Theoretical level energies, radiative lifetimes and transitions in W IX
aa r X i v : . [ phy s i c s . a t o m - ph ] J u l Groundstates and low-lying states of W IX, W X, and W XI tungsten ions
Karol Kozioł ∗ Narodowe Centrum Bada´n J ˛adrowych (NCBJ), Andrzeja Sołtana 7, 05-400 Otwock- ´Swierk, Poland
Abstract
The groundstates and low-lying states of W IX (W ), W X (W ), and W XI (W ) tungsten ions related to 4 f
10. . . 14
2. . . 6 and 4 f
11. . . 14
3. . . 6 valence configurations have been studied theoretically, employing the multi-configuration Dirac–Hartree–Fock method with configuration interaction. The aim of present research is to fill a lack of atomic data for these tungsten ionizationstages, which may help in identification of the measured complex spectra and be a base for collisional-radiative modeling for spectraof tungsten ions occurring in plasma. ∗ Corresponding author.
Email address:
E-mail: [email protected] (Karol Kozioł)
Preprint submitted to Atomic Data and Nuclear Data Tables 2019 ontents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22. Method of calculation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.1. W IX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.2. W X . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.3. W XI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Explanation of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7Tables1. Atomic levels of W IX. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82. Atomic levels of W X. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103. Atomic levels of W XI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1. Introduction
Tungsten has been chosen as a plasma facing material in modern large tokamaks, including JET and ITER [1, 2]. Therefore,spectroscopic studies of tungsten ions can constitute a unique tool for diagnostics relevant for a wide range of electron temperatures,from 0.1 keV at the edge up to 30 keV in the core of the tokamak plasma [3]. The tungsten spectra originating from differentplasma regions with various electron temperatures consist of radiation emitted by many specific ion charges. The atomic data oflow-charged tungsten ions are of growing interest in the tokamak plasma diagnostics [4]. Visible transitions in high- Z ions, e.g.low-charged tungsten ions, are suggested as potential candidates for a precise atomic clock that can be used to laboratory searchfor time variation in the fine-structure constant [5, 6]. However, there is a lack of spectroscopic data for some tungsten ionizationstages, from W VIII to W XXVII, as pointed out by Kramida and Shirai [7] and by Ralchenko [8]. Moreover, tungsten ions fromW VIII (W ) to W XIII (W ) are interested because in these cases the most outer orbitals 4f and 5p are close each other andconfigurations [Kr] 4 d x and [Kr] 4 d x +1 competing for the ground state, as was reported first by Sugarand Kaufman [9]. Last years a few works were focused on W VIII from both experimental and theoretical side. Berengut et al. [5]calculated the energies for four levels belonging to configurations 4 f and 4 f and confirmed the level sequencereported by Kramida and Shirai [7]. Then Ryabtsev et al. [10] observed spectrum of seven times ionized tungsten and reportedthe appropriate level energies. Next, Mita et al. [11] measured the fine-structure splitting of the ground term 4 f F inW VIII. The fine-structure splitting was also measured by Lu et al. [12] and compared to the Multi-configuration Dirac–Hartree–Fock (MCDHF) calculation with configuration interaction (CI) with good agreement. Nonetheless, there is still no data available(except identifying the groundstates) for W IX to W XIII in the Atomic Spectra Database of the National Institute of Standards andTechnology [13].In the present work, the MCDHF-CI calculations have been used to predict the energy levels for groundstates and low-lyingstates of W IX (W ), W X (W ), and W XI (W ) tungsten ions. The total number of 1094 states related to 4 f
10. . . 14
2. . . 6
11. . . 14
3. . . 6 valence configurations have been considered. According to my knowledge, the present compilation presentsthe first extended data set for levels of W X and W XI ions, and importantly extend data set for W IX ion.
2. Method of calculation
The calculations of the radiative transition energies and rates have been carried out by means of the G
RASP N -electron system is expressed by H = N ∑ i = h D ( i ) + N ∑ j > i = C i j , (1)where h D ( i ) is the Dirac operator for the i th electron and the terms C i j account for the electron–electron interactions. In general,the latter is a sum of the Coulomb interaction operator and the transverse Breit operator. An atomic state function (ASF) with totalangular momentum J and parity p is assumed in the form Ψ s ( J p ) = ∑ m c m ( s ) Φ ( γ m J p ) , (2)where Φ ( γ m J p ) are the configuration state functions (CSFs), c m ( s ) are the configuration mixing coefficients for state s , and γ m repre-sents all information required to define a certain CSF uniquely. The CSFs are linear combinations of N -electron Slater determinantswhich are antisymmetrized products of 4-component Dirac orbital spinors: Φ ( γ m J p ) = ∑ i d i (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) ψ ( ) · · · ψ ( N ) ... . . . ... ψ N ( ) · · · ψ N ( N ) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) (3)where the ψ i is the one-electron wavefunction defined as ψ n , κ , j = r P n , κ ( r ) · Ω m j κ , j ( θ , φ ) iQ n , κ ( r ) · Ω m j − κ , j ( θ , φ ) (4)where Ω m j κ , j ( θ , φ ) is a angular 2-component spinor and P n , κ ( r ) and Q n , κ ( r ) are large and small radial part of the wavefunction,respectively.In present calculations, the initial and final states of the considered transitions have been optimized separately and a biorthonor-mal transformation has been used for performing the transition rate calculations [18]. Following this, the so-called relaxation effectis taken into account. In the G RASP ion with3Kr] 4 d electronic configuration. After the radial wavefunctions had been calculated within SCF process, the configurationinteraction calculations between ASFs related to valence configurations with different number of 4f electrons have been carried out,to take into account the correlation effect related to near-degeneracy [22].
3. Results
Table A collects valence electronic configurations used in calculations of energy levels for W IX, W X, and W XI tungsten ions.Tables 1, 2, and 3 collect atomic levels of W IX, W X, and W XI, respectively.Table A Valence electronic configurations used in calculations.Ionization state Even configurations Odd configurationsW IX 4 f , 4 f , 4 f , 4 f W X 4 f , 4 f , 4 f , 4 f , 4 f , 4 f W XI 4 f , 4 f , 4 f , 4 f ,4 f , 4 f , 4 f , 4 f For W IX ion Kramida and Shirai [7] suggested that the groundstate is 4 f P and the first excited level (proba-bly 4 f F ) is located about 14000 cm -1 above the groundstate. Berengut et al. [5] calculated sixteen levels relatedto 4 f , 4 f , and 4 f valence configurations. They confirmed that the groundstate is 4 f P and reported that the first excited level 4 f F is located 6075 cm -1 above the groundstate and the second excited level4 f G is located 6357 cm -1 above the groundstate. Presents calculations confirm that the groundstate is 4 f P and the first excited state is related to the terms 4 f F . The relative energy of first excited state is predicted to be10455 cm -1 above the groundstate. This value is in the middle of numbers provided by Kramida and Shirai [7] and by Berengut etal. [5]. From present calculations the second excited state is described mainly by 4 f F term and it is located 11467 cm -1 above the groundstate. For W X ion Kramida and Shirai [7] reported that the groundstate belongs to 4 f configuration while the lowest excitedlevel belongs to 4 f configuration and is located about 31000 cm -1 above the groundstate. They stated that the ground levelhas 39% of the P character and 34% of S . In present calculations the groundstate is described in similar manner, having38% of the P term and 38% of S term. The first excited state is located 23147 cm -1 above the groundstate and it is describedmostly by 4 f D term (34%) with significant contributions from CSFs related to 4 f configuration. For W XI ion Kramida and Shirai [7] reported that the groundstate is 4 f P and the lowest excited level belongs to4 f configuration and is located about 46000 cm -1 above the groundstate. Present calculations confirm that the groundstate4s 4 f P . The lowest excited level is located 48969 cm -1 above the groundstate, having 40% of the 4 f G character and 36% of 4 f F character. Acknowledgments
The work was partly supported by the Polish Ministry of Science and Higher Education within the framework of the scientificfinancial resources in the years 2016–2019 allocated for the realization of the international co-financed project. This work hasbeen carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom Research andTraining Programme 2014–2019 under Grant Agreement No. 633053. The views and opinions expressed herein do not necessarilyreflect those of the European Commission.
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J P LS -composition E (cm -1 )1 2 + 0.73 4 f ( S ) S s p ( P ) P + 0.25 4 f ( S ) S s p ( D ) D
02 4 + 0.81 4 f ( F ) F s p F + 0.10 4 f ( F ) F s p G + 0.10 4 f ( F ) F s p G f ( F ) F s p F + 0.28 4 f ( F ) F s p D + 0.09 4 f ( F ) F s p F f ( F ) F s p G f ( F ) F s p D + 0.23 4 f ( S ) S s p ( P ) P + 0.14 4 f ( F ) F s p F f ( F ) F s p F + 0.17 4 f ( F ) F s p G + 0.15 4 f ( F ) F s p F f ( S ) S s p ( S ) S + 0.48 4 f ( S ) S s p ( P ) P f ( F ) F s p D + 0.45 4 f ( F ) F s p F f ( F ) F s p G + 0.47 4 f ( F ) F s p G f ( F ) F s p D f ( H ) H s p H f ( F ) F s p F + 0.34 4 f ( G ) G s p G + 0.08 4 f ( H ) H s p H f ( H ) H s p H f ( H ) H s p H + 0.33 4 f ( F ) F s p F + 0.17 4 f ( G ) G s p G f ( F ) F s p F f ( F ) F s p F + 0.26 4 f ( D ) D s p D + 0.03 4 f ( P ) P s p P f ( S ) S s p ( P ) P f ( G ) G s p G + 0.42 4 f ( H ) H s p H + 0.09 4 f ( F ) F s p F f ( S ) S s p ( D ) D + 0.22 4 f ( S ) S s p ( P ) P + 0.04 4 f ( F ) F s p F f ( P ) P s p P + 0.24 4 f ( D ) D s p D + 0.21 4 f ( F ) F s p F f ( F ) F s p D + 0.23 4 f ( F ) F s p F + 0.11 4 f ( F ) F s p F f ( F ) F s p G + 0.32 4 f ( F ) F s p G + 0.16 4 f ( F ) F s p F f ( I ) I s p I f ( P ) P s p P + 0.09 4 f ( S ) S s p S + 0.06 4 f ( S ) S s p ( S ) S f ( P ) P s p P f ( F ) F s p G + 0.16 4 f ( F ) F s p F + 0.05 4 f ( F ) F s p F f ( P ) P s p P + 0.34 4 f ( D ) D s p D + 0.04 4 f ( F ) F s p F f ( F ) F s p D + 0.21 4 f ( P ) P s p P + 0.20 4 f ( S ) S s p ( D ) D f ( S ) S s p S + 0.06 4 f ( P ) P s p P + 0.05 4 f ( S ) S s p ( P ) P f ( S ) S s p ( P ) P + 0.45 4 f ( S ) S s p ( S ) S + 0.04 4 f ( S ) S s p S f ( S ) S s S p P f ( S ) S s S p P + 0.25 4 f ( S ) S s S p P f ( F ) F s F p F J P LS -composition E (cm -1 )34 3 - 0.69 4 f ( F ) F s F p F + 0.31 4 f ( F ) F s F p F f ( F ) F s F p F f ( F ) F s F p F + 0.31 4 f ( F ) F s F p F f ( S ) S s S p P f ( S ) S s S p P + 0.25 4 f ( S ) S s S p P able 2 Atomic levels of W X.No.
J P LS -composition E (cm -1 )1 3/2 - 0.38 4 f ( S ) s p ( S ) S + 0.38 4 f ( S ) s p ( P ) P + 0.22 4 f ( S ) s p ( D ) D
02 3/2 - 0.34 4 f ( F ) s p ( P ) D + 0.18 4 f ( S ) s p ( P ) P + 0.15 4 f ( S ) s p ( S ) S f ( F ) s p ( P ) G + 0.20 4 f ( F ) s p ( D ) H f ( F ) s p ( P ) F + 0.31 4 f ( F ) s p ( D ) G + 0.18 4 f ( F ) s p ( P ) G f ( F ) s p ( P ) D + 0.28 4 f ( F ) s p ( D ) F + 0.16 4 f ( F ) s p ( P ) F f ( F ) s p ( P ) D + 0.26 4 f ( F ) s p ( P ) D + 0.19 4 f ( F ) s p ( D ) D f ( F ) s p ( D ) F + 0.23 4 f ( F ) s p ( P ) D + 0.20 4 f ( F ) s p ( P ) F f ( F ) s p ( P ) D + 0.17 4 f ( F ) s p ( D ) P f ( F ) s p ( P ) D + 0.17 4 f ( F ) s p ( D ) D + 0.16 4 f ( F ) s p ( P ) F f ( F ) s p ( P ) G + 0.35 4 f ( F ) s p ( P ) G + 0.22 4 f ( F ) s p ( D ) H f ( F ) s p ( D ) G + 0.30 4 f ( F ) s p ( P ) F + 0.25 4 f ( F ) s p ( P ) G f ( F ) s p ( S ) F + 0.39 4 f ( F ) s p ( P ) F + 0.08 4 f ( F ) s p ( P ) G f ( S ) s p ( D ) D + 0.43 4 f ( S ) s p ( S ) S + 0.04 4 f ( F ) s p ( P ) D f ( F ) s p ( S ) F + 0.28 4 f ( F ) s p ( P ) F + 0.13 4 f ( F ) s p ( P ) G f ( H ) s p H + 0.12 4 f ( H ) s p I + 0.09 4 f ( H ) s p I f ( S ) s p ( D ) D + 0.09 4 f ( F ) s p ( P ) F + 0.06 4 f ( F ) s p ( S ) F f ( H ) s p H + 0.31 4 f ( H ) s p G + 0.13 4 f ( H ) s p H f ( H ) s p I f ( H ) s p G + 0.17 4 f ( G ) s p G + 0.17 4 f ( F ) s p F f ( F ) s p G + 0.25 4 f ( G ) s p H + 0.15 4 f ( H ) s p H f ( F ) s p D + 0.17 4 f ( G ) s p F + 0.15 4 f ( F ) s p ( S ) F f ( F ) s p D + 0.21 4 f ( G ) s p G + 0.16 4 f ( G ) s p F f ( H ) s p H + 0.23 4 f ( F ) s p G + 0.11 4 f ( H ) s p I f ( H ) s p H + 0.26 4 f ( H ) s p G + 0.15 4 f ( H ) s p H f ( H ) s p G + 0.19 4 f ( H ) s p G + 0.13 4 f ( G ) s p G f ( S ) s p ( P ) P f ( H ) s p I + 0.31 4 f ( H ) s p I f ( F ) s p ( P ) D + 0.25 4 f ( F ) s p ( P ) G + 0.12 4 f ( F ) s p ( P ) G f ( H ) s p G + 0.24 4 f ( H ) s p H + 0.16 4 f ( F ) s p G f ( H ) s p G + 0.24 4 f ( F ) s p F + 0.15 4 f ( F ) s p G f ( F ) s p D + 0.32 4 f ( D ) s p P + 0.04 4 f ( P ) s p S f ( F ) s p F + 0.16 4 f ( H ) s p H + 0.15 4 f ( H ) s p H f ( F ) s p ( P ) F + 0.37 4 f ( F ) s p ( P ) G + 0.15 4 f ( F ) s p ( P ) G J P LS -composition E (cm -1 )34 3/2 - 0.54 4 f ( F ) s p D + 0.36 4 f ( F ) s p D + 0.05 4 f ( F ) s p F f ( H ) s p G + 0.20 4 f ( G ) s p F + 0.17 4 f ( F ) s p D f ( F ) s p ( D ) G + 0.20 4 f ( G ) s p G + 0.12 4 f ( F ) s p F f ( F ) s p F + 0.25 4 f ( F ) s p D + 0.14 4 f ( F ) s p D f ( F ) s p G + 0.18 4 f ( F ) s p G + 0.11 4 f ( H ) s p H f ( F ) s p D + 0.37 4 f ( F ) s p F + 0.05 4 f ( F ) s p F f ( F ) s p F + 0.18 4 f ( F ) s p G + 0.13 4 f ( D ) s p F f ( G ) s p H + 0.26 4 f ( H ) s p I + 0.19 4 f ( F ) s p G f ( F ) s p ( P ) D + 0.12 4 f ( F ) s p ( P ) F + 0.11 4 f ( F ) s p D f ( F ) s p ( D ) G + 0.18 4 f ( F ) s p ( P ) G + 0.12 4 f ( F ) s p D f ( F ) s p F + 0.15 4 f ( G ) s p F + 0.13 4 f ( F ) s p G f ( H ) s p G + 0.20 4 f ( G ) s p G + 0.16 4 f ( G ) s p F f ( F ) s p ( D ) F + 0.12 4 f ( H ) s p H + 0.12 4 f ( D ) s p F f ( F ) s p ( P ) G + 0.22 4 f ( F ) s p ( P ) F + 0.13 4 f ( F ) s p ( P ) D f ( F ) s p G + 0.26 4 f ( F ) s p F + 0.11 4 f ( H ) s p H f ( G ) s p G + 0.14 4 f ( G ) s p H + 0.13 4 f ( F ) s p F f ( F ) s p ( P ) F + 0.11 4 f ( H ) s p G + 0.11 4 f ( F ) s p F f ( H ) s p G + 0.32 4 f ( G ) s p F + 0.03 4 f ( F ) s p D f ( P ) s p S + 0.27 4 f ( F ) s p D + 0.19 4 f ( D ) s p P f ( H ) s p I + 0.23 4 f ( G ) s p H + 0.23 4 f ( H ) s p I f ( F ) s p ( P ) F + 0.17 4 f ( F ) s p ( P ) D + 0.12 4 f ( F ) s p ( P ) D f ( F ) s p ( D ) H + 0.17 4 f ( F ) s p ( P ) G + 0.05 4 f ( H ) s p H f ( F ) s p ( D ) F + 0.19 4 f ( G ) s p F + 0.15 4 f ( F ) s p D f ( P ) s p S + 0.17 4 f ( D ) s p P + 0.11 4 f ( D ) s p D f ( I ) s p I + 0.20 4 f ( I ) s p K + 0.02 4 f ( H ) s p H f ( P ) s p D + 0.14 4 f ( D ) s p F + 0.12 4 f ( F ) s p G f ( F ) s p ( D ) P + 0.11 4 f ( F ) s p D + 0.10 4 f ( F ) s p F f ( F ) s p ( P ) F + 0.19 4 f ( F ) s p G + 0.13 4 f ( F ) s p F f ( F ) s p ( P ) D + 0.16 4 f ( F ) s p ( D ) D + 0.09 4 f ( F ) s p F f ( I ) s p I + 0.20 4 f ( I ) s p H + 0.06 4 f ( F ) s p ( D ) H f ( F ) s p ( D ) H + 0.12 4 f ( G ) s p G + 0.11 4 f ( F ) s p ( P ) G f ( D ) s p P + 0.33 4 f ( P ) s p S + 0.10 4 f ( F ) s p D f ( P ) s p S + 0.14 4 f ( P ) s p P + 0.14 4 f ( D ) s p D f ( F ) s p ( D ) D + 0.07 4 f ( F ) s p ( P ) D + 0.07 4 f ( P ) s p D f ( I ) s p K J P LS -composition E (cm -1 )69 3/2 - 0.30 4 f ( P ) s p D + 0.17 4 f ( F ) s p ( P ) F + 0.16 4 f ( P ) s p D f ( P ) s p D + 0.28 4 f ( P ) s p P + 0.08 4 f ( P ) s p D f ( F ) s p ( D ) P + 0.20 4 f ( P ) s p S + 0.10 4 f ( F ) s p ( P ) D f ( D ) s p F + 0.38 4 f ( P ) s p D + 0.05 4 f ( G ) s p G f ( I ) s p H + 0.18 4 f ( F ) s p ( D ) H + 0.08 4 f ( F ) s p ( P ) G f ( P ) s p D + 0.22 4 f ( P ) s p P + 0.18 4 f ( P ) s p P f ( P ) s p P + 0.17 4 f ( F ) s p ( D ) F + 0.14 4 f ( D ) s p D f ( P ) s p P + 0.17 4 f ( P ) s p D + 0.16 4 f ( F ) s p ( D ) P f ( S ) s p ( P ) P + 0.25 4 f ( S ) s p ( D ) D + 0.09 4 f ( S ) s p ( S ) S f ( H ) s p G + 0.16 4 f ( H ) s p H + 0.15 4 f ( H ) s p H f ( I ) s p I + 0.04 4 f ( K ) s p K f ( H ) s p I + 0.23 4 f ( H ) s p I + 0.20 4 f ( H ) s p H f ( F ) s p D + 0.21 4 f ( G ) s p F + 0.14 4 f ( F ) s p F f ( F ) s p G + 0.24 4 f ( G ) s p H + 0.13 4 f ( F ) s p G f ( H ) s p I + 0.28 4 f ( H ) s p I + 0.15 4 f ( H ) s p H f ( H ) s p I + 0.23 4 f ( H ) s p H + 0.21 4 f ( H ) s p G f ( I ) s p I f ( F ) s p G + 0.17 4 f ( F ) s p F + 0.10 4 f ( H ) s p G f ( I ) s p I + 0.29 4 f ( H ) s p H + 0.03 4 f ( G ) s p G f ( S ) s p P + 0.21 4 f ( D ) s p D + 0.04 4 f ( F ) s p D f ( H ) s p I + 0.22 4 f ( H ) s p H + 0.17 4 f ( H ) s p G f ( F ) s p F + 0.22 4 f ( I ) s p I + 0.18 4 f ( H ) s p H f ( F ) s p G + 0.26 4 f ( F ) s p F + 0.09 4 f ( F ) s p D f ( F ) s p F + 0.17 4 f ( F ) s p D + 0.15 4 f ( F ) s p D f ( F ) s p F + 0.17 4 f ( F ) s p G + 0.13 4 f ( F ) s p G f ( F ) s p D + 0.25 4 f ( F ) s p F + 0.23 4 f ( S ) s p P f ( I ) s p I + 0.39 4 f ( F ) s p F + 0.07 4 f ( H ) s p H f ( G ) s p H + 0.16 4 f ( H ) s p I + 0.15 4 f ( G ) s p G f ( S ) s p S + 0.21 4 f ( P ) s p P + 0.12 4 f ( D ) s p D f ( H ) s p H + 0.21 4 f ( H ) s p I + 0.17 4 f ( I ) s p I f ( F ) s p ( S ) F + 0.09 4 f ( F ) s p G + 0.08 4 f ( F ) s p F f ( F ) s p F + 0.07 4 f ( G ) s p G + 0.04 4 f ( G ) s p G f ( H ) s p G + 0.23 4 f ( G ) s p F + 0.15 4 f ( G ) s p G f ( F ) s p F + 0.22 4 f ( F ) s p ( D ) F + 0.13 4 f ( F ) s p G f ( F ) s p F + 0.19 4 f ( D ) s p D + 0.12 4 f ( S ) s p S J P LS -composition E (cm -1 )104 9/2 - 0.28 4 f ( F ) s p F + 0.19 4 f ( I ) s p I + 0.14 4 f ( G ) s p G f ( D ) s p F + 0.16 4 f ( D ) s p D + 0.14 4 f ( P ) s p D f ( K ) s p K + 0.07 4 f ( L ) s p L + 0.04 4 f ( I ) s p I f ( P ) s p P + 0.20 4 f ( P ) s p D + 0.12 4 f ( D ) s p D f ( G ) s p G + 0.21 4 f ( H ) s p H + 0.14 4 f ( H ) s p H f ( G ) s p G + 0.27 4 f ( G ) s p G + 0.26 4 f ( G ) s p G f ( F ) s p ( S ) F + 0.18 4 f ( F ) s p ( P ) G + 0.10 4 f ( F ) s p ( P ) F f ( I ) s p K + 0.20 4 f ( I ) s p I f ( G ) s p G + 0.10 4 f ( G ) s p H + 0.08 4 f ( H ) s p H f ( P ) s p P + 0.33 4 f ( F ) s p ( D ) P + 0.07 4 f ( F ) s p ( P ) D f ( P ) s p P + 0.29 4 f ( P ) s p D + 0.14 4 f ( P ) s p S f ( K ) s p K + 0.14 4 f ( I ) s p I f ( I ) s p H + 0.24 4 f ( I ) s p I f ( F ) s p F + 0.24 4 f ( P ) s p P + 0.12 4 f ( D ) s p D f ( P ) s p D + 0.33 4 f ( P ) s p P + 0.12 4 f ( P ) s p P f ( G ) s p G + 0.08 4 f ( D ) s p D + 0.06 4 f ( F ) s p F f ( P ) s p D + 0.16 4 f ( P ) s p D + 0.15 4 f ( P ) s p P f ( P ) s p D + 0.23 4 f ( P ) s p D + 0.20 4 f ( D ) s p F f ( G ) s p G + 0.21 4 f ( G ) s p G + 0.10 4 f ( G ) s p G f ( D ) s p D + 0.19 4 f ( F ) s p F + 0.17 4 f ( D ) s p D f ( P ) s p P + 0.18 4 f ( P ) s p P + 0.14 4 f ( D ) s p D f ( H ) s p H + 0.20 4 f ( G ) s p G + 0.15 4 f ( H ) s p H f ( D ) s p D + 0.21 4 f ( D ) s p D + 0.17 4 f ( D ) s p D f ( I ) s p I + 0.29 4 f ( H ) s p H + 0.03 4 f ( G ) s p G f ( L ) s p L f ( D ) s p D + 0.04 4 f ( F ) s p F + 0.04 4 f ( G ) s p G f ( I ) s p I + 0.31 4 f ( I ) s p K + 0.07 4 f ( K ) s p K f ( P ) s p P + 0.26 4 f ( D ) s p D + 0.20 4 f ( D ) s p D f ( D ) s p D + 0.12 4 f ( D ) s p D + 0.11 4 f ( D ) s p D f ( L ) s p L + 0.07 4 f ( K ) s p K f ( H ) s p H + 0.24 4 f ( H ) s p H + 0.03 4 f ( G ) s p G f ( D ) s p D + 0.08 4 f ( P ) s p P f ( D ) s p D + 0.31 4 f ( D ) s p D + 0.09 4 f ( F ) s p F f ( H ) s p H + 0.31 4 f ( I ) s p I + 0.11 4 f ( H ) s p H f ( F ) s p F + 0.36 4 f ( F ) s p F + 0.07 4 f ( D ) s p D J P LS -composition E (cm -1 )139 3/2 - 0.56 4 f ( D ) s p D + 0.22 4 f ( D ) s p D + 0.08 4 f ( D ) s p D f ( S ) s S p ( P ) P + 0.14 4 f ( S ) s S p ( D ) D f ( F ) s p F + 0.17 4 f ( F ) s p F + 0.15 4 f ( D ) s p D f ( G ) s p G + 0.39 4 f ( G ) s p G + 0.04 4 f ( F ) s p F f ( S ) s p P + 0.03 4 f ( P ) s p D f ( G ) s p G + 0.40 4 f ( G ) s p G + 0.03 4 f ( H ) s p H f ( S ) s S p ( P ) P + 0.39 4 f ( S ) s S p ( S ) S f ( S ) s S p ( P ) P + 0.24 4 f ( S ) s S p ( D ) D + 0.14 4 f ( S ) s S p ( P ) P f ( F ) s p F + 0.17 4 f ( F ) s p F + 0.09 4 f ( F ) s p ( S ) F f ( F ) s F p F + 0.18 4 f ( F ) s F p G + 0.04 4 f ( F ) s F p G f ( F ) s p F + 0.37 4 f ( F ) s p F + 0.04 4 f ( F ) s p ( S ) F f ( F ) s F p F + 0.23 4 f ( F ) s F p D + 0.21 4 f ( F ) s F p F f ( F ) s F p G f ( F ) s F p F + 0.27 4 f ( F ) s F p D + 0.17 4 f ( F ) s F p F f ( F ) s F p F + 0.25 4 f ( F ) s F p F + 0.23 4 f ( F ) s F p G f ( F ) s F p F + 0.13 4 f ( F ) s F p D + 0.10 4 f ( F ) s F p G f ( F ) s F p D + 0.24 4 f ( F ) s F p F + 0.18 4 f ( F ) s F p D f ( F ) s F p D + 0.31 4 f ( F ) s F p F f ( F ) s F p D f ( F ) s F p G + 0.21 4 f ( F ) s F p G + 0.20 4 f ( F ) s F p G f ( S ) s S p ( D ) D + 0.23 4 f ( F ) s F p D + 0.23 4 f ( S ) s S p ( P ) P f ( F ) s F p G + 0.15 4 f ( F ) s F p G + 0.14 4 f ( F ) s F p F f ( F ) s F p D + 0.29 4 f ( F ) s F p D + 0.12 4 f ( F ) s F p F f ( F ) s F p D + 0.21 4 f ( F ) s F p F + 0.17 4 f ( F ) s F p G f ( S ) s S p ( D ) D + 0.20 4 f ( F ) s F p D + 0.12 4 f ( F ) s F p F f ( F ) s F p G + 0.39 4 f ( F ) s F p G + 0.08 4 f ( F ) s F p F f ( F ) s F p G + 0.20 4 f ( F ) s F p D + 0.15 4 f ( F ) s F p F f ( F ) s F p D + 0.28 4 f ( F ) s F p F + 0.18 4 f ( F ) s F p D f ( S ) s S p ( P ) P + 0.30 4 f ( S ) s S p ( S ) S + 0.29 4 f ( S ) s S p ( P ) P f ( F ) s F p D + 0.19 4 f ( F ) s F p G + 0.18 4 f ( F ) s F p F f ( H ) s H p H f ( S ) s S p ( P ) P + 0.25 4 f ( S ) s S p ( D ) D f ( H ) s H p H + 0.28 4 f ( H ) s H p H f ( F ) s F p F + 0.25 4 f ( G ) s G p G + 0.05 4 f ( H ) s H p H f ( F ) s F p G + 0.15 4 f ( F ) s F p D + 0.12 4 f ( F ) s F p F J P LS -composition E (cm -1 )174 7/2 + 0.39 4 f ( G ) s G p G + 0.27 4 f ( F ) s F p F + 0.17 4 f ( H ) s H p H f ( H ) s H p H + 0.08 4 f ( H ) s H p H + 0.07 4 f ( F ) s F p F f ( H ) s H p H + 0.28 4 f ( H ) s H p H f ( F ) s F p F + 0.39 4 f ( H ) s H p H + 0.05 4 f ( G ) s G p G f ( F ) s F p F + 0.09 4 f ( D ) s D p D f ( F ) s F p F + 0.21 4 f ( D ) s D p D + 0.05 4 f ( S ) s S p ( D ) D f ( G ) s G p G + 0.38 4 f ( H ) s H p H + 0.20 4 f ( F ) s F p F f ( F ) s F p F + 0.22 4 f ( F ) s F p F + 0.21 4 f ( H ) s H p H f ( F ) s F p F + 0.17 4 f ( F ) s F p F + 0.13 4 f ( F ) s F p D f ( F ) s F p F + 0.27 4 f ( D ) s D p D + 0.06 4 f ( P ) s P p P f ( G ) s G p G + 0.30 4 f ( F ) s F p F + 0.20 4 f ( H ) s H p H f ( F ) s F p G + 0.10 4 f ( F ) s F p G + 0.07 4 f ( F ) s F p F f ( H ) s H p H + 0.33 4 f ( G ) s G p G + 0.10 4 f ( H ) s H p H f ( F ) s F p D + 0.29 4 f ( F ) s F p D + 0.16 4 f ( F ) s F p F f ( P ) s P p P + 0.31 4 f ( F ) s F p F + 0.19 4 f ( D ) s D p D f ( F ) s F p F + 0.22 4 f ( F ) s F p D + 0.15 4 f ( F ) s F p F f ( D ) s D p D + 0.19 4 f ( P ) s P p P + 0.16 4 f ( F ) s F p F f ( F ) s F p G + 0.38 4 f ( F ) s F p G + 0.09 4 f ( F ) s F p G f ( I ) s I p I f ( I ) s I p I f ( P ) s P p P + 0.05 4 f ( S ) s S p S f ( F ) s F p D + 0.12 4 f ( F ) s F p F + 0.05 4 f ( F ) s F p D f ( P ) s P p P + 0.12 4 f ( D ) s D p D + 0.04 4 f ( P ) s P p P f ( D ) s D p D + 0.36 4 f ( P ) s P p P + 0.06 4 f ( F ) s F p F f ( P ) s P p P + 0.11 4 f ( S ) s S p ( P ) P + 0.08 4 f ( S ) s S p ( P ) P f ( P ) s P p P + 0.17 4 f ( D ) s D p D + 0.03 4 f ( S ) s S p ( P ) P f ( S ) s S p ( P ) P + 0.31 4 f ( S ) s S p ( S ) S + 0.11 4 f ( S ) s S p ( P ) P f ( S ) s S p S + 0.09 4 f ( S ) s S p ( P ) P + 0.04 4 f ( P ) s P p P able 3 Atomic levels of W XI.No.
J P LS -composition E (cm -1 )1 0 + 0.77 4 f ( S ) s p ( P ) P + 0.22 4 f ( S ) s p ( S ) S