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Atoms 2015, 3(3), 273-298; doi:10.3390/atoms3030273

Article
Spectra of W VIII and W IX in the EUV Region
Alexander Ryabtsev 1,*, Edward Kononov 1,, Rimma Kildiyarova 1,, Wan-Ü Lydia Tchang-Brillet 2,, Jean-Francois Wyart 2,3,, Norbert Champion 2, and Christophe Blaess 2,
1
Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow 142190, Russia
2
LERMA, Observatoire de Paris-Meudon, PSL Research University, UMR8112 du CNRS, Sorbonne Universités, UPMC Univ. Paris 06, 92195 Meudon, France
3
Laboratoire Aimé Cotton, CNRS UMR9188, Université Paris-Sud, ENS Cachan, Bâtiment 505, F-91405 Orsay Cedex, France
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed; Tel.: +7-495-851-0225.
Academic Editor: Bastiaan J. Braams
Received: 8 April 2015 / Accepted: 15 June 2015 / Published: 30 June 2015

Abstract

: The results obtained on the W VIII spectrum as well as on the isoelectronic spectra Lu V, Hf VI, Ta VII, and Re IX in the VUV wavelength region are summarized with emphasis on the main trends along the isoelectronic sequence. A total of 187 lines of W VIII in the region of 160–271 Å were accurately measured and identified, 98 levels were found, and transition probabilities calculated. The isoelectronic regularities support the data on W VIII. A list of spectral lines in the region of 170–199 Å, considered as belonging to W IX, is presented.
Keywords:
atomic data for tungsten; vacuum ultraviolet; ion spectra; wavelengths; energy levels; transition probabilities; parametric calculations

1. Introduction

One of the key components of the international tokamak ITER, the divertor, is planned to be made from refractory tungsten. Tungsten sputtered from the divertor target plates will be transported to the plasma core where it contributes to radiative losses. The plasma parameters that are expected in the divertor will lead to excitation of tungsten ions up to approximately the 15th stage of ionization [1]. It is thus important to know the influx of tungsten. Emission lines from tungsten ions provide a diagnostic tool to solve this problem. However, as was shown in the compilation by Kramida and Shirai in 2009 [2] and the subsequent update [3], experimental data on classified line wavelengths and on energy levels were available only for the ions up to the sixth ionization stage. The W VIII–W XXVII spectra had never been analysed before.

An emission spectrum from a tokamak was recorded [4] in 1996 where the tungsten was injected by a blow-off method as an impurity in the plasma of the tokamak. The spectrum was taken with a low resolution of 5 Å and two broad peaks around 190 and 230 Å were tentatively assigned to radiations from the W7+ ion (W VIII). It was even uncertain to which configuration the ground state of this ion belongs. The authors of the compilation [2], based on the analysis of the 4f135s25p6ns and 4f145s25p5(2P3/2)ns series of W VII by Sugar and Kaufman [5], asserted that the ground state of W VIII is probably 4f135s25p6 F7/2, whereas 4f145s25p5 2P3/2 is located 800 ± 700 cm−1 above it. They also estimated the fine structure splitting of 4f135s25p62F7/2-2F5/2 to be 17440 ± 60 cm−1. More recently, a tungsten spectrum excited in a spheromak and recorded in the range of 180–450 Å with a resolution of 0.3 Å was published [6]. Along with 10 known W VI–W VII lines, an incompletely resolved structure was observed for the tungsten lines with maxima at about 200 and 250 Å; 17 peaks of this structure were attributed to the transitions in W VI–W VIII. However, the low resolution of the instruments used in both experimental studies [5,6] did not allow any reliable interpretation of the W VIII spectrum. Except for the calculations showing the position of W IX resonance transitions [7], there was no other information on the W IX spectrum.

To extend the data on tungsten ions needed for fusion plasma modeling, we undertook an investigation of the W VIII and W IX spectra. Given the complexity of these spectra, it was relevant to perform a systematic study of neighboring isoelectronic spectra making use of possible isoelectronic regularities. The present project “Spectra of W VIII and W IX and Isoelectronic Ions of Hf, Ta and Re” has been carried out within the framework of the IAEA Coordination Research Project (CRP) entitled “Spectroscopic and Collisional Data for Tungsten from 1 eV to 20 keV” [8]. An extensive analysis of the W VIII spectrum was published [9,10], followed by the analyses of the isoelectronic Hf VI [11], Ta VII [12], and Re IX [13]. In this paper, we will summarize our results obtained on W VIII and its isoelectronic spectra [9,10,11,12,13] with an emphasis on the main trends along the isoelectronic sequence. Preliminary results on the W IX spectrum will be reported and discussed.

2. Experimental Techniques

For all studied isoeletronic spectra with the W VIII (Hf, Ta, Re), two complementary experimental settings were used.

At the Institute of Spectroscopy in Troitsk, the spectra were recorded in the region 130–350 Å on a 3-m grazing incidence spectrograph equipped with a 3600 lines/mm, gold-coated holographic grating. The spectra were excited in a three-electrode, low-inductance vacuum spark with the peak current varied in the range of 9–50 kA. The spectra were recorded on Kodak SWR photographic plates and FUJI Imaging Plate BAS-TR2025. The photographic plate spectra were measured on an Epson Expression 1000 XL scanner. The observed wavelength resolution was about 0.015 Å. The anode was made of the appropriate element rod, whereas titanium was used for the cathode. Wavelengths were calibrated using titanium ion lines [14] as standards with the estimated uncertainty of the measured wavelengths ± 0.005 Å.

The spectra recorded on the FUJI Imaging Plate were scanned with a Typhoon FLA 9500 reader using a 10 µm sample step. Produced images were processed and analysed with ImageQuant TL 7.0 image analysis software, giving a digitized spectrum by signal integration along spectrum lines. This spectrum was further reduced using the program GFit [15], resulting in a table of line centres and intensities. The wavelength resolution in the case of image plates was about 0.03 Å, keeping in mind the 25 µm optical resolution of the Typhoon FLA 9500 reader. Therefore, these spectra were used for the intensity measurement, taking advantage of the linear intensity response of the image plate. It should be noticed that the wavelength dependence of the spectrograph efficiencies and image plate sensitivity were not taken into account.

At the Meudon Observatory, a similar but different triggered spark source was used to produce emission spectra. Spectra were recorded on a 10 m normal incidence spectrograph. This instrument is equipped with a 3600 lines/mm concave grating, resulting in a plate factor of ~0.25 Å/mm in the first order and a resolution of 0.008Å with a slit width of 30 µm in the range of 200–3000 Å. In the present work at the Meudon Observatory, spectra were recorded in the region of 180–500 Å on phosphor image plates (Fuji BAS-TR 2040), which were processed by a specific reader as described in a previous work on Nd V [16]. A Perkin-Elmer CYCLONE reader with a 43 µm sample step had been used in some earlier recordings, and more recent recordings were read using a FUJI FLA 9000 reader with a 10 µm sample step. In the last case, the high resolution of 0.008 Å of the spectrograph was preserved.

Well exposed spectra were obtained down to 180 Å on this normal incidence instrument, which provides an overlapping wavelength range with the grazing incidence instrument at Troitsk. A comparison of line intensities in the region of the overlap was helpful in selecting lines belonging to the spectrum under study.

Line identifications were made with the aid of the program IDEN [17]. IDEN uses an experimental spectrum, calculated energy levels, and transition probabilities. Ab initio calculations were performed by the Hartree–Fock method with relativistic corrections (HFR) with the use of the RCN-RCN2-RCG chain of the Cowan codes [18]. The derivation of radial energy parameters that leads to minimal deviations between experimental and theoretical energies, and optimal eigenfunctions, was performed with the last code RCE of the Cowan package [18].

The level energies derived from the line identifications were optimized by using the least-squares program LOPT [19].

3. Results and Discussion

3.1. W VIII and Isoelectronic Ion Spectra

According to ab initio calculations with the Cowan code [18], the spectrum of the resonance transitions of W VIII is expected to be formed by the decays from the interacting 4f125s25p65d + 4f135s25p5(5d+6s) + 4f145s25p4(5d+6s) + 4f145s5p6 excited configurations of the even parity to the 4f135s25p6 and 4f145s25p5 odd parity configurations. For better prediction of the spectrum, the ab initio calculations had to be properly scaled. Usually, the scaling factors are estimated by extrapolation along an isoelectronic sequence. However, of all these even configurations, only 4f125s25p65d was studied in the isoelectronic sequence of W VIII, the last spectrum being Lu V [20]. No other even configuration was known in any of the ions of the sequence, nor was the 4f145s25p5 odd parity configuration observed in this isoelectronic sequence. Therefore, a study of the isoelectronic spectra of the neighbouring chemical elements with the aim of finding these unknown configurations was necessary for reliable identifications in the W VIII spectrum.

Figure 1 shows the positions of low-lying configurations relative to the 4f135s25p6 configuration in the sequence Lu V–Re IX according to the Hartree-Fock calculations. It is seen that the configurations of both parities cross along the sequence, W VIII being the most intricate case.

Figure 1. Calculated average energies of the low-lying configurations in the W VIII isoelectronic sequence.
Figure 1. Calculated average energies of the low-lying configurations in the W VIII isoelectronic sequence.
Atoms 03 00273 g001 1024

The structure of the energy levels in Hf VI–Re IX spectra is shown in Figure 2. Red bars mark experimentally found levels. Grey bars correspond to the calculated positions of unknown levels. Dashed vertical lines divide two systems formed by excitation of one electron from one of the two lowest configurations 4f145s25p5 and 4f135s25p6. Electric dipole (E1) transitions are possible inside these two systems. There is also one intersystem E1 transition array connecting levels from the two systems: 4f145s25p5–4f135s25p55d. The general trend along the isoelectronic sequence is that the configurations formed by an excitation from the 5p5 subshell of the 4f145s25p5 configuration move down and the 4f125s25p6(5d+6s) configurations move up relative to the 4f135s25p5(5d+6s) configurations as the ion change increases. Because of the large spread of the even configurations, they overlap to some extent in all ions, depending on the change of relative positions along the isoelectronic sequence. The configuration interactions lead to a mixture of their wave functions, resulting in the observations of different electric dipole forbidden transitions. These transitions contribute to establishing the connection between the levels of two excitation systems with higher reliability. It is visible from Figure 2 that we found the levels in all but the 4f145s5p6 excited configurations of the even parity that decay to the low-lying odd 4f145s25p5 and 4f135s25p6 configurations. The 4f125s25p66s configuration is metastable. It does not decay down by E1 transitions. However, due to configuration interactions, transitions from this configuration were detected and they helped to establish some of its levels in Ta VII. Below, we discuss some individual features of the studied spectra.

Figure 2. Energy levels of low-lying configurations of Hf VI, Ta VII, W VIII, and Re IX. Red horizontal bars show levels established in this work. Calculated positions of unknown levels are shown in grey colour. Dashed vertical lines divide systems formed by excitation of the two lowest configurations 4f145s25p5 and 4f135s25p6 (the subshell 5s2 is omitted from the configuration names except for 4f145s5p6). Arrows indicate electron dipole transitions between the configurations.
Figure 2. Energy levels of low-lying configurations of Hf VI, Ta VII, W VIII, and Re IX. Red horizontal bars show levels established in this work. Calculated positions of unknown levels are shown in grey colour. Dashed vertical lines divide systems formed by excitation of the two lowest configurations 4f145s25p5 and 4f135s25p6 (the subshell 5s2 is omitted from the configuration names except for 4f145s5p6). Arrows indicate electron dipole transitions between the configurations.
Atoms 03 00273 g002 1024

W VIII [9,10]. Figure 3 shows an experimental spectrum of tungsten excited in a vacuum spark source from Troitsk, with a peak current of 50 kA. Our spectrum reproduced, with a resolution an order of magnitude higher, the entire structure in the regions 200 and 250 Å, as well as the individual peaks of tungsten emission in other regions, which were detected in the spheromak spectrum [6]. Because of the large spin-orbit splitting of the 5p electron, the spectrum of W VIII is roughly divided into three groups located approximately at 170, 200, and 250 Å. The lines around 170 Å are identified with the 4f135s25p6–4f135s25p5j = 1/26s and 4f145s25p5–4f145s25p46s transitions. The lines of the group at 200 Å are mostly identified as the 4f135s25p6– (4f135s25p5j = 1/25d + 4f135s25p5j = 3/26s) transitions, contrary to a former suggestion [6] that they could belong to transitions from the 4f145s25p45d configuration. Intense lines in the 250 Å region belong mostly to the 4f135s25p6–4f135s25p5j = 3/25d transitions.

The list of 187 identified W VIII lines is presented in Table 1. It also contains the products gA of the upper level statistical weight and the transition probability per unit time (Einstein coefficient A) and the energies of the lower and the upper levels of the transitions, respectively. The transition probabilities were calculated with wavefunctions obtained by Cowan’s code with optimised energy parameters. The wavefunctions show mixtures of states within the same configuration, as well as mixtures of states belonging to different interacting configurations. Therefore, in Table 1, the upper levels of the transitions are designated by their energies and their J-values, whereas for convenience, a configuration name is given according to the output files from Cowan’s code in spite of possible ambiguity in some cases.

Figure 3. Spectrum of tungsten excited in a vacuum spark with the peak current 50 kA with identification of the lines.
Figure 3. Spectrum of tungsten excited in a vacuum spark with the peak current 50 kA with identification of the lines.
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It was firmly established that the ground state of W VIII is 4f135s25p6 2F7/2. A splitting of 17410 ± 5 cm−1 for the 4f135s25p6 2F term was found in close agreement with the predicted [2] value 17440 ± 60 cm−1. The 4f145s25p5 2P3/2 level was found to be located 1231 ± 3 cm−1 above the ground state, again in agreement with the predicted value 800 ± 700 cm−1 [2,5]. The 2P3/22P1/2 interval was derived as 87890 ± 6 cm−1, slightly different from the predicted [2] value 87100 ± 300 cm−1. Overall, 97 levels of the excited configurations were located.

Table 1. Identified lines in the spectrum of W VIII.
Table 1. Identified lines in the spectrum of W VIII.
λ (Å)ho-ca (Å)σ (cm−1)Int.gA (108·s−1)Lower LevelUpper Level
Config.bTermE (cm−1)Config.cJE(cm−1)
160.940−0.0026213515104f135p62F7/204f135p56s5/2621343
161.057−0.0026208974104f145p52P3/212334f135p56s3/2622123
161.260−0.002620118271474f145p52P3/212334f135p56s5/2621343
163.5960.00661126180124f135p62F7/204f135p56s7/2611283
164.143−0.005609225644f135p62F7/204f135p56s5/2609206
164.479−0.0026079792114f145p52P3/212334f135p56s5/2609206
165.3690.00160470813013654f135p62F5/2174104f135p56s3/2622123
165.5830.002603927869004f135p62F5/2174104f135p56s5/2621343
166.8270.00059942241033974f135p62F7/204f135p56s9/2599423
166.971−0.00159890521013734f135p62F7/204f135p56s7/2598904
167.382 59743532021724f135p62F7/204f135p56s5/2597436
168.084 5949411606494f135p62F7/204f135p56s7/2594941
168.381−0.00559389130025784f135p62F5/2174104f135p56s7/2611283
168.9800.0035917872505844f135p62F5/2174104f135p56s5/2609206
171.7270.002582320213474f145p52P3/212334f145p46s3/2583560
171.9730.0025814888464f135p62F5/2174104f135p56s7/2598904
172.2950.00158040026014314f145p52P3/212334f145p46s5/2581635
175.199−0.003570781385614f145p52P3/212334f145p46s1/2572004
176.237−0.002567418402994f145p52P3/212334f145p46s3/2568644
176.630−0.002566156541114f135p62F5/2174104f145p46s3/2583560
176.6940.0025659511504054f145p52P3/212334f145p46s3/2567191
177.232−0.00256423223904f135p62F5/2174104f145p46s5/2581635
181.410−0.001551237172024f135p62F5/2174104f145p46s3/2568644
181.888−0.003549788124194f135p62F5/2174104f145p46s3/2567191
187.608−0.00953302712564f145p52P1/2891234f135p56s3/2622123
189.616−0.002527381621304f135p62F7/204f135p56s7/2527376
189.667−0.004527241587184f145p52P3/212334f145p45d1/2528462
191.348e0.0015226071110694f135p62F7/204f125p65d5/2522610
191.6170.00152187594954f135p62F7/204f135p56s5/2521876
192.0700.0005206433234f145p52P3/212334f135p56s5/2521876
193.6140.0015164923201024f135p62F7/204f135p55d5/2516493
194.0770.00051525961774f145p52P3/212334f135p55d5/2516493
194.3150.00051462852594f135p62F7/204f135p56s5/2514628
194.3970.0015144113402494f135p62F7/204f135p56s7/2514413
194.527−0.00251406861022784f135p62F7/204f135p56s5/2514063
194.9980.00251282547574f145p52P3/212334f135p56s5/2514063
195.0210.009512765162514f135p62F7/204f135p55d7/2512790
195.598−0.00451125254021664f135p62F5/2174104f135p56s3/2528652
196.0930.00250996164028684f135p62F5/2174104f135p56s7/2527376
197.8350.00050547272089234f135p62F5/2174104f125p65d3/2522881
197.941e0.00050520241015694f135p62F5/2174104f125p65d5/2522610
198.171 50461359050134f135p62F7/204f135p56s9/2504615
198.2290.00050446767039504f135p62F5/2174104f135p56s5/2521876
198.625−0.0015034611654f145p52P3/212334f125p65d3/2504691
198.779 50307074058404f135p62F7/204f135p56s7/2503071
199.875 50031271019584f135p62F7/204f135p56s5/2500313
200.3670.000499085710186644f135p62F5/2174104f135p55d5/2516493
200.483−0.001498796730301074f135p62F7/204f135p55d7/2498792
200.787−0.001498041580208354f135p62F7/204f135p55d5/2498037
201.079−0.00449731769020274f145p52P3/212334f145p45d3/2498541
201.1190.00049721744031544f135p62F5/2174104f135p56s5/2514628
201.205−0.00149700670013884f135p62F5/2174104f135p56s7/2514413
201.2880.00149680028022384f145p52P3/212334f135p55d5/2498037
201.739 495691770381104f135p62F7/204f135p55d9/2495690
201.864−0.001495382710303204f135p62F5/2174104f135p55d7/2512790
202.2500.00049443733013364f145p52P1/2891234f145p46s3/2583560
203.6230.00049110431081104f145p52P3/212334f145p45d1/2492337
205.2210.00148728062063844f135p62F5/2174104f125p65d3/2504691
205.479 48666866030634f145p52P3/212334f145p46s3/2487901
206.634−0.00248394734016464f145p52P3/212334f135p55d5/2485175
207.0920.0024828782707464f145p52P1/2891234f145p46s1/2572004
207.4660.00148200734028164f145p52P3/212334f135p55d3/2483243
207.690−0.006481488431374f135p62F7/204f145p46s5/2481473
207.7360.0014813811702524f135p62F5/2174104f135p55d7/2498792
207.8500.00748111651544f135p62F5/2174104f145p45d3/2498541
207.884−0.0014810382608134f135p62F7/204f145p45d5/2481035
208.227−0.0024802451701764f145p52P3/212334f145p46s5/2481473
208.4200.001479800660145264f145p52P3/212334f145p45d5/2481035
208.5430.00247951749051194f145p52P1/2891234f145p46s3/2568644
209.1750.00047807037069424f145p52P1/2891234f145p46s3/2567191
211.0270.00547387367044274f145p52P3/212334f145p45d3/2475117
213.436−0.00146852413034f135p62F7/204f125p65d5/2468523
213.6610.0014680304224f135p62F7/204f125p65d5/2468034
213.7850.003467759271304f135p62F5/2174104f135p55d5/2485175
214.0010.0014672871701404f145p52P3/212334f125p65d5/2468523
214.2290.00546679169020804f145p52P3/212334f125p65d5/2468034
214.488−0.0034662261574f135p62F7/204f125p65d5/2466219
215.055−0.0054649966009464f145p52P3/212334f125p65d5/2466219
215.4960.0084640462674f135p62F5/2174104f145p46s5/2481473
215.6920.00146362469834f135p62F5/2174104f145p45d5/2481035
216.5960.0024616894603694f145p52P3/212334f125p65d3/2462927
217.6010.00645955664164f135p62F7/204f125p65d5/2459570
218.174−0.006458350350284f145p52P3/212334f125p65d5/2459570
218.429 4578145502154f135p62F7/204f125p65d9/2457815
218.477−0.00345771433174f135p62F5/2174104f145p45d3/2475117
218.5070.0004576514001184f135p62F7/204f135p55d5/2457652
218.747−0.0014571481802384f145p52P3/212334f125p65d3/2458380
219.0970.0004564192014f145p52P3/212334f135p55d5/2457652
220.2390.0074540531624f135p62F7/204f125p65d7/2454067
221.4430.0024515836004834f145p52P3/212334f125p65d3/2452821
221.908−0.0064506372202604f135p62F5/2174104f125p65d5/2468034
222.8180.00644879733654f135p62F5/2174104f125p65d5/2466219
223.2600.00044790862674f135p62F7/204f125p65d5/2447909
224.573−0.002445289964f135p62F7/204f125p65d5/2445286
225.2030.005444044110394f145p52P3/212334f125p65d5/2445286
227.497−0.0034395663402004f135p62F7/204f125p65d7/2439561
227.5190.00343952356134f145p52P1/2891234f135p56s3/2528652
227.6170.00343933544057864f145p52P1/2891234f145p45d1/2528462
229.011−0.0024366614101864f135p62F5/2174104f125p65d7/2454067
229.5410.003435652490154f135p62F7/204f145p45d7/2435658
229.5900.0014355581601254f135p62F7/204f125p65d5/2435561
229.666−0.00243541558294f135p62F5/2174104f125p65d3/2452821
230.2460.0054343182101564f145p52P3/212334f125p65d5/2435561
230.5440.00143375756034f145p52P1/2891234f125p65d3/2522881
230.964−0.00343296775574f135p62F7/204f125p65d5/2432963
231.6290.0034317255103194f145p52P3/212334f125p65d5/2432963
232.176 4307084601094f135p62F7/204f125p65d7/2430708
232.2880.0004304994401954f135p62F5/2174104f125p65d5/2447909
233.2250.0044287718404254f135p62F7/204f125p65d7/2428777
233.525−0.0024282211901964f135p62F7/204f125p65d7/2428216
233.709−0.0034278835503284f135p62F5/2174104f125p65d5/2445286
235.4180.003424776140784f135p62F7/204f125p65d5/2424781
235.509−0.00142461247104f145p52P3/212334f125p65d3/2425843
236.8840.002422148291174f135p62F5/2174104f125p65d7/2439561
238.243 4197393101254f135p62F5/2174104f125p65d5/2437149
238.330−0.0014195862464f135p62F7/204f125p65d7/2419585
239.004 4184022801194f135p62F7/204f125p65d9/2418403
239.089−0.00341825558024f135p62F5/2174104f145p45d7/2435658
239.142−0.0064181621501014f135p62F5/2174104f125p65d5/2435561
240.107 4164808104994f135p62F7/204f125p65d9/2416481
240.468−0.0024158551094f135p62F7/204f125p65d5/2415852
240.6340.000415569267284f145p52P1/2891234f125p65d3/2504691
241.0370.00841487469894f135p62F7/204f125p65d7/2414888
241.183−0.0024146231274f145p52P3/212334f125p65d5/2415852
241.867 4134519607164f135p62F7/204f125p65d9/2413450
242.8190.002411829420724f135p62F7/204f125p65d7/2411832
242.8290.004411813270174f135p62F7/204f125p65d5/2411819
243.088−0.00441137452264f135p62F5/2174104f125p65d7/2428777
243.4260.002410802120214f135p62F5/2174104f125p65d7/2428216
243.434 410788260364f135p62F5/2174104f125p65d3/2428199
243.5180.00441064710104f135p62F7/204f125p65d7/2410654
243.551−0.0034105917174f145p52P3/212334f125p65d5/2411819
244.281−0.002409364330744f135p62F7/204f125p65d5/2409362
244.8330.001408442190524f145p52P3/212334f125p65d5/2409676
244.8390.0014084311501024f135p62F5/2174104f125p65d3/2425843
245.0460.0004080875801914f135p62F7/204f125p65d7/2408086
245.334−0.00540760712144f145p52P3/212334f125p65d3/2408833
245.474−0.002407375470744f135p62F5/2174104f125p65d5/2424781
246.362 4059077802914f135p62F7/204f125p65d9/2405907
248.0070.000403215361044f145p52P1/2891234f145p45d1/2492337
248.508 4024014902624f135p62F5/2174104f125p65d5/2419811
248.6490.0014021746903294f135p62F5/2174104f125p65d7/2419585
248.765−0.0014019858106764f135p62F7/204f145p45d5/2401984
249.5330.00140074896013694f145p52P3/212334f145p45d5/2401984
249.873 4002038203404f135p62F7/204f125p65d9/2400203
250.010 3999841901044f135p62F5/2174104f125p65d3/2417394
250.811 3987061201064f135p62F7/204f135p55d9/2398707
250.9780.0013984414201264f135p62F5/2174104f125p65d5/2415852
251.500−0.001397614340874f135p62F7/204f125p65d5/2397612
251.584−0.0023974817905284f135p62F5/2174104f125p65d7/2414888
252.203−0.0013965069605914f135p62F7/204f135p55d7/2396505
252.2850.0013963773201094f145p52P3/212334f125p65d5/2397612
252.740−0.00239566493014714f145p52P3/212334f135p55d3/2396894
252.862−0.00139547379024f135p62F7/204f135p55d7/2395471
252.9890.001395274210484f135p62F7/204f135p55d5/2395276
253.534−0.0013944245901874f135p62F5/2174104f125p65d7/2411832
253.541−0.00339441382014114f135p62F5/2174104f125p65d5/2411819
253.6530.0013942397104434f145p52P3/212334f145p45d1/2395474
253.726−0.00439412623144f145p52P1/2891234f135p55d3/2483243
253.779−0.0013940437174f145p52P3/212334f135p55d5/2395276
253.812 393992100019604f135p62F7/204f125p65d7/2393992
254.294−0.00139324593015354f135p62F5/2174104f125p65d7/2410654
254.551 392849100013924f135p62F5/2174104f125p65d3/2410258
254.928−0.0013922674401684f135p62F5/2174104f125p65d5/2409676
255.1400.0073919426344f135p62F5/2174104f125p65d5/2409362
255.401 39154186029814f135p62F7/204f135p55d9/2391541
255.4790.0013914222001104f135p62F5/2174104f125p65d3/2408833
255.9670.0013906753905104f135p62F5/2174104f125p65d7/2408086
258.592−0.00438671098014334f135p62F7/204f135p55d5/2386704
259.069−0.0023859982801544f145p52P1/2891234f145p45d3/2475117
259.419−0.0043854769206334f145p52P3/212334f135p55d5/2386704
260.027−0.00138457614314f135p62F5/2174104f145p45d5/2401984
260.146 384400290544f135p62F7/204f135p55d9/2384400
261.002−0.0043831395494f135p62F7/204f135p55d5/2383133
261.767 3820196801554f135p62F7/204f135p55d7/2382019
261.8490.000381899450154f145p52P3/212334f135p55d5/2383133
262.537 380899530534f135p62F7/204f135p55d9/2380899
263.5210.0063794762314f135p62F5/2174104f135p55d3/2396894
263.7870.001379094300734f135p62F5/2174104f135p55d7/2396505
264.5080.00137806023854f135p62F5/2174104f135p55d7/2395471
264.644d0.0013778673201114f135p62F7/204f135p55d5/2377867
264.644d0.000377867320724f135p62F5/2174104f135p55d5/2395276
265.168 3771204601334f135p62F7/204f135p55d9/2377119
265.5100.00037663330784f145p52P3/212334f135p55d5/2377867
265.9190.000376054400114f145p52P3/212334f135p55d3/2377288
267.518−0.0023738077434f145p52P1/2891234f125p65d3/2462927
270.7940.0073692845124f135p62F5/2174104f135p55d5/2386704
270.8160.00236925410764f145p52P1/2891234f125p65d3/2458380

a The difference between the observed wavelength and the wavelength derived from the final level energies (Ritz wavelength). A blank value indicates that the upper level is derived from that line only; b The closed subshell 5s2 is omitted from configuration labelling; c Configuration attribution is arbitrary in a few cases (see text); d Doubly identified; e Questionable identification; h Estimated uncertainty ±0.005 Å.

Lu V The unique analysis of Lu V by Kaufman and Sugar [20] reports transitions between the configurations 4f13, 4f125d, 4f126s, and 4f126p. In addition to levels with the highest J-values often established from one single strong line, several levels were derived from two transitions according to selection rules taking into account the J-J coupling scheme that dominates in the 4f126s and 4f126p configurations, and the intermediate coupling between LS and J-J limits in the 4f125d configuration. However, no transition probabilities were reported. Indeed, large hyperfine structures could not be resolved because of the line broadening in the high-current spark used, and consequently their line list contained many blends and 15 doubly classified lines [20].

In the present work, parametric calculations were performed with the Cowan codes and the agreement between the intensities of classified lines and the calculated transition probabilities was checked. We paid attention to several unknown levels, mostly with small J-values and relatively weak transition probabilities. In the absence of new observations of lutetium spark spectra, the unique set of data available for extending the Lu V analysis is an unpublished line list of wavelengths initially considered as Lu V by Kaufman and Sugar before 1980 [21]. As transitions between high levels of Lu IV were excited under conditions similar to Lu V, some of these lines [21] were later interpreted as the 4f135f–4f135d transitions of Lu IV in [22], the corresponding transition array being traced up from Lu IV to W VII. As for Lu V, by comparing the transition probabilities for missing levels to the intensities of assumed Lu V lines, the following levels have been determined from some of their most probable transitions:

  • E = 291733.0 (4f123P2, 6p1/2) J = 3/2,

  • E = 291764.8 (4f123P2, 6p1/2) J = 5/2,

  • E = 296226.7 (4f121G4, 6p3/2) J = 5/2,

  • E = 160846.4 (4f123H4, 5d5/2) J = 3/2,

  • E = 176831.6 (4f123F3, 5d5/2) J = 11/2,

  • E = 177390.0 (4f123F3, 5d5/2) J = 5/2,

  • E = 197304.0 (4f121I6, 5d3/2) J = 13/2.

Table 2 gives 20 lines used for the present determination of new levels. Three of them are doubly identified. Two of these, 563.723 Å and 880.543 Å, were already reported in [20] with different identifications. All the other lines are from the line list of [21]. One weak line has been identified as the transition between previously known levels [20] confirming the latter. The absence of a predicted strong transition 313347.6 (4f121I6, 6p3/2) 9/2–243552.86 (4f121I6, 6s1/2) 11/2 with gA = 1.456 × 1010 s−1 and Ritz wavelength 1495.488 Å in the available line lists is unexplained. In the case of the isoelectronic spectrum Yb IV, a similar situation had been the starting point of a revised analysis [23].

Table 2. Newly identified lines of Lu V. Experimental wavelengths (estimated uncertainty ±0.005 Å) and intensities (in arbitrary units) are taken from the line list of [21]. Calculated gA values are from the present work.
Table 2. Newly identified lines of Lu V. Experimental wavelengths (estimated uncertainty ±0.005 Å) and intensities (in arbitrary units) are taken from the line list of [21]. Calculated gA values are from the present work.
λexp (Å)λRitz (Å)σRitz (cm−1)Intensity (arb.)gA (106·s−1)Eodd (cm−1)JoddEeven (cm−1)Jeven
563.723a,d563.708177396.91004250.07/2177396.99/2
563.723a,d563.730177390.010021080.07/2177390.05/2
786.582786.572127134.0167287980.45/2160846.43/2
806.043806.046124062.41668284908.85/2160846.43/2
856.592856.593116741.561552277587.95/2160846.43/2
874.638874.640114332.762451296226.75/2181894.07/2
875.645875.644114201.763034296226.75/2182025.05/2
880.543b,d880.534113567.5203306274413.95/2160846.43/2
880.543b,d880.556113564.6204832280099.97/2166535.37/2
898.980898.985111236.64015750288068.29/2176831.611/2
909.941909.941109897.21797287287.25/2177390.05/2
910.156910.160109870.841693291764.85/2181894.07/2
911.242911.246109739.852090291764.85/2182025.05/2
911.509911.511109708.051915291733.03/2182025.05/2
914.012914.012109407.831327296226.75/2186818.95/2
914.326914.326109370.23910286201.89/2176831.611/2
919.071919.076108804.93654286201.89/2177396.99/2
920.269920.265108664.33901285495.911/2176831.611/2
952.873952.872104945.911638291764.85/2186818.95/2
953.165953.161104914.111317291733.03/2186818.95/2
974.890d974.886102576.111498291764.85/2189188.77/2
974.890d974.889102575.815339299879.811/2197304.013/2
978.015978.017102247.749081299551.713/2197304.013/2

a Line already reported in [20] now interpreted as a blend of two resonance transitions with different gA values; b Line already reported in [20] now interpreted as a blend of two transitions with close gA values; d Doubly identified.

Hf VI [11]. A total of 189 lines in the region 193–474 Å were identified in our spectra. In comparison with W VIII, the analysis was extended by the identification of the 4f135s25p6–4f125s25p66d transitions. The interaction between the 4f135s25p55d and the 4f125s25p66s configurations appeared to be very important in this spectrum. The 4f125s25p66s levels were not established, but this configuration is present as the second or the third component of several 4f135s25p55d levels that helped to estimate its average energy by the appropriate fitting of calculations to measured level energies. Fine structure splittings and relative positions of the odd terms were established, and 142 levels of the excited, even configurations were found.

Ta VII [12]. The same set of transitions as in W VIII was studied in Ta VII in our observed spectra. A total of 237 lines in the region 191–354 Å were identified as transitions between four odd, low-lying levels and 126 even, excited levels. The 4f125s25p66s configuration in Ta VII, contrary to Hf VI, only partly overlaps with the upper part of the 4f125s25p65d configuration, and does not undergo a strong interaction from the latter. On the other hand, the 4f125s25p66s configuration strongly interacts with the 4f135s25p56s, 4f145s25p46s, and 4f145s25p45d configurations. The levels of the 4f125s25p66s configuration have large contributions from these three configurations, resulting in the observation of many “forbidden” E1 transitions to both low-lying 4f135s25p6 and 4f145s25p5 configurations. Six energy levels of the 4f125s25p66s configuration were found, which permitted the 4f125s25p66s configuration to be explicitly included in the parametric description of the Ta VII even energy levels.

Re IX [13]. Unlike the previous isoelectronic spectra Hf VI–W VIII, where the ground level is 4f135s25p6 2F7/2, Re IX is the first spectrum in the isoelectronic sequence where the ground level is found to be 4f145s25p5 2P3/2, whereas the 4f135s25p6 2F7/2 level is located 63,439 cm−1 above it. The 4f125s25p66s configuration now lies above all the other even configurations that give the resonance transitions, and their mutual interactions are not as important as in the previous spectra. A total of 112 lines in the region 146–244 Å have been identified in our observed spectra and 87 levels have been found.

As was mentioned in Section 2, the spectra (energy levels, wavelengths, and transition probabilities) were calculated with the use of Cowan codes [18]. In these calculations, ab initio Hartree-Fock values of radial integrals are improved by fitting the theoretical to experimental energy levels. In a case as complex as these spectra, involving strong interaction between seven configurations based on open 4f, 5s, and 5p sub-shells, the fitting process meets divergence problems if too many parameters are left free. Table 3, where the fitted energy parameters (FIT) for W VIII are listed, shows the numerous constraints applied. Due to this situation, the standard deviations of the fits, 340, 380, 440, and 494 cm−1 in Hf VI, Ta VII, W VIII and Re IX, respectively, are larger than in lower Z elements of the same sequence in which configuration interactions are weaker. For instance, a standard deviation of 77 cm−1 was obtained for the even configurations 4f12(5d+6s+6d+7s) in Yb IV [23] and 54 cm−1 for the even configurations 4f12(5d+6s) in Lu V [20].

Table 3. Fitted (FIT) energy parameters (in cm−1) of W VIII with uncertainties of their definition (Unc.) in comparison with the HFR parameters.
Table 3. Fitted (FIT) energy parameters (in cm−1) of W VIII with uncertainties of their definition (Unc.) in comparison with the HFR parameters.
ConfigurationParameterFITUnc.Status aHFRFIT/HFR b
Odd
4f135s25p6Eav74610 7546−85
ζ(4f)49740 50300.989
4f145s25p5Eav305290 40520−9991
ζ(5p)585930 589760.994
Even
4f145s5p6Eav377512 f384795−7283
4f135s25p55dEav403014241 3993113703
ζ(4f)502042r1150450.995
ζ(5p)60627116r2617130.982
ζ(5d)4668109r1047730.978
F2(4f,5p)524991446r12673760.779
F2(4f,5d)338471845r4453260.747
F4(4f,5d)16437896r4220120.747
F2(5p,5d)652572675r7784820.831
G2(4f,5p)284191152r3274661.035
G4(4f,5p)23650959r3228571.035
G1(4f,5d)14185369r5159750.888
G3(4f,5d)13292346r5149690.888
G5(4f,5d)10627277r5119680.888
G1(5p,5d)67784615r1952790.711
G3(5p,5d)42727388r1600600.711
4f135s25p56dEav775400 f7721713229
4f135s25p56sEav542202127 5410491153
ζ(4f)503142r1150590.994
ζ(5p)61816118r2629250.982
F2(4f,5p)530151460r12680410.779
G2(4f,5p)286121160r3276711.034
G4(4f,5p)23881968r3230811.035
G3(4f,6s)62911804 53121.184
G1(5p,6s)9567686r13106550.898
4f135s25p57sEav813134 f8131340
4f145s25p45dEav420075415 426261−6186
F2(5p,5p)766052809r14923680.829
ζ(5p)58700112r2596610.984
ζ(5d)4419104r1045200.978
F2(5p,5d)641162628r7771070.832
G1(5p,5d)66465603r1933270.712
G3(5p,5d)41891380r1588210.712
4f145s25p46dEav778313 f786313−8000
4f145s25p46sEav550168240 557405−7237
F2(5p,5p)774972842r14929900.833
ζ(5p)59855114r2608350.984
G1(5p,6s)9579687r13106690.898
4f145s25p47sEav813793 f825793−12000
4f145s5p56pEav992590 f9925900
4f145s5p55fEav1092223 f10922230
4f125s25p65dEav429242123 41711412128
F2(4f,4f)1482202174 1767870.838
F4(4f,4f)1067976059 1124720.95
F6(4f,4f)726853157 813730.893
α(4f)22 f0
β(4f)−1000 f0
γ(4f)−70 f0
ζ(4f)519843r1152270.994
ζ(5d)4926115r1050380.978
F2(4f,5d)362711297r6462270.785
F4(4f,5d)17578629r6224040.785
G1(4f,5d)14023365r5157920.888
G3(4f,5d)13329347r5150110.888
G5(4f,5d)10710279r5120620.888
4f125s25p66dEav819431 f80343116000
4f125s25p66sEav579803 f5700869717
F2(4f,4f)147636 f1772350.833
F4(4f,4f)110752 f1127830.982
F6(4f,4f)78585 f816060.963
α(4f)22 f0
β(4f)−1000 f0
γ(4f)−70 f0
ζ(4f)5161 f52410.985
G3(4f,6s)3974 f52450.758
4f135s25p55d–5s25p45dD2(4f,5p,4f,4f)−566099r8−65530.864
D4(4f,5p,4f,4f)−3095r8−3590.864
D2(5p,5p,4f,5p)−34863611r8−403590.864
D2(5p,5d,4f,5d)−27245478r8−315400.864
D4(5p,5d,4f,5d)−17854313r8−206690.864
E1(5p,5d,4f,5d)−24106423r8−279070.864
E3(5p,5d,4f,5d)−18066317r8−209150.864
4f135s25p55d–4f125s25p65dD2(4f,4f,4f,5p)−378752r9−45860.826
D4(4f,4f,4f,5p)85712r910390.826
D2(4f,5p,5p,5p)−32514444r9−393730.826
D2(4f,5d,5p,5d)−25571349r9−309660.826
D4(4f,5d,5p,5d)−16823230r9−203720.826
E1(4f,5d,5p,5d)−22364305r9−270810.826
E3(4f,5d,5p,5d)−16960231r9−205380.826
4f145s25p45d–4f125s25p65dD2(4f,4f,5p,5p)24561335r9297430.826
D4(4f,4f,5p,5p)20265277r9245400.826
4f135s25p56s–4f145s25p46sD2(4f,5p,4f,4f)−6391 f 1.0
D4(4f,5p,4f,4f)−244 f 1.0
D2(5p,5p,4f,5p)−40487 f 1.0

a f—fixed parameter, rn, n = 1–14—parameters linked by their corresponding HFR ratios; b For Eav, the difference between the fitted and ab initio values is given; the omitted electrostatic parameters of unknown configurations, as well as interaction parameters not listed in the table, are scaled by a factor of 0.85 with respect to the ab initio values; the omitted spin-orbit parameters are not scaled.

The spectra are calculated with the use of the fitted energy parameters. Table 3 also contains so-called scaling factors: ratios of the fitted to Hartree-Fock parameters (FIT/HFR). It is important that the scaling factors behave regularly along the isoelectronic sequence. For the average energies of configurations, instead of the scaling factors, the differences between fitted and ab initio values are shown in Figure 4. To guide the eye, straight lines connect the points in Figure 4. The points related to the 4f125s25p66s configuration (brown squares) are not connected because fittings were performed only in Lu V [20] and Ta VII [12] and the corresponding points are only roughly estimated in Hf VI [11] and W VIII [10]. It is seen that the differences between fitted and Hartree-Fock average energies of configurations are similar for groups of the same 4f sub-shell and progress quite regularly along the isoelectronic sequence.

Figure 4. Differences between the experimental and HFR average energies of configurations in the W VIII isoelectronic sequence.
Figure 4. Differences between the experimental and HFR average energies of configurations in the W VIII isoelectronic sequence.
Atoms 03 00273 g004 1024

The scaling factors for electrostatic energy parameters are presented in Figure 5 and Figure 6. They represent all electrostatic energy parameters in the configurations with the 4f14, 4f13, and 4f12 inner sub-shell because, as was mentioned above, for preventing instability of the least-squares fits, similar parameters were varied simultaneously, keeping their ratios fixed and equal to the corresponding ratios of their Hartree-Fock values. Figure 7 shows the scaling factors for spin-orbit parameters, which are connected by similar ratios for all even configurations. It is seen that all scaling factors within the limits of the definition errors behave regularly and can be approximated by a straight line or a polynomial of second degree.

Figure 5. Scaling factors (ratios FIT/HFR) for main electrostatic parameters in the 4f135p5nl and 4f145p4nl configurations.
Figure 5. Scaling factors (ratios FIT/HFR) for main electrostatic parameters in the 4f135p5nl and 4f145p4nl configurations.
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Figure 6. Scaling factors for main electrostatic parameters in the 4f125p65d configuration.
Figure 6. Scaling factors for main electrostatic parameters in the 4f125p65d configuration.
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Figure 7. Scaling factors for spin-orbit parameters (ZETA) in the even configurations.
Figure 7. Scaling factors for spin-orbit parameters (ZETA) in the even configurations.
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3.2. Spectrum of the W8+ Ion (W IX)

On the experimental spectrum recorded for the W VIII study (see Figure 3), a group of previously unidentified lines (marked by red colour) was observed between 170 Å and 200 Å, which could be due to W IX emission. It was possible to select lines that might belong to the W IX spectrum by measuring the variation of their intensities according to the plasma conditions. In the isoelectronic sequence of W IX, the last known members were Tm IV [24] and Yb V [25]. A systematic evaluation of energy ranges of low configurations along the isoelectronic sequence from Er III to W IX was given in Figure 2 of reference [25]. It predicted a change of the ground configuration from 4f125s25p6 (Er III–Hf VII) to 4f145s25p4 (Ta VIII and W IX).

Figure 8 shows a detailed structure of energy levels belonging to the 4f125s25p6 configuration from Er III to Re IX. It was derived from calculations for the group of even configurations 4f125s25p6 + 4f135s25p5 + 4f145s25p4, where all the HFR electrostatic integrals were scaled by a factor of 0.85 and the spin-orbit parameters were unscaled. The average energy Eav (5s25p64f12) was set to zero for all the spectra, which explains the negative energies for many levels on the figure. The highest level of the 4f125s25p6 configuration has a zero total angular momentum (J = 0), showing a 1S03P0 mixing that increases with the increasing importance of the spin-orbit parameter ζ4f relative to the Slater integrals Fk (4f,4f). Irregularity in its relative position along the isoelectronic sequence is a consequence of configuration interaction (CI) resulting from the crossing with the 4f145s25p4 configuration, which has a downward trend from Er III to W IX as shown in Figure 2 of Reference [25]. Indeed, the other nearby even configuration 4f135s25p5 has no level of J = 0 and produces CI effects only for levels of J = 1–4. The two J = 0 levels in the 4f145s25p4 configuration have calculated energies of 55634 and 211895 cm−1 in Ta VIII, −68449 and 112556 cm−1 in W IX, −206333 and −7437 cm−1 in Re X. The resulting CI energy shifts on the highest J = 0 levels of the 4f125s25p6 configurations in these ions are −3158, −4312, and +1682 cm−1, respectively. This simple case shows the order of magnitude of possible CI shifts for all perturbed levels with other J values. Although this case is of limited practical interest as no strong transitions are involved, it illustrates a complexity that is even higher in the odd parity configurations in the W IX isoelectronic sequence.

Therefore, the structure of W IX is significantly more complex than in W VIII. Figure 9 shows the presently predicted structure of the W IX low-lying configurations, in which the ground configuration is 4f145s25p4, and the 4f125s25p6 configuration is even higher than the first excited configuration 4f135s25p5. These three low-lying, even configurations result in three corresponding systems of excitations and E1 allowed transitions. Strongly interacting odd, excited configurations are all overlapping in the approximate energy range of 300,000 to 800,000 cm−1 above the ground state, which makes the predictions of the W IX spectrum critically dependent on the estimation of relative positions for energy levels. Figure 10 compares the W IX spectrum calculated in two approximations. In the approximation of Figure 10a the ab initio Hartree-Fock calculations were improved by a “standard” scaling of the energy parameters: scaling factors 0.85 for all electrostatic parameters and no scaling for spin-orbit parameters. The results in Figure 10b were obtained using the scaling factors from W VIII [10], which were derived from experimental levels (Table 3). Although these values do not significantly differ from the “standard” scaling factors, they nevertheless lead to drastic changes in the calculated spectra in the positions as well as in the intensities of the lines.

Figure 8. Isoelectronic comparison of the energy levels belonging to the 4f125s25p6 configuration from Er III to Re IX (black bars). Black dashed lines trace the highest J = 0 level. Red dashed lines show the trend of changes for the two perturbing J = 0 levels of 4f145s25p4. Only one J = 0 perturber could be represented (short red bars) on the chosen scale. Their perturbation effects are indicated by vertical arrows.
Figure 8. Isoelectronic comparison of the energy levels belonging to the 4f125s25p6 configuration from Er III to Re IX (black bars). Black dashed lines trace the highest J = 0 level. Red dashed lines show the trend of changes for the two perturbing J = 0 levels of 4f145s25p4. Only one J = 0 perturber could be represented (short red bars) on the chosen scale. Their perturbation effects are indicated by vertical arrows.
Atoms 03 00273 g008 1024
Figure 9. Low-lying energy levels of W IX according to Hartree-Fock calculations. Dashed vertical lines divide systems formed by excitation of the three lowest configurations: 4f145s25p4, 4f135s25p5, and 4f125s25p6. Arrows indicate electric dipole transitions between the configurations.
Figure 9. Low-lying energy levels of W IX according to Hartree-Fock calculations. Dashed vertical lines divide systems formed by excitation of the three lowest configurations: 4f145s25p4, 4f135s25p5, and 4f125s25p6. Arrows indicate electric dipole transitions between the configurations.
Atoms 03 00273 g009 1024
Figure 10. Calculated W IX spectrum: (a) “standard” scaling of Hartree-Fock parameters; (b) the Hartree-Fock parameters are scaled by the scaling factors taken from the W VIII spectrum. The colours of calculated lines correspond to the colours of transitions in Figure 9.
Figure 10. Calculated W IX spectrum: (a) “standard” scaling of Hartree-Fock parameters; (b) the Hartree-Fock parameters are scaled by the scaling factors taken from the W VIII spectrum. The colours of calculated lines correspond to the colours of transitions in Figure 9.
Atoms 03 00273 g010 1024

A list of the 189 strongest observed lines with intensities in the range of 50–1000, which could belong to W IX, is given in Table 4 (the full list consists of 483 spectral lines, see table S1 in Supplementary Materials). The wavelengths have an estimated uncertainty ±0.005 Å. The intensities of the lines are given in the same relative scale without correction for response of recording. It is impossible to reliably identify the W IX spectrum with the present predictions. More work is needed in the analyses of the isoelectronic spectra of the neighbouring chemical elements for making better calculations of the W IX spectrum. At this stage, it is only reasonable to suggest that the line at 193.830 Å can belong to the 4f135p53G6–4f135p45d (3P) 3H6 transition.

Table 4. Lines of W IX excited in a vacuum spark with intensities greater than 50 a.
Table 4. Lines of W IX excited in a vacuum spark with intensities greater than 50 a.
Int aλ (Å)σ(cm−1)
63170.006588215.3
84170.203587535.1
120170.269587306.0
339170.336587076.3
95170.353587017.1
120170.648586001.9
95171.216584056.2
309172.038581265.3
79174.997571437.4
56175.490569834.3
59176.002568174.1
81176.493566595.7
63176.660566060.4
82176.752565763.8
69177.197564342.1
102177.468563483.1
178177.504563367.9
66177.591563092.9
54178.005561782.3
97178.115561435.0
95178.140561355.3
67178.220561104.9
76178.473560308.2
104178.490560256.4
64178.508560199.6
86178.956558797.5
59179.023558588.7
110179.631556696.2
56180.080555310.0
69180.164555049.6
94180.570553802.8
109180.922552725.6
71180.955552624.8
128180.986552529.6
61181.247551733.3
51181.428551184.1
115181.818550000.3
100181.835549949.1
69181.958549578.9
74182.184548896.8
72182.437548135.0
143182.505547928.7
76182.614547604.1
77182.824546973.6
54182.932546652.4
166182.990546478.9
156183.081546205.8
107183.093546169.9
110183.271545640.7
53183.305545537.9
54183.573544743.0
51183.771544154.0
110184.033543380.8
63184.070543271.6
64184.156543018.2
248184.200542887.0
117184.271542680.2
58184.438542188.2
86184.538541893.8
95184.545541872.9
56184.818541072.3
59185.727538424.7
67186.218537004.4
54186.297536778.4
252186.428536399.6
51186.456536318.4
74186.479536253.7
79186.506536175.2
71186.539536080.1
166186.680535676.3
51187.890532225.4
92188.104531621.1
77188.114531591.4
104188.197531357.6
105188.706529925.1
82189.264528363.3
161190.062526143.6
66190.391525234.9
56190.596524670.6
107191.103523278.3
82191.464522291.7
304191.933521016.0
243191.984520876.5
54192.090520589.6
84192.117520516.2
87192.468519567.4
370192.591519234.0
199192.715518901.5
102192.771518749.7
541192.834518581.8
194192.859518514.3
132193.091517889.5
87193.174517667.5
115193.229517519.6
53193.342517218.7
118193.411517032.3
95193.428516987.7
290193.490516822.8
443193.549516664.0
303193.636516432.4
209193.719516210.8
181193.771516073.6
696193.830515915.8
362193.999515467.9
408194.105515184.6
148194.140515091.1
245194.173515006.0
229194.201514930.2
58194.268514752.3
500194.355514522.1
94194.553513998.2
1000194.646513752.1
66194.792513368.4
99194.803513339.9
77194.832513262.7
84194.910513057.8
66195.114512520.6
130195.192512315.8
153195.259512141.3
255195.432511685.6
102195.469511590.1
51195.483511552.7
439195.679511040.5
66195.745510869.3
67195.794510741.2
77195.921510410.6
140196.129509869.5
51196.242509573.9
53196.371509239.9
99196.577508707.6
192196.592508667.4
61196.665508478.4
66196.732508306.8
51196.947507751.1
357196.966507702.1
77197.013507579.9
120197.057507467.9
138197.136507263.3
169197.350506714.7
311197.607506056.2
72197.736505724.8
110197.810505535.9
66198.008505031.4
53198.095504807.3
114198.196504551.3
53198.378504088.7
71198.391504056.4
64198.464503869.7
128198.543503668.5
161198.562503621.8

a Relative intensity in arbitrary units not corrected for response of recording.

4. Conclusions

This work extended the state of knowledge on spectra of tungsten ions relevant for fusion plasma diagnostics. Using the spectrum of tungsten recorded on high resolution vacuum spectrographs under excitation in vacuum spark sources, a total of 187 lines of W VIII in the region 160–271 Å were identified for the first time. One hundred and two levels were found and transition probabilities were calculated [9,10]. For confirmation of the identifications of a spectrum as complex as W VIII, the isoelectronic spectra of neighboring chemical elements Hf VI, Ta VII, and Re IX were studied [11,12,13]. In each of these spectra, the transitions from 4f145s25p4nl and 4f135s25p6nl configurations to the low-lying configurations 4f145s25p5 and 4f135s25p6 were analyzed and, respectively 146, 130, and 87 energy levels were found. Previous analysis of Lu V [20] was extended by 22 newly identified lines and seven new levels. Parametric calculations of the spectra were performed with the aid of the Cowan codes [18], leading to fitted energy parameters together with their ratios to the corresponding ab initio values (scaling factors). In spite of sharp changes in relative positions of strongly interacting configurations along the isoelectronic sequence, resulting in noticeable variation in intensities and relative positions of lines, the scaling factors for the energy parameters show a rather regular trend. These isoelectronic regularities of scaling factors along the sequence Lu V – Hf VI – Ta VII – W VIII – Re IX can be considered as a proof of reliability of our atomic data for W VIII. Furthermore, the set of consistent scaling factors could be useful for predictions of other spectra of the 5d elements.

A list of 483 spectral lines in the region 170–199 Å, considered to belong to W IX, was prepared. The current state of the theory of atomic spectra does not allow for calculation of W IX with the accuracy needed for detailed identification of this spectrum and its application for quantitative diagnostics of tokamak plasmas.

Spectral lines from moderately charged tungsten ions (W IV–VI), in particular the 6p–6d and 6p–7s transitions of W V and the transitions between known levels of W III and W IV not reported in the compilation [2], are also present on our spectrograms. Their analyses are currently in progress.

Supplementary Materials

Table S1. Lines of W IX excited in a vacuum spark

Acknowledgments

This work was partly supported by the RFBR grant 10-02-00390a, by the Russian Academy of Sciences, by the French state funds managed by the Agence Nationale de Recherche (ANR) within the Investissements d'Avenir programme under reference ANR-11-IDEX-0004-02, and by a PPF grant of the Université Pierre et Marie Curie (UPMC). It is a part of the IAEA Coordinated Research Project “Spectroscopic and Collisional Data for Tungsten from 1 eV to 20 keV”. One of us (JFW) is indebted to his late colleagues Victor Kaufman and Jack Sugar from the National Institute of Standards and Technology (USA) for communication of the wavelengths of the lutetium spark spectrum.

Author Contributions

All authors contributed equally to this work.

Conflicts of Interest

The authors declare no conflict of interest.

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