Revised energy levels of singly ionized lanthanum

Journal of Quantitative Spectroscopy & Radiative Transfer 211 (2018) 188–199

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Revised energy levels of singly ionized lanthanum Feyza Güzelçimen a,∗, Mehdi Tonka b, Zaheer Uddin c,d, Naveed Anjum Bhatti c, Laurentius Windholz d, Sophie Kröger e, Gönül Bas¸ ar a a

Istanbul University, Faculty of Science, Physics Department, Vezneciler, Istanbul Tr-34134, Turkey Graduate School of Engineering and Sciences, Istanbul University, Beyazıt, Istanbul TR-34452, Turkey c Institute of Materials Research and Quantum Engineering, Department of Physics, University of Karachi, Karachi 75270, Pakistan d Institut für Experimentalphysik, Technische Universität Graz, Petersgasse 16, Graz A-8010, Austria e Hochschule für Technik und Wirtschaft Berlin, Fachbereich 1, Wilhelminenhofstr. 75A, Berlin D-12459, Germany b

a r t i c l e

i n f o

Article history: Received 26 January 2018 Revised 23 February 2018 Accepted 25 February 2018 Available online 27 February 2018

a b s t r a c t Based on the experimental wavenumbers of 344 spectral lines from calibrated Fourier transform (FT) spectra as well as wavenumbers of 81 lines from the wavelength tables from literature, the energy of 115 fine structure levels of singly ionized lanthanum has been revised by weighted global fits. The classifications of the lines are provided by numerous previous investigations of lanthanum by different spectroscopic methods and authors. For the high accurate determination of the center of gravity wavenumbers from the experimental spectrum, the hyperfine constants of the involved levels have been taken into account, if possible. For the 94 levels with known hyperfine constants the accuracy of energy values is better than 0.01 cm−1 . For 34 levels the magnetic dipole hyperfine constants A have been determined from FT spectra as part of this work. For four of these 34 levels even electric quadrupole hyperfine constants B could be estimated. For levels, which have experimentally unknown hyperfine constants and which are connected only by lines not found in the FT spectra but taken from literature, the uncertainties of energy values are about a factor of 10 higher. A list of all revised level energies together with a compilation of hyperfine structure data is given as well as a list of all lines used. © 2018 Elsevier Ltd. All rights reserved.

1. Introduction With the atomic number of 57 lanthanum (La) is the first and namesake element of the rare-earth metals, also called lanthanides. It has two naturally occurring isotopes 139 La and 138 La with a natural abundance of 99.910% and 0.090%, respectively. When using La in its natural abundance, the less abundant isotope carries no weight in Doppler-limited spectroscopic measurements. The predominant isotope 139 La has a nuclear spin of 7/2, a quite large nuclear magnetic dipole moment of μI = 2.7830455(9) μN and relatively small nuclear electric quadrupole moment of Q = 0.20(1) b [1]. The large magnetic dipole moment causes a broad hyperfine structure in La spectra. La is an important element for estimating the life time of stars. The knowledge of abundance of La and other rare elements helps in understanding the nucleosynthesis process of astrophysical objects and supports the determination of the age of various stars [2]. Precise atomic and especially ionic data are essential for this pur-

∗

Corresponding author. E-mail address: [email protected] (F. Güzelçimen).

https://doi.org/10.1016/j.jqsrt.2018.02.029 0022-4073/© 2018 Elsevier Ltd. All rights reserved.

pose. In the present work we are focused on improving the fine structure energy values for singly ionized La. In the NIST atomic spectra data base [3], in total 118 fine structure energy levels of La II are listed, 70 levels of even parity in the energy range from 0 cm−1 to 69,505 cm−1 and 48 levels of odd parity in the energy range from 14,148 cm−1 to 64,411 cm−1 . During the last decades the spectrum La has been subject of several investigations. Experimental data for radiative lifetimes, branching fractions, oscillator strengths and hyperfine structure have been provided for atomic La in [4–24] and for ionic La in [24–44]. In these papers a large number of La I and La II lines have been classified and several new energy levels belonging to both, La I and La II, have been found. In many cases the difference between the experimental wavenumber and the calculated energy difference between the upper and the lower level was relatively high, i.e. larger than 0.1 cm−1 . This fact points out a large uncertainty of the energy values for La II. Hence, a revision of energy levels for La II was urgently required. Thanks to the knowledge of classifications and hyperfine constants, which result from previously works, this step was made possible.

F. Güzelçimen et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 211 (2018) 188–199

2. Experimental data The experimental basis is given by calibrated Fourier transform (FT) spectra in the spectral range from 330 nm to 1450 nm (30,0 0 0 cm−1 –690 0 cm−1 ), measured by some of the authors at the Laser Centre of the University of Latvia and already discussed in ref. [23]. Here only briefly summarized: The spectrum has been produced with a hollow cathode discharge lamp and recorded with a high-resolution Bruker IFS 125 HR FT spectrometer. La was used in its natural abundance with a purity of the 99.9%. The hollow cathode discharge was produced in an argon atmosphere at a pressure of about 1.0 mbar with a discharge current between 50 mA and 100 mA. The cathode lamp was cooled with liquid nitrogen to reduce Doppler line broadening. For more details see [45]. The calibration of the FT spectra was verified by comparing special ionic Ar lines, for which the wavelengths are nearly independent on discharge conditions, with wavelengths from our FT spectrum. Such lines are given by Learner and Thorne [46] in the wavelength range 372.9–514.7 nm (26,807–19,429 cm−1 ; the wavelengths were re-calculated using the energies given in the NIST tables [3]). For the calibration outside of this wavelength range we calculated wavelengths using the same upper Ar II – levels as in ref. [46], but now in combination with other lower energy levels. Here we made the assumption, that these wavelengths are also more or less independent from the discharge conditions. The absolute accuracy of the wavenumber is estimated to be better than 0.003 cm−1 in the entire wavelength range from 330 nm to 1450 nm. The original FT spectrum is given in wavenumbers. The classification program "Elements" [47,48] used for determination of the center of gravity (cg) of lines (see below) needs the spectra given in wavelengths in standard air. The global fit is done in wavenumbers. Therefore the data are transformed from cm−1 to nm and later back from nm to cm−1 , both using the dispersion formula of Peck and Reeder [49]. Transformation from wavenumber to wave-

a)

189

length (straight forward) and back (iteratively) causes a wavenumber deviation smaller than 10−5 cm−1 . Additionally to the lines from the FT spectra, experimental data from the literature i.e. form the MIT wavelength tables [50] have been taken into account, if for a La II level no lines were available in our FT spectra. 3. Hyperfine Structure; center of gravity Following the Ritz combination principle, the reciprocal value of the wavelength in vacuum λvac of a spectral line is equal to the difference of energy values (given in cm−1 ) of the two fine structure levels involved in the transition. On the other hand this is equal to the wavenumber ˜ v:

v˜ =

1

λvac

= Eupper − Elower

(1)

If the fine structure levels split into hyperfine structure sublevels, this rule applies for the wavenumber of a single component of the hyperfine structure and the corresponding hyperfine structure sublevels as well as for the centers of gravity (cg) of lines and levels. In the present study we deal with centers of gravity. However, the hyperfine structure must be taken into account for the determination of the cg of spectral lines, because many lines show very broad hyperfine structure patterns. For the determination of the cg of a line the program "Elements" [47,48] was used. Based on a list of all of the known fine structure levels of atomic and singly ionized La, the classification program calculates for a given wavelength interval all possible transitions which meet the selection rules for optical dipole transitions. Fine structure and hyperfine structure input data for the classification program comes from the above cited La papers. The program offers a variety of functionalities, from which only a small part was used in the present study, as described below. With the classification program the hyperfine structure of the line can be simulated using a Gaussian profile with adjustable full

b)

c)

d)

Fig. 1. Examples of lines with different weighting factors (wf): experimental curves are shown together with simulated hyperfine spectra using a Gaussian profile with adjustable the full width of half maximum. At the x-axis the offset frequency (from cg) in MHz is given.

190

F. Güzelçimen et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 211 (2018) 188–199

Fig. 2. Part of the energy level scheme of La II including the levels from Table 1 and 2, which are only connected to other levels by one or two transitions. Energy levels are given in/cm. Energy levels symbolized with thick bars are well established (transitions not shown). Levels marked by an asterisk are calculated by use of MIT wavelengths [50].

width of half maximum (FWHM). The simulated hyperfine spectrum is shown in a graphic window together with the experimental curve from the FT spectrum. The simulated curve can be shifted along the wavenumber axis to best match the experimental curve. In this way, the cg of the line can be determined very accurately, if the hyperfine structure constants of both involved levels are known. As long as the signal-to-noise ratio (S/N) is higher as 10, the accuracy of the cg is almost independent of the S/N and we estimate an uncertainty better than 0.003 cm-1 . If in a transition the experimental hyperfine structure constants for one level have been unknown up to now, the A values and sometimes even B values have been estimate by adjusting the simulated spectrum of corresponding lines to the intensity profile of the FT spectrum. Because no saturation effects occur in the FT spectra – in contrast to laser spectroscopic measurements – the experimental spectra are well reproduced by the theoretical intensity distribution of hyperfine structure peaks. Therefore this method leads to appropriate values for the hyperfine structure constants, even if the hyperfine structure is not well resolved. By using this method, new experimental hyperfine structure constants were obtained for 34 levels. For 21 levels with unknown hyperfine structure constants, no corresponding lines are detectable in our FT spectra. For these levels all classified lines are in the UV region outside the wavelength range of our FT spectrum. Therefore for these levels neither the cg nor the hyperfine constants could be determined from our FT spectrum. Nevertheless, we could take into account these levels in our investigation, because there are lines listed the MIT wavelength ta-

bles [50]. However the cg given in [50] is less accurate compared with lines form the FT spectra. 4. Global fit To determine revised values for the fine structure level energies for La II a weighted global fit was performed. For this purpose a weighting factor (wf) was assigned to each line corresponding to the quality of the line. The following criteria have been used to assign weighting factors to the spectral lines: Weighting factor (wf)

Criteria

10 5

well resolved, strong lines with 100 > S/N ≥ 20 partly resolved, strong lines with S/N ≥ 20 or well resolved, moderate lines with 20 > S/N ≥ 10 hardly resolved, strong lines with S/N ≥ 20 or well resolved, weak lines with S/N < 10 partly resolved weak lines with S/N < 10 or unresolved lines independent from S/N

3

1

Number of lines from FT spectra with this weight 3 36

100

205

Well resolved means that minimum three strong hyperfine structure peaks are well separated. For well resolved lines with S/N greater as 100 a weighting factor of 50 could have been assigned, but in our FT spectra no ionic line but only atomic lines have such high S/N.

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191

Table 1 La II levels of even parity; for explanations of column 3 to 6 see text; A and B: magnetic dipole and electric quadrupole hyperfine structure constants. Energy calculation J 1

Energy (cm−1 ) 2

No. of lines used 3

Stat. uncert. (cm−1 ) 4

Total uncert. (cm−1 ) 5

No. of class. lines 6

A (MHz) 7

B (MHz) 8

Ref. to col. 7, 8 9

2 3 2 1 4 2 3 0 1 2 0 4 2 3 2 3 4 3 4 2 1 5 4 3 2 1 2 3 2 3 1 2 3 1 4 3 2 1 5 3 4 2 1 4 5 4 2 6 2 3 4 4 2 0 1 1 2 6 2 0 1 2 1 2 3 0 3 0

0.0 0 0 1016.090 1394.471 1895.130 1970.708 2591.613 3250.381 5249.687 5718.115 6227.414 7394.550 7473.342 10,094.889 35,452.602 35,787.522 36,954.640 37,172.789 37,209.729 37,790.609 38,221.488 38,534.074 39,018.744 39,221.688 39,402.522 40,457.733 49,733.140 49,884.446 51,228.648 51,524.005 52,137.777 52,169.784 52,734.998 52,858.064 53,302.781 53,333.485 53,689.775 53,885.394 54,366.231 54,434.925 54,840.409 55,107.152 55,184.254 55,230.528 55,321.502 55,981.83 56,035.909 56,036.788 56,838.06 57,399.524 57,918.49 58,259.53 59,527.58 59,900.236 60,094.76 60,660.15 61,128.87 62,026.24 62,408.50 62,506.30 63,464.00 63,703.19 64,278.96 64,361.26 64,529.82 64,692.59 66,591.74 69,234.11 69,505.13

16 17 19 13 11 21 14 5 11 14 4 8 9 9 7 12 11 11 9 6 4 7 10 10 6 6 6 7 4 3 4 4 4 5 3 5 4 2 1 3 3 4 3 2 5 2 3 2 1 4 4 5 1 2 2 9 9 2 6 1 6 4 3 2 3 1 1 2

0.0 0 05 0.0 0 05 0.0 0 04 0.0 0 07 0.0 0 06 0.0 0 06 0.0 0 05 0.0012 0.0 0 04 0.0 0 05 0.0014 0.0 0 03 0.0 0 07 0.0010 0.0010 0.0 0 06 0.0 0 06 0.0 0 07 0.0 0 06 0.0 0 04 0.0013 0.0 0 07 0.0 0 09 0.0010 0.0011 0.0011 0.0010 0.0011 0.0013 0.0015 0.0018 0.0016 0.0015 0.0018 0.0016 0.0015 0.0013 0.0 0 09 – 0.0012 0.0018 0.0015 0.0021 0.0 0 03 0.039 0.0012 0.0025 0.0346 – 0.063 0.045 0.019 – 0.019 0.121 0.035 0.035 0.029 0.033 – 0.050 0.091 0.097 0.051 0.111 – – 0.029

0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.005 0.004 0.004 0.005 0.004 0.004 0.005 0.005 0.004 0.004 0.004 0.004 0.004 0.005 0.004 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.004 0.006∗ 0.005 0.005 0.005 0.006 0.004 0.07 0.005 0.006 0.07 0.006∗ 0.10 0.08 0.05 0.006∗ 0.05∗ 0.15∗∗ 0.07 0.07 0.06 0.07 0.07∗ 0.08 0.13 0.13 0.08 0.15 0.07∗ 0.07∗ 0.07

22 22 30 16 17 25 19 6 17 18 7 10 13 15 10 16 18 20 14 12 14 8 16 14 9 10 11 9 8 8 8 10 10 7 6 6 7 6 3 5 9 5 5 6 5 6 4 2 4 4 4 6 6 2 2 9 9 2 6 1 6 4 3 2 3 1 1 2

397.6(2) 101.3(2) 949.5(1.6) −1128.1(9) −18.6(1) −8.7(3.0) 1066.3(3.3) 0 −225.2(2) −158.2(4) 0 150.1(2) 48.1(1) 440.9(4.0) 242.6(5.7) 177.1(4.4) 253.8(4.1) 202.2(4.0) 232.3(3.9) 197.2(1.0) 419(5) 169.1(1.0) 208.4(4.2) 149.9(2.0) 165.1(5.0) 100(10) 690(10) 285(5) −220(10) 165(15) 270(15) 50(10) 190(15) 0(20) 110(20) 30(15) 250(20) −30(10) 40(15) 80(15) 185(15) 40(10) 160(15) 90(15) – 80(20) 30(15) – 350(50) – – – 250(50) 0 – – – – – 0 – – – – – 0 – 0

19.8(1.8) 25.2(3.3) 49.8(12.6) 49.8(6.5) 37.5(3.0) 56.7(6.9) 60.3(9.3) 0 25.8(9) −45(11) 0 151.8(5.4) 39.9(1.8) 30(10) 0(5) 22(8) 22(11) 25(12) 80(20) 7(5) 22(8) 140(20) 85(20) 25(10) 55(10)

[25] [25] [25] [25] [25] [25] [25]

30(20)

−450(100)

Remarks 10

[25] [25] [25] [25] [31] [31] [31] [31] [31] [31] [31] [31] [31] [31] [31] [31] This This This This This This This This This This This This This This This This This This This

work work work work work work work work work work work work work work work work work work work

–

wl from MIT This work This work

–

wl from MIT This work

– – –

wl from MIT wl from MIT wl from MIT This work

0 – – – – – 0 – – – – – 0 – 0

wl wl wl wl wl wl wl wl wl wl wl wl wl wl wl

from from from from from from from from from from from from from from from

MIT MIT MIT MIT MIT MIT MIT MIT MIT MIT MIT MIT MIT MIT MIT

References for Table 1: [25,31]. ∗ For these levels, only 1 line could be treated, thus a statistical uncertainty is not available. Instead, a wavenumber error of 0.003 cm−1 was supposed for lines appearing in the FT spectrum. This leads, together with the calibration error of 0.003 cm−1 , to a total uncertainty of 0.006 cm−1 . For lines from the MIT table [50] the total uncertainty was assumed to be 0.07 cm−1 . ∗∗ It may be that one or both wavelengths in the MIT table [50] are given not correctly.

192

F. Güzelçimen et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 211 (2018) 188–199

Table 2 La II levels of odd parity; for explanations of column 3 to 6 see text; A and B: magnetic dipole and electric quadrupole hyperfine structure constants. Energy calculation J 1

Energy (cm−1 ) 2

No. of lines used 3

Stat. uncert. (cm−1 ) 4

Total uncert. (cm−1 ) 5

No. of class. lines 6

A (MHz) 7

B (MHz) 8

Ref. to col. 7, 8 9

2 3 4 3 4 2 3 3 5 2 4 6 3 4 1 2 5 3 0 1 2 2 3 1 2 3 2 1 0 1 3 5 4 2 1 0 1 3 2 1 3 4 3 4 3 3+ 3

14,147.954 14,375.198 15,698.782 15,773.814 16,599.258 17,211.915 17,825.604 18,235.558 18,580.482 18,895.372 19,214.527 19,749.649 20,402.810 21,331.594 21,441.685 22,106.016 22,282.808 22,537.291 22,683.643 22,705.126 23,246.892 24,462.681 24,522.694 25,973.367 26,414.022 26,837.656 27,388.135 27,423.919 27,545.818 28,154.540 28,315.299 28,525.720 28,565.423 29,498.079 30,353.375 31,785.814 32,160.965 32,201.058 33,204.388 45,692.19 57,364.200 58,748.813 59,612.512 60,744.142 61,017.580 61,514.413 64,411.332

10 14 9 10 7 8 6 8 3 9 9 1 5 3 6 9 3 8 2 6 8 11 10 12 10 12 16 12 3 9 15 2 10 10 12 2 6 8 7 7 7 6 10 6 1 1 2

0.0 0 07 0.0 0 06 0.0 0 07 0.0 0 08 0.0010 0.0 0 08 0.0011 0.0 0 08 0.0013 0.0 0 06 0.0 0 05 – 0.0 0 02 0.0018 0.0010 0.0 0 08 0.0016 0.0 0 04 0.0012 0.0010 0.0013 0.0 0 08 0.0 0 05 0.0 0 08 0.0 0 09 0.0 0 05 0.0 0 07 0.0 0 08 0.0014 0.0010 0.0 0 06 0.0 0 07 0.0 0 08 0.0 0 06 0.0 0 08 0.0038 0.0 0 08 0.0 0 08 0.0 0 06 0.048 0.0 0 05 0.0011 0.0 0 05 0.0 0 08 – – 0.0025

0.004 0.004 0.004 0.004 0.005 0.004 0.005 0.004 0.005 0.004 0.004 0.006∗ 0.004 0.006 0.005 0.004 0.005 0.004 0.005 0.005 0.005 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.005 0.005 0.004 0.004 0.004 0.004 0.004 0.007 0.004 0.004 0.004 0.08 0.004 0.005 0.004 0.004 0.006∗ 0.006∗ 0.006

34 16 12 14 12 14 13 14 5 20 12 3 14 9 15 20 15 19 4 15 12 16 15 19 17 14 24 16 6 17 21 5 13 16 17 5 14 17 23 7 8 6 10 6 1 1 3

−468.8(5.5) 1110.9(5.1) 792.8(1.8) −431.0(5.0) 220.4(2.5) 365.9(2) 267.9(2.5) 148.7(4) 173(5) 197.6(2.1) 64.8(1) 190(10) 332.7(3.5) 170.7(1.9) 412.4(5) 127.8(2.4) 136.1(3.0) 100.9(1.2) 0 72.2(7.0) 34.5(3) 446.5(1.8) 161.9(2) 547.3(3.0) 250.5(2) 258.9(1.5) 68.8(7) 886.9(1.5) 0 791.8(2.3) 82.9(5.0) 175(5) 126.1(9.5) 610.2(3.3) −157.7(6) 0 1383.9(9.0) 193.7(3.0) 30(10) – 360(20) 170(15) 240(20) 220(20) 20(20) 60(10) 180(20)

80(20) 130(15) 155(20) 145(15) 116(15) −3.9(1.8) 91(20) 5.0(4.2)

[30] [30] [30] [30] [30] [25] [30] [25] This work [30] [25] This work [30] [30] [30] [29] [30] [29]

−16(8) 8.4(4.8) 450(100) 60(15) 180(20) 8(4) 2.6(7.5) 60(30) −31.2(6.9) 0 −28(10) 11.1(2.4) 21(8) 22.1(4.2) 27(7) 51.9(1.8) 114.3(7.6) 30(15) −18.9(4.8) 0 −24(10) −28(10) 250(30) 150(30) 88(15) 33(6) 0 −35(10) 143(20)

Remarks 10

[30] [25] [30] [26] [30] [25] [29] [30] [29] [30] [30] This work [30] [30] [30] [30] [30] This work

–

wl from MIT This This This This This This This

work work work work work work work

References for Table 2: [25,26,29,30]. + The J-value of the level 61,514 cm−1 is given in ref. [43] as 3 or 4, but may also be 2. The given value for A is determined assuming J = 3. ∗ For these levels, only 1 line could be treated, thus a statistical uncertainty is not available. Instead, a wavenumber error of 0.003 cm−1 was supposed for lines appearing in the FT spectrum. This leads, together with the calibration error of 0.003 cm−1 , to a total uncertainty of 0.006 cm−1 .

Examples of lines with different weighting factors are shown in Fig. 1a–d. For easy extraction of all needed data of the spectral lines selected for the energy determination (cg wavelength from the FT spectrum, classification) an additional tool was implemented in the classification program "Elements" [47,48] and additionally the program "GlobalFit" [51] was written by one of the authors (L.W.). Altogether the cg wavelengths of 344 classified La II lines were accurately determined from the FT spectra. Based on these lines, a transition matrix was build up, in which each level of even parity corresponds to a column and each level of odd parity to a row. The matrix elements comprise the experimental cg wavenumbers as well as the weighting factors. Corresponding to this transition matrix, an over-determined system of linear equations is prepared. Each spectral line results in one equation, in terms of its structure equivalent to Eq. (1). Then the over-determined system of linear

equations was solved using a least squares method, resulting in improved energy values as well as the corresponding confidence intervals. The cg of the ground level is also varied during the fit as well as the cg energy of all levels. Finally the ground state energy is set to zero, and the deviation is added to all calculated energies. The statistical uncertainty of all level energies depends on the quality and number of the lines, which are connecting the levels. In order to verify easily the results a color coding for the deviation between experimental cg wavenumber and calculated difference between levels is show graphically by the program (for reasons of space no illustration is shown here). In the first step the 344 lines already mentioned have been evaluated and 92 revised energy values had been determined. For all these lines the differences between cg wavenumbers deter-

F. Güzelçimen et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 211 (2018) 188–199

193

Table 3 List of La II lines from the FT spectrum, which have been used for weighted global fit to determine revised level energies; ν = ν − |Eodd –Eeven |, wf: weighting factor for global fit.

λ in nm

ν in cm−1

ν in cm−1

Eodd in cm−1

Jodd

Eeven in cm−1

Jeven

wf

333.74918 337.63305 338.09094 345.21806 350.99866 351.29153 353.36256 355.08105 355.72458 357.00580 358.16628 358.54873 359.06204 359.65977 360.10495 360.12343 360.63956 360.81531 360.91858 361.23265 361.85986 362.88178 363.71429 363.91157 364.10611 364.16476 364.54132 365.01757 366.20667 366.52164 367.02232 369.42596 369.61148 370.17995 370.58102 371.35394 371.48572 371.55216 371.79690 372.07093 372.50486 373.14172 373.50249 373.58492 373.64058 375.90774 376.65813 376.70106 376.89413 377.31064 378.04964 379.08170 379.47681 384.07123 384.90059 386.30614 386.44599 387.16340 388.50434 388.63663 389.24611 391.08066 391.60366 392.15333 392.50876 392.92125 393.62132 393.98520 394.41443 394.91025 394.97205 395.14314 395.60703 397.90768 398.13533

29,954.006 29,609.449 29,569.349 28,958.901 28,481.990 28,458.246 28,291.459 28,154.540 28,103.608 28,002.753 27,912.025 27,882.253 27,842.394 27,796.123 27,761.761 27,760.337 27,720.609 27,707.106 27,699.179 27,675.097 27,627.129 27,549.330 27,486.273 27,471.373 27,456.696 27,452.274 27,423.917 27,388.137 27,299.208 27,275.749 27,238.542 27,061.321 27,047.738 27,006.203 26,976.976 26,920.829 26,911.279 26,906.467 26,888.756 26,868.953 26,837.654 26,791.850 26,765.972 26,760.066 26,756.080 26,594.714 26,541.733 26,538.708 26,525.113 26,495.833 26,444.041 26,372.048 26,344.590 26,029.453 25,973.368 25,878.867 25,869.502 25,821.568 25,732.445 25,723.686 25,683.409 25,562.932 25,528.792 25,493.010 25,469.926 25,443.188 25,397.937 25,374.481 25,346.867 25,315.044 25,311.083 25,300.124 25,270.458 25,124.351 25,109.985

−0.001 0.004 −0.003 −0.003 0.001 0.001 0.004 0.0 0 0 0.0 0 0 0.0 0 0 −0.002 0.005 0.001 0.004 −0.001 0.002 −0.001 0.003 0.001 0.001 0.005 −0.003 0.0 0 0 0.001 0.004 0.0 0 0 −0.002 0.002 −0.001 −0.004 −0.001 −0.003 0.0 0 0 0.0 0 0 0.002 0.001 0.001 0.001 −0.003 −0.002 −0.002 −0.003 0.005 −0.003 0.001 −0.001 0.004 −0.001 0.003 0.004 −0.001 0.003 −0.001 0.005 0.001 0.005 0.0 0 0 0.002 −0.004 0.0 0 0 −0.004 0.005 0.003 0.005 −0.003 0.003 0.005 0.005 0.004 0.002 0.004 0.003 −0.001 −0.001 0.002

33,204.388 32,201.058 32,160.965 30,353.375 29,498.079 30,353.375 21,441.685 28,154.540 29,498.079 26,837.656 25,973.367 28,154.540 27,388.135 27,388.135 30,353.375 27,423.919 28,315.299 24,462.681 32,201.058 24,462.681 22,106.016 28,565.423 33,204.388 26,414.022 64,411.332 27,388.135 27,423.919 27,388.135 28,315.299 26,414.022 64,411.332 24,462.681 26,837.656 28,315.299 33,204.388 28,315.299 32,160.965 29,498.079 26,414.022 28,315.299 26,837.656 28,315.299 24,462.681 28,154.540 28,565.423 28,565.423 28,565.423 29,498.079 28,315.299 26,837.656 26,414.022 27,388.135 28,315.299 27,423.919 25,973.367 27,423.919 28,565.423 26,837.656 29,498.079 28,315.299 30,353.375 28,154.540 27,423.919 27,388.135 27,388.135 26,837.656 26,414.022 28,315.299 27,388.135 28,565.423 27,423.919 26,837.656 24,462.681 28,565.423 26,414.022

2 3 1 1 2 1 1 1 2 3 1 1 2 2 1 1 3 2 3 2 2 4 2 2 3 2 1 2 3 2 3 2 3 3 2 3 1 2 2 3 3 3 2 1 4 4 4 2 3 3 2 2 3 1 1 1 4 3 2 3 1 1 1 2 2 3 2 3 2 4 1 3 2 4 2

3250.381 2591.613 2591.613 1394.471 1016.090 1895.130 49,733.140 0.0 0 0 1394.471 54,840.409 53,885.394 56,036.788 55,230.528 55,184.254 2591.613 55,184.254 56,035.909 52,169.784 59,900.236 52,137.777 49,733.140 1016.090 5718.115 53,885.394 36,954.640 54,840.409 0.0 0 0 0.0 0 0 1016.090 53,689.775 37,172.789 51,524.005 53,885.394 55,321.502 6227.414 1394.471 5249.687 2591.613 53,302.781 55,184.254 0.0 0 0 55,107.152 51,228.648 1394.471 55,321.502 1970.708 55,107.152 56,036.788 54,840.409 53,333.485 52,858.064 1016.090 1970.708 1394.471 0.0 0 0 53,302.781 54,434.925 1016.090 55,230.528 2591.613 56,036.788 2591.613 1895.130 1895.130 52,858.064 1394.471 1016.090 53,689.775 52,734.998 3250.381 52,734.998 52,137.777 49,733.140 53,689.775 51,524.005

3 2 2 2 3 1 1 2 2 3 2 2 1 2 2 2 4 1 2 3 1 3 1 2 3 3 2 2 3 3 4 2 2 4 2 2 0 2 1 2 2 4 3 2 4 4 4 2 3 4 3 3 4 2 2 1 5 3 1 2 2 2 1 1 3 2 3 3 2 3 2 3 1 3 2

3 1 5 3 1 3 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 3 3 1 1 1 3 1 1 1 1 3 1 1 3 3 3 3 1 1 1 1 1 1 1 3 1 1 1 1 1 3 3 1 1 1 1 1 1 3 1 1 5 5 1 3 1 1 1 10 3 1 3 1 3

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194

F. Güzelçimen et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 211 (2018) 188–199 Table 3 (continued)

λ in nm

ν in cm−1

ν in cm−1

Eodd in cm−1

Jodd

Eeven in cm−1

Jeven

wf

398.85117 399.45030 399.57446 399.59626 401.86161 402.35768 402.58744 402.61061 403.16845 403.63169 403.65854 404.29026 404.96774 405.00761 405.80759 405.99370 406.71241 406.73820 407.67046 407.73368 408.67055 409.87176 409.95364 411.32733 411.53110 412.32211 413.18965 413.24838 413.79210 414.17196 414.20423 414.37444 415.19578 415.27683 415.45964 418.09837 419.23428 419.33583 419.43550 419.60907 419.65451 420.23503 420.40364 420.76090 421.75554 423.09484 423.83805 424.12433 424.83323 424.99782 426.35794 426.94897 427.56365 428.69650 429.60471 430.04396 432.25058 433.37516 433.49611 433.77795 435.43987 435.54034 435.61871 436.30421 436.44237 436.46606 437.81031 438.34479 438.51969 441.11956 441.22380 441.91500 442.75640 442.98972 443.29542 443.58451

25,064.920 25,027.326 25,019.549 25,018.185 24,877.157 24,846.486 24,832.306 24,830.877 24,796.521 24,768.063 24,766.415 24,727.718 24,686.351 24,683.921 24,635.262 24,623.969 24,580.456 24,578.898 24,522.692 24,518.890 24,462.682 24,390.991 24,386.119 24,304.680 24,292.645 24,246.043 24,195.136 24,191.698 24,159.911 24,137.753 24,135.872 24,125.958 24,078.233 24,073.534 24,062.941 23,911.077 23,846.291 23,840.517 23,834.852 23,824.992 23,822.413 23,789.505 23,779.964 23,759.773 23,703.741 23,628.708 23,587.276 23,571.355 23,532.023 23,522.910 23,447.871 23,415.412 23,381.750 23,319.964 23,270.665 23,246.897 23,128.225 23,068.209 23,061.773 23,046.790 22,958.830 22,953.534 22,949.404 22,913.348 22,906.095 22,904.851 22,834.526 22,806.684 22,797.588 22,663.226 22,657.871 22,622.433 22,579.443 22,567.550 22,551.988 22,537.291

0.002 0.002 −0.002 −0.001 0.004 −0.004 0.0 0 0 −0.002 −0.001 0.001 0.0 0 0 0.002 0.002 0.002 0.002 0.003 −0.002 0.002 −0.002 −0.002 0.001 −0.001 −0.001 −0.004 0.004 0.0 0 0 0.0 0 0 0.002 0.001 −0.001 0.002 −0.003 −0.004 0.0 0 0 0.0 0 0 −0.002 0.001 0.004 0.001 0.002 0.004 0.003 0.0 0 0 0.0 0 0 0.001 0.0 0 0 0.001 0.002 0.004 0.004 −0.003 0.001 −0.004 0.002 0.0 0 0 0.005 0.002 −0.001 −0.002 0.0 0 0 0.005 0.001 −0.002 −0.001 0.001 −0.002 −0.005 −0.002 −0.003 0.001 −0.001 0.003 0.001 −0.001 0.002 0.0 0 0

28,315.299 14,375.198 26,414.022 28,315.299 30,353.375 14,375.198 27,423.919 30,353.375 27,388.135 28,565.423 32,160.965 32,201.058 26,837.656 15,773.814 30,353.375 27,545.818 28,154.540 25,973.367 24,522.694 26,414.022 24,462.681 26,837.656 14,147.954 61,514.413 28,565.423 26,837.656 33,204.388 29,498.079 59,612.512 27,388.135 27,388.135 30,353.375 25,973.367 14,147.954 36,954.640 25,973.367 14,375.198 27,388.135 32,201.058 59,612.512 26,414.022 60,744.142 29,498.079 25,973.367 15,698.782 15,773.814 26,837.656 60,744.142 30,353.375 15,698.782 15,773.814 14,375.198 25,973.367 15,698.782 29,498.079 23,246.892 24,522.694 24,462.681 14,147.954 26,837.656 30,353.375 60,744.142 30,353.375 28,315.299 32,201.058 28,154.540 14,375.198 14,147.954 14,375.198 28,565.423 59,612.512 16,599.258 14,375.198 24,462.681 24,522.694 22,537.291

3 3 2 3 1 3 1 1 2 4 1 3 3 3 1 0 1 1 3 2 2 3 2 2, 3 or 4 4 3 2 2 3 2 2 1 1 2 3 1 3 2 3 3 2 4 2 1 4 3 3 4 1 4 3 3 1 4 2 2 3 2 2 3 1 4 1 3 3 1 3 2 3 4 3 4 3 2 3 3

3250.381 39,402.522 1394.471 53,333.485 55,230.528 39,221.688 2591.613 55,184.254 2591.613 53,333.485 7394.550 7473.342 51,524.005 40,457.733 5718.115 52,169.784 52,734.998 1394.471 0.0 0 0 1895.130 0.0 0 0 51,228.648 38,534.074 37,209.729 52,858.064 2591.613 57,399.524 53,689.775 35,452.602 3250.381 51,524.005 6227.414 1895.130 38,221.488 61,017.580 49,884.446 38,221.488 51,228.648 56,035.909 35,787.522 2591.613 36,954.640 5718.115 49,733.140 39,402.522 39,402.522 3250.381 37,172.789 53,885.394 39,221.688 39,221.688 37,790.609 2591.613 39,018.744 6227.414 0.0 0 0 1394.471 1394.471 37,209.729 49,884.446 7394.550 37,790.609 53,302.781 51,228.648 55,107.152 5249.687 37,209.729 36,954.640 37,172.789 51,228.648 36,954.640 39,221.688 36,954.640 1895.130 1970.708 0.0 0 0

3 3 2 4 1 4 2 2 2 4 0 4 2 2 1 1 2 2 2 1 2 3 1 3 3 2 2 3 3 3 2 2 1 2 4 2 2 3 4 2 2 3 1 1 3 3 3 4 2 4 4 4 2 5 2 2 2 2 3 2 0 4 1 3 4 0 3 3 4 3 3 4 3 1 4 2

5 3 3 1 1 3 3 3 3 1 3 3 3 5 1 1 3 3 1 5 1 1 5 3 1 1 1 5 1 5 1 1 3 3 3 3 5 1 3 1 3 1 3 3 5 3 1 1 1 3 3 3 1 3 3 1 3 5 3 1 1 3 1 1 1 5 3 3 1 1 1 1 3 5 1 1

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F. Güzelçimen et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 211 (2018) 188–199

195

Table 3 (continued)

λ in nm

ν in cm−1

ν in cm−1

Eodd in cm−1

Jodd

Eeven in cm−1

Jeven

wf

444.39249 445.51324 445.57874 447.40168 449.87463 450.21731 450.58138 450.84735 452.23563 452.52915 452.60999 455.84608 455.92831 456.25138 457.09700 457.48696 458.00503 458.12680 458.70964 460.05240 460.16182 460.57726 461.33780 461.98700 463.33363 463.34760 463.49538 463.64119 464.14239 464.50100 464.52798 464.61948 464.74952 465.54892 466.25068 466.37620 466.89005 467.18125 467.24441 467.35497 468.43693 468.86443 469.11751 469.24975 469.96307 470.32697 471.29265 471.64390 471.75869 471.99300 472.41649 472.44156 472.84151 474.02738 474.30903 474.87289 480.40399 480.90046 482.40493 482.68764 483.96203 484.00245 485.05476 485.91384 486.08982 488.01659 489.14171 489.82972 489.99172 490.27974 490.38701 490.44453 492.09742 492.18003 493.48249 493.56127

22,496.315 22,439.723 22,436.425 22,345.009 22,222.181 22,205.267 22,187.325 22,174.236 22,106.167 22,091.829 22,087.883 21,931.082 21,927.126 21,911.600 21,871.065 21,852.422 21,827.704 21,821.902 21,794.176 21,730.566 21,725.399 21,705.803 21,670.020 21,639.569 21,576.677 21,576.027 21,569.147 21,562.364 21,539.081 21,522.452 21,521.202 21,516.964 21,510.943 21,474.007 21,441.687 21,435.916 21,412.325 21,398.978 21,396.086 21,391.024 21,341.618 21,322.159 21,310.656 21,304.651 21,272.315 21,255.856 21,212.304 21,196.506 21,191.349 21,180.829 21,161.842 21,160.719 21,142.821 21,089.929 21,077.405 21,052.379 20,809.997 20,788.513 20,723.682 20,711.544 20,657.006 20,655.281 20,610.471 20,574.033 20,566.584 20,485.385 20,438.265 20,409.558 20,402.811 20,390.825 20,386.365 20,383.974 20,315.508 20,312.098 20,258.488 20,255.255

0.004 0.0 0 0 0.0 0 0 0.004 0.006 0.001 0.003 0.004 −0.002 0.002 −0.002 0.001 0.0 0 0 0.002 −0.003 0.001 0.001 −0.001 0.003 −0.003 0.001 −0.001 0.0 0 0 0.001 −0.001 0.003 0.0 0 0 0.003 −0.003 −0.002 0.001 −0.003 −0.004 0.0 0 0 0.002 0.001 0.001 0.003 0.002 0.0 0 0 −0.002 0.0 0 0 0.001 0.003 0.002 −0.002 0.004 0.001 −0.002 0.003 −0.001 −0.002 0.001 0.003 0.001 0.001 0.001 0.0 0 0 0.002 −0.001 0.0 0 0 0.002 0.0 0 0 0.0 0 0 0.001 −0.002 0.003 −0.002 0.001 0.001 −0.002 0.004 0.004 −0.002 0.002 0.003

27,388.135 59,612.512 28,154.540 27,388.135 18,235.558 32,160.965 27,545.818 27,423.919 32,201.058 15,698.782 28,315.299 24,522.694 28,154.540 57,364.200 24,462.681 23,246.892 27,545.818 59,612.512 58,748.813 29,498.079 60,744.142 27,423.919 27,388.135 14,147.954 57,364.200 58,748.813 28,315.299 18,895.372 58,748.813 60,744.142 22,537.291 31,785.814 15,698.782 15,698.782 21,441.685 15,773.814 14,375.198 15,773.814 17,825.604 59,612.512 60,744.142 17,211.915 22,705.126 14,147.954 24,522.694 15,698.782 24,462.681 27,423.919 16,599.258 15,773.814 33,204.388 27,388.135 22,537.291 22,106.016 14,375.198 28,525.720 22,705.126 22,683.643 25,973.367 22,106.016 32,201.058 23,246.892 16,599.258 32,160.965 22,537.291 33,204.388 18,580.482 57,364.200 20,402.810 59,612.512 29,498.079 31,785.814 21,331.594 22,282.808 30,353.375 25,973.367

2 3 1 2 3 1 0 1 3 4 3 3 1 3 2 2 0 3 4 2 4 1 2 2 3 4 3 2 4 4 3 0 4 4 1 3 3 3 3 3 4 2 1 2 3 4 2 1 4 3 2 2 3 2 3 5 1 0 1 2 3 2 4 1 3 2 5 3 3 3 2 0 4 5 1 1

49,884.446 37,172.789 5718.115 49,733.140 40,457.733 54,366.231 49,733.140 5249.687 10,094.889 37,790.609 6227.414 2591.613 6227.414 35,452.602 2591.613 1394.471 5718.115 37,790.609 36,954.640 51,228.648 39,018.744 5718.115 5718.115 35,787.522 35,787.522 37,172.789 49,884.446 40,457.733 37,209.729 39,221.688 1016.090 53,302.781 37,209.729 37,172.789 0.0 0 0 37,209.729 35,787.522 37,172.789 39,221.688 38,221.488 39,402.522 38,534.074 1394.471 35,452.602 3250.381 36,954.640 3250.381 6227.414 37,790.609 36,954.640 54,366.231 6227.414 1394.471 1016.090 35,452.602 7473.342 1895.130 1895.130 5249.687 1394.471 52,858.064 2591.613 37,209.729 52,734.998 1970.708 53,689.775 39,018.744 36,954.640 0.0 0 0 39,221.688 49,884.446 52,169.784 1016.090 1970.708 10,094.889 5718.115

2 4 1 1 2 1 1 0 2 4 2 2 2 3 2 2 1 4 3 3 5 1 1 2 2 4 2 2 3 4 3 1 3 4 2 3 2 4 4 2 3 1 2 3 3 3 3 2 4 3 1 2 2 3 3 4 1 1 0 2 3 2 3 2 4 3 5 3 2 4 2 1 3 4 2 1

3 1 5 1 1 3 1 1 3 3 3 1 5 3 1 5 3 1 1 1 3 3 3 5 1 3 3 1 1 1 1 1 3 3 1 3 5 3 1 1 1 3 3 3 3 3 1 3 1 3 1 1 3 1 3 3 5 10 3 1 1 1 1 5 1 5 1 1 1 1 1 1 1 1 3 1

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196

F. Güzelçimen et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 211 (2018) 188–199 Table 3 (continued)

λ in nm

ν in cm−1

ν in cm−1

Eodd in cm−1

Jodd

Eeven in cm−1

Jeven

wf

494.64476 494.66663 495.12187 495.20570 496.02942 497.03948 497.41336 498.68326 499.12755 499.64030 499.68159 499.94782 500.21249 501.44723 504.80227 506.29176 506.69932 508.01990 509.05671 510.75008 511.45654 511.96558 512.29923 515.67336 515.74243 516.36144 516.72714 516.75099 517.29049 518.34203 518.82121 520.41385 522.24662 522.61998 525.93851 529.08281 530.19798 530.26246 530.35440 537.70739 538.09783 538.17701 538.19086 544.75677 545.86795 546.43721 548.07276 548.22685 549.34510 553.56675 556.69217 567.15435 570.33223 571.24060 572.72850 576.90632 579.75724 580.57706 580.83175 580.86789 584.89342 586.37006 587.39916 588.06395 589.26727 592.77167 593.62145 597.35108 606.71223 610.03742 612.60807 612.95580 614.65271 617.27223 618.80834 626.23047

20,210.888 20,209.994 20,191.412 20,187.994 20,154.470 20,113.513 20,098.395 20,047.215 20,029.371 20,008.816 20,007.163 19,996.509 19,985.929 19,936.717 19,804.214 19,745.952 19,730.069 19,678.782 19,638.703 19,573.592 19,546.556 19,527.121 19,514.404 19,386.720 19,384.124 19,360.886 19,347.184 19,346.291 19,326.115 19,286.909 19,269.096 19,210.127 19,142.712 19,129.036 19,008.339 18,895.375 18,855.633 18,853.340 18,850.071 18,592.305 18,578.815 18,576.082 18,575.603 18,351.716 18,314.359 18,295.280 18,240.684 18,235.557 18,198.437 18,059.652 17,958.262 17,626.993 17,528.776 17,500.903 17,455.438 17,329.031 17,243.817 17,219.468 17,211.917 17,210.846 17,092.394 17,049.351 17,019.481 17,0 0 0.241 16,965.526 16,865.229 16,841.086 16,735.938 16,477.716 16,387.900 16,319.133 16,309.876 16,264.848 16,195.826 16,155.622 15,964.146

0.002 0.004 0.001 −0.001 −0.001 0.0 0 0 0.002 0.001 0.002 −0.003 0.002 −0.002 −0.001 −0.002 −0.003 −0.001 0.0 0 0 −0.006 0.001 0.001 0.001 −0.004 0.001 0.0 0 0 −0.001 0.0 0 0 −0.001 0.0 0 0 −0.001 −0.001 0.001 0.0 0 0 0.0 0 0 0.0 0 0 0.0 0 0 0.003 −0.002 −0.004 −0.001 −0.002 −0.002 0.0 0 0 −0.004 −0.001 0.002 0.0 0 0 −0.003 −0.001 0.0 0 0 0.001 0.0 0 0 −0.005 −0.001 0.002 −0.001 0.001 −0.002 0.0 0 0 0.002 0.005 0.005 −0.001 0.003 −0.001 −0.002 −0.002 −0.001 0.002 0.004 −0.001 0.0 0 0 −0.001 −0.002 0.001 −0.008 0.0 0 0

22,106.016 59,612.512 57,364.200 19,214.527 57,364.200 22,705.126 33,204.388 21,441.685 27,423.919 32,160.965 19,214.527 23,246.892 18,235.558 32,201.058 19,214.527 25,973.367 58,748.813 15,773.814 18,895.372 57,364.200 21,441.685 58,748.813 22,106.016 20,402.810 17,825.604 21,331.594 17,825.604 58,748.813 18,895.372 22,537.291 19,749.649 18,580.482 57,364.200 17,825.604 20,402.810 18,895.372 22,106.016 16,599.258 21,441.685 18,580.482 25,973.367 19,214.527 17,211.915 22,106.016 18,895.372 24,522.694 17,211.915 18,235.558 19,214.527 28,154.540 19,214.527 17,825.604 23,246.892 18,895.372 22,705.126 27,423.919 19,214.527 18,235.558 17,211.915 23,246.892 21,441.685 24,522.694 23,246.892 18,895.372 22,683.643 22,537.291 18,235.558 22,282.808 22,705.126 22,106.016 26,414.022 22,537.291 18,235.558 17,211.915 23,246.892 19,214.527

2 3 3 4 3 1 2 1 1 1 4 2 3 3 4 1 4 3 2 3 1 4 2 3 3 4 3 4 2 3 6 5 3 3 3 2 2 4 1 5 1 4 2 2 2 3 2 3 4 1 4 3 2 2 1 1 4 3 2 2 1 3 2 2 0 3 3 5 1 2 2 3 3 2 2 4

1895.130 39,402.522 37,172.789 39,402.522 37,209.729 2591.613 53,302.781 1394.471 7394.550 52,169.784 39,221.688 3250.381 38,221.488 52,137.777 39,018.744 6227.414 39,018.744 35,452.602 38,534.074 37,790.609 1895.130 39,221.688 2591.613 1016.090 37,209.729 1970.708 37,172.789 39,402.522 38,221.488 3250.381 39,018.744 37,790.609 38,221.488 36,954.640 1394.471 0.0 0 0 3250.381 35,452.602 2591.613 37,172.789 7394.550 37,790.609 35,787.522 40,457.733 37,209.729 6227.414 35,452.602 0.0 0 0 1016.090 10,094.889 37,172.789 35,452.602 5718.115 1394.471 5249.687 10,094.889 1970.708 1016.090 0.0 0 0 40,457.733 38,534.074 7473.342 6227.414 1895.130 5718.115 39,402.522 1394.471 39,018.744 6227.414 5718.115 10,094.889 6227.414 1970.708 1016.090 39,402.522 3250.381

1 3 4 3 3 2 1 2 0 1 4 3 2 3 5 2 5 3 1 4 1 4 2 3 3 4 4 3 2 3 5 4 2 3 2 2 3 3 2 4 0 4 2 2 3 2 3 2 3 2 4 3 1 2 0 2 4 3 2 2 1 4 2 1 1 3 2 5 2 1 2 2 4 3 3 3

1 1 3 1 1 1 3 1 5 3 1 5 1 1 1 1 3 3 1 3 5 1 1 1 1 1 1 3 1 5 1 1 3 1 1 1 1 1 3 1 5 1 1 1 1 1 1 1 1 3 1 1 1 3 1 3 1 1 1 1 1 1 1 5 1 1 3 1 1 3 1 1 1 1 1 5

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F. Güzelçimen et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 211 (2018) 188–199

197

Table 3 (continued)

λ in nm

ν in cm−1

ν in cm−1

Eodd in cm−1

Jodd

Eeven in cm−1

Jeven

wf

627.37428 629.60422 639.04815 639.90302 644.65870 649.81632 652.69827 663.65329 664.27758 667.14184 671.86543 677.42425 680.88608 683.40638 683.79160 685.90675 695.25025 695.45072 695.80927 706.62110 728.23355 748.34680 748.92045 761.29691 787.98936 789.17592 792.78857 805.93803 815.91419 848.40534 851.46880 865.08798 934.67520 1018.65670 1027.67200 1095.48030 1135.98980 1192.44070 1204.42120 1404.69690 1448.48980

15,935.041 15,878.602 15,643.948 15,623.049 15,507.798 15,384.713 15,316.783 15,063.949 15,049.792 14,985.178 14,879.825 14,757.725 14,682.692 14,628.545 14,620.304 14,575.219 14,379.344 14,375.199 14,367.791 14,147.955 13,728.076 13,359.109 13,348.877 13,131.864 12,687.036 12,667.961 12,610.235 12,404.491 12,252.822 11,783.581 11,741.186 11,556.343 10,695.969 9814.160 9728.065 9125.916 8800.486 8383.867 8300.472 7117.028 6901.855

0.002 0.0 0 0 0.003 0.003 −0.003 0.001 −0.002 0.0 0 0 0.0 0 0 0.001 −0.003 0.001 0.0 0 0 −0.005 0.002 −0.004 0.001 0.001 −0.001 0.001 0.002 0.001 0.0 0 0 0.0 0 0 0.001 0.003 −0.002 0.001 −0.002 −0.004 0.001 0.002 0.001 0.005 −0.001 0.0 0 0 0.003 0.003 0.0 0 0 0.002 −0.001

24,522.694 22,106.016 18,235.558 21,331.594 22,282.808 20,402.810 17,211.915 22,537.291 20,402.810 18,235.558 24,522.694 15,773.814 15,698.782 16,599.258 17,211.915 17,825.604 15,773.814 14,375.198 24,462.681 14,147.954 15,698.782 14,375.198 16,599.258 14,147.954 24,522.694 18,895.372 22,705.126 14,375.198 14,147.954 14,375.198 19,214.527 14,147.954 28,525.720 25,973.367 59,612.512 16,599.258 18,895.372 59,612.512 15,773.814 17,211.915 14,375.198

3 2 3 4 5 3 2 3 3 3 3 3 4 4 2 3 3 3 2 2 4 3 4 2 3 2 1 3 2 3 4 2 5 1 3 4 2 3 3 2 3

40,457.733 6227.414 2591.613 36,954.640 37,790.609 35,787.522 1895.130 7473.342 35,452.602 3250.381 39,402.522 1016.090 1016.090 1970.708 2591.613 3250.381 1394.471 0.0 0 0 10,094.889 0.0 0 0 1970.708 1016.090 3250.381 1016.090 37,209.729 6227.414 10,094.889 1970.708 1895.130 2591.613 7473.342 2591.613 39,221.688 35,787.522 49,884.446 7473.342 10,094.889 51,228.648 7473.342 10,094.889 7473.342

2 2 2 3 4 2 1 4 3 3 3 3 3 4 2 3 2 2 2 2 4 3 3 3 3 2 2 4 1 2 4 2 4 2 2 4 2 3 4 2 4

1 1 1 1 1 3 5 1 1 3 1 3 3 1 1 1 3 5 1 10 5 5 1 3 1 1 1 5 1 1 1 1 1 1 1 1 1 1 5 1 5

mined from the FT spectrum and wavenumbers calculated from the revised energy values are smaller than 0.005 cm−1 . In a second step further 81 lines from the MIT wavelength tables [50] have been treated in the same manner. But this time the 94 previously determined newly lower combining levels were treated as fixed in the least squares fit. For all 81 lines the same weight is used in this fit, i.e. an unweighted fit is performed. With this procedure the level energy of 21 further levels could be determined. 5. Results The results of the global fits are given in Table 1 for the levels of even parity and in Table 2 for the levels of odd parity. In these both tables in the first two columns the total angular momentum of the electrons J and the energy is given. In the next four columns information concerning the energy calculation are listed, i.e. - the number of lines, which has been used to determine the energy, - the statistical uncertainty, resulting from the fit, - the total uncertainty, which additionally takes into account the calibration uncertainty of the FT spectrum, and - the number of classified lines for this level. In the last columns the hyperfine constants together with corresponding reference are given, as well as a comment, if all used lines originate from MIT wavelength tables [50].

A list of all lines from the FT spectra is given in Table 3. For the sake of completeness, the lines used from MIT wavelength tables [50] are listed in Table 4. Many levels show up a dense array of lines, which means that in mean each level is connected by about 7 lines with other combining levels. The maximum lies at 21 connecting lines for one level. Only a few energetically high lying levels and one level with high angular momentum quantum number of J = 6 are connected by only one line. In Fig. 2, a level scheme is shown for the levels which are only connected to other levels by one or two lines. Levels for which the energy could be determined only from MIT wavelengths [50] are marked with an asterisk. For the even level 59,900.236 cm−1 only one line is inside the wavelength range of our FT spectrum, but altogether 6 lines are classified as transitions involving this level. The energy value given for this level is based on this one FT line (360.91858 nm). Only one line could be classified by the level 61,514.413 cm−1 (J = 2, 3 or 4). This line is quite strong in the FT spectrum (S/N = 165). But it is possible that the classification is wrong, and a not yet discovered level having lower energy is involved in the formation of this line. Thus the existence of this level is not sure. Three levels listed in the NIST tables [3] could not yet be confirmed in the course of years of research on the analysis of the lanthanum spectrum:

54793.82 cm−1 , J = 0, 54964.19 cm−1 J = 0, and 63598.87 cm−1 , J = 4.

198

F. Güzelçimen et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 211 (2018) 188–199 Table 4 List of La II lines from MIT wavelength tables [50], which have been used for global fit to determine revised level energies; ν = ν − |Eodd – Eeven |.

λ in nm

ν in cm−1

ν in cm−1

Eodd in cm−1

Jodd

Eeven in cm−1

Jeven

216.136 218.787 223.074 225.676 228.094 231.782 231.9441 232.8753 236.550 239.7237 240.328 241.761 243.713 243.839 245.815 247.106 247.1900 247.243 247.984 250.118 251.456 251.9215 253.160 253.314 254.24 254.64 255.3398 256.0374 256.1848 257.7921 260.0869 260.1777 261.0335 262.003 263.193 263.8988 266.136 266.475 266.562 266.654 267.2906 267.3743 267.986 268.4142 269.5458 270.649 273.2415 275.2858 275.9156 276.0504 276.1111 277.8757 277.9778 279.1513 279.8546 280.839 284.050 284.3659 284.669 285.372 285.5902 288.5141 289.3071 292.390 293.9618 295.0492 295.145 296.2910 296.605 296.657 297.683 301.895 307.551 311.263

46,252.64 45,692.26 44,814.24 44,297.59 43,828.04 43,130.73 43,100.59 42,928.26 42,261.44 41,701.99 41,597.14 41,350.60 41,019.43 40,998.23 40,668.69 40,456.23 40,442.49 40,433.82 40,313.01 39,969.08 39,756.42 39,682.96 39,488.84 39,464.83 39,321.10 39,259.34 39,151.75 39,045.08 39,022.62 38,779.34 38,437.20 38,423.79 38,297.82 38,156.11 37,983.61 37,882.02 37,563.60 37,515.81 37,503.57 37,490.63 37,401.35 37,389.64 37,304.30 37,244.79 37,088.44 36,937.27 36,586.83 36,315.15 36,232.26 36,214.57 36,206.61 35,976.69 35,963.48 35,812.31 35,722.31 35,597.10 35,194.72 35,155.62 35,118.19 35,031.69 35,004.92 34,650.19 34,555.21 34,190.89 34,008.08 33,882.75 33,871.75 33,740.75 33,705.03 33,699.12 33,582.98 33,114.45 32,505.49 32,117.86

0.21 0.07 −0.08 −0.13 0.02 −0.13 0.02 −0.06 −0.06 0.01 −0.03 0.01 −0.12 0.17 0.00 −0.06 −0.02 −0.11 −0.05 0.07 0.15 0.03 −0.11 0.06 −0.01 −0.07 0.00 0.08 −0.23 −0.01 0.00 0.04 0.18 −0.12 0.00 0.05 0.04 0.13 0.02 0.00 −0.01 0.00 −0.16 0.02 0.03 −0.07 −0.07 0.09 0.07 0.05 −0.11 −0.03 −0.18 −0.17 0.07 −0.20 0.21 0.12 0.03 −0.05 0.04 −0.06 −0.04 −0.11 0.19 −0.03 0.05 0.01 0.08 0.09 −0.07 0.12 −0.12 −0.14

15,773.814 45,692.19 17,211.915 45,692.19 18,580.482 18,895.372 45,692.19 16,599.258 21,441.685 17,825.604 22,106.016 28,154.540 22,683.643 22,705.126 28,565.423 23,246.892 45,692.19 17,825.604 19,214.527 22,537.291 24,522.694 18,235.558 22,537.291 45,692.19 22,705.126 23,246.892 30,353.375 19,214.527 22,106.016 23,246.892 28,154.540 22,705.126 45,692.19 17,825.604 24,522.694 23,246.892 24,462.681 20,402.810 24,522.694 25,973.367 18,580.482 22,705.126 27,388.135 22,282.808 19,749.649 27,423.919 21,331.594 27,388.135 19,749.649 28,315.299 28,154.540 22,282.808 28,315.299 22,106.016 22,537.291 45,692.19 29,498.079 25,973.367 27,388.135 29,498.079 24,522.694 21,331.594 22,282.808 28,315.299 30,353.375 28,525.720 28,154.540 27,388.135 27,423.919 22,282.808 27,545.818 27,545.818 28,154.540 32,160.965

3 1 2 1 5 2 1 4 1 4 2 1 0 1 4 2 1 4 4 3 3 3 3 1 1 2 1 4 2 2 1 1 1 4 3 2 2 3 3 1 5 1 2 5 6 1 4 2 6 3 1 5 3 2 3 1 2 1 2 2 3 4 5 3 1 5 1 2 1 5 0 0 1 1

62,026.24 0 62,026.24 1394.471 62,408.50 62,026.24 2591.613 59,527.58 63,703.19 59,527.58 63,703.19 69,505.13 63,703.19 63,703.19 69,234.11 63,703.19 5249.687 58,259.53 59,527.58 62,506.30 64,278.96 57,918.49 62,026.24 6227.414 62,026.24 62,506.30 69,505.13 58,259.53 61,128.87 62,026.24 66,591.74 61,128.87 7394.55 55,981.84 62,506.30 61,128.87 62,026.24 57,918.49 62,026.24 63,464.00 55,981.84 60,094.76 64,692.59 59,527.58 56,838.06 64,361.26 57,918.49 63,703.19 55,981.84 64,529.82 64,361.26 58,259.53 64,278.96 57,918.49 58,259.53 10,094.889 64,692.59 61,128.87 62,506.30 64,529.82 59,527.58 55,981.84 56,838.06 62,506.30 64,361.26 62,408.50 62,026.24 61,128.87 61,128.87 55,981.84 61,128.87 60,660.15 60,660.15 64,278.96

2 2 2 2 6 2 2 4 1 4 1 0 1 1 3 1 0 4 4 2 2 3 2 2 2 2 0 4 1 2 0 1 0 5 2 1 2 3 2 0 5 0 3 4 6 1 3 1 5 2 1 4 2 3 4 2 3 1 2 2 4 5 6 2 1 6 2 1 1 5 1 1 1 2

(continued on next page)

F. Güzelçimen et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 211 (2018) 188–199

199

Table 4 (continued)

λ in nm

ν in cm−1

ν in cm−1

Eodd in cm−1

Jodd

Eeven in cm−1

Jeven

316.056 317.488 321.712 329.444 357.8871∗ 358.00685∗ 365.83989∗

31,630.81 31,488.14 31,074.73 30,345.43 27,933.80 27,924.45 27,326.58

0.01 −0.06 0.15 0.10 0.00 −0.03 0.05

29,498.079 33,204.388 33,204.388 32,160.965 32,160.965 33,204.388 32,201.058

2 2 2 1 1 2 3

61,128.87 64,692.59 64,278.96 62,506.30 60,094.76 61,128.87 59,527.58

1 3 2 2 0 1 4

∗ These wavelengths are from the FT spectrum, but the SNR is very bad. In MIT is given 357.889, 358.0099 and 365.841 nm, respectively.

6. Conclusion In the present work we determined revised fine structure level energies for all except three La II levels, which are listed in [3], i.e. for 115 levels. 94 of these 115 levels are connected by spectral lines from wavenumber calibrated FT spectra and the hyperfine structure constants of these 94 levels were known or could be determined. The energy uncertainty for these 94 levels lies below 0.01 cm−1 . For the remaining 21 levels we used wavenumbers from the MIT wavelength tables [50] for the determination of the level energy, which results in less accurate energy values with an uncertainty on average of 0.07 cm−1 . For 34 levels the hyperfine structure constants were previously unknown but could be estimated from the FT spectra. In comprehensive tables the levels are compiled with all hyperfine structure data available in the literature. Additionally the list of all lines is given. Acknowledgments We would like to thank Prof. Ruvin Ferber and Maris Tamanis from Laser Centre of the University of Latvia (Rainis Bulevard 19, LV-1586 Riga) for providing the FT spectra data. This work was supported by Istanbul University Scientific Research Project with Nos: BEK-2017-26232, UDP-54979, UDP-43660. References [1] Raghavan P. 1989. At Data Nucl Data Tables 1989;42:189. [2] Giora S. The synthesis of the elements: the astrophysical quest for nucleosynthesis and what it can tells us about the universe. Berlin: Springer-Verlag; 2012. [3] NIST atomic spectra database, Version 5 http://physics.nist.gov/PhysRefData/ ASD/levels_form.html. [4] Childs WJ, Goodman LS. Phys Rev A 1971;3:25. [5] Wilson M. Phys Rev A 1971;3:45. [6] Fischer W, Hühnermann H, Mandrek K, Ihle H. Phys Lett B 1972;40:87. [7] Ben Ahmed Z, Bauche-Arnoult C, Wyart JF. Physica 1974;77:148. [8] Childs WJ, Goodman LS. J Opt Soc Am 1977;67:1230. [9] Childs WJ, Goodman LS. J Opt Soc Am 1978;68:1348. [10] Childs WJ, Nielsen U. Phys Rev A 1988;37:6. [11] Govindarajan J, Pramila T. J Opt Soc Am B 1989;6:1275. [12] Caiyan L, Fucheng L, Jianan C, Lizhou Z. Phys D Appl Phys 1990;23:1327. [13] Shaw RW, Young JP, Smith DH, Bonanno AS, Dale JM. Phys Rev A 1990;41:2566. [14] Jia L, Jing C, Lin F. Opt Commun 1992;94:331.

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