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Article

Extended Atomic Structure Calculations for W11+ and W13+

by
Narendra Singh
1,
Sunny Aggarwal
1,* and
Man Mohan
2
1
Department of Physics, Shyamlal College, University of Delhi, Delhi 110032, India
2
Department of Physics & Astrophysics, University of Delhi, Delhi 110007, India
*
Author to whom correspondence should be addressed.
Atoms 2020, 8(4), 92; https://doi.org/10.3390/atoms8040092
Submission received: 1 August 2020 / Revised: 26 November 2020 / Accepted: 3 December 2020 / Published: 7 December 2020
(This article belongs to the Special Issue Atomic Structure Calculations of Complex Atoms)
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Abstract

We report an extensive and elaborate theoretical study of atomic properties for Pm-like and Eu-like Tungsten using Flexible Atomic Code (FAC). Excitation energies for 304 and 500 fine structure levels are presented respectively, for W11+ and W13+. Properties of the 4f-core-excited states are evaluated. Different sets of configurations are used and the discrepancies in identifications of the ground level are discussed. We evaluate transition wavelength, transition probability, oscillator strength, and collisional excitation cross section for various transitions. Comparisons are made between our calculated values and previously available results, and good agreement has been achieved. We have predicted some new energy levels and transition data where no other experimental or theoretical results are available. The present set of results should be useful in line identification and interpretation of spectra as well as in modelling of fusion plasmas.
Keywords:
oscillator strength; FAC; NIST; EBIT; spectroscopy
PACS:
32.70; Cs oscillator strengths

1. Introduction

There has been strong interest in the spectroscopy of tungsten as it is planned to be used in plasma facing components of future fusion devices, such as International Thermonuclear Experimental Reactor (ITER) due to its favourable physical and chemical properties, e.g., high energy threshold of sputtering, low sputtering yield, low tritium retention, and high melting temperature [1,2]. Since tungsten is a high-Z element (Z = 74), where Z is the atomic number, it will contribute a large fraction of energy carried out from the plasma, which leads to plasma cooling. Atomic data such as energy levels, radiative transition rates, and photoionization cross sections for low-charged and medium-charged ions are of great importance in the ITER plasma diagnostics [3]. In the past few decades, atomic data for several highly charged tungsten ions have been determined using different experimental and theoretical methods [4,5,6,7,8], but still there is demand for more accurate atomic data, especially for low and medium ionization states of tungsten.
In the present work, spectra of moderately charged states of tungsten (W11+ and W13+) are theoretically investigated. Several observations and theoretical calculations have been performed for Pm-like W but, for Eu-like W, only a few experimental data are available in the literature. In fact, only one theoretical energy value can be found for Eu-like W in the Atomic Spectra Database of the National Institute of Standards and Technology (NIST) [9]. These ionized states of tungsten are complex due to an open 4f shell, and obtaining accurate atomic data for these ions is a largely unsolved problem. For example, by inclusion of different configuration sets in the calculations, one will obtain a different ground state. The accuracy of a calculation can be estimated by considering (i) the convergence rate, (ii) the agreement between experimental measurements and theoretical calculations, and (iii) the difference between the velocity and length gauges of oscillator strength. Furthermore, results of calculations depend on the configuration-interaction (CI) effects, and, to ensure good accuracy, the most essential interactions must be included. In the past few years, we have calculated accurate atomic data by taking into account the essential interactions [10,11,12,13,14,15]. Brage and Froese Fischer [16] and Froese Fischer [17] presented a detailed review of analysis and evaluation of the CI effect in different atomic structure codes. In our present work, we have compared our calculated results with the available theoretical and experimental results and found good agreement.

2. Available Atomic Data

2.1. Pm-Like W (W13+)

Promethium-like ions have been studied both experimentally and theoretically over many years. There is still no full understanding of this sequence due to the open 4f shell, and obtaining accurate atomic data for this sequence is a largely unsolved problem. There is contradiction over the ground state for various charged states of Pm-like ions. Reliable atomic data for Pm-like ions are much needed, as some of these ions are promising candidates for the development of future optical clocks [18] and measurement of variation of the fine structure constant [19,20]. Curtis and Ellis [21] by their Hartree-Fock-Pauli (HFP) calculations showed that, in Pm-like W, the ground state is 4f145s 2S1/2 and dominant resonance lines are 5s-5p doublets. Theodosiou and Raftopoulos [22] performed a fully relativistic but single configuration calculation, using the Dirac-Fock approximation, and determined that the ground state of W13+ is odd parity 4f135s2 2F7/2. Hutton et al. [23] identified the transitions 4f145s 2S1/2- 4f145p 2P1/2,3/2 using an electron beam ion trap (EBIT). Vilkas et al. [24] evaluated transition wavelengths and lifetimes in Pm-like ions (including W13+) by taking 4f135s2, 4f135p2, 4f135s5p, 4f125s25p, 4f125s5p2, and 4f125p3 configurations using relativistic multi-reference Møller-Plesset second order perturbation theory (MR-MP). They claim to have accuracy of a predicted wavelength of about 0.25 Å for Pm-like W. Their [24] work targeted the 4f145s 2S1/2- 4f145p 2P1/2,3/2 transitions between excited states.
Kramida and Shirai [25] predicted that the ground state of Pm-like W is 4f135s2 2F7/2 while the first excited state is 4f135s2 2F5/2, which is separated by 18,000 cm−1 from the ground state. Wu and Hutton [26] discussed the behaviour of relative intensities of strong lines at different electron beam energies. Kramida [27] in his review noted the effect on the calculated energies from inclusion of two additional configurations (4f115s25p2 and 4f105s25p3). Safronova et al. [28] calculated excitation energies of some levels in Pm-like ions (including Pm-like W) using relativistic many body perturbation theory (RMBPT), Hebrew university Lawrence Livermore atomic code (HULLAC), and Hartree-Fock relativistic method (Cowan’s code). They confirmed that the ground state is 4f135s2 2F7/2. Qiu et al. [29] studied the visible and soft X-ray spectral regions and concluded that 4f collapse is not complete in W13+. According to them [29], four lines that were identified in the Berlin EBIT spectra [30] do not appear to originate from tungsten. Kobayashi et al. [31] observed extreme ultraviolet and visible spectra of W13+ using EBIT. Zhao et al. [32] observed visible transitions in W13+ using Shanghai high temperature superconducting EBIT. They predicted that, out of eight observed lines, five belong to transitions from 4f125s25p. Recently, Ding et al. [33] calculated wavelengths and transition rates of the 5s-5p transitions of tungsten ions (including W13+) using the relativistic configuration interaction method as implemented in the Flexible Atomic Code (FAC) [34].

2.2. Eu-Like W (W11+)

Ions of the Eu isoelectronic sequence (63 electron systems) are complex systems due to open 5s, 5p, and 4f subshells, but atomic structure calculations for these ions are needed to interpret the observed features. In the past, no extensive calculations for Eu-like W have been carried out. In fact, no spectral lines are available at the NIST website [9] for this particular ion. However, some authors reported selected transition wavelengths. Several studies contradict over the ground state for this ion. Kramida and Shirai [25] predicted that the ground state of Eu-like W is 4f135s25p2 4F7/2, while the first excited state is 4f145s25p 2P1/2 located approximately 11,000 cm−1 above it. They showed that the ground state of this ion is uncertain. Li et al. [30] reported spectra for some transitions in the range of 150–400 Å using the Shanghai high-temperature superconducting electron beam ion trap (SH-HtscEBIT). They have also performed calculations using the fully relativistic FAC using nine configurations, which generated 2538 fine-structure levels. They confirmed that the ground state is 4f135s25p2 4F7/2. Mita et al. [34] observed EUV spectra for multiple charged tungsten ions (including W11+). They have compared experimental measurements with collisional-radiative (CR) model calculations.

3. Theoretical Method

In spite of calculations performed by different authors for Pm-like and Eu-like W, there are no medium-scale calculations for these ions, and the shortage of complete and accurate data for these ions motivates this work. Most past calculations included very limited CI with an arbitrary choice of configurations. Therefore, in the present work, extensive calculations for W11+ and W13+ have been performed within the framework of FAC, which was developed by Gu [35]. FAC is a fully relativistic program used to compute the atomic structure, photoionization cross sections, and other atomic data. It is based on the Dirac-Hartree-Fock-Slater (DHFS) method, which uses perturbation theory. Optimization of orbitals is performed in a self-consistent-field iterative procedure in which the average energy of a fictitious mean configuration is minimized. This mean configuration represents the average electron cloud of the configurations retained in the CI expansion. In FAC, the Hamiltonian and configuration atomic state functions are similar to those of the MCDF (multi-configuration Dirac-Fock) method, including relativistic effects and higher-order QED effects, e.g., the Breit interaction in the zero-energy limit for the exchanged photon, and hydrogenic approximations for self-energy and vacuum polarization effects.
The effective Hamiltonian for an N-electron system is given by:
H   ^ = ∑ i = 1 N H ^ i + ∑ i = 1 N − 1 ∑ j = i + 1 N V i j ,
where H ^ i is the Dirac one-particle operator for the ith-electron and Vij represents effective electron-electron interactions.
An atomic state function (ASF) with total angular momentum J, its z-projection M, and parity p is assumed in the following form.
    ψ s ( J M P ) = ∑ m c m ( s ) ϕ ( γ m J M P )
where ϕ ( γ m J M P ) are configuration state functions (CSF), cm(s) are configuration mixing coefficients for the states, and γ m represents all information required to uniquely define a certain CSF. A detailed description of this theoretical approach can be found in the literature [35].

4. Result and Discussion

4.1. Eu-Like W

There is scarcity of complete, consistent, and reliable atomic data for Eu-like W in the literature. Therefore, in the present calculations, we have evaluated energy levels and radiative transition rates using FAC for Eu-like W with a set of electronic configurations ([Kr]4d10) 4f125s25p5d2, 4f125s25p25d, 4f125s25p3, 4f125s5p25d2, 4f135s25p5d, 4f135s25p2, 4f135p25d2, 4f135s5p5d2, 4f135s5p25d, 4f135s5p3, 4f145s25d, 4f145d5f2, 4f145d25f, 4f145d3, 4f145s25f, 4f145f3, 4f145s25p, 4f145p5d5f, 4f145p5d2, 4f145p5f2, 4f145p25d, 4f145p25f, 4f145p3, 4f145s5d2, 4f145s5f2, 4f145s5p5d, 4f145s5p5f, and 4f145s5p2, which generate 20,573 fine structure levels. Previous studies have not included so many configurations. Our ground state with this set of configurations is 4f135s25p2 2F7/2, which is also shown by Li et al. [30].
We found complexity in the energy levels of Eu-like W. We have performed several calculations with different configurations included and found significant differences in the results, especially for the ground state. We are discussing one such difference. We have performed calculations by including the 4f145l3 (l = s,p,d,f,g), 4f135s25p2, 4f135s5p3, 4f135s25p5d, 4f135s5p25d, 4f125s25p3, and 4f125s25p25d configurations, which generate 4653 fine structure levels. Using these configurations, the ground state is found to be 4f145s25p 2P1/2. This problem is due to an insufficient account for inter-electron correlations, as accurate calculation of energies of open-f-shell configurations requires accounting for single and double excitations not only from the valence shells (including 4f), but also from the core shells such as 4d, which makes the study of Eu-like W more difficult. Therefore, we decided to check the reliability of our calculated results by comparison with the other available theoretical and experimental results, as suggested by Froese Fischer [17].
We present energy levels (in Ryd.) of the lowest 304 levels in Table 1 calculated using FAC. In the column “configuration,” we give the configuration in LS coupling, while, in the “2J” column, the relativistic designation ending with the 2J value of a particular level is provided. Each shell is denoted so that 4f+7(7) represents seven electrons in the 4f7/2 subshell (J = 7/2), and 4f-5(5) represents five electrons in the 4f5/2 subshell (J = 5/2). The number in parentheses is two times the total angular momentum of the coupled shell. Immediately after the parentheses, there is a number indicating the 2J value obtained after all preceding shells are coupled. Completely filled relativistic subshells, such as (4f5/2)6 and (5s1/2)2, are omitted in the ‘2J’ designations. For example, 4f+6(8)p+1(3)11 represents [(4f5/26)0(4f7/26)4(5s2)0(5p1/22)0(5p3/21)3/2] (J = 11/2).
A widely used method of accuracy assessment is to match the calculated results with the critically evaluated data compiled by National institute of Standard and Technology (NIST). For Eu-like W, there is only one energy value present in the Atomic Spectra Database (ASD) [9] for the level 4f145s25p 2P1/2, which is 0.10 Rydberg (Ryd) with the uncertainty of 0.18 Ryd., while our calculated result for the same level is 0.105 Ryd. The NIST value was obtained in a very primitive Cowan-code (HFR) calculation made with only a few configurations included. Furthermore, Li et al. [36] reported the calculated value for the energies of the lowest 18 levels for W11+. They have included 4f135s25p2, 4f145s25p, 4f125s25p3, 4f135s25p5l, 4f135s25p6l, 4f125p25s25l, 4f125p25s26l, 4f145s25l, and 4f145s26l configurations, which generate 16,752 levels. The 4f145s25p 2P1/2 level does not appear among their list of the lowest 18 levels, while, in our calculation, this is the second level, which is also suggested by Kramida and Shirai [25]. We have performed a calculation by taking the same configurations as Li et al. [37] and found that 4f145s25p 2P1/2 is the second level, but they have not reported that. Our level designations for the first three levels are unambiguous, as the dominant eigenvector components constitute 96.3%, 97%, and 95.7%, respectively. For some levels, designations can be ambiguous due to mixing. The basis state given as the label of our calculated level 211 (59%) is mixed with that of level 217 (23%). Level designations of Li et al. [37] differ from our present calculation for some levels. This is because they have not included many important configurations within n = 5. Furthermore, for the 4f135s25p2 2F°7/2–2F°5/2 transition, Li et al. [37] reported the transition wavelength calculated using FAC. They have also measured the transition wavelength for the same transition using SH-HtscEBIT, which is 527.60 ± 0.06 nm, while their calculated wavelength is 516.37 nm for the same transition. Our wavelength for this transition calculated using FAC is 472.06 nm.
In Table 2, we present a comparison of wavelengths calculated with FAC with other experimental and theoretical wavelengths [30] for the (4f135s25p2)5/2–(4f135s5p3)3/2,5/2,7/2 transitions in Eu-like W, which is also shown in Figure 1. For all transitions, our calculated transition wavelengths agree with the experimental results of Li et al. [30] within 4.7%, while the theoretical results of Li et al. [30] deviate from their experimental results by up to 3.1%. Li et al. [30] also used FAC as in the present calculations, but with a different number of configurations. They have included the 4f145s25p, 4f145s5p2, 4f145s5p5d, 4f135s25p2, 4f135s25p5d, 4f135s5p3, 4f135s5p25d, 4f125s25p3, and 4f125s25p25d configurations, which generate 2538 fine structure levels.
Table 3 presents transition data for some strong electric dipole (E1) transitions (transition probability A > 108 s−1), respectively, from the ground state to various levels among the lowest 304 levels. We present a transition wavelength λ (in nm), a weighted oscillator strength gf (dimensionless) (both the length and velocity forms), and a transition rate Aji (s−1) calculated using FAC for Eu-like W. In Figure 2, a comparison of the ‘length’ and ‘velocity’ forms of gf (actually, results in the Babushkin and Coulomb gauges) is made for a few of the strongest transitions given in Table 3. One can see that the plot has the usual regular behaviour of increasing scatter with a decreasing line strength. However, for the strongest transitions, although the scatter is small, there is a systematic offset. The velocity form is smaller than the length form by 30%. Thus, all E1 transitions in Table 3 are estimated to have a common uncertainty of 30%.
Table 4 and Table 5 present transition data for magnetic dipole (M1) and magnetic quadrupole (M2) transitions from the ground state to some of the lowest 304 levels. We have presented transition wavelength λ (in nm), weighted oscillator strength gf (dimensionless), and transition rate Aji (s−1) calculated using FAC for Eu-like W. We predict new oscillator strength and transition probability data, where no other theoretical or experimental results are available, which will form the basis for future experimental work.
In Table 6, we provide collisional excitation cross-sections of Eu-like W from the ground state for the incident electron energy range of 65 to 125 eV. To the best of our knowledge, there are no other data points for collisional cross sections of Eu-like W in the literature within the given energy range.

4.2. Pm-Like W

Realizing the importance of Pm-like W and considering the paucity of atomic data for this ion, in the present work, we have calculated energy levels and radiative transition rates using FAC. To check the convergence of results, we have calculated results with different sets of configurations. Table 7 shows the configurations used in various calculations and the number of levels generated using these configurations. In the present work, we have increased the number of configurations in the sets in a systematic way to study the CI effect. In INP1, we have included 4f145s, 4f135s2, 4f135s5p, 4f145p, and 4f135p2 configurations, which generate 59 fine structure levels. In INP2, we have added the 4f125s25p, 4f125s5p2, and 4f125p3 configurations. These three configurations generate 621 levels. Furthermore, in order to check the effect on energies, INP3 forms a complex system by adding 4f115s25p2, 4f115s5p3, 4f105s25p3, and 4f105s5p4 to INP2, which generates a total of 7790 fine structure levels. We observe that the energies of these additional configurations are distributed inside the interval between the 4f145s and 4f145p energies, which shows the importance of adding these configurations. Finally, in the INPF column of Table 7, we have considered a larger CI for Pm-like W, which includes 4f145s, 4f135s2, 4f135s5p, 4f145p, 4f135p2, 4f125s25p, 4f125s5p2, 4f125p3, 4f115s25p2, 4f115s5p3, 4f105s25p3, 4f105s5p4, 4f125s25d, 4f125s5d2, 4f135d2, 4f135p5d, 4f135d2, 4f135p5d, 4f125p5d2, 4f125p25d, and 4f135s5d configurations. This set generates 13,160 levels. Table 8 shows the list of configurations included and the number of fine structure levels arising from each configuration of Pm-like W. The ground state configuration in each case is the same. Table 9 lists the energy values from each input for the 4f135s5p configuration. To check convergence, the difference between various output levels (Out1, Out2, Out3) and OutF is plotted in Figure 3. The different colors correspond to the different levels of Table 9. For levels 19 to 24, the difference is very large. Although the differences do not tend to zero with an increasing size of the calculation, the level splitting is almost the same in each output using different configuration sets for the first 18 levels, as shown in Figure 4. The root-mean-square (rms) difference from OUTF for the intervals ΔEj is 0.16 eV for OUT1, 0.10 eV for OUT2, and 0.08 eV for OUT3.
Table 10 presents the energy levels (in Rydberg) for the lowest 500 levels calculated with FAC for Pm-like W. As can be seen from this table, we report results for many new levels that are not listed in the NIST tables [9]. The format of Table 10 is the same as in Table 1. Since 85 levels out of 500 of Table 8 have the same ‘2J’ label as some other levels, we report the eigenvector compositions and mixing coefficients of W13+ in Table S2 of the supplementary material. In this table, we report the composition of the levels given in Table 10. In the column, the ‘Comp. No.’ of Table S2 contains sequential numbers of the basis states in decreasing order of contribution. We have included only a few basis states with the largest contributions. For each basis state, Table S2 gives an electronic configuration in the JJ coupling scheme. In these designations, ‘4f13’ represents that there are 13 electrons in the 4f subshell. In ‘4f+7(7)7,’ the ‘+’ sign denotes the larger of the two possible values of the angular momentum for the f electron, i.e., ‘4f+’ corresponds to 4f7/2. ‘7’ after the ‘+’ sign shows the number of electrons in the relativistic subshell 4f7/2, ‘(7),’ which means that the total 2J value of the 4f7/2 subshell is 7, and ‘7’ at the end denotes the final 2J value of the configuration.
In Table 11, some of the calculated energies are compared with those from critically evaluated data compiled by NIST [9], which are commonly used as a reference set for atomic results. The calculated values of Safronova et al. [28] and Zhou et al. [32] are also presented for comparison in Table 11. For the level 4f135s2 2F5/2, our calculated value matches the results of Zhou et al. [32]. For this level, the NIST value is from Vilkas et al. [24] whose results have been proven wrong by many authors in the recent past. They have used the MR-MP method for their calculation. For the 4f135s5p levels, the maximum difference between our calculation using FAC and the calculation of Safronova et al. [28] is 3.1%.
In Table 12, we present the transition data for the 4f135s2–4f135s5p and 4f145s-4f145p transitions including transition wavelengths (in nm), transition probabilities (Aji in s−1), and oscillator strengths (gfij, dimensionless). We give the oscillator strengths both in the velocity and length forms to check the accuracy of the calculated results, as it is one of the criteria used to assess the accuracy. The ratio of the velocity and length forms of the oscillator strength should be close to unity in accurate calculations. It is a necessary condition, even though it is not sufficient. As one can see in Table 12, this ratio is close to unity for most of the strong transitions. It is plotted in Figure 5 against line strength. For the Pm-like W, the systematic offset between the length and velocity forms is significantly smaller, at only about 10%. Therefore, the strongest E1 transitions with the line strength SV > 0.017 a.u. can be assigned an uncertainty of 10%. Those with 0.004 a.u. < SV < 0.017 a.u. can be assigned an uncertainty of 15%, and weaker transitions can be estimated as accurate to 30%. In Table 12, we also present the transition rates from the OUT3 results for comparison since, for magnetic transitions, the velocity form is not available. From Table 12, one can see that transition rates of OUTF have large differences from OUT3 for many levels, which is due to additional configurations in OUTF. In Table S1 of the supplementary material, we report M1 and E2 transition data for the transitions to various levels for 4f125s25p of Pm-like W, as these transitions could help to analyze experimental EBIT and tokamak spectra.
In the 4f135s2 2F7/2 and 4f135s2 2F5/2 levels, the mixing is very low, and their labeling is unambiguous. For both levels, the dominant eigenvector component contributes 98.3% and 98.4%, respectively. We would also like to mention that mixing among some of the levels is strong in our calculations. We found that level 250 is strongly coupled with level 317 with percentages of the corresponding components of 71% and 23%, respectively. We found that the level 277 is composed of 52% of the basis state used in its label mixed with 39% of the state used to label the level 357. Similarly, mixing among some other levels is very strong. Hence, the labeling of a particular level is not always based on the dominant eigenvector component. The configuration and J values given in Table 8 are definite, but the labels are not unique and can be interchanged.
Table S1 provides the means to estimate the uncertainties of the M1 and E2 transitions in Pm-like W. For example, Figure 6 plots the natural logarithm of the ratio AoutF/Aout3 of the E2 transition rates calculated in the two largest calculations. From this figure, one can see that, except for a few strongly discrepant transitions, the two data sets agree with each other fairly well. This figure is consistent with a typical behavior of calculated transition rates. For the strongest transitions (in this case, SoutF > 0.94 a.u.), the mean (i.e., root-mean-square, rms) of the logarithmic ratio is 0.014, corresponding to an agreement within 1.4% on average. For weaker transitions, the scatter of the data points increases, but, even for the weakest transitions with S < 0.00212 a.u., the mean disagreement is only 52%.
For M1 transitions, if three strongly discrepant transitions are excluded, the comparison of out3 and outF looks qualitatively similar, as shown in Figure 7. Here again, the strongest transitions (SoutF > 2.8 a.u. in this case) exhibit a mean discrepancy of 3.2%, while, for weaker transitions, it increases, but, even for the weakest transitions with S < 0.1 a.u., the mean discrepancy is only 15%. The three transitions excluded from this plot are 47 → 38, 65 → 38, and 74 → 38. For them, the discrepancies amount to a factor between 10 and 100.
In Table 13, we compare transition wavelengths (in nm) calculated using FAC with the data compiled by NIST [9] and with experimental and theoretical results of Kobayashi et al. [31] along with theoretical results of Safronova et al. [28] and Ding et al. [33]. For the transitions 0–91, 0–263, and 0–326, our calculated transition wavelengths are comparable (maximum difference of 5%) with the data compiled by NIST. For the transitions 0–433, 0–434, and 0–451, our calculated transition wavelength agrees well with the experimental results of Kobayashi et al. [31] (error within 0.4%) and are more accurate than the theoretical results of Safronova et al. [28] and Kobayashi et al. [31]. Furthermore, our calculated transition wavelengths for all transitions are in excellent agreement with the recent results of Ding et al. [33]. This is a clear indication of accuracy of our results.
In Table 14, we have compared transition wavelength (in nm) calculated with FAC for the transition 4f135s2 2F5/2–2F7/2 with other results for Pm-like W. The theoretical wavelengths are calculated in vacuum, while the experimental wavelengths are measured in standard air. Li et al. [30] and Zhao et al. [32] in Shanghai and Kobayashi et al. [31] in Tokyo observed similar spectra, but the charge state assignments differ by one. Recently, the Shanghai group confirmed [36] that their assignment made in References [30,32] was wrong and confirmed the assignment in Reference [31]. In addition, recent theoretical calculations by Ding et al. [33] also support the assignment in Reference [31]. Our theoretical result agrees within 2% with the experimental wavelengths of Kobayashi et al. [31]. This is better than the result of Safronova et al. [28], who used the COWAN code, and Vilkas et al. [24]. The differences of those two results from the measurement of Kobayashi et al. are larger (4% and 30%, respectively). The maximum discrepancy of 29% is between the experimental wavelength and the results of Vilkas et al. [24], which are responsible for discrepancies between our calculated results and the NIST data [9] quoted from Vilkas et al. [24]. Furthermore, our transition wavelength is in good agreement with the recent results of Ding et al. [33] as well as with other theoretical results listed in Table 14. In Table 15, we give the collisional excitation cross-sections of Pm-like W from the ground state for incident electron energy ranging from 45 to 75 eV. The collision cross section is given in units of 100 Mb.

5. Conclusions

Motivated by the need of atomic data for fusion plasma research, in the present paper, we have reported energy levels and radiative data, such as transition wavelengths and oscillator strengths, as well as collisional excitation cross sections for W11+ and W13+. For the calculations, the fully relativistic FAC has been adopted with the inclusion of CI. The effect of CI has been examined and investigated systematically by including different configurations. The present calculations provide new energy level data and are useful for accuracy assessments. Based on several comparisons with NIST and other available results, our listed energies are accurate (error <1%) for most levels of both ions. Energies have been listed for the lowest 304 and 500 levels of W11+ and W13+, respectively, but the remaining data for higher levels can be obtained from the authors on request. We have also presented radiative transition rates for both ions that are expected to be highly useful in analysis and modeling of plasmas. We have presented oscillator strengths in both velocity and length forms for both ions. We have compared our calculated data with the other available theoretical and experimental data and no (major) discrepancies have been found, except for some levels of Pm-like W calculated by Vilkas et al. [24]. Furthermore, we observed discrepancies in the ground state of Eu-like W, which depends on the configurations included. There is scope for further work in these complex systems.

Supplementary Materials

The following are available online at https://www.mdpi.com/2218-2004/8/4/92/s1. Table S1: Magnetic dipole (M1) and electric quadrupole (E2) transition data for transitions within the 4f13.5s2 and 4f12.5s2.5p configurations of Pm-like W. Table S2: Eigenvector compositions and mixing coefficients for Pm-like W.

Author Contributions

All authors have contributed equally in preparation of the manuscript. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by IAEA grant number 23244.

Acknowledgments

We are thankful to IAEA for providing financial support through a research coordination project entitled “Atomic data for vapour shielding in fusion devices” contract no. 23244. “Drafts of Figure 2, Figure 3, Figure 4, Figure 5, Figure 6 and Figure 7, as well as Tables S1 and S2 of the Supplementary Materials, were made for us by an anonymous Reviewer, whose help in preparation of this article for publication is gratefully acknowledged”.

Conflicts of Interest

The authors declare no conflict of interest.

References

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Atoms 08 00092 g001
Figure 1. Comparison of theoretical wavelengths with the experimental wavelengths of Reference [30].
Figure 1. Comparison of theoretical wavelengths with the experimental wavelengths of Reference [30].
Atoms 08 00092 g001
Atoms 08 00092 g002
Figure 2. A comparison of the length and velocity forms of oscillator strengths for a few of the strongest transitions of W11+.
Figure 2. A comparison of the length and velocity forms of oscillator strengths for a few of the strongest transitions of W11+.
Atoms 08 00092 g002
Atoms 08 00092 g003
Figure 3. Difference of energy values of each output OUTn (n = 1, 2, 3) from the final calculation for the 4f135s5p configuration.
Figure 3. Difference of energy values of each output OUTn (n = 1, 2, 3) from the final calculation for the 4f135s5p configuration.
Atoms 08 00092 g003
Atoms 08 00092 g004
Figure 4. Differences of energy intervals relative to the lowest level (with index 1) for each output OUTn (n = 1, 2, 3) from the final calculation for the 4f135s5p configuration.
Figure 4. Differences of energy intervals relative to the lowest level (with index 1) for each output OUTn (n = 1, 2, 3) from the final calculation for the 4f135s5p configuration.
Atoms 08 00092 g004
Atoms 08 00092 g005
Figure 5. A comparison of the velocity and length forms of oscillator strength for a few of the strongest transitions (E1) of W13+.
Figure 5. A comparison of the velocity and length forms of oscillator strength for a few of the strongest transitions (E1) of W13+.
Atoms 08 00092 g005
Atoms 08 00092 g006
Figure 6. Natural logarithm of the ratio AoutF/Aout3 of the E2 transition rates calculated in the two largest calculations for W13+. The horizontal axis contains the line strengths SoutF of the largest calculation in atomic units.
Figure 6. Natural logarithm of the ratio AoutF/Aout3 of the E2 transition rates calculated in the two largest calculations for W13+. The horizontal axis contains the line strengths SoutF of the largest calculation in atomic units.
Atoms 08 00092 g006
Atoms 08 00092 g007
Figure 7. Natural logarithm of the ratio AoutF/Aout3 of the M1 transition rates calculated in the two largest calculations for W13+. The horizontal axis contains the line strengths SoutF of the largest calculation in atomic units.
Figure 7. Natural logarithm of the ratio AoutF/Aout3 of the M1 transition rates calculated in the two largest calculations for W13+. The horizontal axis contains the line strengths SoutF of the largest calculation in atomic units.
Atoms 08 00092 g007
Table 1. Energies (in eV) of 304 lowest levels of Eu-like W.
Table 1. Energies (in eV) of 304 lowest levels of Eu-like W.
LevelConfiguration2JEnergy (eV)
04f135s25p24f+7(7)70.000000
14f145s25p15p-1(1)11.487410
24f135s25p24f-5(5)52.635751
34f135s25p24f+7(7)7.5p-1(1)6.5p+1(3)910.406621
44f135s25p24f+7(7)7.5p-1(1)8.5p+1(3)511.338412
54f135s25p24f+7(7)7.5p-1(1)6.5p+1(3)311.495144
64f135s25p24f+7(7)7.5p-1(1)8.5p+1(3)711.982615
74f135s25p24f-5(5)5.5p-1(1)6.5p+1(3)312.116363
84f135s25p24f+7(7)7.5p-1(1)8.5p+1(3)1112.306080
94f135s25p24f+7(7)7.5p-1(1)6.5p+1(3)512.599174
104f135s25p24f+7(7)7.5p-1(1)8.5p+1(3)912.897008
114f135s25p24f+7(7)7.5p-1(1)6.5p+1(3)712.986980
124f125s25p34f+6(12)12.5p+1(3)1513.168432
134f135s25p24f-5(5)5.5p-1(1)4.5p+1(3)713.903781
144f135s25p24f-5(5)5.5p-1(1)6.5p+1(3)514.122897
154f125s25p34f+6(8)8.5p+1(3)1114.291251
164f135s25p24f-5(5)5.5p-1(1)6.5p+1(3)914.621510
174f125s25p34f+6(12)12.5p+1(3)1314.631127
184f135s25p24f-5(5)5.5p-1(1)4.5p+1(3)114.679897
194f125s25p34f+6(8)8.5p+1(3)914.759824
204f125s25p34f-5(5)5.4f+7(7)10.5p+1(3)715.082206
214f135s25p24f+7(7)7.5p-1(1)8.5p+1(3)915.398633
224f125s25p34f+6(8)8.5p+1(3)1115.501744
234f135s25p24f-5(5)5.5p-1(1)4.5p+1(3)515.508532
244f145s25p15p+1(3)315.538168
254f125s25p34f+6(8)8.5p+1(3)715.864304
264f135s25p24f-5(5)5.5p-1(1)4.5p+1(3)315.922657
274f125s25p34f-5(5)5.4f+7(7)10.5p+1(3)1316.076542
284f125s25p34f+6(8)8.5p+1(3)516.145582
294f125s25p34f-5(5)5.4f+7(7)8.5p+1(3)716.400673
304f125s25p34f+6(4)4.5p+1(3)516.824471
314f125s25p34f-5(5)5.4f+7(7)10.5p+1(3)916.857139
324f125s25p34f-5(5)5.4f+7(-7)10.5p+1(3)1117.125132
334f125s25p34f+6(4)4.5p+1(3)317.421249
344f125s25p34f-5(5)5.4f+7(7)6.5p+1(3)717.509417
354f125s25p34f-5(5)5.4f+7(7)8.5p+1(3)1117.527564
364f125s25p34f-5(5)5.4f+7(7)8.5p+1(3)917.779745
374f125s25p34f-4(8)8.5p+1(3)517.834973
384f125s25p34f+6(4)4.5p+1(3)117.891446
394f125s25p34f-5(5)5.4f+7(7)6.5p+1(3)518.053266
404f125s25p34f-5(5)5.4f+7(7)6.5p+1(3)718.202150
414f125s25p34f-5(5)5.4f+7(7)6.5p+1(3)918.356867
424f125s25p34f-5(5)5.4f+7(7)8.5p+1(3)718.596612
434f125s25p34f-5(5)5.4f+7(7)6.5p+1(3)319.061518
444f125s25p34f-5(5)5.4f+7(7)8.5p+1(3)519.422447
454f125s25p34f-4(8)8.5p+1(3)719.635564
464f125s25p34f-4(8)8.5p+1(3)1119.732177
474f125s25p34f-4(8)8.5p+1(3)919.983774
484f125s25p34f-5(5)5.4f+7(7)4.5p+1(3)520.239222
494f125s25p34f-5(5)5.4f+7(7)12.5p+1(3)1520.693116
504f125s25p34f-5(5)5.4f+7(7)4.5p+1(3)720.821427
514f125s25p34f+6(4)4.5p+1(3)120.856783
524f125s25p34f+6(4)4.5p+1(3)320.905069
534f125s25p34f-5(5)5.4f+7(7)12.5p+1(3)921.326702
544f125s25p34f+6(0)0.5p+1(3)321.575392
554f125s25p34f-5(5)5.4f+7(7)2.5p+1(3)522.169730
564f125s25p34f-5(5)5.4f+7(7)12.5p+1(3)1122.498936
574f125s25p34f-5(5)5.4f+7(7)2.5p+1(3)122.737919
584f125s25p34f-5(5)5.4f+7(7)12.5p+1(3)1322.989126
594f125s25p34f-4(4)4.5p+1(3)523.102462
604f125s25p34f-5(5)5.4f+7(7)2.5p+1(3)323.176613
614f125s25p34f-4(4)4.5p+1(3)723.443646
624f125s25p34f-5(5)5.4f+7(7)4.5p+1(3)323.652780
634f125s25p34f-4(4)4.5p+1(3)124.886345
644f125s25p34f+6(12)12.5p-1(1)11.5p+2(4)1525.198660
654f135s25p24f+7(7)7.5p+2(4)1125.225674
664f135s25p24f+7(7)7.5p+2(4)925.463906
674f135s25p24f+7(7)7.5p+2(4)725.560618
684f135s25p24f+7(7)7.5p+2(4)325.845469
694f125s25p34f+6(12)12.5p-1(1)11.5p+2(4)1326.159966
704f135s25p24f+7(7)7.5p+2(4)526.641175
714f125s25p34f+6(8)8.5p-1(1)7.5p+2(4)1126.677789
724f125s25p34f+6(12)12.5p-1(1)13.5p+2(4)926.929062
734f125s25p34f+6(12)12.5p-1(1)13.5p+2(4)1127.017239
744f135s25p24f-5(5)5.5p+2(4)527.183576
754f125s25p34f+6(8)8.5p-1(1)9.5p+2(4)727.403642
764f135s25p24f-5(5)5.5p+2(4)327.583722
774f125s25p34f+6(8)8.5p-1(1)7.5p+2(4)927.737449
784f135s25p24f-5(5)5.5p+2(4)927.825543
794f135s25p24f-5(5)5.5p+2(4)127.843724
804f125s25p34f+6(8)8.5p-1(1)9.5p+2(4)528.013025
814f135s25p24f-5(5)5.5p+2(4)728.016205
824f125s25p34f+6(12)12.5p-1(1)13.5p+2(4)1728.046730
834f125s25p34f-5(5)5.4f+7(7)10.5p-1(1)11.5p+2(4)928.073077
844f125s25p34f-5(5)5.4f+7(7)10.5p-1(1)11.5p+2(4)1128.092883
854f125s25p34f-5(5)5.4f+7(7)10.5p-1(1)9.5p+2(4)1328.093387
864f125s25p34f+6(12)12.5p-1(1)13.5p+2(4)1528.284992
874f125s25p34f-5(5)5.4f+7(7)10.5p-1(1)11.5p+2(4)728.296631
884f125s25p34f+6(12)12.5p-1(1)13.5p+2(4)1328.439835
894f125s25p34f-5(5)5.4f+7(7)8.5p-1(1)9.5p+2(4)728.636467
904f125s25p34f-5(5)5.4f+7(7)8.5p-1(1)9.5p+2(4)528.890217
914f125s25p34f-5(5)5.4f+7(7)6.5p-1(1)5.5p+2(4)929.031733
924f125s25p34f+6(8)8.5p-1(1)9.5p+2(4)1329.106108
934f125s25p34f-5(5)5.4f+7(7)8.5p-1(1)7.5p+2(4)1129.109282
944f125s25p34f+6(12)12.5p-1(1)11.5p+2(4)729.138058
954f125s25p34f-5(5)5.4f+7(7)6.5p-1(1)7.5p+2(4)529.247008
964f125s25p34f-5(5)5.4f+7(7)10.5p-1(1)11.5p+2(4)929.463518
974f125s25p34f-5(5)5.4f+7(7)6.5p-1(1)7.5p+2(4)329.510742
984f125s25p34f+6(4)4.5p-1(1)3.5p+2(4)729.581339
994f125s25p34f+6(8)8.5p-1(1)7.5p+2(4)329.660947
1004f125s25p34f-5(5)5.4f+7(7)8.5p-1(1)7.5p+2(4)1129.690268
1014f125s25p34f+6(4)4.5p-1(1)5.5p+2(4)129.785016
1024f125s25p34f-5(5)5.4f+7(7)6.5p-1(1)7.5p+2(4)729.802755
1034f125s25p34f+6(8)8.5p-1(1)9.5p+2(4)1129.835407
1044f125s25p34f+6(12)12.5p-1(1)11.5p+2(4)929.935173
1054f125s25p34f+6(8)8.5p-1(1)7.5p+2(4)929.992789
1064f125s25p34f-4(8)8.5p-1(1)9.5p+2(4)530.135794
1074f125s25p34f+6(8)8.5p-1(1)7.5p+2(4)730.208798
1084f125s25p34f-4(0)0.5p+1(3)330.252252
1094f125s25p34f-5(5)5.4f+7(7)10.5p-1(1)11.5p+2(4)1530.315463
1104f125s25p34f-5(5)5.4f+7(7)6.5p-1(1)7.5p+2(4)530.367034
1114f125s25p34f-5(5)5.4f+7(7)10.5p-1(1)11.5p+2(4)1330.420168
1124f125s25p34f-4(8)8.5p-1(1)9.5p+2(4)530.515569
1134f125s25p34f-5(5)5.4f+7(7)10.5p-1(1)9.5p+2(4)1130.618863
1144f125s25p34f-4(8)8.5p-1(1)9.5p+2(4)930.650657
1154f125s25p34f+6(8)8.5p-1(1)7.5p+2(4)330.755836
1164f125s25p34f-4(8)8.5p-1(1)9.5p+2(4)730.950833
1174f135s25p24f+7(7)7.5p+2(0)731.028018
1184f125s25p34f-5(5)5.4f+7(7)10.5p-1(1)9.5p+2(4)531.135297
1194f125s25p34f-5(5)5.4f+7(7)8.5p-1(1)9.5p+2(4)1331.239437
1204f125s25p34f-5(5)5.4f+7(7)10.5p-1(1)9.5p+2(4)931.300041
1214f125s25p34f+6(12)12.5p-1(1)11.5p+2(0)1131.395345
1224f125s25p34f-5(5)5.4f+7(7)6.5p-1(1)5.5p+2(4)131.455875
1234f125s25p34f-4(8)8.5p-1(1)9.5p+2(4)1131.524113
1244f125s25p34f-5(5)5.4f+7(7)10.5p-1(1)9.5p+2(4)931.631040
1254f125s25p34f+6(4)4.5p-1(1)5.5p+2(4)531.660101
1264f125s25p34f-5(5)5.4f+7(7)10.5p-1(1)9.5p+2(4)731.690291
1274f125s25p34f-5(5)5.4f+7(7)6.5p-1(1)7.5p+2(4)1131.716101
1284f125s25p34f-4(8)8.5p-1(1)9.5p+2(4)731.778531
1294f125s25p34f-5(5)5.4f+7(7)8.5p-1(1)7.5p+2(4)331.849222
1304f145s15p25s+1(1)131.888981
1314f125s25p34f-5(5)5.4f+7(7)8.5p-1(1)9.5p+2(4)1132.085578
1324f125s25p34f+6(4)4.5p-1(1)3.5p+2(4)132.085592
1334f125s25p34f-5(5)5.4f+7(7)8.5p-1(1)7.5p+2(4)532.119796
1344f125s25p34f+6(4)4.5p-1(1)3.5p+2(4)332.155819
1354f125s25p34f-5(5)5.4f+7(7)10.5p-1(1)9.5p+2(4)732.172054
1364f125s25p34f+6(4)4.5p-1(1)5.5p+2(4)932.219276
1374f125s25p34f+6(12)12.5p-1(1)13.5p+2(0)1332.250253
1384f125s25p34f-5(5)5.4f+7(7)6.5p-1(1)5.5p+2(4)332.284567
1394f125s25p34f-5(5)5.4f+7(7)6.5p-1(1)7.5p+2(4)932.310825
1404f125s25p34f+6(4)4.5p-1(1)3.5p+2(4)532.430748
1414f125s25p34f-4(8)8.5p-1(1)7.5p+2(4)732.599412
1424f125s25p34f-5(5)5.4f+7(7)2.5p-1(1)1.5p+2(4)532.710532
1434f125s25p34f+6(8)8.5p-1(1)9.5p+2(0)932.722893
1444f125s25p34f-5(5)5.4f+7(7)6.5p-1(1)5.5p+2(4)332.726514
1454f125s25p34f-4(8)8.5p-1(1)9.5p+2(4)1332.788252
1464f125s25p34f-5(5)5.4f+7(7)6.5p-1(1)7.5p+2(4)732.803691
1474f135s25p24f-5(5)5.5p+2(0)533.190258
1484f125s25p34f-5(5)5.4f+7(7)12.5p-1(1)13.5p+2(4)933.311662
1494f125s25p34f-4(8)8.5p-1(1)9.5p+2(4)1133.320945
1504f125s25p34f-5(5)5.4f+7(7)12.5p-1(1)11.5p+2(4)1533.356951
1514f125s25p34f+6(8)8.5p-1(1)7.5p+2(0)733.409179
1524f125s25p34f-4(8)8.5p-1(1)7.5p+2(4)333.506910
1534f125s25p34f-4(8)8.5p-1(1)7.5p+2(4)533.541559
1544f125s25p34f-4(4)4.5p-1(1)5.5p+2(4)133.637808
1554f125s25p34f-5(5)5.4f+7(7)8.5p-1(1)7.5p+2(0)733.638887
1564f125s25p34f-5(5)5.4f+7(7)12.5p-1(1)13.5p+2(4)1133.703349
1574f125s25p34f-5(5)5.4f+7(7)10.5p-1(1)9.5p+2(0)933.705428
1584f125s25p34f-5(5)5.4f+7(7)8.5p-1(1)9.5p+2(0)933.869720
1594f125s25p34f-4(8)8.5p-1(1)7.5p+2(4)333.944386
1604f125s25p34f-4(8)8.5p-1(1)9.5p+2(4)1334.004247
1614f125s25p34f-4(8)8.5p-1(1)7.5p+2(4)334.099755
1624f125s25p34f+6(4)4.5p-1(1)5.5p+2(0)534.102104
1634f125s25p34f-5(5)5.4f+7(7)10.5p-1(1)11.5p+2(0)1134.135950
1644f125s25p34f-4(8)8.5p-1(1)7.5p+2(4)734.455709
1654f125s25p34f-4(8)8.5p-1(1)7.5p+2(4)534.503115
1664f125s25p34f-5(5)5.4f+7(7)4.5p-1(1)5.5p+2(4)134.566251
1674f125s25p34f-5(5)5.4f+7(7)6.5p-1(1)7.5p+2(0)734.581228
1684f125s25p34f-4(8)8.5p-1(1)7.5p+2(4)934.785497
1694f125s25p34f-4(4)4.5p-1(1)5.5p+2(4)934.912240
1704f125s25p34f-4(4)4.5p-1(1)3.5p+2(4)534.933144
1714f125s25p34f-5(5)5.4f+7(7)4.5p-1(1)5.5p+2(4)335.233127
1724f125s25p34f-5(5)5.4f+7(7)12.5p-1(1)11.5p+2(4)1335.331629
1734f125s25p34f-4(4)4.5p-1(1)5.5p+2(4)735.335261
1744f125s25p34f-5(5)5.4f+7(7)2.5p-1(1)3.5p+2(4)135.353611
1754f125s25p34f-4(8)8.5p-1(1)7.5p+2(4)535.358568
1764f125s25p34f-5(5)5.4f+7(7)4.5p-1(1)3.5p+2(4)335.443479
1774f125s25p34f-5(5)5.4f+7(7)12.5p-1(1)13.5p+2(4)1735.506997
1784f125s25p34f-5(5)5.4f+7(7)12.5p-1(1)11.5p+2(4)1135.519342
1794f125s25p34f-5(5)5.4f+7(7)12.5p-1(1)13.5p+2(4)1535.687177
1804f125s25p34f-5(5)5.4f+7(7)2.5p-1(1)3.5p+2(4)535.832089
1814f125s25p34f-4(8)8.5p-1(1)9.5p+2(0)935.889007
1824f125s25p34f-5(5)5.4f+7(7)8.5p-1(1)7.5p+2(0)735.953208
1834f125s25p34f-4(4)4.5p-1(1)3.5p+2(4)136.137604
1844f125s25p34f-5(5)5.4f+7(7)2.5p-1(1)3.5p+2(4)336.266912
1854f125s25p34f-5(5)5.4f+7(7)6.5p-1(1)5.5p+2(0)536.417751
1864f125s25p34f-5(5)5.4f+7(7)12.5p-1(1)11.5p+2(4)736.686838
1874f125s25p34f-5(5)5.4f+7(7)12.5p-1(1)11.5p+2(4)936.981241
1884f125s25p34f-5(5)5.4f+7(7)2.5p-1(1)1.5p+2(4)336.996846
1894f125s25p34f+6(4)4.5p-1(1)5.5p+2(0)537.131836
1904f125s25p34f-5(5)5.4f+7(7)4.5p-1(1)3.5p+2(4)137.136391
1914f125s25p34f-5(5)5.4f+7(7)12.5p-1(1)11.5p+2(4)737.253204
1924f125s25p34f-4(4)4.5p-1(1)3.5p+2(4)537.454373
1934f125s25p34f-5(5)5.4f+7(7)2.5p-1(1)3.5p+2(4)737.610500
1944f125s25p34f-4(4)4.5p-1(1)3.5p+2(4)337.748395
1954f125s25p34f-4(4)4.5p-1(1)5.5p+2(4)937.811969
1964f125s25p34f-4(8)8.5p-1(1)7.5p+2(0)738.345107
1974f125s25p34f-5(5)5.4f+7(7)4.5p-1(1)3.5p+2(0)338.556955
1984f125s25p34f-5(5)5.4f+7(7)2.5p-1(1)3.5p+2(4)538.846072
1994f125s25p34f-5(5)5.4f+7(7)12.5p-1(1)13.5p+2(0)1339.722163
2004f135s15p34f+7(7)7.5s+1(1)8.5p+1(3)1139.977587
2014f125s25p34f-5(5)5.4f+7(7)2.5p-1(1)1.5p+2(0)140.009869
2024f135s15p34f+6(0)0.5p-1(1)1.5p+2(0)140.143273
2034f125s25p34f-4(4)4.5p-1(1)3.5p+2(0)340.319889
2044f125s25p34f-5(5)5.4f+7(7)12.5p-1(1)11.5p+2(0)1140.349004
2054f145s15p25s+1(1)1.5p-1(1)0.5p+1(3)340.558843
2064f125s25p34f-5(5)5.4f+7(7)4.5p-1(1)5.5p+2(0)540.642163
2074f135s15p34f+7(7)7.5s+1(1)6.5p+1(3)540.988890
2084f135s15p34f+7(7)7.5s+1(1)8.5p+1(3)941.140485
2094f135s15p34f+7(7)7.5s+1(1)6.5p+1(3)741.198875
2104f125s25p34f-5(5)5.4f+7(7)2.5p-1(1)3.5p+2(0)341.215262
2114f135s15p34f+7(7)7.5s+1(1)6.5p+1(3)341.408168
2124f135s15p34f-5(5)5.5s+1(1)4.5p+1(3)142.003775
2134f125s25p34f+6(12)12.5p+3(3)1343.025335
2144f125s25p34f+6(12)12.5p+3(3)1143.297322
2154f125s25p34f-4(0)0.5p-1(1)1.5p+2(4)343.350760
2164f135s15p34f-5(5)5.5s+1(1)4.5p+1(3)343.392389
2174f125s25p34f+6(12)12.5p+3(3)1543.406285
2184f145s15p25s+1(1)1.5p-1(1)2.5p+1(3)543.608173
2194f135s15p34f-5(5)5.5s+1(1)6.5p+1(3)943.884680
2204f125s25p34f+6(8)8.5p+3(3)944.013274
2214f135s15p34f-5(5)5.5s+1(1)4.5p+1(3)544.086014
2224f125s25p34f+6(8)8.5p+3(3)1144.238316
2234f135s15p34f-5(5)5.5s+1(1)6.5p+1(3)744.238615
2244f125s25p34f-4(0)0.5p-1(1)1.5p+2(4)544.585410
2254f125s25p34f+6(8)8.5p+3(3)545.006992
2264f125s25p34f-5(5)5.4f+7(7)10.5p+3(3)1145.017933
2274f125s25p34f-5(5)5.4f+7(7)10.5p+3(3)945.045473
2284f125s25p34f+6(8)8.5p+3(3)745.090392
2294f125s25p34f-5(5)5.4f+7(7)8.5p+3(3)945.574024
2304f125s25p34f-5(5)5.4f+7(7)10.5p+3(3)1345.776380
2314f125s25p34f-5(5)5.4f+7(7)8.5p+3(3)745.858203
2324f125s25p34f-5(5)5.4f+7(7)10.5p+3(3)746.339124
2334f125s25p34f+6(4)4.5p+3(3)146.446157
2344f125s25p34f+6(12)12.5p+3(3)946.472647
2354f125s25p34f-5(5)5.4f+7(7)6.5p+3(3)346.568953
2364f135s15p34f+7(7)7.5s+1(1)8.5p+1(3)546.616534
2374f125s25p34f-5(5)5.4f+7(7)8.5p+3(3)546.666498
2384f135s15p34f+7(7)7.5s+1(1)6.5p+1(3)946.718090
2394f125s25p34f-5(5)5.4f+7(7)6.5p+3(3)546.804436
2404f125s25p34f-5(5)5.4f+7(7)8.5p+3(3)1146.818182
2414f125s25p34f+6(4)4.5p+3(3)346.867630
2424f125s25p34f-5(5)5.4f+7(7)6.5p+3(3)946.897059
2434f125s25p34f+6(4)4.5p+3(3)747.131872
2444f125s25p34f-4(8)8.5p+3(3)747.498949
2454f125s25p34f-4(0)0.5p-1(1)1.5p+2(0)147.601261
2464f145s15p25s+1(1)1.5p-1(1)2.5p+1(3)347.867842
2474f135s15p34f+7(7)7.5s+1(1)8.5p+1(3)747.963146
2484f125s25p34f-5(5)5.4f+7(7)6.5p+3(3)748.284880
2494f125s25p34f-4(8)8.5p+3(3)948.314230
2504f125s25p34f-4(8)8.5p+3(3)1148.357492
2514f125s25p34f+6(4)4.5p+3(3)548.358299
2524f125s25p34f-4(8)8.5p+3(3)548.625980
2534f125s25p34f-5(5)5.4f+7(7)4.5p+3(3)148.890449
2544f135s15p34f-5(5)5.5s+1(1)6.5p+1(3)348.914054
2554f125s25p34f-5(5)5.4f+7(7)12.5p+3(3)1349.313778
2564f135s15p34f-5(5)5.5s+1(1)6.5p+1(3)749.571514
2574f125s25p34f+6(4)4.5p+3(3)349.586195
2584f125s25p34f-5(5)5.4f+7(7)4.5p+3(3)749.919408
2594f125s25p34f-5(5)5.4f+7(7)12.5p+3(3)1150.371537
2604f145s15p25s+1(1)1.5p-1(1)2.5p+1(3)150.452949
2614f135s15p34f-5(5)5.5s+1(1)6.5p+1(3)550.744707
2624f125s25p34f-4(4)4.5p+3(3)150.746650
2634f125s25p34f-4(4)4.5p+3(3)350.893695
2644f125s25p34f+6(4)4.5p+3(3)550.970529
2654f135s15p34f+7(7)7.5s+1(1)8.5p-1(1)7.5p+2(4)1151.131667
2664f125s25p34f-5(5)5.4f+7(7)12.5p+3(3)1551.788425
2674f125s25p34f-4(4)4.5p+3(3)751.985278
2684f125s25p34f-5(5)5.4f+7(7)2.5p+3(3)552.093916
2694f135s15p34f+7(7)7.5s+1(1)8.5p-1(1)7.5p+2(4)952.398490
2704f125s25p34f+6(0)0.5p+3(3)352.440969
2714f135s15p34f+7(7)7.5s+1(1)6.5p-1(1)7.5p+2(4)352.516271
2724f135s15p34f+7(7)7.5s+1(1)6.5p-1(1)7.5p+2(4)752.871630
2734f135s15p34f+7(7)7.5s+1(1)6.5p-1(1)7.5p+2(4)552.967365
2744f135s15p34f-5(5)5.5s+1(1)4.5p-1(1)5.5p+2(4)153.136186
2754f125s25p34f-5(5)5.4f+7(7)12.5p+3(3)953.148205
2764f125s25p34f-5(5)5.4f+7(7)4.5p+3(3)353.432744
2774f125s25p34f-4(4)4.5p+3(3)553.482487
2784f135s15p34f-5(5)5.5s+1(1)4.5p-1(1)5.5p+2(4)353.556245
2794f135s15p34f-5(5)5.5s+1(1)4.5p-1(1)5.5p+2(4)554.072377
2804f125s25p34f-5(5)5.4f+7(7)2.5p+3(3)154.212902
2814f145s15p25s+1(1)1.5p+2(4)554.710411
2824f135s15p34f-5(5)5.5s+1(1)6.5p-1(1)5.5p+2(4)954.778699
2834f135s15p34f+7(7)7.5s+1(1)8.5p-1(1)9.5p+2(4)1355.063904
2844f135s15p34f+7(7)7.5s+1(1)8.5p-1(1)9.5p+2(4)1155.118007
2854f135s15p34f-5(5)5.5s+1(1)4.5p-1(1)5.5p+2(4)755.233560
2864f135s15p34f+7(7)7.5s+1(1)6.5p-1(1)7.5p+2(4)955.423570
2874f135s15p34f+7(7)7.5s+1(1)6.5p-1(1)7.5p+2(4)755.687604
2884f135s15p34f+7(7)7.5s+1(1)6.5p-1(1)5.5p+2(4)156.090306
2894f135s15p34f+7(7)7.5s+1(1)6.5p-1(1)5.5p+2(4)356.104775
2904f145s15p25s+1(1)1.5p+2(4)557.091806
2914f135s15p34f-5(5)5.5s+1(1)6.5p-1(1)7.5p+2(4)1157.767247
2924f135s15p34f-5(5)5.5s+1(1)6.5p-1(1)5.5p+2(4)758.051208
2934f135s15p34f-5(5)5.5s+1(1)4.5p-1(1)3.5p+2(4)358.085215
2944f135s15p34f-5(5)5.5s+1(1)4.5p-1(1)5.5p+2(4)958.102775
2954f135s15p34f-5(5)5.5s+1(1)4.5p-1(1)3.5p+2(4)558.108579
2964f135s15p34f-5(5)5.5s+1(1)4.5p-1(1)3.5p+2(4)158.157443
2974f135s15p34f+7(7)7.5s+1(1)8.5p-1(1)7.5p+2(0)758.332193
2984f135s25p15d14f+7(7)7.5p-1(1)6.5d-1(3)358.415197
2994f135s25p15d14f+7(7)7.5p-1(1)8.5d-1(3)958.772385
3004f135s25p15d14f+7(7)7.5p-1(1)6.5d-1(3)558.867240
3014f135s25p15d14f+7(7)7.5p-1(1)8.5d-1(3)1159.062629
3024f135s25p15d14f+7(7)7.5p-1(1)6.5d-1(3)759.176646
3034f135s15p34f+7(7)7.5s+1(1)6.5p-1(1)7.5p+2(0)759.486179
3044f125s25p34f-4(0)0.5p+3(3)359.792970
Table 2. Comparison of calculated wavelengths (in nm) using FAC with other wavelengths for various transitions in Eu-like W. i and j represent the sequential numbers assigned in Table 1 to the lower and upper levels, respectively.
Table 2. Comparison of calculated wavelengths (in nm) using FAC with other wavelengths for various transitions in Eu-like W. i and j represent the sequential numbers assigned in Table 1 to the lower and upper levels, respectively.
TransitionijOur WorkExperimental 1Other Theory 1
{[(4f13)5/25s]3(5p21/25p3/2)3/2}3/2→{[(4f 13)5/25s2]5/2(5p21/2)0}5/2227824.34924.623 ± 0.01225.084
{[(4f13)5/25s]2(5p21/25p3/2)3/2}7/2→{[(4f 13)5/25s2]5/2(5p21/2)0}5/2225626.41625.225 ± 0.01825.746
{[(4f13)5/25s]3(5p21/25p3/2)3/2}5/2→{[(4f 13)5/25s2]5/2(5p21/2)0}5/2226125.77225.409 ± 0.01726.198
1 Reference [30].
Table 3. Oscillator strengths (length and velocity form) gfL and gfv, vacuum wavelengths λ (in nm), and transition probabilities Aji (in s−1) for some strong electric dipole (E1) transitions from the ground state to various levels of Eu-like W.
Table 3. Oscillator strengths (length and velocity form) gfL and gfv, vacuum wavelengths λ (in nm), and transition probabilities Aji (in s−1) for some strong electric dipole (E1) transitions from the ground state to various levels of Eu-like W.
Ijλ (nm)gfLgfvAji
020730.24821.532E-021.181E-021.861E+08
020930.09411.647E-021.400E-021.516E+08
021928.25236.616E-026.040E-025.529E+08
022328.02621.887E-021.607E-022.003E+08
023626.59668.246E-016.311E-011.296E+10
023826.53881.685E+001.322E+001.596E+10
024725.84991.118E+008.577E-011.395E+10
025625.01123.056E-012.369E-014.073E+09
028222.63371.033E-021.017E-021.345E+08
029721.25483.173E-024.308E-025.857E+08
Table 4. Oscillator strengths gfij, vacuum wavelengths λ (in nm), and transition probabilities Aji (in s−1) for magnetic dipole (M1) transitions from the ground state calculated for Eu-like W.
Table 4. Oscillator strengths gfij, vacuum wavelengths λ (in nm), and transition probabilities Aji (in s−1) for magnetic dipole (M1) transitions from the ground state calculated for Eu-like W.
iJλ (nm)gfijAji(s−1)
02470.39423.751E-061.885E+02
03119.13971.653E-057.768E+03
04109.34889.150E-068.507E+03
06103.47001.244E-059.688E+03
0998.40662.064E-072.369E+02
01096.13412.104E-061.519E+03
01195.46811.038E-069.496E+02
01389.17302.619E-082.746E+01
01487.78955.872E-078.470E+02
01684.79582.574E-092.388E+00
01984.00124.295E-084.060E+01
02082.20561.588E-071.959E+02
02180.51641.239E-071.275E+02
02379.94583.759E-106.538E-01
02578.15309.817E-091.340E+01
02876.79141.085E-082.045E+01
02975.59701.530E-072.232E+02
03073.69281.854E-083.795E+01
03173.55005.146E-086.345E+01
03470.81008.218E-101.367E+00
03669.73346.906E-099.473E+00
03769.51751.369E-083.149E+01
03968.67693.374E-107.953E-01
04068.11512.651E-114.764E-02
04167.54101.421E-092.078E+00
04266.67032.688E-085.042E+01
04463.83556.616E-091.805E+01
04563.14271.790E-083.743E+01
04762.04242.034E-093.525E+00
04861.25944.736E-101.403E+00
05059.54641.348E-093.170E+00
05358.13571.264E-082.495E+01
05555.92501.177E-094.184E+00
05953.66715.867E-102.265E+00
06152.88601.829E-115.452E-02
06648.69022.296E-096.460E+00
07545.24377.166E-102.919E+00
08044.25952.668E-101.514E+00
08144.25453.462E-101.474E+00
08344.16487.762E-092.654E+01
08743.81596.396E-092.778E+01
08943.29592.130E-099.474E+00
09042.91568.688E-105.244E+00
09142.70646.188E-092.263E+01
09442.55065.833E-092.686E+01
09542.39211.434E-118.871E-02
09642.08065.565E-092.096E+01
09841.91301.867E-098.861E+00
010241.60162.435E-091.173E+01
010441.41768.900E-093.461E+01
010541.33801.757E-096.858E+00
010641.14182.075E-091.363E+01
010741.04244.872E-092.412E+01
011040.82861.550E-111.034E-01
011240.62981.542E-091.038E+01
011440.45072.878E-101.173E+00
011640.05841.399E-107.269E-01
011839.82113.407E-092.389E+01
012039.61151.780E-087.567E+01
012439.19703.920E-091.702E+01
012539.16107.961E-095.771E+01
012639.12371.382E-107.528E-01
012839.01512.709E-091.484E+01
013338.60066.222E-094.642E+01
013538.53796.191E-113.476E-01
013938.37232.555E-091.157E+01
014038.23046.538E-104.973E+00
014138.03271.381E-097.960E+00
014237.90353.474E-092.688E+01
014337.88912.346E-091.090E+01
014637.79582.487E-101.452E+00
014737.35566.913E-095.508E+01
014837.21955.742E-102.765E+00
015336.96443.356E-102.731E+00
015536.85745.074E-103.114E+00
015736.78461.956E-099.642E+00
015836.60628.529E-104.246E+00
016435.98364.992E-113.215E-01
016535.93421.351E-101.163E+00
016735.85301.308E-108.484E-01
016835.64252.604E-101.367E+00
016935.51311.517E-108.025E-01
017035.49192.602E-092.296E+01
017335.08802.364E-091.601E+01
018034.60141.203E-091.117E+01
018134.54662.024E-091.131E+01
018234.48492.403E-091.685E+01
018534.04501.289E-091.236E+01
018633.79533.482E-092.542E+01
018733.52625.150E-093.056E+01
018933.39032.300E-102.293E+00
019133.28151.441E-081.085E+02
019233.10271.192E-101.209E+00
019332.96532.964E-112.274E-01
019532.78977.813E-104.847E+00
019632.33384.930E-103.932E+00
019831.91681.226E-101.338E+00
020630.50631.277E-101.525E+00
022527.54787.954E-111.165E+00
023127.03645.195E-115.926E-01
023226.75581.034E-101.204E+00
023426.67905.105E-114.784E-01
023726.56819.262E-121.459E-01
023926.48983.333E-115.280E-01
024226.43753.896E-113.718E-01
024326.30587.933E-119.558E-01
024825.67768.008E-111.013E+00
024925.66202.285E-112.314E-01
025125.63871.583E-112.677E-01
025824.83692.726E-113.685E-01
026723.84999.560E-111.401E+00
026823.80012.857E-115.607E-01
027523.32801.146E-101.405E+00
Table 5. Oscillator strengths gfij, vacuum wavelengths λ (in nm), and transition probabilities Aji (in s−1) for magnetic quadrupole (M2) transitions from the ground state in Eu-like W.
Table 5. Oscillator strengths gfij, vacuum wavelengths λ (in nm), and transition probabilities Aji (in s−1) for magnetic quadrupole (M2) transitions from the ground state in Eu-like W.
ijλ (nm)gfijAji (s−1)
020031.01344.147E-092.397E+01
020530.56903.013E-105.377E+00
020730.24821.820E-092.211E+01
020830.13683.279E-092.408E+01
020930.09412.665E-092.454E+01
021129.94208.454E-101.572E+01
021628.57285.206E-101.063E+01
021828.43146.824E-119.385E-01
021928.25233.457E-102.889E+00
022128.12334.822E-106.778E+00
022328.02623.373E-103.580E+00
023626.59665.529E-128.689E-02
023826.53882.201E-132.084E-03
024625.90146.804E-111.691E+00
024725.84991.913E-112.387E-01
025425.34747.382E-121.916E-01
025625.01128.935E-121.191E-01
026124.43296.642E-131.237E-02
026524.24801.490E-091.409E+01
026923.66181.444E-091.720E+01
027123.60875.501E-101.646E+01
027223.45009.282E-101.407E+01
027323.40777.612E-101.544E+01
027823.15039.312E-122.897E-01
027922.92934.199E-118.879E-01
028122.66195.448E-111.179E+00
028422.49431.238E-111.360E-01
028522.44731.773E-102.934E+00
028622.37031.152E-111.536E-01
028722.26424.283E-117.204E-01
028922.09875.163E-131.763E-02
029021.71665.489E-121.294E-01
029121.46276.646E-128.020E-02
029221.35774.977E-129.097E-02
029421.33881.916E-122.807E-02
029521.33662.720E-126.642E-02
029721.25497.816E-111.443E+00
029821.22463.513E-111.300E+00
029921.09573.285E-114.924E-01
030021.06174.574E-121.146E-01
030120.99202.376E-112.997E-01
030220.95151.754E-113.332E-01
030320.84253.451E-126.624E-02
Table 6. Collisional excitation cross-sections (100 Mb) of Eu-like W from the ground state to various levels.
Table 6. Collisional excitation cross-sections (100 Mb) of Eu-like W from the ground state to various levels.
Energy (eV)
/Transition		0–30–40–5Energy (eV)
/Transition		0–1Energy (eV)
/Transition		0–2Energy (eV)
/Transition		0–29
4.47E-012.63E+021.07E+021.79E+021.61E-013.14E+021.11E-012.73E+036.30E-018.61E+00
1.42E+011.03E+024.29E+018.40E+016.82E+008.81E+015.37E+009.22E+021.74E+014.29E+00
4.80E+013.40E+011.34E+013.68E+012.65E+012.55E+012.24E+012.79E+025.51E+011.98E+00
1.31E+029.42E+003.14E+001.61E+018.48E+016.25E+007.77E+017.50E+011.40E+028.90E-01
3.30E+022.60E+005.62E-017.06E+002.55E+021.08E+002.54E+021.49E+013.28E+024.06E-01
7.95E+028.12E-017.11E-023.01E+007.34E+022.30E-017.95E+021.60E+007.34E+021.83E-01
Energy (eV)
/Transition		0–60–70–80–90–100–110–130–140–16
8.77E-011.65E+024.82E+017.03E+022.79E+021.39E+023.13E+028.94E+009.00E+002.89E+01
2.22E+015.29E+011.85E+012.70E+021.08E+024.93E+011.23E+023.93E+003.03E+001.21E+01
6.79E+011.78E+018.14E+001.18E+024.74E+011.80E+015.50E+012.12E+009.23E-015.35E+00
1.66E+026.34E+003.86E+005.57E+012.23E+016.60E+002.67E+011.30E+002.44E-012.47E+00
3.72E+022.59E+001.87E+002.69E+011.08E+012.63E+001.34E+017.94E-015.98E-021.18E+00
7.95E+021.22E+008.94E-011.28E+015.10E+001.12E+006.67E+004.56E-011.47E-025.62E-01
Energy (eV)
/Transition		0–180–220–24Energy (eV)
/Transition		0–120–150–170–190–20
8.77E-011.27E+006.97E+018.56E+006.08E-017.78E+013.22E+025.48E+015.88E+013.03E+01
2.22E+014.80E-013.06E+013.56E+002.14E+012.64E+011.35E+022.01E+012.25E+011.29E+01
6.79E+011.73E-011.40E+011.48E+007.59E+016.78E+005.42E+015.67E+006.98E+005.09E+00
1.66E+025.76E-026.64E+006.19E-012.17E+021.06E+002.19E+011.15E+001.78E+002.07E+00
3.72E+021.95E-023.21E+002.71E-015.74E+021.37E-018.93E+002.86E-015.32E-019.19E-01
7.95E+027.33E-031.54E+001.21E-011.43E+032.02E-023.60E+001.06E-011.93E-013.78E-01
Energy (eV)
/Transition		0–210–230–250–260–27Energy (eV)
/Transition		0–280–300–31
6.08E-015.35E+029.02E+015.04E+022.71E+017.70E+011.22E+007.15E+016.76E+012.60E+02
2.14E+012.39E+023.80E+012.41E+021.08E+013.43E+013.42E+012.51E+012.38E+019.53E+01
7.59E+011.02E+021.44E+011.19E+023.54E+001.41E+011.09E+021.04E+019.56E+004.08E+01
2.17E+024.34E+015.40E+006.74E+011.11E+005.69E+002.78E+024.95E+004.14E+001.88E+01
5.74E+021.81E+012.15E+003.88E+014.41E-012.32E+006.50E+022.52E+001.86E+008.68E+00
1.43E+037.33E+008.78E-011.71E+011.99E-019.37E-011.43E+031.22E+008.44E-014.00E+00
Energy (eV)
/Transition		0–280–300–310–320–330–340–350–360–37
1.22E+007.15E+016.76E+012.60E+026.66E+017.88E+018.88E+012.09E+014.37E+011.34E+02
3.42E+012.51E+012.38E+019.53E+012.34E+012.94E+013.23E+016.37E+001.53E+015.09E+01
1.09E+021.04E+019.56E+004.08E+019.30E+001.26E+011.34E+011.94E+005.94E+002.21E+01
2.78E+024.95E+004.14E+001.88E+014.05E+005.73E+006.11E+006.65E-012.52E+001.02E+01
6.50E+022.52E+001.86E+008.68E+001.84E+002.62E+002.88E+002.94E-011.14E+004.74E+00
1.43E+031.22E+008.44E-014.00E+008.46E-011.20E+001.35E+001.46E-015.23E-012.18E+00
Energy (eV)
/Transition		0–380–390–400–410–420–430–440–450–46
1.22E+004.06E+003.24E+014.00E+012.40E+014.00E+012.37E+017.58E+002.61E+002.05E+00
3.42E+011.17E+001.17E+011.59E+018.06E+001.58E+019.02E+002.33E+009.78E-017.32E-01
1.09E+022.81E-014.61E+007.79E+002.85E+007.52E+003.76E+005.88E-014.14E-012.70E-01
2.78E+024.71E-021.98E+004.75E+001.12E+004.40E+001.68E+001.05E-012.24E-011.08E-01
6.50E+028.72E-038.87E-012.98E+005.00E-012.70E+007.70E-012.10E-021.42E-014.79E-02
1.43E+032.32E-034.05E-011.61E+002.36E-011.44E+003.54E-015.58E-037.83E-022.21E-02
Energy (eV)
/Transition		0–470–480–490–50
1.22E+001.27E+019.06E+002.66E+011.08E+01
3.42E+014.46E+003.00E+008.92E+003.48E+00
1.09E+021.51E+009.06E-012.87E+009.59E-01
2.78E+025.11E-012.70E-011.02E+002.37E-01
6.50E+022.04E-011.03E-014.61E-017.70E-02
1.43E+038.86E-024.63E-022.30E-013.09E-02
Table 7. Configurations included in the different inputs with the number of fine structure levels for Pm-like W.
Table 7. Configurations included in the different inputs with the number of fine structure levels for Pm-like W.
INP1INP2INP3INPF
Configuration4f145s, 4f135s2, 4f135s5p, 4f145p, 4f135p24f145s, 4f135s2, 4f135s5p, 4f145p, 4f135p2, 4f125s25p, 4f125s5p2, 4f125p34f145s, 4f135s2, 4f135s5p, 4f145p, 4f135p2, 4f125s25p, 4f125s5p2, 4f125p3, 4f115s25p2, 4f115s5p3, 4f105s25p3, 4f105s5p44f145s, 4f135s2, 4f135s5p, 4f145p, 4f135p2, 4f125s25p, 4f125s5p2, 4f125p3, 4f115s25p2, 4f115s5p3, 4f105s25p3, 4f105s5p4, 4f125s25d, 4f125s5d2, 4f135d2, 4f135p5d, 4f135d2, 4f135p5d, 4f125p5d2, 4f125p25d, 4f135s5d
Levels59680779013,160
Ground state4f135s2 2F7/24f135s2 2F7/24f135s2 2F7/24f135s2 2F7/2
Table 8. List of configurations included and the number of fine-structure levels arising from each configuration of Pm-like W.
Table 8. List of configurations included and the number of fine-structure levels arising from each configuration of Pm-like W.
ConfigurationTotal
4f145s11
4f135s22
4f135s1 5p124
4f145p12
4f135p236
4f125s25p169
4f125s15p2335
4f125p3231
4f115s25p2594
4f115s15p31542
4f105s25p31971
4f105s15p42947
4f125s25d1139
4f125s15d2910
4f135d282
4f135p15d1121
4f125p15d22617
4f125p25d11499
4f135s15d138
Table 9. Energy values (in eV) from each input for the 4f135s5p configuration of Pm-like W.
Table 9. Energy values (in eV) from each input for the 4f135s5p configuration of Pm-like W.
S. No.Level Index2Jout1out2out3outF
1694f+7(7)7.5s+1(1)8.5p-1(1)728.3408428.2303228.3380428.05699
2854f+7(7)7.5s+1(1)6.5p-1(1)730.4984530.3920730.4946330.07793
3894f-5(5)5.5s+1(1)4.5p-1(1)530.5190430.4278330.5314630.24463
4914f+7(7)7.5s+1(1)8.5p-1(1)930.9358830.8138530.9173530.53786
5944f+7(7)7.5s+1(1)6.5p-1(1)531.5938431.4881831.5951031.22191
61084f-5(5)5.5s+1(1)6.5p-1(1)533.5159133.3992533.4862333.07156
71104f-5(5)5.5s+1(1)6.5p-1(1)733.5923433.5023033.6073033.22125
81144f-5(5)5.5s+1(1)4.5p-1(1)333.9400133.7942433.8913333.52918
92224f+7(7)7.5s+1(1)8.5p+1(3)1142.2867042.1779042.2127441.88907
102504f+7(7)7.5s+1(1)6.5p+1(3)343.3396743.1671143.2170842.84671
112634f+7(7)7.5s+1(1)6.5p+1(3)543.6965543.4800743.5413243.20679
122664f-5(5)5.5s+1(1)4.5p+1(3)143.7302343.5596643.6303443.25833
132774f+7(7)7.5s+1(1)6.5p+1(3)744.1476043.8822043.9481843.64971
142794f+7(7)7.5s+1(1)8.5p+1(3)944.1589843.8869343.9502243.67102
153174f-5(5)5.5s+1(1)4.5p+1(3)345.5253545.3025845.3626245.02438
163264f-5(5)5.5s+1(1)6.5p+1(3)945.6522245.4402845.5227345.17111
173514f-5(5)5.5s+1(1)4.5p+1(3)546.4720846.2291546.2938645.99735
183574f-5(5)5.5s+1(1)6.5p+1(3)746.6154446.3768246.4484546.14563
194334f+7(7)7.5s+1(1)8.5p+1(3)551.2120550.8540550.8980049.88168
204344f+7(7)7.5s+1(1)6.5p+1(3)951.3123750.9961551.0514049.98717
214514f+7(7)7.5s+1(1)8.5p+1(3)752.8096352.1443152.2055151.07045
224604f-5(5)5.5s+1(1)6.5p+1(3)353.1214952.7499652.8075251.79452
234754f-5(5)5.5s+1(1)4.5p+1(3)753.8958753.4250753.4885952.41451
244934f-5(5)5.5s+1(1)6.5p+1(3)555.3142654.6389654.7055753.48189
Table 10. Energy levels (in eV) for the lowest 500 levels calculated with FAC using INPF configurations for Pm-like W.
Table 10. Energy levels (in eV) for the lowest 500 levels calculated with FAC using INPF configurations for Pm-like W.
Level No.Configuration2JFAC
04f135s24f+7(7)70.000000
14f135s24f-5(5)52.255395
24f125s25p14f+6(12)12.5p-1(1)117.276828
34f125s25p14f+6(12)12.5p-1(1)138.000018
44f125s25p14f+6(8)8.5p-1(1)78.504221
54f125s25p14f+6(8)8.5p-1(1)98.898153
64f125s25p14f-5(5)5.4f+7(7)10.5p-1(1)119.837877
74f125s25p14f-5(5)5.4f+7(7)10.5p-1(1)99.857320
84f125s25p14f-5(5)5.4f+7(7)8.5p-1(1)710.537519
94f125s25p14f-5(5)5.4f+7(7)6.5p-1(1)510.821138
104f125s25p14f+6(4)4.5p-1(1)310.938403
114f125s25p14f-5(5)5.4f+7(7)8.5p-1(1)911.036302
124f125s25p14f-5(5)5.4f+7(7)6.5p-1(1)511.306358
134f125s25p14f-5(5)5.4f+7(7)6.5p-1(1)711.775166
144f125s25p14f-4(8)8.5p-1(1)912.546322
154f125s25p14f-5(5)5.4f+7(7)4.5p-1(1)313.724712
164f125s25p14f-4(8)8.5p-1(1)713.755493
174f125s25p14f-4(4)4.5p-1(1)513.957189
184f125s25p14f-5(5)5.4f+7(7)12.5p-1(1)1314.902679
194f125s25p14f-5(5)5.4f+7(7)2.5p-1(1)115.077341
204f125s25p14f+6(0)0.5p-1(1)115.148716
214f125s25p14f-5(5)5.4f+7(7)12.5p-1(1)1115.246453
224f125s25p14f-5(5)5.4f+7(7)2.5p-1(1)316.064828
234f125s25p14f-4(4)4.5p-1(1)516.335222
244f125s25p14f-4(4)4.5p-1(1)316.845319
254f115s25p24f+5(15)1520.958997
264f125s25p14f+6(12)12.5p+1(3)1521.711928
274f125s25p14f+6(12)12.5p+1(3)1122.687480
284f125s25p14f+6(12)12.5p+1(3)922.793061
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4164f115s25p24f-4(8)8.4f+7(7)5.5p-1(1)4.5p+1(3)148.876547
4174f125s15p24f-5(5)5.4f+7(7)4.5s+1(1)348.891319
4184f115s25p24f-4(8)8.4f+7(7)15.5p-1(1)14.5p+1(3)1348.923501
4194f115s25p24f-4(4)4.4f+7(7)7.5p-1(1)6.5p+1(3)548.991206
4204f115s25p24f-4(8)8.4f+7(7)15.5p-1(1)14.5p+1(3)1549.005761
4214f115s25p24f-4(4)4.4f+7(7)7.5p-1(1)8.5p+1(3)949.073201
4224f115s25p24f-4(8)8.4f+7(7)1.5p-1(1)0.5p+1(3)349.092208
4234f115s25p24f-5(5)5.4f+6(4)7.5p-1(1)8.5p+1(3)749.107584
4244f125s15p24f+6(8)8.5s+1(1)9.5p-1(1)8.5p+1(3)1149.225409
4254f115s25p24f-4(4)4.4f+7(7)7.5p-1(1)6.5p+1(3)349.318118
4264f115s25p24f-4(4)4.4f+7(7)5.5p-1(1)4.5p+1(3)549.398585
4274f115s25p24f-3(3)3.5p-1(1)4.5p+1(3)749.458758
4284f125s15p24f+6(12)12.5s+1(1)13.5p-1(1)12.5p+1(3)1349.511467
4294f125s15p24f+6(8)8.5s+1(1)9.5p-1(1)8.5p+1(3)949.549600
4304f115s25p24f-5(5)5.4f+6(4)7.5p-1(1)6.5p+1(3)949.803106
4314f115s25p24f-3(3)3.5p-1(1)4.5p+1(3)349.819068
4324f115s25p24f-4(4)4.4f+7(7)5.5p-1(1)6.5p+1(3)749.856027
4334f135s15p14f+7(7)7.5s+1(1)8.5p+1(3)549.881682
4344f135s15p14f+7(7)7.5s+1(1)6.5p+1(3)949.987168
4354f115s25p24f-3(3)3.5p-1(1)2.5p+1(3)350.028605
4364f115s25p24f-5(5)5.4f+6(4)7.5p-1(1)8.5p+1(3)550.077842
4374f115s25p24f-4(4)4.4f+7(7)9.5p-1(1)10.5p+1(3)750.111402
4384f125s15p24f-5(5)5.4f+7(7)10.5s+1(1)9.5p-1(1)10.5p+1(3)750.183762
4394f125s15p24f+6(8)8.5s+1(1)9.5p-1(1)8.5p+1(3)950.198350
4404f115s25p24f+5(15)15.5p+2(4)1950.226742
4414f125s15p24f-5(5)5.4f+7(7)8.5s+1(1)7.5p-1(1)8.5p+1(3)550.328400
4424f125s15p24f+6(8)8.5s+1(1)7.5p-1(1)8.5p+1(3)750.426385
4434f115s25p24f-3(3)3.5p-1(1)2.5p+1(3)150.466901
4444f115s25p24f-4(4)4.4f+7(7)9.5p-1(1)10.5p+1(3)750.502712
4454f125s15p24f+6(8)8.5s+1(1)9.5p-1(1)8.5p+1(3)1150.590776
4464f115s25p24f-5(5)5.4f+6(4)7.5p-1(1)6.5p+1(3)950.597918
4474f115s25p24f-5(5)5.4f+6(4)7.5p-1(1)8.5p+1(3)1150.610624
4484f115s25p24f-4(4)4.4f+7(7)9.5p-1(1)8.5p+1(3)550.949017
4494f115s25p24f-3(5)5.5p-1(1)6.5p+1(3)951.020195
4504f115s25p24f-4(4)4.4f+7(7)9.5p-1(1)8.5p+1(3)1151.068131
4514f135s15p14f+7(7)7.5s+1(1)8.5p+1(3)751.070448
4524f115s25p24f+5(15)15.5p+2(4)1751.116024
4534f125s15p24f-5(5)5.4f+7(7)10.5s+1(1)11.5p-1(1)10.5p+1(3)1351.334835
4544f115s25p24f-5(5)5.4f+6(4)7.5p-1(1)6.5p+1(3)351.363160
4554f125s15p24f-5(5)5.4f+7(7)6.5s+1(1)5.5p-1(1)6.5p+1(3)551.370276
4564f115s25p24f-5(5)5.4f+6(4)7.5p-1(1)6.5p+1(3)751.373528
4574f125s15p24f+6(12)12.5s+1(1)13.5p-1(1)14.5p+1(3)1751.564277
4584f115s25p24f-5(5)5.4f+6(4)7.5p-1(1)6.5p+1(3)551.616242
4594f115s25p24f-3(5)5.5p-1(1)6.5p+1(3)951.669738
4604f135s15p14f-5(5)5.5s+1(1)6.5p+1(3)351.794518
4614f125s15p24f+6(12)12.5s+1(1)11.5p-1(1)12.5p+1(3)951.808742
4624f115s25p24f+5(15)15.5p+2(4)1551.873567
4634f115s25p24f-4(4)4.4f+7(7)9.5p-1(1)10.5p+1(3)1351.894895
4644f115s25p24f-3(5)5.5p-1(1)4.5p+1(3)751.949134
4654f115s25p24f-3(5)5.5p-1(1)4.5p+1(3)152.008321
4664f125s15p24f-5(5)5.4f+7(7)10.5s+1(1)9.5p-1(1)10.5p+1(3)752.026776
4674f115s25p24f-5(5)5.4f+6(4)7.5p-1(1)6.5p+1(3)552.033636
4684f125s15p24f-5(5)5.4f+7(7)8.5s+1(1)9.5p-1(1)8.5p+1(3)1152.083735
4694f125s15p24f+6(4)4.5s+1(1)3.5p-1(1)4.5p+1(3)352.119437
4704f115s25p24f-3(5)5.5p-1(1)4.5p+1(3)352.127458
4714f115s25p24f-4(4)4.4f+7(7)9.5p-1(1)10.5p+1(3)1152.249539
4724f125s15p24f-4(8)8.5s+1(1)7.5p-1(1)8.5p+1(3)552.272296
4734f115s25p24f+5(15)15.5p+2(4)1352.359709
4744f125s15p24f+6(12)12.5s+1(1)13.5p-1(1)14.5p+1(3)1552.368597
4754f135s15p14f-5(5)5.5s+1(1)4.5p+1(3)752.414510
4764f115s25p24f+5(15)15.5p+2(4)1152.547263
4774f125s15p24f+6(12)12.5s+1(1)11.5p-1(1)12.5p+1(3)1352.589880
4784f115s25p24f-3(5)5.5p-1(1)4.5p+1(3)552.607852
4794f125s15p24f-5(5)5.4f+7(7)10.5s+1(1)9.5p-1(1)10.5p+1(3)952.686118
4804f115s25p24f-5(5)5.4f+6(12)13.5p+2(4)1752.735714
4814f125s15p24f+6(4)4.5s+1(1)3.5p-1(1)4.5p+1(3)152.825991
4824f125s15p24f+6(8)8.5s+1(1)7.5p-1(1)8.5p+1(3)552.888739
4834f115s25p24f-4(4)4.4f+7(7)9.5p-1(1)10.5p+1(3)952.889924
4844f125s15p24f+6(12)12.5s+1(1)13.5p-1(1)12.5p+1(3)1152.905137
4854f115s25p24f-5(5)5.4f+6(12)13.5p+2(4)1553.036541
4864f125s15p24f+6(8)8.5s+1(1)9.5p-1(1)10.5p+1(3)1353.151612
4874f115s25p24f-5(5)5.4f+6(12)13.5p+2(4)1353.161837
4884f125s15p24f-5(5)5.4f+7(7)8.5s+1(1)9.5p-1(1)8.5p+1(3)1153.245023
4894f125s15p24f+6(8)8.5s+1(1)9.5p-1(1)10.5p+1(3)1153.248825
4904f125s15p24f+6(12)12.5s+1(1)11.5p-1(1)10.5p+1(3)953.381515
4914f125s15p24f+6(8)8.5s+1(1)7.5p-1(1)8.5p+1(3)753.404688
4924f115s25p24f-4(4)4.4f+7(7)9.5p-1(1)8.5p+1(3)753.434223
4934f135s15p14f-5(5)5.5s+1(1)6.5p+1(3)553.481890
4944f125s15p24f+6(12)12.5s+1(1)11.5p-1(1)10.5p+1(3)753.583051
4954f115s25p24f-5(5)5.4f+6(12)13.5p+2(4)1153.620775
4964f115s25p24f-5(5)5.4f+6(0)5.5p-1(1)6.5p+1(3)353.620908
4974f115s25p24f+5(9)9.5p+2(4)1353.694318
4984f115s25p24f-5(5)5.4f+6(12)13.5p+2(4)953.695742
4994f115s25p24f+5(11)11.5p+2(4)1553.722950
5004f125s15p24f+6(8)8.5s+1(1)7.5p-1(1)8.5p+1(3)953.767747
6344f145p15p-1(1)158.282075
12924f145p15p+1(3)372.160271
Table 11. Comparison of energy levels (in Rydberg) calculated with FAC for Pm-like W with other available results.
Table 11. Comparison of energy levels (in Rydberg) calculated with FAC for Pm-like W with other available results.
Level No.Configuration2JFACNISTSafronova a
14f135s250.16580.24(3) + x0.165 b
434f145s111.84821.62(3) + y1.79
914f135s5p92.24452.3379(12)2.294
2634f135s5p53.17563.350(3)3.212
3264f135s5p93.32003.490(3)3.361
4514f135s5p73.75363.826(3)3.878
a—Reference [28]. b—Reference [32].
Table 12. Transition data for the 4f135s2 2F-4f135s5p and 4f145s-4f145p transitions in Pm-like W. Oscillator strength are given in both the length form (gfL) and velocity form (gfv).
Table 12. Transition data for the 4f135s2 2F-4f135s5p and 4f145s-4f145p transitions in Pm-like W. Oscillator strength are given in both the length form (gfL) and velocity form (gfv).
4f135s2 2F-4f135s5p Transition
j2Jji2Jiλ(nm)gfLgfvAji(s−1)
OUT3		Aji(s−1)
OUTF		Type
6970744.19012.41E-022.20E-028.84E+071.03E+08E1
6971548.05296.40E-048.21E-043.20E+062.31E+06E1
6970744.19019.18E-129.18E-122.95E-023.92E-02M2
6971548.05291.16E-121.16E-123.81E-034.18E-03M2
8570741.22102.75E-012.40E-011.40E+091.35E+09E1
8571544.56251.67E-021.68E-027.72E+077.02E+07E1
8570741.22102.05E-122.05E-121.15E-021.01E-02M2
8571544.56256.20E-146.20E-144.67E-042.60E-04M2
8950740.99388.27E-027.26E-024.68E+085.47E+08E1
8951544.29714.68E-034.16E-032.93E+072.65E+07E1
8950740.99381.81E-121.81E-129.39E-031.19E-02M2
8951544.29714.19E-124.19E-121.92E-022.38E-02M2
9190740.60025.38E-015.00E-012.18E+092.18E+09E1
9190740.60027.31E-127.31E-122.23E-022.96E-02M2
9191543.83782.25E-122.25E-121.01E-027.81E-03M2
9450739.71062.42E-012.19E-011.78E+091.71E+09E1
9451542.80265.97E-025.49E-023.36E+083.62E+08E1
9450739.71061.48E-111.48E-119.30E-021.04E-01M2
9451542.80261.10E-131.10E-131.35E-036.68E-04M2
10850737.48975.80E-025.69E-024.50E+084.59E+08E1
10851540.23351.76E-011.50E-011.29E+091.21E+09E1
10850737.48978.94E-138.94E-131.10E-027.07E-03M2
10851540.23353.24E-123.24E-121.31E-022.22E-02M2
11070737.32082.07E-021.76E-021.31E+081.24E+08E1
11071540.03904.29E-013.86E-012.17E+092.23E+09E1
11070737.32083.07E-123.07E-121.50E-021.84E-02M2
11071540.03908.68E-128.68E-123.70E-024.51E-02M2
11431539.64482.25E-011.95E-012.38E+092.38E+09E1
114307 36.97804.52E-124.52E-126.28E-025.51E-02M2
11431539.64487.47E-127.47E-126.67E-027.93E-02M2
222110729.59823.95E-093.95E-092.50E+012.51E+01M2
25031530.54454.58E-033.26E-038.20E+078.18E+07E1
25030728.93671.25E-091.25E-092.45E+012.48E+01M2
25031530.54453.70E-103.70E-106.94E+006.62E+00M2
26350728.69551.85E-021.53E-022.10E+082.50E+08E1
26351530.27591.96E-021.80E-022.04E+082.37E+08E1
26350728.69552.16E-092.16E-092.98E+012.92E+01M2
26351530.27592.74E-102.74E-103.47E+003.32E+00M2
26611530.23797.45E-107.45E-102.74E+012.72E+01M2
27770728.40443.29E-023.06E-022.69E+083.40E+08E1
27771529.95204.30E-034.51E-033.61E+074.00E+07E1
27770728.40443.21E-093.21E-093.44E+013.32E+01M2
27771529.95201.24E-101.24E-101.26E+001.15E+00M2
27990728.39052.12E-021.76E-021.30E+081.75E+08E1
27990728.39054.13E-094.13E-093.53E+013.42E+01M2
27991529.93669.21E-119.21E-117.97E-016.85E-01M2
31731528.98932.36E-022.32E-023.72E+084.68E+08E1
31730727.53715.07E-105.07E-101.15E+011.12E+01M2
31731528.98931.16E-091.16E-092.36E+012.30E+01M2
32690727.44774.27E-024.56E-023.18E+083.78E+08E1
32690727.44771.26E-101.26E-101.12E+001.12E+00M2
32691528.89023.90E-093.90E-093.02E+013.12E+01M2
35150726.95461.60E-021.60E-021.80E+082.45E+08E1
35151528.34452.01E-032.06E-032.35E+072.79E+07E1
35150726.95463.86E-103.86E-106.32E+005.91E+00M2
35151528.34452.22E-092.22E-093.17E+013.07E+01M2
35770726.86801.38E-021.33E-021.21E+081.59E+08E1
35771528.24875.85E-025.66E-025.11E+086.11E+08E1
35770726.86801.59E-101.59E-102.11E+001.84E+00M2
35771528.24873.26E-093.26E-093.55E+013.41E+01M2
43350724.85573.27E+003.03E+006.52E+105.88E+10E1
43351526.03273.84E-023.41E-027.37E+086.29E+08E1
43350724.85573.52E-143.52E-148.78E-046.33E-04M2
43351526.03271.45E-111.45E-112.74E-012.38E-01M2
43490724.80325.16E+004.84E+006.74E+105.59E+10E1
43490724.80326.56E-126.56E-123.56E-037.11E-02M2
43491525.97523.47E-113.47E-113.20E-013.43E-01M2
45170724.27713.97E+003.75E+004.92E+105.62E+10E1
45171525.39884.19E-014.00E-014.99E+095.42E+09E1
45170724.27711.29E-111.29E-111.45E-011.83E-01M2
45171525.39881.73E-121.73E-121.80E-022.23E-02M2
46031525.02752.23E+002.06E+006.66E+105.93E+10E1
46030723.93771.38E-121.38E-127.80E-024.03E-02M2
46031525.02756.03E-126.03E-122.44E-011.61E-01M2
47570723.65464.17E-013.92E-018.91E+096.21E+09E1
47571524.71823.77E+003.54E+005.84E+105.14E+10E1
47570723.65469.03E-129.03E-122.22E-011.35E-01M2
47571524.71822.69E-112.69E-113.70E-013.66E-01M2
49350723.18254.11E-023.86E-028.33E+088.51E+08E1
49351524.20313.28E+003.09E+006.74E+106.23E+10E1
49350723.18251.09E-111.09E-112.19E-012.26E-01M2
49351524.20311.82E-121.82E-121.32E-023.45E-02M2
4f145s-4f145p transition
J2Jji2Jiλ(in nm)gfLgfvAji(s−1) OUT3Aji(s−1) OUTF Type
634143137.41714.89E-014.61E-011.29E+101.16E+10E1
1292343126.37181.33E+001.29E+003.50E+103.18E+10E1
1292343126.37182.40E-092.40E-095.53E+015.75E+01M2
Table 13. Comparison of a transition wavelength (in nm) calculated using FAC with NIST [9] and other results for Pm-like W. The indexes of the lower and upper levels, i and j, respectively, correspond to those given in Table 10.
Table 13. Comparison of a transition wavelength (in nm) calculated using FAC with NIST [9] and other results for Pm-like W. The indexes of the lower and upper levels, i and j, respectively, correspond to those given in Table 10.
iJλ (This Work)λ (NIST)λ (Others)
09140.60038.978(20)---------
026328.69627.205(20)---------
032627.44826.110(20)---------
043324.856---------24.91 c
24.70 a
24.71 b
24.76 d
043424.803---------24.83 c
24.64 a
24.53 b
24.69 d
045124.277---------24.32 c
24.06 a
23.95 b
24.17 d
145125.39925.384(20)
a—Reference [28] results using COWAN code. b—Reference [31] results using the HULLAC code. c—Experimental results of Reference [31]. d—Reference [33] using FAC.
Table 14. Comparison of transition wavelength (nm) calculated with FAC for the transition 4f135s2 2F5/2-2F7/2 with other results for Pm-like W. Experimental wavelengths are given in standard air, while theoretically calculated wavelengths are in vacuum.
Table 14. Comparison of transition wavelength (nm) calculated with FAC for the transition 4f135s2 2F5/2-2F7/2 with other results for Pm-like W. Experimental wavelengths are given in standard air, while theoretically calculated wavelengths are in vacuum.
MethodWavelength (nm)
FAC (this work)549.72
Experiment f560.25
Experiment a549.95 ± 0.06
RMBPT a567.64
FAC a552.08
Safronova et al. (COWAN) b537.63
Vilkas et al. (MR-MP) c388.71
Nandy (CCSD-T) d556.60
FAC e550.80
a—Reference [32]. b—Reference [28]. c—Reference [24]. d—Reference [38]. e—Reference [33]. f—Reference [31].
Table 15. Collisional excitation cross-sections (100 Mb) of Pm-like W from the ground state to various levels.
Table 15. Collisional excitation cross-sections (100 Mb) of Pm-like W from the ground state to various levels.
Energy (eV)
/Transition		0–20–30–4Energy (eV)
/Transition		0–50–60–7Energy (eV)
/Transition		0–43
0.00E+002.54E+042.54E+042.54E+040.00E+002.54E+042.54E+042.54E+040.00E+003.00E+04
3.72E-011.72E+021.12E+028.80E+013.72E-018.14E+015.64E+011.13E+021.20E+003.06E+01
1.32E+015.98E+014.14E+013.36E+011.32E+013.19E+012.35E+014.93E+012.43E+011.52E+01
4.70E+011.89E+011.37E+011.11E+014.70E+011.07E+018.24E+001.91E+016.85E+017.18E+00
1.36E+024.65E+003.87E+002.93E+001.36E+022.94E+002.36E+006.91E+001.52E+023.21E+00
3.64E+028.57E-011.10E+006.36E-013.64E+027.57E-016.19E-012.54E+003.11E+021.47E+00
9.32E+021.97E-014.12E-011.85E-019.32E+022.63E-011.96E-019.75E-016.04E+027.42E-01
Energy (eV)
/Transition		0–80–90–100–11Energy (eV)
/Transition		0–120–130–140–15
0.00E+002.54E+042.54E+042.54E+042.54E+040.00E+002.54E+042.54E+042.54E+042.54E+04
7.44E-014.67E+012.78E+012.96E+011.50E+027.44E-017.69E+011.78E+021.77E+011.62E+01
2.11E+011.64E+019.12E+009.88E+005.42E+012.11E+012.77E+016.76E+016.84E+006.19E+00
6.78E+016.91E+003.02E+003.32E+002.17E+016.78E+011.08E+012.78E+012.76E+002.22E+00
1.74E+023.25E+009.09E-011.01E+009.12E+001.74E+024.27E+001.20E+011.14E+007.23E-01
4.13E+021.71E+002.85E-013.13E-013.99E+004.13E+021.79E+005.32E+004.88E-012.44E-01
9.32E+027.91E-011.11E-011.21E-011.78E+009.32E+027.87E-012.39E+002.16E-019.65E-02
Energy (eV)
/Transition		0–160–170–180–190–200–210–220–230–24
0.00E+002.54E+042.54E+042.54E+042.54E+042.54E+042.54E+042.54E+042.54E+042.54E+04
7.44E-011.11E+014.92E+013.25E+015.56E+006.88E+002.18E+023.76E+013.07E+012.40E+01
2.11E+014.71E+002.02E+011.24E+012.16E+002.69E+009.61E+011.69E+011.39E+011.11E+01
6.78E+012.09E+008.33E+004.08E+007.25E-019.17E-014.22E+017.40E+006.13E+004.98E+00
1.74E+029.88E-013.47E+001.03E+001.94E-012.52E-011.87E+013.23E+002.68E+002.23E+00
4.13E+024.94E-011.50E+002.12E-014.75E-026.39E-028.42E+001.44E+001.20E+001.01E+00
9.32E+022.44E-016.68E-015.14E-021.49E-022.12E-023.81E+006.48E-015.38E-014.57E-01
Energy (eV)
/Transition		0–260–270–280–300–310–320–330–360–37
0.00E+002.54E+042.54E+042.54E+042.54E+042.54E+042.54E+042.54E+042.54E+042.54E+04
1.48E+003.44E+016.29E+011.73E+021.83E+002.50E+011.63E+015.08E+014.80E+012.57E+01
3.30E+011.15E+012.58E+017.67E+017.06E-019.14E+005.97E+002.20E+012.14E+011.03E+01
9.59E+013.46E+001.12E+013.69E+012.67E-013.15E+002.03E+001.00E+011.01E+014.20E+00
2.21E+028.42E-015.07E+001.86E+019.95E-021.05E+006.36E-014.81E+004.99E+001.79E+00
4.66E+021.97E-012.47E+009.59E+004.19E-024.11E-012.25E-012.41E+002.54E+008.53E-01
9.32E+024.72E-021.24E+004.96E+002.09E-021.96E-019.44E-021.23E+001.31E+004.40E-01
Energy (eV)
/Transition		0–380–390–410–420–450–460–470–490–50
0.00E+002.54E+042.54E+042.54E+042.54E+042.54E+042.54E+042.54E+042.54E+042.54E+04
1.48E+001.38E+015.47E+017.00E+011.12E+013.03E+012.14E+011.31E+012.71E+013.43E+01
3.30E+015.39E+002.42E+013.25E+014.53E+001.38E+019.78E+005.37E+001.25E+011.63E+01
9.59E+012.10E+001.12E+011.60E+011.77E+006.51E+004.63E+002.18E+006.04E+008.19E+00
2.21E+028.62E-015.46E+008.18E+006.91E-013.20E+002.28E+009.22E-013.02E+004.41E+00
4.66E+024.12E-012.75E+004.26E+003.02E-011.63E+001.16E+004.41E-011.55E+002.57E+00
9.32E+022.19E-011.41E+002.22E+001.46E-018.42E-015.99E-012.30E-017.99E-011.54E+00
Energy (eV)
/Transition		0–250–290–340–350–400–440–48Energy (eV)
/Transition		0–1
0.00E+002.54E+042.54E+042.54E+042.54E+042.54E+042.54E+042.54E+040.00E+003.00E+04
1.40E+001.37E-011.56E-019.11E+007.74E-011.50E-012.15E-011.30E+001.13E-012.79E+03
4.18E+013.78E-025.01E-022.89E+002.69E-016.03E-028.22E-025.14E-012.21E+001.47E+03
1.37E+028.92E-031.55E-028.48E-019.60E-022.57E-023.25E-022.12E-016.17E+007.72E+02
3.58E+021.66E-034.96E-032.65E-013.77E-021.13E-021.35E-029.14E-021.36E+014.02E+02
8.57E+022.51E-041.89E-031.01E-011.63E-025.00E-035.83E-034.03E-022.77E+012.06E+02
1.91E+033.28E-058.74E-044.29E-027.56E-032.28E-032.66E-031.84E-025.41E+011.03E+02
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Singh, N.; Aggarwal, S.; Mohan, M. Extended Atomic Structure Calculations for W11+ and W13+. Atoms 2020, 8, 92. https://doi.org/10.3390/atoms8040092

AMA Style

Singh N, Aggarwal S, Mohan M. Extended Atomic Structure Calculations for W11+ and W13+. Atoms. 2020; 8(4):92. https://doi.org/10.3390/atoms8040092

Chicago/Turabian Style

Singh, Narendra, Sunny Aggarwal, and Man Mohan. 2020. "Extended Atomic Structure Calculations for W11+ and W13+" Atoms 8, no. 4: 92. https://doi.org/10.3390/atoms8040092

APA Style

Singh, N., Aggarwal, S., & Mohan, M. (2020). Extended Atomic Structure Calculations for W11+ and W13+. Atoms, 8(4), 92. https://doi.org/10.3390/atoms8040092

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