b) Even parity configurations.
Figure 2. Energy levels of U II belonging to the configurations included in the present study as predicted by ab initio HFR calculations. (a) Odd parity configurations. (b) Even parity configurations.
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Table 1. Summary of experimental data available for the parametric interpretation of U II levels. N t o t : total number of levels; N Z E : number of levels with Landé factor measured by Zeeman effect, N I S : number of levels with measured isotope shift; N i d e n t : number of levels with empirical identification. The number of classified lines per level was not given in [6].
Table 1. Summary of experimental data available for the parametric interpretation of U II levels. N t o t : total number of levels; N Z E : number of levels with Landé factor measured by Zeeman effect, N I S : number of levels with measured isotope shift; N i d e n t : number of levels with empirical identification. The number of classified lines per level was not given in [6].
Odd Parity LevelsEven Parity Levels
N t o t 354809
N Z E 137355
N I S 114401
N i d e n t 109113
Table 2. Fitted parameters (in cm 1 ) for odd parity configurations of U II compared with HFR radial integrals. The scaling factors S F ( P ) = P f i t / P H F R (dimensionless) are replaced by Δ E = E f i t E H F R for E a v average energies (in cm 1 ). Constraints on some parameters are in the second column under ’Cstr.’ (denoted ’f’ for fixed parameters or ’rn’ , which link parameters of the same ’rn’ to vary in a constant ratio). The H F R values of E a v parameters are relative to the ground state configuration 5 f 3 7 s 2 taken as zero value.
Table 2. Fitted parameters (in cm 1 ) for odd parity configurations of U II compared with HFR radial integrals. The scaling factors S F ( P ) = P f i t / P H F R (dimensionless) are replaced by Δ E = E f i t E H F R for E a v average energies (in cm 1 ). Constraints on some parameters are in the second column under ’Cstr.’ (denoted ’f’ for fixed parameters or ’rn’ , which link parameters of the same ’rn’ to vary in a constant ratio). The H F R values of E a v parameters are relative to the ground state configuration 5 f 3 7 s 2 taken as zero value.
5 f 3 7 s 2 5f 3 6 d 7 s 5f 3 6 d 2
Param. P Cstr. P fit Unc. P HFR Δ E / SF P fit Unc. P HFR Δ E / SF P fit Unc. P HFR Δ E / SF
E a v 2271154022711301413547162542541875291545926916
F 2 ( f f ) r147923244701590.68347163241690470.68346426237679690.683
F 4 ( f f ) r231974437454480.70431411429446480.70430868422438770.704
F 6 ( f f ) r321971563332100.66221568552326010.66221180542320150.662
α r436.31 36.31 36.31
β f−600 −600 −600
γ f1500 1500 1500
F 2 ( d d ) 23885401339220.704
F 4 ( d d ) 12305782223070.551
α d 2 f 10
ζ f r51732.441868.50.9271705.741839.80.9271681.241813.40.927
ζ d r6 1531.8141793.10.8541410.4131650.90.854
F 1 ( f d ) r7 880202 880202
F 2 ( f d ) r8 19605205280260.70018724196267660.700
F 4 ( f d ) r9 13940363151510.92013251345144040.920
G 1 ( f d ) r10 1130481181560.6231099578176600.623
G 2 ( f d ) r11 833295 833295
G 3 ( f d ) r12 11699227130540.89611236218125350.896
G 4 ( f d ) r13 2858355 2858355
G 5 ( f d ) r14 805435396820.832769633792500.832
G 3 ( f s ) 25838841980.615
G 2 ( d s ) 13609247210810.646
5 f 4 7 p 5f 5
Param. P Cstr. P fit Unc. P HFR Δ E / SF Cstr. P fit Unc. P HFR Δ E / SF
E a v 601581964294317215f61000 584562544
F 2 ( f f ) r143973224643760.683f38003 554780.686
F 4 ( f f ) r229072397413230.704f24513 351180.691
F 6 ( f f ) r319894509300710.662f17151 254100.675
α r437.71 36.51
β f−600 −600
γ f1500 1500
ζ f r51550.441672.20.927 1333.531437.90.927
ζ p f3325.82093293.71.01
F 1 ( f p ) f100
F 2 ( f p ) f7215 80160.900
G 2 ( f p ) f2058 20581.000
G 4 ( f p ) f1800 18001.000
Param. P Cstr. P fit Unc. P HFR Δ E / SF
Configuration Interaction
5 f 3 7 s 2 5 f 3 6 d 7 s
R 2 ( f s , f d ) r15−661471−101040.65
R 3 ( f s , d f ) r15−144215−22040.65
5 f 3 s 2 5 f 3 d 2
R 2 ( s s , d d ) r1514670157224120.65
5 f 3 7 s 2 5 f 5
R 3 ( s s , f f ) r1545164869000.65
5 f 3 6 d 7 s 5 f 3 6 d 2
R 2 ( f s , f d ) r15−660571−99550.65
R 3 ( f s , d f ) r15−150016−22840.65
R 2 ( d s , d d ) r15−16091172−245840.65
5 f 3 6 d 7 s 5 f 4 7 p
R 1 ( d s , f p ) r15−9384101−143370.65
R 3 ( d s , p f ) r15−280530−42860.65
5 f 3 6 d 7 s 5 f 5
R 3 ( d s , f f ) r15−350738−53570.65
5 f 3 6 d 2 5 f 4 7 p
R 1 ( d d , f p ) r1555806085260.66
R 3 ( d d , f p ) r1524902738050.66
5 f 3 6 d 2 5 f 5
R 1 ( d d , f f ) r1515269164233260.66
R 3 ( d d , f f ) r1510171109155370.66
R 5 ( d d , f f ) r15732578111910.66
5 f 4 7 p 5 f 5
R 2 ( f p , f f ) r15−288731−44100.66
R 4 ( f p , f f ) r15−250127−38210.66
Table 3. Energy levels of U II, odd parity. Comparison of experimental energies and Landé factors with values calculated from the parameter set of Table 2. Δ E = E e x p E t h . The percentage of the leading term (notations from Cowan codes) and its configuration are specified by columns 7–9. The dominant configuration and its percentage are reported in the last two columns.
Table 3. Energy levels of U II, odd parity. Comparison of experimental energies and Landé factors with values calculated from the parameter set of Table 2. Δ E = E e x p E t h . The percentage of the leading term (notations from Cowan codes) and its configuration are specified by columns 7–9. The dominant configuration and its percentage are reported in the last two columns.
J E exp
( cm 1 )
E th
( cm 1 )
Δ E
( cm 1 )
g L th g L exp % 1 st comp Conf Term Main conf %
4.50.000−56.8560.7560.76577f3s2(4I)4If3s291.7
5.5289.041224.4640.6560.65577f3ds(4I)6Lf3ds99.9
4.5914.765930.2−150.6040.60571f3ds(4I)6Kf3ds96.2
6.51749.1231715.5330.8640.86545f3ds(4I)6Lf3ds93.8
5.52294.6962320.7−260.8680.86547f3ds(4I)6Kf3ds97.5
5.54420.8714406.4140.9710.9789f3s2(4I)4If3s293.6
6.54585.4344577.970.7930.78528f3d2(4I)6Mf3d251.8
2.54706.2734674.8310.4770.48033f3ds(4I)6Hf3ds96.8
7.55259.6535247.0121.0071.01568f3ds(4I)6Lf3ds97.6
3.55401.5035352.6480.7670.69026f3ds(4I)6If3ds98.0
6.55526.7505549.1−221.0191.02070f3ds(4I)6Kf3ds98.3
3.55667.3315695.5−280.6570.73551f3ds(4I)6If3ds96.9
5.55790.6415827.3−360.8510.86039f3ds(4I)6Kf3ds95.5
6.56283.4316392.9−1090.7850.79039f3d2(4I)6Mf3ds54.5
4.56445.0356471.2−260.8350.84043f3ds(4I)6If3ds97.6
0.5 6999.4 2.398 20f3ds(4F)4Paf3ds97.8
1.57017.1727096.0−780.6120.62058f3s2(4F)4Ff3s290.8
4.57166.6327259.7−930.9450.94020f3ds(4I)6Hf3ds94.9
5.57598.3537626.3−270.9710.98018f3ds(4I)4Iaf3ds98.0
3.57547.3747629.2−810.8020.79021f3ds(4I)4Haf3ds84.8
6.58276.7338248.0281.0931.09084f3s2(4I)4If3s289.9
4.58379.6978357.5220.8410.84014f3ds(4I)6If3ds76.1
1.58400.1258426.1−250.0860.15068f3ds(4I)6Gf3ds97.7
2.58430.1858432.6−20.7190.72038f3ds(4I)6Gf3ds94.3
7.58394.3628437.9−431.0520.96055f3ds(4I)6Kf3ds74.2
5.58510.8668446.9630.8540.86011f3ds(4I)4Kbf3ds78.7
7.58521.9228535.6−130.9681.06041f3d2(4I)6Mf3d257.1
6.58755.6408767.9−121.0421.04014f3ds(4I)4Lbf3ds92.2
8.58853.7488815.5381.1051.10583f3ds(4I)6Lf3ds98.6
3.59075.7329020.5550.8730.87015f3ds(4I)6Hf3ds68.6
2.59344.6259250.9930.7510.7925f3s2(4G)4Gf3s247.1
4.59241.9719254.9−121.0231.01512f3ds(4I)6Hf3ds77.6
5.59553.1879584.8−311.0531.06056f3ds(4I)6If3ds96.4
6.59626.1139637.3−110.9460.95039f3ds(4I)4Kbf3ds83.9
4.59690.6659707.7−170.9910.99510f3s2(2H)2H2f3ds60.9
1.59881.6189911.4−290.272 51f3ds(4F)6Gf3ds98.3
3.59933.2269916.5160.8230.8227f3ds(4I)4Hbf3ds88.1
4.59882.7269967.6−840.8780.87516f3s2(4I)4Ibf3ds43.9
2.510285.07210178.11060.4540.4235f3ds(4F)6Hf3ds93.1
7.510198.31210250.6−520.9680.96044f3ds(4I)4Lbf3ds79.5
2.510366.25310437.7−710.922 58f3s2(4F)4Ff3s268.1
3.510444.43210437.760.8780.86512f3ds(4F)4Hbf3ds74.7
1.5-10643.1 1.731 30f3ds(4F)6Df3ds97.8
5.510740.95810688.6520.6900.68568f3d2(4I)6Lf3d284.1
2.510732.08710867.1−1350.953 29f3ds(4F)6Gf3ds92.0
2.511350.71411227.91221.254 17f3ds(4F)6Df3ds95.3
1.5-11230.7 1.617 58f3s2(4S)4Sf3s291.6
3.511363.53711289.2741.033 13f3d2(4I)6Iaf3ds69.2
8.511382.32111330.6511.1791.18575f3ds(4I)6Kf3ds96.4
4.511544.67211426.01180.6730.69045f3d2(4I)6Kaf3d261.1
3.5-11571.9 0.994 23f3s2(4F)4Ff3s252.5
7.511708.48311664.6431.1751.17577f3s2(4I)4If3s292.2
3.511707.83511743.7−350.7810.70537f3ds(4G)6If3ds60.0
5.511784.95311809.2−241.097 36f3ds(4I)6Hf3ds97.0
6.511813.45011833.5−201.0081.0926f3ds(4I)6If3ds81.0
6.511787.31511841.2−531.0300.94037f3ds(4I)6If3ds83.9
4.511797.34311854.3−561.005 16f3ds(4I)6Gf3ds96.3
0.5-11902.1 1.361 22f3ds(4F)2Pf3ds95.6
2.512112.40212095.7160.957 10f3ds(4F)6Gf3ds94.6
4.512055.78812117.5−610.976 18f3ds(4G)6If3ds93.8
8.512033.37812121.2−871.0141.00578f3d2(4I)6Mf3d290.9
3.512092.31912161.5−690.823 22f3ds(4F)6Hf3ds86.6
9.512350.55512255.1951.1761.20089f3ds(4I)6Lf3ds99.0
1.5-12392.5 0.562 19f3ds(4G)4Faf3ds90.4
5.512530.61312519.6100.9871.00012f3d2(4I)6Kaf3ds74.9
6.512629.35512578.1511.0441.09523f3d2(4I)6Lf3ds65.8
3.512627.82612582.6450.965 24f3s2(4G)4Gf3ds49.3
7.512660.55912591.2691.0721.0158f3ds(4I)4Lbf3ds88.1
5.512638.06012690.0−510.997 14f3ds(4I)4Ibf3ds78.1
2.5-12691.9 0.713 33f3s2(4G)4Gf3ds47.4
4.512687.30812718.0−300.916 13f3d2(4I)6Iaf3d249.9
1.5-12891.3 0.905 8f3ds(4F)4Dbf3ds78.5
7.513015.83812958.6571.0701.12530f3ds(4I)4Kbf3ds96.0
3.513183.79313117.1660.982 22f3ds(4F)6Gf3ds70.5
2.5-13125.8 0.997 20f3ds(4F)6Gf3ds83.5
5.513089.59013133.0−430.9410.94034f3d2(4I)6Kaf3d253.3
4.513275.36513247.5270.956 15f3ds(4I)6Hf3ds78.9
5.513270.61213272.1−11.134 20f3ds(4I)6Gf3ds92.7
6.513344.19813275.1690.9050.91035f3d2(4I)6Lf3d260.6
3.513450.36213423.3270.979 19f3ds(4I)6Gf3ds80.0
4.513450.49013449.011.014 15f3ds(4G)6If3ds69.0
7.513503.31913524.3−201.1011.1319f3ds(4I)6If3ds87.2
4.513695.73713683.4121.058 21f3ds(4F)6Hf3ds85.3
3.513733.50013730.820.934 22f3ds(4F)6Gf3ds64.9
2.5-13751.0 0.638 17f3d2(4I)6Haf3ds61.8
0.5-13817.0 0.009 51f3ds(4F)6Ff3ds94.3
6.513975.27813932.4421.021 19f3ds(4I)2Kf3ds81.3
2.513967.81213944.8230.734 18f3ds(4I)4Gaf3ds87.9
5.513961.85013980.2−180.972 14f3ds(4I)4Ibf3ds63.9
3.514107.32914042.4640.829 16f3ds(4F)4Hbf3ds84.4
9.5-14049.9 1.232 72f3ds(4I)6Kf3ds97.9
1.5-14142.4 1.176 34f3ds(4F)6Ff3ds88.8
8.514177.72314148.0291.0721.08560f3ds(4I)4Lbf3ds86.1
4.514265.97614230.0351.110 17f3ds(4I)4Hbf3ds81.3
4.514366.88914399.2−321.078 8f3ds(4I)6Hf3ds90.1
1.5-14477.7 1.043 14f3ds(4S)6Df3ds65.8
6.5-14496.9 1.142 16f3ds(4I)4Iaf3ds96.8
6.514599.60014557.6420.934 17f3d2(4I)6Lf3d261.8
4.514654.18114628.3251.057 12f3ds(4F)6Gf3ds75.8
2.5-14660.8 0.777 17f3ds(4F)4Gbf3ds71.4
7.514724.77614738.1−131.1701.17034f3ds(4I)6If3ds96.5
5.514709.26614771.1−610.9250.92010f3ds(4I)4Kaf3ds49.4
3.514900.13414873.4261.010 7f3ds(4G)6Gf3ds84.7
0.5-14905.3 1.636 32f3ds(4S)6Df3ds92.3
4.5-14981.0 1.177 44f3s2(4F)4Ff3s271.3
6.514991.37714993.8−21.180 17f3ds(4F)6Hf3ds88.6
2.5-15013.4 1.198 13f3ds(4F)6Pf3ds89.2
3.515147.87815080.0670.989 9f3ds(4F)4Gbf3ds79.0
1.5-15205.3 1.007 10f3ds(4G)6Gf3ds66.4
5.515234.38315205.3291.058 7f3ds(4F)6Hf3ds78.7
2.5-15280.5 1.147 33f3ds(4F)6Ff3ds71.8
1.5-15308.6 1.985 55f3ds(4F)6Pf3ds93.4
5.515330.43415334.3−31.123 14f3ds(4I)6Gf3ds82.6
4.515413.34615397.6150.984 14f3ds(4G)6If3ds52.3
0.5-15411.9 0.611 25f3ds(4S)4Dbf3ds81.9
3.515587.28015423.31641.031 9f3ds(4I)4Gaf3ds63.2
5.515430.90015483.0−521.073 16f3s2(2H)2H2f3ds54.4
9.515534.86815604.8−691.0931.09589f3d2(4I)6Mf3ds97.5
7.515692.65515633.9581.005 62f3d2(4I)6Lf3d292.4
10.5-15655.2 1.230 91f3ds(4I)6Lf3ds99.7
8.515767.76215683.0841.200 36f3ds(4I)6If3ds96.2
3.5-15689.4 1.136 11f3ds(4F)6Pf3ds82.3
6.515717.45215736.5−191.0261.0435f3d2(4I)6Kaf3d269.0
5.515863.75515811.3521.027 14f3d2(4I)6Iaf3d251.9
4.515916.16615879.5360.971 28f3d2(4I)6Kbf3ds55.2
2.5-15883.4 0.628 10f3d2(4I)6Haf3d249.2
6.515884.56015900.5−151.0721.15012f3ds(4I)4Kaf3ds72.3
7.516156.48716066.8891.150 19f3ds(4I)6Hf3ds82.9
2.516213.94516073.41401.010 7f3ds(4G)2Ff3ds84.5
0.5-16099.202.345 32f3ds(4F)6Df3ds93.9
4.516063.24416101.2−370.889 21f3d2(4I)6Kbf3ds44.9
5.516003.16316120.1−1161.091 20f3ds(4G)6If3ds75.8
3.5-16140.4 1.052 15f3ds(4G)6Hf3ds75.0
1.5-16176.8 1.130 9f3ds(4F)4Paf3ds85.5
2.516336.51416281.8541.161 7f3ds(4F)6Pf3ds74.4
3.516239.75716285.9−461.230 14f3ds(4F)6Pf3ds83.5
4.516338.71916290.5481.040 6f3ds(4I)4Iaf3ds87.9
8.5-16419.3 1.098 22f3ds(4I)4Laf3ds78.7
3.516376.82016443.1−661.048 9f3ds(4I)4Gbf3ds63.7
6.516532.58916466.5661.043 14f3ds(4I)2If3ds77.6
1.5-16471.3 1.008 12f3ds(4F)2Df3ds86.2
2.516473.74716481.7−70.952 13f3ds(4F)6Ff3ds65.1
5.516397.82816490.5−921.045 13f3s2(2H)2H2f3ds51.3
1.5-16528.6 0.844 10f3s2(4D)4Df3ds49.5
4.516514.26516528.9−140.986 16f3s2(4G)4Gf3ds51.5
6.516618.36916650.2−310.987 60f3s2(2K)2Kf3s268.2
2.5-16660.2 1.339 22f3ds(4F)6Pf3ds80.3
3.516672.39916723.4−511.019 7f3ds(4G)6Gf3ds69.2
7.516690.21216731.2−400.986 14f3ds(2K)4Mf3ds51.9
4.516819.69416758.4611.033 11f3ds(4F)6Gf3ds68.2
5.516699.40916782.6−831.114 16f3ds(4I)6Hf3ds78.5
2.516838.25816808.1300.982 10f3ds(4G)6Hf3ds83.1
0.5-16830.2 0.230 14f3d2(4I)6Ff3d271.1
2.5-16867.1 1.060 8f3ds(4G)6Hf3ds58.8
3.516857.01516868.5−110.838 10f3d2(4F)6If3ds54.8
5.516758.02416899.5−1411.026 12f3ds(4I)4Kaf3ds65.5
8.516982.51016958.9231.143 22f3ds(4I)4Kbf3ds91.3
4.5-16964.3 1.026 11f3ds(4F)4Hbf3ds64.7
6.516990.27117005.7−151.118 12f3ds(4I)4Ibf3ds59.7
1.5-17006.8 0.859 9f3d2(4I)6Ff3ds55.0
2.517008.22917102.2−941.154 10f3ds(4F)6Df3ds84.7
3.5-17117.2 0.920 8f3ds(4G)4Hbf3ds60.7
5.517205.37217170.4341.120 28f3ds(4F)6Gf3ds76.8
1.5-17192.9 0.957 17f3ds(4F)2Pf3ds82.7
0.5-17217.5 0.499 30f3s2(2P)2Pf3s253.9
4.517200.90317280.6−790.9790.97010f3ds(4G)4Ibf3d250.5
7.517259.21617301.3−421.118 12f3ds(4I)4Ibf3ds79.9
2.5-17320.0 0.619 18f3ds(4G)6Hf3ds48.2
3.517381.93017363.1181.184 17f3ds(4F)6Df3ds84.2
1.5-17364.5 0.679 7f3ds(4F)4Faf3ds77.1
4.517388.63117392.7−41.010 13f3ds(4I)4Hbf3ds65.2
6.517461.88317423.5381.155 18f3ds(4I)6Gf3ds84.6
3.5-17481.4 1.163 15f3ds(4S)6Df3ds67.6
7.517556.77617523.7331.055 11f3d2(4I)6Lf3ds68.6
1.5-17579.4 0.960 15f3d2(4I)6Ff3ds57.4
2.517621.17517607.3130.941 5f3d2(4I)6Hbf3ds57.1
3.517560.92217619.6−580.991 10f3ds(4G)4Gbf3ds72.9
5.517755.02817785.9−301.050 11f3ds(2H)4K2f3ds84.0
6.517775.96017808.2−321.046 15f3d2(4I)6Kaf3d257.7
0.5-17812.2 0.076 13f3d2(4I)6Ff3ds51.0
3.517823.43417820.920.950 12f3d2(4F)6If3d251.4
2.5-17857.4 0.987 5f3s2(4D)4Df3d244.1
5.517922.76917934.8−120.973 11f3d2(4I)4Kaf3d265.0
6.517888.31217935.3−471.157 21f3ds(4F)6Hf3ds90.7
3.5-17959.5 0.963 12f3d2(4I)6Haf3ds48.7
4.518009.83817965.3441.119 12f3ds(4F)6Ff3ds71.6
9.5-17995.9 1.146 68f3ds(4I)4Lbf3ds81.7
8.518032.56418015.8161.044 25f3d2(4I)6Lf3d292.4
3.518041.43718095.3−530.913 9f3d2(4F)6If3ds51.0
2.518178.85418128.3501.074 5f3s2(4D)4Df3ds54.7
5.518102.95818150.0−471.117 7f3ds(4F)6Ff3ds79.1
4.5-18182.7 1.081 8f3d2(4I)6Haf3ds70.3
3.5-18232.9 0.974 7f3d2(4I)6Haf3d240.4
3.518291.41218326.3−340.893 19f3d2(4I)6Ibf3d263.0
1.5-18385.9 0.921 8f3ds(4F)6Ff3ds59.8
4.5-18424.3 1.061 8f3ds(4F)4Hbf3ds68.1
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7.518539.15418523.8151.098 10f3ds(4I)4Iaf3ds50.6
6.518451.97918576.6−1241.116 40f3ds(4G)6If3ds89.1
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1.5-18664.9 1.001 11f3ds(4F)4Pbf3ds57.2
2.518852.92218728.51241.145 5f3ds(4S)6Df3ds72.2
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6.518788.82718792.5−31.042 14f3d2(4I)4Laf3d267.4
8.5-18796.5 1.153 29f3ds(2H)4K2f3ds90.2
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5.519129.39419157.3−271.019 11f3ds(4I)4Gbf3ds62.9
8.519242.36419215.9261.042 48f3d2(4I)6Lf3d289.0
4.519237.39419219.6171.174 12f3s2(4G)4Gf3ds66.2
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4.519375.29219300.7741.031 11f3d2(4G)6Kf3ds58.0
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4.519627.05619598.3281.093 9f3d2(4G)6Kf3ds64.9
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1.5-19743.7 0.654 26f3d2(4I)6Gf3d248.0
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6.519694.32919779.6−851.023 9f3ds(2K)4Kf3ds61.3
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4.519869.60919841.7271.053 7f3d2(4I)6Hbf3d252.8
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4.520018.68519953.9640.910 28f3d2(4G)6Kf3d252.5
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3.520084.77520039.4450.978 6f3ds(4F)4Gbf3d245.1
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3.520263.43420107.41561.038 11f3d2(4F)6Hf3d254.8
7.520148.47420124.4240.985 18f3d2(4I)4Maf3d251.4
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0.5-20796.7 1.267 16f3ds(4G)6Df3ds65.5
4.520899.42920808.9901.065 8f3ds(4G)6Gf3ds61.3
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3.520890.42620965.3−741.130 9f3ds(4F)4Fbf3ds50.1
5.5-21022.3 1.084 7f3ds(2H> 2I2f3ds59.9
7.520946.23921023.1−761.008 23f3d2(4I)4Mbf3d279.4
4.521103.43221118.7−151.078 7f3d2(4F)6Hf3ds50.6
1.5-21159.6 0.906 11f3ds(4G)6Ff3ds54.0
3.521107.88121165.2−570.870 14f3d2(4G)6If3d249.3
7.5-21215.3 1.111 13f3ds(4F)6Hf3ds84.4
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1.5-21288.7 1.046 5f3ds(4S)6Df3ds71.5
4.521387.04021309.6770.940 9f3d2(4G)6If3d274.1
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8.5-21531.9 1.072 12f3ds(2K)4Mf3d258.7
2.5-21553.7 1.045 7f3ds(4D)6Ff3ds65.9
8.5-21582.8 1.058 24f3ds(4I)4Kbf3ds78.3
6.521645.93921597.3481.152 12f3d2(4I)6Haf3ds51.0
0.5-21604.6 0.518 11f3s2(2P)2Pf3ds44.8
9.5-21618.8 1.159 73f3d2(4I)6Lf3d299.9
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4.5-21656.8 1.177 21f3ds(2H)4F2f3ds82.7
5.5-21662.8 1.075 6f3d2(4I)6Hbf3d265.7
2.5-21718.6 1.114 7f3d2(4F)6Gaf3ds51.7
0.5-21721.7 0.048 14f3d2(4S)6Ff3d258.4
4.521793.33421750.4421.067 10f3d2(4F)6Gaf3d265.1
7.5-21768.7 1.100 9f3ds(2H)2K2f3ds92.0
6.5-21803.0 1.117 7f3ds(4I)4Haf3ds75.2
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4.5-21821.1 1.070 7f3d2(4G)6If3ds52.6
3.5-21855.1 1.096 6f3ds(2H> 2F2f3ds63.9
6.521858.43321863.2−41.015 31f3d2(4I)6Kbf3d280.9
2.5-21873.3 1.090 7f3ds(4F)4Pbf3ds70.7
5.5-21886.1 1.088 7f3ds(4F)4Gbf3ds53.7
2.5-21942.1 1.178 8f3d2(4F)6Pf3d270.4
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5.5-22123.0 1.023 14f3d2(4G)6Kf3d262.3
1.5-22127.9 1.207 88f3d2(4I)6Mf3d2100.
8.5-22150.9 1.120 16f3ds(4I)6If3ds84.2
3.5-22152.9 1.206 18f3ds(4G)6Ff3ds74.8
3.5-22197.0 1.101 8f3d2(4I)6Ff3d259.6
4.522230.45322197.0331.114 7f3s2(2G)2G1f3d241.3
6.5-22225.0 1.093 4f3ds(4G)6Gf3d251.3
2.5-22226.7 1.125 8f3ds(2H)4F2f3ds70.4
4.5-22262.3 0.943 8f3d2(4G)6If3ds49.9
1.5-22269.6 1.121 6f3ds(4D)6Df3d250.6
6.5-22273.6 1.086 10f3ds(4F)4Hbf3ds64.9
4.522305.30522289.0161.090 15f3ds(4I)2Gf3ds55.5
7.5-22300.7 1.062 15f3ds(4I)4Ibf3ds58.6
3.5-22350.7 0.985 9f3d2(4I)4Hcf3d261.8
4.5-22398.8 1.054 8f3s2(2G)2G1f3ds42.7
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3.5-22449.8 1.049 7f3ds(4G)6Gf3d250.1
5.5-22470.4 1.019 17f3d2(4G)6Kf3d278.5
5.522567.16722555.9111.080 11f3d2(4G)6Kf3d250.3
7.5-22582.5 1.220 23f3ds(4G)6Hf3ds68.3
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4.5-22604.6 1.115 5f3ds(4I)4Gaf3ds49.4
0.5-22620.1 0.894 11f3ds(4D)6Df3ds60.9
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6.5-22692.1 1.223 23f3ds(4G)6Gf3ds80.8
2.5-22693.8 1.021 6f3ds(2D)4F2f3ds61.9
5.5-22708.2 1.185 6f3ds(4G)6Gf3ds53.5
3.5-22729.6 1.131 7f3ds(4D)6Df3ds58.6
5.522813.79222788.4251.049 6f3ds(2K)4If3ds52.7
3.5-22793.4 1.215 8f3s2(4D)4Df3ds68.0
7.5-22819.3 1.048 12f3d2(4I)6Kbf3d264.3
6.5-22820.8 1.050 7f3ds(4G)4Ibf3ds55.7
0.5-22833.5 1.834 20f3ds(2D)2S1f3ds80.9
1.5-22833.8 1.287 9f3d2(4F)6Pf3d259.8
5.5-22851.9 1.043 7f3d2(4F)6If3d261.3
3.5-22857.0 1.182 7f3s2(4D)4Df3ds58.4
8.5-22888.2 1.135 34f3d2(4I)6Kaf3d282.6
1.5-22942.6 1.091 7f3ds(4G)6Df3ds72.5
3.5-22963.0 1.051 8f3ds(2H> 2F2f3ds64.5
2.5-22972.1 1.012 5f3ds(4G)4Fbf3ds62.2
1.5-22991.6 0.806 8f3d2(4F)6Gaf3ds51.1
4.5-23006.5 1.047 3f3d2(4I)6Ibf3d246.1
2.5-23031.6 1.181 4f3ds(2H> 2F2f3ds53.7
2.5-23062.2 1.204 14f3ds(4G)6Df3ds66.3
4.523106.35023094.0121.023 7f3d2(4G)6If3d263.8
6.523013.22223100.7−871.066 9f3ds(4G)6Hf3d253.5
8.5-23125.4 1.173 34f3ds(4G)6If3ds84.5
5.523043.89623135.7−911.111 11f3s2(4G)4Gf3ds49.8
0.5-23170.1 0.636 11f3d2(4F)6Faf3d253.0
5.5-23170.0 1.131 9f3ds(2H)4G2f3ds76.9
1.5-23225.8 1.043 5f3ds(2D)4P1f3ds54.4
3.5-23259.0 1.082 6f3d2(4F)6Fbf3d251.4
7.523371.61123282.8881.047 26f3d2(4I)6Kbf3d282.3
2.5-23293.3 0.964 5f3d2(4F)6Faf3ds48.9
9.5-23318.7 1.196 47f3d2(4I)6Kaf3d299.9
6.5-23329.5 1.092 7f3d2(4F)6Hf3d269.3
2.5-23330.0 1.174 6f3ds(2D)4P1f3ds73.2
1.5-23364.1 1.369 14f3d2(4F)6Pf3d249.4
0.5-23375.3 1.338 23f3ds(2D)2S1f3ds78.6
4.5-23397.0 1.097 11f3ds(4F)4Fbf3ds60.5
3.5-23461.6 1.152 6f3d2(4F)6Pf3d254.8
4.5-23474.8 1.020 13f3d2(4I)6Gf3d269.7
8.5-23507.1 1.032 28f3d2(4I)4Maf3d279.9
6.5-23534.5 1.060 5f3ds(2K)4Lf3ds53.0
2.5-23557.4 1.091 6f3d2(4I)6Ff3d245.6
5.523528.30523572.0−431.079 6f3d2(4F)6Hf3d259.3
3.5-23585.2 1.047 4f3ds(2H)4G2f3ds54.3
5.5-23594.8 1.146 9f3ds(2H)4H2f3ds56.3
3.5-23601.2 1.214 9f3ds(4G)6Df3ds51.7
1.5-23648.2 0.829 9f3ds(2D)4F1f3ds62.1
7.5-23651.9 1.084 15f3ds(2H)4K2f3ds75.8
5.5-23671.9 1.137 6f3d2(4F)6Gaf3d258.2
0.5-23688.3 0.487 15f3d2(4F)6Faf3ds49.3
4.5-23706.2 1.100 8f3d2(4I)6Gf3d258.8
3.5-23726.6 1.131 3f3ds(4D)6Ff3ds56.0
9.5-23730.0 1.088 41f3ds(2K)4Mf3ds99.9
6.5-23735.2 1.093 8f3d2(4F)6If3ds62.3
4.5-23760.6 1.112 10f3d2(4I)6Ff3d251.8
0.5-23774.7 0.513 14f3s2(4D)4Df3ds46.4
2.5-23811.4 0.973 9f3d2(4S)6Ff3d264.0
1.5-23813.8 0.906 15f3d2(4F)6Faf3d247.4
5.5-23814.8 1.095 5f3s2(4G)4Gf3d265.2
6.5-23819.7 1.094 5f3ds(4G)4Ibf3d251.7
7.5-23823.9 1.037 21f3d2(4I)4Mbf3d289.3
2.5-23844.1 1.166 5f3ds(2D)4P1f3ds62.3
6.5-23916.1 1.130 11f3d2(4I)6Ibf3d265.2
2.5-23926.4 1.092 6f3ds(4F)4Gaf3ds75.7
1.5-23940.0 0.948 6f3ds(4D)6Gf3ds65.3
3.5-23945.5 1.031 4f3d2(4G)6If3d252.2
4.523924.33323956.4−321.100 5f3ds(2K)4If3ds70.9
0.5-23978.6 1.410 10f3d2(4S)6Ff3d266.6
8.5-23985.8 0.995 13f3d2(4I)4Nf3d254.4
5.5-24014.6 1.150 11f3d2(4F)6Hf3ds49.7
5.5-24061.4 1.115 8f3ds(4G)6Ff3ds70.7
7.5-24091.8 1.123 10f3d2(4I)6Haf3d264.6
4.5-24098.6 1.129 7f3d2(4I)6Gf3ds50.5
1.5-24104.3 0.872 10f3d2(4F)6Gbf3ds43.9
5.5-24163.8 1.111 8f3ds(4G)4Gbf3ds54.0
3.5-24199.1 0.952 6f3d2(4I)4Hcf3d262.1
0.5-24202.1 0.767 9f3ds(2D)4P1f3ds61.4
2.5-24214.8 1.139 5f3ds(4F)4Dbf3ds62.7
3.5-24215.6 1.249 8f3ds(4G)6Ff3ds48.6
4.5-24232.9 1.084 11f3d2(4F)6Gaf3d258.8
6.5-24278.4 1.060 7f3d2(4G)6Kf3d264.9
9.5-24314.3 1.013 50f3d2(4I)4Nf3d299.9
2.5-24319.2 0.969 8f3d2(4G)6Haf3d257.6
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1.5-24369.2 1.084 6f3ds(2D)4P1f3ds53.5
4.5-24377.2 1.100 4f3ds(4F)2Hf3d263.1
5.5-24383.2 1.098 7f3ds(2K)4If3ds65.1
6.5-24388.0 1.063 10f3ds(2K)4Kf3ds57.9
3.5-24403.0 1.168 8f3ds(4D)6Gf3ds51.2
10.5-24433.6 1.209 71f3d2(4I)6Lf3d299.9
7.5-24441.5 1.077 12f3ds(2K)4Kf3ds53.7
1.5-24488.1 0.673 20f3d2(4F)6Gbf3d257.1
1.5-24505.5 1.121 5f3ds(2D)4P1f3ds65.9
4.524446.49124505.8−591.070 4f3d2(4I)2Haf3d247.6
3.5-24548.7 1.089 5f3ds(4D)4Gbf3ds53.8
2.5-24570.0 1.060 6f3d2(4I)4Gaf3d259.3
1.5-24602.0 1.162 9f3ds(4D)6Df3ds63.0
8.5-24605.5 1.069 19f3d2(4I)4Mbf3d258.0
4.5-24707.3 0.959 4f3d2(4I)4Ibf3ds46.1
5.524771.46324720.3511.096 7f3d2(4G)6If3ds58.6
6.5-24735.1 1.056 36f3d2(4G)6Kf3d291.9
2.5-24740.2 1.161 11f3ds(4G)4Dbf3d249.4
7.5-24754.0 1.125 8f3d2(4I)6Haf3d252.1
3.5-24790.7 1.124 4f3ds(4D)6Df3d255.0
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7.5-24851.5 1.093 10f3ds(2K)4Lf3ds53.1
3.5-24861.8 1.247 9f3ds(4G)6Df3ds60.8
2.5-24877.5 1.259 6f3ds(4D)6Df3ds53.9
1.5-24889.3 0.985 3f3d2(4F)6Faf3d254.6
5.5-24920.7 1.094 5f3ds(4G)6Ff3d258.8
4.524888.13224945.0−561.161 9f3ds(4G)6Ff3ds50.8
2.5-24964.3 1.135 5f3ds(2P)4Ff3ds52.9
6.5-24986.3 1.073 5f3d2(4G)6Kf3ds50.2
4.524984.71125008.7−231.023 3f3ds(2H)4I1f3ds57.1
8.5-25008.2 1.077 14f3d2(4I)6Iaf3d252.8
7.5-25019.1 1.182 11f3d2(4F)6Hf3d278.6
3.5-25045.7 1.077 4f3ds(2P)2Faf3d254.7
5.525111.92425063.7481.170 6f3ds(4F)4Gbf3ds56.2
3.5-25082.7 1.126 5f3ds(4G)6Gf3d249.5
1.5-25084.7 1.215 11f3d2(4F)6Daf3d256.5
6.5-25130.0 1.110 10f3ds(4G)6Hf3ds50.0
4.5-25154.2 1.173 7f3ds(2H> 2G2f3ds51.7
2.5-25158.7 1.017 8f3ds(2H)2F2f3d249.9
2.5-25179.5 1.213 5f3d2(4F)6Faf3d251.9
1.5-25219.2 0.913 7f3d2(4I)4Fbf3ds51.9
4.5-25236.5 1.036 9f3s2(2H)2H1f3ds48.1
5.525245.18325237.471.021 25f3d2(4G)6If3d271.9
8.5-25302.6 1.037 23f3d2(4I)4Mbf3d254.4
2.5-25320.0 1.094 8f3d2(4S)6Ff3d249.8
4.5-25325.8 1.152 6f3ds(4F)4Fbf3ds58.6
6.5-25376.5 1.091 8f3s2(2I)2If3d268.6
0.5-25379.7 1.245 11f3ds(4D)6Df3ds67.7
3.5-25396.3 1.018 5f3ds(4F)2Gf3d247.5
6.5-25411.7 1.092 9f3s2(2I)2If3d250.4
3.5-25453.7 1.070 4f3d2(4I)2Gf3d247.5
4.525439.10325463.6−241.076 5f3d2(4S)6Ff3d258.6
5.525423.49025476.5−530.977 7f3ds(2I)4Kf3d254.5
1.5-25482.2 1.014 8f3ds(2D)4S1f3ds53.0
3.5-25516.3 1.045 4f3d2(4G)6If3d256.6
0.5-25521.6 0.983 6f3ds(2D> 2P1f3ds53.1
5.525514.65625537.8−231.082 10f3ds(4G)2If3ds49.4
4.5-25545.5 1.169 12f3d2(4S)6Ff3d258.7
6.5-25558.5 1.096 7f3ds(4G)4Iaf3ds63.1
2.5-25582.3 1.134 9f3d2(4F)6Faf3ds53.6
2.5-25603.8 0.986 6f3ds(4D)4Fbf3d248.7
6.5-25647.8 1.088 42f3s2(2I)2If2s244.7
4.5-25665.7 1.137 4f3ds(4G)6Ff3d257.5
1.5-25666.4 1.063 7f3ds(4D)6Gf3d249.1
7.5-25671.0 1.079 7f3ds(2L)4Mf3ds67.3
5.525726.26025729.7−31.101 4f3d2(4I)6Gf3ds60.1
1.5-25754.9 1.030 6f3d2(4F)6Gbf3d264.2
Table 4. Transitions of the U II odd parity level at 13695.737 cm 1 with J = 4.5 to even levels of J = 3.5 .
Table 4. Transitions of the U II odd parity level at 13695.737 cm 1 with J = 4.5 to even levels of J = 3.5 .
wl Ritz
in Air (Å)
wn Ritz
( cm 1 )
wn exp
( cm 1 )
E even
( cm 1 )
J E odd
( cm 1 )
JInt Ref
14539.4646875.9536875.95020571.6903.513695.7374.518.15[14]
13112.0827624.4697624.46821320.2063.513695.7374.59.22[14]
4566.339621893.24321893.23935588.9803.513695.7374.5142[7]
4452.149322454.75822454.75736150.4953.513695.7374.5112[7]
4354.314422959.27422959.27636655.0113.513695.7374.5135[7]
4343.345623017.25623017.27436712.9933.513695.7374.5139[7]
4299.601623251.43023251.42936947.1673.513695.7374.5131[7]
4103.889724360.25324360.29338055.9903.513695.7374.5236[7]
4058.372424633.46324633.45938329.2003.513695.7374.5269[7]
4036.983024763.97724763.97338459.7143.513695.7374.5138[7]
4026.755024826.87824826.89938522.6153.513695.7374.5151[7]
3990.692725051.22325051.23338746.9603.513695.7374.5126[7]
3965.947625207.52425207.54638903.2613.513695.7374.5133[7]
3891.944125686.82125686.81539382.5583.513695.7374.5171[7]
3765.451726549.69726549.70640245.4343.513695.7374.5166[7]
3734.831126767.35926767.36140463.0963.513695.7374.5157[7]
3728.608126812.03326812.08340507.7703.513695.7374.5141[7]
3697.770727035.62827035.60340731.3653.513695.7374.5217[7]
Table 5. Fitted parameters (in cm 1 ) for even parity configurations of U II with 5 f 2 and 5 f 4 cores compared with HFR radial integrals. The scaling factors are S F ( P ) = P f i t / P H F R (dimensionless). They are replaced by Δ E = E f i t E H F R for E a v average energies (in cm 1 ). Constraints on some parameters are in the ’Cstr’ columns (denoted ’f’ for fixed parameters or ’rn’ , which link parameters of the same ’rn’ to vary in a constant ratio). The H F R values of E a v parameters are relative to the lowest odd configuration 5 f 3 7 s 2 taken as zero value.
Table 5. Fitted parameters (in cm 1 ) for even parity configurations of U II with 5 f 2 and 5 f 4 cores compared with HFR radial integrals. The scaling factors are S F ( P ) = P f i t / P H F R (dimensionless). They are replaced by Δ E = E f i t E H F R for E a v average energies (in cm 1 ). Constraints on some parameters are in the ’Cstr’ columns (denoted ’f’ for fixed parameters or ’rn’ , which link parameters of the same ’rn’ to vary in a constant ratio). The H F R values of E a v parameters are relative to the lowest odd configuration 5 f 3 7 s 2 taken as zero value.
5 f 4 7 s 5 f 4 6 d
aram. P P f i t Cstr.Unc. P H F R Δ E / S F P f i t Cstr.Unc. P H F R Δ E / S F
E a v 32165 112158721629346815 1532904417771
F 2 ( f f ) 42100r1471638210.66041167r1461624080.660
F 4 ( f f ) 25599r2810409340.62524977r2790399390.625
F 6 ( f f ) 18480r3814297790.62118016r3794290300.621
α 19.5r42 19.5r42
β −600f −600f
γ 1600f 1600f
ζ f 1557r5916610.9381529r5916310.938
ζ d 1145r61913690.836
F 1 ( f d ) 509f
F 2 ( f d ) 20390r8520249060.819
F 4 ( f d ) 14468r9776134771.074
G 1 ( f d ) 11163r10248181090.616
G 2 ( f d ) 1524f197
G 3 ( f d ) 13293r11511123421.077
G 4 ( f d ) 2691f
G 5 ( f d ) 7527r1292389630.840
G 3 ( f s ) 2132 11345610.467
5 f 2 6 d 7 s 2 5 f 2 6 d 2 7 s
Param. P P f i t Cstr.Unc. P H F R Δ E / S F P f i t Cstr.Unc. P H F R Δ E / S F
E a v 39115 305118412727443050 2081297330077
F 2 ( f f ) 49005r1548742890.66048413r1542733810.660
F 4 ( f f ) 30284r2958484240.62529870r2945477630.625
F 6 ( f f ) 22025r3971354900.62121710r3957349840.621
α 19.5r42 19.5r42
β −600f −600f
γ 1600f 1600f
F 2 ( d d ) 23302r131546377560.617
F 4 ( d d ) 14997r163057250800.598
α ( d d ) 10f
ζ f 1908r51120360.9371884r51120100.937
ζ d 1889r63222590.9311760r6 21040.837
F 1 ( f d ) 509f 509f
F 2 ( f d ) 25399r8647310250.81924437r8623298500.819
F 4 ( f d ) 18040r9968168031.07417283r9927160991.074
G 1 ( f d ) 11285r10250183060.61611030r10245178920.616
G 2 ( f d ) 1524f 1524f
G 3 ( f d ) 14821r11570137601.07714324r11551132991.077
G 4 ( f d ) 2691f 2691f
G 5 ( f d ) 8727r121071103890.8408394r12103099960.840
G 3 ( f s ) 1578f 24500.6441885r610040330.467
G 2 ( d s ) 12984 597208740.622
5 f 2 6 d 3
Param. P P f i t Cstr.Unc. P H F R Δ E / S F
E a v 520934012088231211
F 2 ( f f ) 47830r1535742890.660
F 4 ( f f ) 29460r2932441310.625
F 6 ( f f ) 21410r3943345000.621
α 19.5r42
β −600f
γ 1600f
F 2 ( d d ) 22416r131488363190.617
F 4 ( d d ) 14359r162926240130.598
α ( d d ) 10f
ζ f 1860r51119860.937
ζ d 1635r62719560.836
F 1 ( f d ) 509f
F 2 ( f d ) 25399r8647310250.819
F 4 ( f d ) 18040r9968168031.074
G 1 ( f d ) 11285r10250183060.616
G 2 ( f d ) 1524f
G 3 ( f d ) 13799r11570128111.077
G 4 ( f d ) 2691f
G 5 ( f d ) 8050r1298895870.840
Configuration Interaction
5 f 4 7 s 5 f 4 6 d
R 2 ( f s , f d ) −6216r14357−105740.588
R 3 ( f s , d f ) −1875r14108−31890.588
5 f 4 7 s 5 f 2 6 d 7 s 2
R 3 ( f f , d s ) −2310r14133−39300.588
5 f 4 7 s 5 f 2 6 d 2 7 s
R 1 ( f f , d d ) 10962r15214231170.474
R 3 ( f f , d d ) 7708r15150162250.474
R 5 ( f f , d d ) 5672r15111119610.474
5 f 4 6 d 5 f 2 6 d 7 s 2
R 3 ( f f , s s ) 3556r1420460500.588
5 f 4 6 d 5 f 2 6 d 2 7 s
R 3 ( f f , d s ) −2385r14137−40560.588
5 f 4 6 d 5 f 2 6 d 3
R 1 ( f f , d d ) 10762r15210226940.474
R 3 ( f f , d d ) 7466r15146157450.474
R 5 ( f f , d d ) 5465r15107115250.474
5 f 2 6 d 7 s 2 5 f 2 6 d 2 7 s
R 2 ( f s , f d ) −5657r14324−96210.588
R 3 ( f s , d f ) −908r1452−15450.588
R 2 ( d s , d d ) −14874r14853−253020.588
5 f 2 6 d 7 s 2 5 f 2 6 d 3
R 2 ( s s , d d ) 13119r14752223160.588
5 f 2 6 d 2 7 s 5 f 2 6 d 3
R 2 ( f s , f d ) −5558r14319−94540.588
R 4 ( f s , d f ) −938r1454−15960.588
R 2 ( d s , d d ) −14638r14840−249000.588
Table 6. Energy levels of U II, even parity with 5 f 2 and 5 f 4 parent configurations. Comparison of experimental energies and Landé factors with values calculated from the parameter set of Table 5. Δ E = E e x p E t h . The percentage, the configuration and the L S name of the leading component in the corresponding configuration are given in the last three columns.
Table 6. Energy levels of U II, even parity with 5 f 2 and 5 f 4 parent configurations. Comparison of experimental energies and Landé factors with values calculated from the parameter set of Table 5. Δ E = E e x p E t h . The percentage, the configuration and the L S name of the leading component in the corresponding configuration are given in the last three columns.
J E exp
( cm 1 )
E th
( cm 1 )
Δ E
( cm 1 )
g L th g L exp % 1 st comp Conf Term
3.54663.8034647160.5000.49071f4s(5I)6I
4.55716.44955641520.8300.83040f4s(5I)6I
5.58347.6908327191.0301.04062f4s(5I)6I
4.58423.4188423 0.7970.79041f4s(5I)4I
6.510740.26510772−311.1421.14572f4s(5I)6I
1.510987.20410954320.6900.64524f4s(5F)6F
2.511252.337111381141.175 22f4s(5F)6F
5.511389.46911419−300.9610.97059f4s(5I)4I
0.5 12254 −0.516 70f4s(5F)6F
5.512513.88112493190.6760.68061f4s(5I)6L
3.512804.95012821−160.922 12f4s(3G)4G2
7.512862.15512880−171.2061.2269f4s(5I)6I
4.513023.114129051181.134 11f4s(3G)4G2
1.513006.99013044−370.701 34f4s(5F)6F
5.513783.03013733490.6950.68556f2d2s(3H)6L
2.513758.14213807−490.931 30f4s(5G)6G
6.513865.96913875−91.0681.1061f4s(5I)4I
3.514018.82113979391.260 46f4s(5F)6F
1.5 14204 0.370 34f4s(5F)4F
2.514239.50314439−1991.517 34f4s(5S)6S
8.514796.72514742541.245 61f4s(5I)6I
3.514767.4661475981.044 30f4s(5G)6G
2.514848.57514955−1071.004 26f4s(5F)4F
2.515087.78515088 0.951 23f4s(5G)4G
6.515392.41615353380.8710.88072f4d(5I)6L
3.515679.55515734−550.5890.61520f2d2s(3H)6Ia
3.515812.49815857−440.5880.59017f2d2s(5I)6I
1.515888.90515870181.529 42f4s(5S)4S
7.515992.76515937551.1291.2053f4s(5I)4I
6.515962.3201595930.9030.90046f2d2s(3H)6L
4.516211.70416356−1450.6630.61553f4d(5I)6K
5.516379.87816364141.283 24f4s(5F)6F
4.516804.920165462590.7590.84519f2d2s(3H)6K
4.516656.41216711−551.318 52f4s(5F)6F
5.516706.30316913−2070.7880.79036f4s(3K)4K2
4.517225.8851721690.991 14f4s(3H)6K
5.517434.36317438−40.7950.80020f2ds2(3K)4K2
6.517380.86817463−820.973 31f4s(3K)4K2
4.517392.21117604−2120.8600.78516f2d2s(3H)6K
3.5 17683 1.115 49f4s(5F)4F
2.5 18060 0.680 17f4d(5I)4G
7.518136.36618062731.0041.00576f4d(5I)6L
4.518084.43518154−690.971 19f4d(5G)6G
4.518200.09218334−1340.8360.78027f2ds2(3H)4I
3.5 18599 0.980 25f4s(5G)4G
4.518536.70518600−630.967 26f4d(5I)6I
2.5 18675 0.575 10f4d(5I)6H
5.518827.008186941330.9080.94536f2d2s(3H)6K
7.518656.35518699−421.053 21f4s(3L)4L
0.5 18737 2.635 39f4s(5D)6D
6.518617.80718791−1730.908 42f4s(3L)4L
5.518654.31618850−1960.8740.88070f4d(5I)6K
2.5 19047 0.751 12f4s(3G)4G2
5.519097.5941909611.330 42f4s(5F)6F
2.5 19134 0.933 10f4s(5F)6F
1.5 19159 0.448 17f2d2s(3F)6Ga
3.5 19246 1.001 13f4s(3G)4G2
2.519395.16819330640.779 7f2d2s(3H)6Ha
2.5 19354 1.001 10f4s(3H)6Ha
1.5 19412 0.996 17f4s(5F)6F
3.519517.72919546−280.8210.81515f4d(5I)6I
7.519743.51119756−121.0171.00067f2d2s(3H)6L
1.5 19796 0.191 48f4d(5I)6G
2.5 19863 0.909 12f2d2s(3H)6Ha
5.519840.51419899−580.947 8f4d(5I)6K
6.519977.10019935410.9690.96032f2d2s(3H)6L
3.519971.32819977−50.8570.86011f4d(5I)4H
8.520230.479201271021.099 20f4s(5I)6I
5.520353.99220310431.0291.01529f2d2s(3H)6Ia
4.5 20365 1.208 50f4s(5F)4F
7.520425.56720445−200.975 32f4s(3M)4M
3.520571.69020474970.9470.9358f4d(3H)6Ha
0.5 20496 1.065 26f4s(3P)4P2
1.5 20530 1.274 20f4s(5D)6D
8.520739.844206121271.0951.1174f4d(5I)6L
2.520678.7792067261.066 8f4s(1D)2D3
4.520635.27220721−860.9140.94513f2d2s(3H)6Ia
6.520702.03720789−871.0340.99040f4d(5I)6K
1.5 20828 1.079 12f4s(3P)4P2
6.520934.18620858761.265 45f4s(5G)6G
3.520961.72020901600.8770.85511f4d(5I)6H
2.5 20917 0.750 14f4d(5I)6H
5.520742.87820940−1971.012 29f4d(5I)6I
5.520932.13921050−1181.173 25f4s(5G)6G
1.5 21053 1.534 31f4s(5D)6D
4.521154.55721066881.0611.01013f4d(5I)4H
4.521053.52821089−351.215 21f4s(3F)4F4
3.521207.73821190171.3031.15019f4s(5D)6D
3.521320.20621514−1940.8220.83514f4d(3H)6Ia
5.521691.517215321590.9610.97515f2d2s(3H)4I
4.521555.27521619−630.9151.0259f2d2s(3H)4Ic
6.521710.76821641680.9170.91531f2d2s(3H)4Lb
3.5 21650 1.062 9f4s(3F)2F4
2.5 21719 0.862 15f4d(5F)6G
4.5 21720 1.001 26f4s(5G)4G
1.5 21728 0.478 12f4s(3F)4F3
0.5 21778 0.852 34f4s(5D)4D
0.5 21942 1.493 33f4s(3P)4P2
2.5 21953 1.186 15f4s(3D)2D1
3.521860.05121954−940.7180.6716f2d2s(3H)6Ia
3.522158.070220531040.910 11f4d(5I)6H
5.522157.16222058981.171 39f4s(5G)4G
6.521975.59022058−821.0301.0329f4d(5I)6K
2.5 22142 1.003 8f4s(3F)4F3
1.5 22153 0.300 25f4d(5F)6G
4.522165.17922197−321.0070.89512f4d(5F)6H
3.522250.39822216340.8630.88512f2d2s(3F)6I
4.522429.865223031260.8740.93513f4s(3I)4I1
5.522389.57422326620.9921.0406f2d2s(3H)6K
6.522615.31922534800.9860.99528f2d2s(3H)4K
0.5 22613 1.207 14f2ds2(3F)2P
5.522764.904226251391.0300.98017f4s(1H)2H1
4.522642.4782263480.9360.8758f2d2s(3I)4I1
2.5 22696 1.168 14f2d2s(5D)6D
3.522815.12322740740.786 26f2ds2(3F)4H
7.5 22776 1.032 40f4d(5I)6K
3.522960.66722891690.9970.9459f2d2s(3H)6Ha
4.522868.03322902−340.9430.9809f2d2s(5I)6H
5.522917.45322942−250.7590.86038f2d3(3H)6L
6.523107.566229451611.1201.06029f2d2s(3H)6Ia
2.523029.45823039−90.988 17f4d(5I)6G
9.5 23076 1.160 71f4d(5I)6L
1.5 23104 1.446 15f2d2s(3H)6D
5.523241.365231211190.9680.9617ds2(3H)4I *
2.5 23148 1.070 13f2d2s(5D)6D
4.523241.03323168720.9591.0506f2d2s(5I)6I
3.523257.61323205520.597 21f4d(5G)6I
6.523234.82023223111.0241.09029f4d(5I)6I
2.523353.60123264890.779 20f2d2s(3H)6Ha
7.523262.35923350−871.1021.07024f2d2s(3H)6K
3.5 23412 0.960 13f4d(5I)6G
0.5 23428 2.116 14f2d2s(3H)6D
8.5 23441 1.107 73f2d2s(3H)6L
6.5 23492 1.202 24f4s(3H)4H3
4.5 23501 1.073 12f4s(3G)4G2
5.5 23628 1.033 11f4d(5I)4H
3.5 23644 0.849 11f2d2s(3H)6Ib
1.523673.64923648251.276 25f4d(5D)4D
6.523635.91923712−770.9860.92018f2d2s(3H)4Lb
2.523700.94623739−380.868 17f2d2s(3F)6H
5.5 23792 0.923 22f2ds2(3H)4I
4.523817.50823802150.9580.87011f2d2s(3H)6K
0.5 23827 1.989 9f4d(5S)6D
2.523905.87723828771.085 9f4d(3F)6H
3.523803.25223831−270.991 7f4d(3F)4G
7.524071.418239271431.023 41f4s(3L)4L
1.5 23943 0.969 7f2d2s(3H)6Ga
4.5 23962 0.947 8f2d2s(3H)6K
3.523895.47124064−1690.9690.73510f4s(3G)2G2
6.524159.69624072860.9220.96531f4s(3L)4L
8.5 24074 1.069 42f4s(3L)4L
5.524010.46724077−660.9340.97518f4d(5I)4K
7.524247.529241221241.113 22f4d(5I)6I
4.524220.67524158621.094 7f4d(5F)6G
5.5 24168 0.989 7f2d2s(3H)2H3
2.5 24213 1.052 11f4d(5F)6F
3.524209.30324243−341.086 12f2d2s(3F)6Ga
1.5 24292 0.768 17f2d2s(5F)6F
2.5 24299 1.004 17f4d(5F)6G
6.5 24375 1.024 9f4d(5I)4K
7.524423.65624381420.995 38f4d(3L)2L
5.5 24432 1.037 12f4s(5G)4G
4.5 24440 1.016 12f2d2s(3F)6I
3.5 24491 1.262 17f4s(5D)6D
1.5 24501 0.628 15f2d2s(3H)6Ga
4.5 24593 1.023 13f4d(3H)6K
0.5 24650 0.273 29f2d2s(3F)6Fa
7.5 24675 0.974 17f4d(3K)4M2
8.5 24686 1.084 30f4d(5I)6K
0.5 24712 −0.082 43f4d(5F)6F
3.524709.44924720−100.943 16f2d2s(3H)6Ib
5.5 24722 1.007 11f4d(5I)6H
1.5 24746 1.386 15f4d(5F)6D
4.524684.13524802−1170.9810.9357f2d2s(3H)6K
2.5 24840 0.805 12f2d2s(3F)4G
9.5 24845 1.114 46f4s(3L)4L
5.524857.57024893−351.068 7f2d2s(3H)4Ga
4.5 24928 0.975 11f2d2s(3H)6K
3.524862.69824946−830.993 10f2d2s(3H)6Ib
6.5 24977 1.111 18f4s(3I)4I1
4.5 24981 1.159 16f4s(3F)4F2
2.5 24984 0.830 8f2d2s(3H)4Gc
8.525053.00525075−221.063 43f4s(3M)4M
3.5 25132 1.140 9f4d(3F)4F3
2.5 25247 0.917 7f4s(3F)2F3
6.5 25248 1.000 14f2d2s(3H)6L
3.5 25294 1.056 8f4d(5I)6G
5.525356.97225334220.9971.0209f4d(3H)4Kb
4.5 25343 1.003 9f2d2s(3H)4H
3.5 25346 1.020 10f4d(3H)6Ha
4.5 25424 0.904 23f2d2s(3H)6Ib
1.5 25434 0.868 7f4d(5F)6F
8.5 25458 1.157 22f4d(5I)6I
0.5 25477 1.513 12f4d(5G)4D
7.525399.46525518−1190.986 32f4s(3M)4M
3.5 25532 0.989 9f4s(3F)2F2
4.5 25537 0.950 7f2d2s(3H)4I
1.525582.63125561211.305 14f4d(5S)6D
2.5 25564 0.793 9f4d(5G)6H
8.5 25575 1.040 44f4s(3M)2M
2.5 25628 0.942 7f2d2s(3H)6Ga
5.525626.94125635−81.038 8f4s(5I)6H
3.5 25637 1.038 8f2d2s(5F)6F
10.5 25657 1.215 72f4d(5I)6L
1.5 25669 0.638 15f2d2s(3H)4F
6.5 25714 1.088 14f4d(3H)6L
7.525667.90625733−651.1641.10029f4s(3I)4I1
5.5 25746 0.978 20f2d2s(3H)4Kb
2.5 25748 1.061 6f2d2s(3F)6Ga
3.5 25784 1.051 13f2d2s(3H)6Ga
7.5 25784 1.078 15f2d2s(3H)6L
2.5 25875 1.115 9f4d(5F)6F
6.5 25892 0.998 20f2d2s(3H)6L
5.5 25894 1.083 22f2d2s(3H)6Ha
1.5 25981 0.913 21f2d2s(3F)6Fa
0.5 26012 1.555 14f4d(5S)6D
4.5 26038 1.116 7f2d2s(5F)6G
6.5 26058 1.176 12f4d(5I)6G
2.5 26094 1.261 16f4s(3P)4P2
0.5 26143 0.461 29f4s(3D)4D1
5.526158.89726164−51.010 18f2d2s(3F)6I
1.5 26166 1.167 18f4s(3P)4P2
3.5 26246 0.996 7f2d2s(3H)4Hb
5.5 26321 1.134 8f4d(3G)4G2
4.5 26343 1.008 9f2d2s(3H)6Ib
2.5 26364 1.209 16f4s(5D)4D
6.5 26375 1.035 18f4s(3I)2I1
8.5 26386 1.162 13f2d2s(3H)4Ka
1.5 26397 1.140 12f4s(3P)2P2
3.5 26446 1.063 4f4d(3H)4H2
4.5 26457 1.042 7f4d(5F)6G
2.5 26470 0.912 5f4s(3H)6D
7.526527.10626493331.0951.07517f4d(3H)4Lb
1.5 26521 1.308 10f4d(5F)6P
5.5 26544 1.093 9f2d2s(3H)4Kb
4.5 26569 1.066 7f4d(5D)6D
3.5 26623 1.160 6f4d(5S)6D
5.526628.49626633−51.0651.15519f4d(3H)6K
9.5 26641 1.176 41f4d(5I)6K
0.5 26642 0.493 8f2d2s(5G)6F
8.5 26703 1.050 30f4d(5I)6K
4.5 26717 1.094 7f4s(1G)2G4
0.5 26793 0.457 14f4d(5F)4D
2.5 26801 1.049 18f2d2s(3F)6Fa
3.5 26811 0.980 7f2.d(3H)4Hh
6.5 26842 1.015 12f4d(3H)4I
4.5 26856 1.076 6f2d2s(3G)2G2
5.526989.437268631251.1031.09513f4d(3H)6K
7.5 26868 1.061 34f4s(3H)6K
5.5 26903 1.059 12f4d(3H)6K
1.5 26918 0.766 6f2d2s(5F)6G
3.5 26919 1.111 14f4s(3F)4F4
7.526931.69926961−291.058 18f4d(5I)4L
2.5 26966 1.098 4f2d2s(3H)6D
3.5 26974 1.143 5f4d(5D)4D
4.5 26984 1.056 9f4d(5F)6F
5.5 27019 1.135 9f4d(5I)6G
6.5 27037 0.995