Energy levels, radiative rates, and lifetimes for transitions in W LVIII
aa r X i v : . [ phy s i c s . a t m - c l u s ] J un Energy levels, radiative rates, and lifetimes for transitions in W LVIII
Kanti M. Aggarwal and
Francis P. Keenan
Astrophysics Research Centre, School of Mathematics and Physics, Queen’s University Belfast,Belfast BT7 1NN, Northern Ireland, UK.
ABSTRACT
Energy levels and radiative rates are reported for transitions in Cl-like W LVIII. Configuration interaction (CI) has beenincluded among 44 configurations (generating 4978 levels) over a wide energy range up to 363 Ryd, and the general-purposerelativistic atomic structure package (
GRASP ) adopted for the calculations. Since no other results of comparable complexity areavailable, calculations have also been performed with the flexible atomic code (
FAC ), which help in assessing the accuracy ofour results. Energies are listed for the lowest 400 levels (with energies up to ∼
98 Ryd), which mainly belong to the 3s ,3s3p , 3s , 3s3p , 3s , and 3p
3d configurations, and radiative rates are provided for four types oftransitions, i.e. E1, E2, M1, and M2. Our energy levels are assessed to be accurate to better than 0.5%, whereas radiative rates(and lifetimes) should be accurate to better than 20% for a majority of the strong transitions.Received January 29, 2014; accepted June 11, 2014————————————————————————————————————————————————
Running Title : K. M. Aggarwal and F. P. Keenan / Atomic Data and Nuclear Data Tables xxx (2014) xxx-xxx ontents
1. Introduction ......................................... 002. Energy levels ........................................ 003. Radiative rates .................................... 004. Lifetimes ......................................... 005. Conclusions .................................... 00Acknowledgments ............................. 00References ........................................ 00Explanation of TablesTables1. Configurations and levels of W LVIII. ................................................. 002. Energies (Ryd) for the lowest 400 levels of W LVIII and their lifetimes (in s). ................................................. 003. Transition wavelengths ( λ ij in ˚ A ), radiative rates (A ji in s − ), oscillator strengths .................................... 00(f ij , dimensionless), line strengths S (in atomic unit) for electric dipole (E1), and ............................................. 00A ji for electric quadrupole (E2), magnetic dipole (M1), and magnetic quadrupole (M2) transitions in W LVIII. ..... 002 . Introduction Recently there have been several studies ( [1] – [4]) of atomic parameters (mainly energy levels and radiative decay rates)for tungsten (W) ions. Similarly, laboratory measurements have been made for emission lines of W ions – see for example, Utteret al. [5] and Clementson et al. [6]. These data have been compiled by the NIST (National Institute of Standards and Technology)team [7], and are available at their website http://physics.nist.gov/PhysRefData/ASD/levels form.html .It is important to have such results because W is a major constituent of fusion reactor devices, and hence data are required forassessing and controlling the radiation loss. With the ongoing ITER project, the need for atomic data for several W ions hasbecome even greater.Unfortunately, the only calculation available in the literature for (Cl-like) W LVIII is by Mohan et al. [8], who haverecently reported results for energy levels, oscillator strengths (f- values), radiative rates (A- values), line strengths (S- values),and lifetimes ( τ ). However, they listed energies for only 31 levels of the 3s , 3s3p , and 3s
3d configurations, and A-values for only transitions from the two levels of the ground state, i.e. (3s ) P o / , / . This amount of data is too limited forthe modelling of plasmas, as demonstrated in Fig. 2 and Table 6 of Del Zanna et al. [9] for Cl-like iron (Fe X). Level populationsdeduced using restricted and larger sets of atomic data may differ by up to a factor of five. Therefore, in this paper we provideenergies (and lifetimes) for the lowest 400 levels of W LVIII, which mainly belong to the 3s , 3s3p , 3s ,3s3p , 3s , and 3p
3d configurations. Furthermore, we also list A-values for all transitions among these levels, andfor four types, namely electric dipole (E1), electric quadrupole (E2), magnetic dipole (M1), and magnetic quadrupole (M2).For the calculations, we have adopted the multi-configuration Dirac-Fock (MCDF) code, developed by Grant et al. [10].It is a fully relativistic code, based on the jj coupling scheme. Further higher-order relativistic corrections arising from the Breitinteraction and QED (quantum electrodynamics) effects have also been included. However, this initial version has undergoneseveral revisions, known as GRASP (general-purpose relativistic atomic structure package) [11], GRASP2 [12], and GRASP2K[13]–[14]. The version adopted here has been revised by one of its authors (Dr. P. H. Norrington), and is referred to as GRASP0.It is freely available at http://web.am.qub.ac.uk/DARC/ , and has been successfully used by ourselves and others tocalculate atomic data for a wide range of ions. Furthermore, GRASP0 provides comparable results with other versions, and hasalso been employed by Mohan et al. [8].
2. Energy levels
Since W is a heavy element (Z = 74), the contributions of various relativistic operators are (expectedly) important inthe determination of energy levels and subsequently other parameters. However, the inclusion of configuration interaction (CI)is equally important for several of its ions – see for example, Fournier [1]. Furthermore, the importance of CI for Cl-like ionshas already been established – see for example, Ti VI [15], Cr VIII [16], Fe X [17], and Co XI [18]. For this reason Mohanet al. [8] included CI among 15 configurations, namely 3s , 3s3p , 3s ℓ , 3s3p , 3s3p ,3p , 3p , 3s , and 3s . However, inclusion of this limited CI is not fully sufficient for an accuratedetermination of energy levels and radiative rates (A- values), as recently discussed by us [19].In our earlier work [19], we included extensive CI among 20 even (1–20) and 18 odd (25–42) configurations, listed in Table1. These 38 configurations generate a total of 3749 levels and cover a wide range of energy up to 363 Ryd. The 15 configurationsincluded by Mohan et al. [8] are also listed in Table 1 (called GRASP1). It is clear from the table that these authors omittedseveral important configurations, such as 3s3p , 3s , and 3s3p , which together generate 1716 levels in the 92–196Ryd energy range. The inclusion of these configurations substantially increases the size of a calculation, especially given thatthe 15 configurations of Mohan et al. generate only 1163 levels. However, the energy range of these three configurations iswell below that of 3s ℓ included by Mohan et al. Levels of these three and other configurations (listed in Table 1) closelyinteract, intermix, and influence the energies of others, such as 3s and 3s for even and odd parity levels. It ispossible that Mohan et al. excluded most of the relevant configurations because they were only interested in the 31 levels of the3s , 3s3p , and 3s
3d configurations, for which discrepancies in energy levels and A- values are not very appreciable[19]. However, two of the configurations included by them, namely (3s ) 4d and 4f , are not important, because their levelslie in a very high energy range, i.e. ≥
413 Ryd, and hence have little effect on the lower levels. Therefore, we have excluded these two configurations from our calculations, but will discuss their impact later. However, we have included a further 4 even33s , 3p , 3s3d , and 3d ) and 2 odd (3s3p3d and 3p3d ) configurations, which generate 1229 levels in the 157–303 Rydenergy range. All the 44 configurations included in our calculations are listed in Table 1 under the column GRASP2. Finally, asin our earlier work and that of Mohan et al., we have adopted the option of extended average level (EAL), in which a weighted(proportional to 2 j +1) trace of the Hamiltonian matrix is minimised. This yields results comparable to other options, such as average level (AL) – see for example, Aggarwal et al. for several ions of Kr [20] and Xe [21].Energies for the lowest 400 levels of W LVIII are listed in Table 2, which correspond to the GRASP2 calculations with 44configurations (listed in Table 1) generating 4978 levels in total. These listed levels mostly belong to the 3s , 3s3p , 3s , 3s3p , 3s , and 3p
3d configurations, but energies for all levels may be obtained electronically on requestfrom one of the authors (KMA: [email protected]). Unfortunately, experimental energies for W LVIII (see the NIST web-site) are limited to only a few levels and are not very accurate because most are determined by interpolation and extrapolation.Nevertheless, detailed comparisons with the NIST listings and those of Mohan et al. [8] were undertaken in our earlier work [19]for the lowest 31 levels belonging to the 3s , 3s3p , and 3s
3d configurations. As noted earlier, the Mohan et al. results arehigher by up to 0.07 Ryd for some of the levels, mainly because of the limited CI included by them. We also note that for these 31levels there are no differences between the present calculations (with a slightly larger CI) and the earlier ones [19], in both magni-tude and ordering. For the levels of other configurations, listed in Table 2, it is difficult to fully assess the accuracy of our energylevels, because no other theoretical or experimental results exist. Therefore, to make such an assessment we have employed the
Flexible Atomic Code ( FAC ) of Gu [22], available from the website http://sprg.ssl.berkeley.edu/ ∼ mfgu/fac/ .This is also a fully relativistic code which provides results of comparable accuracy, particularly for energy levels and A- values,as already shown for several other ions, see for example: Aggarwal et al. for Kr [20] and Xe [21] ions, and Aggarwal and Keenanfor Ti ions ([15] and [23]–[24]), and W XL [25].As with GRASP , we have performed a series of calculations with the
FAC code with increasing amount of CI, but focusonly on three, namely (i) FAC1, which includes 5821 levels among 3*7, 3s
3d 4*1; (ii) FAC2; which includes an additional 3339 levels of 3s
3d 6*1; and finally (iii) FAC3, which includes a further 9299 levels of 3s
3d 4*1, i.e. 18,459 levels in total.For Cl-like ions, CI is very important [15]–[18], and levels from different configurations mix strongly. Therefore, it isvery difficult to assign a unique label for each level. Mixing coefficients for the 31 levels of the 3s , 3s3p , and 3s and 3s3p configurations, but only a few of 3s
3d and 3s .Moreover, these coefficients are from our GRASP2 calculations and hence differ from those of [19], particularly because allcoefficients with magnitude ≥ | | are listed here.Some of the levels are almost pure, such as 3s P o / , / , and some are unambiguously identifiable (because of theirclear dominance), such as: 3s ( P)3d D / , / , / , i.e. 2, 3 and 7. However, some of the levels, such as 3s ( P)3d P / , / , / , are highly mixed, and can therefore easily interchange with others. Unfortunately, a majority of the W LVIII levelsare highly mixed, as shown in Table A. For this reason, the LSJ designations provided in Table 2 are only for guidance andshould not be taken as definitive. The only confirm values associated with the levels are those of J π .In Table B we compare our energies for the lowest 50 levels from the GRASP2 calculations with those from FAC. Resultsfrom all three FAC calculations (FAC1, FAC2, and FAC3) described above are included in this table. Differences between theGRASP2 and FAC energies are up to 0.2 Ryd ( ∼ ∼
3. Radiative rates f ij ), a dimensionless quantity, and radiative rate A ji (in s − ) for a transition i → j arerelated by the following expression: f ij = mc π e λ ji ω j ω i A ji = 1 . × − λ ji ω j ω i A ji (1)where m and e are the electron mass and charge, respectively, c the velocity of light, λ ji the transition wavelength in ˚ A , and ω i and ω j the statistical weights of the lower i and upper j levels, respectively. Similarly, the oscillator strength f ij (dimensionless)and the line strength S (in atomic units, 1 a.u. = 6.460 × − cm esu ) are related by the following standard equations:for the electric dipole (E1) transitions: A ji = 2 . × ω j λ ji S and f ij = 303 . λ ji ω i S, (2)for the magnetic dipole (M1) transitions: A ji = 2 . × ω j λ ji S and f ij = 4 . × − λ ji ω i S, (3)for the electric quadrupole (E2) transitions: A ji = 1 . × ω j λ ji S and f ij = 167 . λ ji ω i S, (4)and for the magnetic quadrupole (M2) transitions: A ji = 1 . × ω j λ ji S and f ij = 2 . × − λ ji ω i S. (5)In our calculations with the GRASP code the S- (and subsequently A- and f-) values have been determined in both thelength and velocity forms, i.e. the Babushkin and Coulomb gauges in the relativistic nomenclature. Since the velocity form isconsidered to be comparatively less accurate, in Table 3 we present results in the length form alone. Included in this table arethe transition wavelengths ( λ ij in ˚ A ), radiative rates (A ji in s − ), oscillator strengths ( f ij , dimensionless), and line strengths ( S in a.u.) for all 19,862 electric dipole (E1) transitions among the lowest 400 levels of W LVIII. Also, in calculating the aboveparameters we have used the Breit and QED-corrected theoretical energies listed in Table 2, where the indices used to representthe lower and upper levels of a transition are also defined. However, only A- values are included in Table 3 for the 30,058 electricquadrupole (E2), 40,771 magnetic dipole (M1), and 28,365 magnetic quadrupole (M2) transitions. Corresponding results for f-or S- values can be easily obtained using Eqs. (1-5).To assess the accuracy of our radiative data, in Table C we compare the f- values from our GRASP2 calculations withthose from FAC1 and FAC2. All transitions with I ≤ ≤
50 are included in the table. Also, the ratio of the velocity/lengthforms is listed, because it gives an indication of the accuracy of the f- (or A-) values. However, we emphasise here althoughgood agreement between the two forms is desirable, it is not a necessary condition for accuracy. This is because different setsof configurations may lead to good agreement between the two forms, but entirely different results in magnitude, mostly for5he weaker (inter-combination) transitions, but sometimes also for allowed ones, which are comparatively stable and larger inmagnitude. Examples of the differences between the two forms can be seen in some of our earlier papers, such as [26]–[27].The velocity/length ratio is generally within 20% of unity for most of the transitions listed in Table C. However, forsome weak transitions (such as 1–11, 2–38, 3–16, and 5–44/46), the ratio is higher, up to factor of 1.7. Nevertheless, mostsuch transitions have f ∼ − (or less) and their magnitudes are highly variable with differing amount of CI. Generally, withincreasing amount of CI, the f- values for strong transitions converge, but this is not necessarily the case for weaker ones. For thesame reasons, differences between the f- values from the GRASP and FAC calculations are up to a factor of two for some weaktransitions, such as 1–11 and 5–26. Otherwise, for most transitions listed in Table C the f- values from the GRASP and FACcalculations agree within 20%, which is highly satisfactory. Finally, as for the energy levels, f- values from FAC1 and FAC2 arecomparable for most transitions, and therefore confirm, yet again, that the CI included in the GRASP2 and FAC1 calculations issufficient to produce accurate radiative rates.Quinet [2] has calculated the energy interval of the 3s P o / , / levels (1 and 10) to be 25.5738 Ryd which compareswell with our result of 25.5358 Ryd – see Table 2. Like us he adopted the same GRASP0 version of the code and also calculatedA- value for the 1–10 (M1 and E2) forbidden transition to be 3.95 × s − , which fully agrees with our result of 3.93 × s − .However, this comparison is too restricted and in the absence of the availability of other similar data, assessing the reliability ofthe present calcuations is not a simple task, as large discrepancies (of even orders of magnitude) have been noted in the past [28].Nevertheless, based on the comparisons shown in Table C and our experience on a variety of ions, the accuracy of our radiativedata is estimated to be better than 20%, for a majority of transitions, particularly the stronger ones.
4. Lifetimes
The lifetime τ of a level j is defined as follows: τ j = 1 P i A ji . (6)In Table 2 we list lifetimes for all 400 levels from our calculations with the GRASP code, which include A- values from all typesof transitions, i.e. E1, E2, M1, and M2. Unfortunately, there are no measurements available with which to compare the lifetimes.However, theoretical results by Mohan et al. [8] are available for 31 levels of the the 3s , 3s3p , and 3s
3d configurations,based on calculations with the same
GRASP code. However, these results are in error for several levels, by up to four orders ofmagnitude, as discussed and demonstrated in our earlier paper [19].
5. Conclusions
In this work, energy levels and radiative rates (for E1, E2, M1, and M2 transitions) obtained with the
GRASP code havebeen reported for the lowest 400 levels of W LVIII. To assess the accuracy of our data, similar calculations with differing amountof CI have also been performed with the
FAC code, as no other results are available in the literature. Based on comparisonsof several calculations with the two independent codes, our energy levels are assessed to be accurate to ∼ ∼ ∼ Acknowledgment
KMA is thankful to AWE Aldermaston for financial support. 6 ppendix A. Supplementary data
Owing to space limitations, only part of Table 3 is presented here, the full table being made available as supplementalmaterial in conjunction with the electronic publication of this work. Supplementary data associated with this article can be found,in the online version, at doi:nn.nnnn/j.adt.2014.nn.nnn.
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Mixing coefficients (MC) for the lowest 50 levels of W LVIII. Numbers outside and inside a bracket correspond to MCand the level, respectively. See Table 2 for definitions of levels up to 400.Index Configuration Level Mixing coefficients1 3s P o / ( P)3d D / -0.59( 2)+0.44( 12)-0.28( 56)+0.16(137)+0.46( 45)-0.28( 40)-0.23( 6)3 3s ( P)3d D / -0.36( 30)+0.61( 3)-0.25(165)-0.18( 47)+0.31( 13)+0.45( 39)-0.31( 50)4 3s ( P)3d P / ( P)3d F / ( S)3d D / ( P)3d D / -0.23( 42)+0.65( 7)+0.47( 5)+0.21( 31)+0.50( 52)8 3s ( P)3d F / ( P)3d P / -0.11( 19)+0.24( 22)+0.35( 4)-0.67( 9)+0.36( 58)+0.47( 41)10 3s P o / ( S)3d D / ( P)3d P / ( P)3d D / -0.28( 30)-0.41( 3)+0.22(165)-0.14( 47)+0.52( 13)+0.35( 39)+0.35( 50)-0.41( 11)14 3s ( D)3d ( F) D o / ( P)3d ( F) D o / -0.45( 71)-0.24(415)-0.26(113)-0.11( 85)-0.31(299)-0.20( 51)-0.15(131)-0.59( 15)-0.11( 24)-0.33(368)16 3s ( S)3d ( D) D o / -0.35( 93)-0.26(121)-0.22( 16)-0.36( 68)-0.25(141)+0.10(187)-0.20(154)-0.28( 78)+0.41(290)-0.19(351)+0.29( 25)-0.14(171)+0.27( 44)17 3s ( D)3d ( F) H o / ( D)3d ( P) F o / S / ( D)3d ( F) H o / -0.43( 92)-0.23(116)-0.14( 35)+0.35( 20)-0.12(423)-0.21( 73)+0.24(176)-0.13(133)-0.55(349)+0.28( 49)-0.24(168)-0.11(127)+0.17(381)21 3s ( P)3d ( F) F o / -0.34( 94)-0.15(160)+0.14( 87)-0.23(352)+0.11( 32)+0.18(144)-0.30( 70)-0.10( 53)+0.16(122)-0.16(163)+0.13( 99)-0.17(124)-0.19(289)-0.25(108)+0.39( 21)+0.10(293)+0.24(360)-0.31( 29)-0.11(374)+0.11(139)+0.26( 46)22 3s ( P)3d D / -0.15( 19)-0.89( 22)-0.21( 4)-0.31( 9)+0.22( 58)23 3s ( P)3d ( F) D o / -0.30( 67)+0.29(111)+0.19( 81)-0.18(357)-0.27( 88)-0.21(151)-0.22(188)+0.18( 18)+0.18(482)-0.11(294)-0.47( 23)+0.30(398)-0.23(322)+0.13(385)-0.24( 36)-0.10( 97)24 3s ( P)3d ( P) S o / -0.21( 71)+0.37(145)-0.15(434)+0.17(415)-0.14(113)-0.11(299)+0.14(126)-0.41(169)+0.15(196)+0.13( 51)+0.14(131)-0.26( 15)-0.38(118)+0.44( 24)+0.25(368)25 3s ( P)3d ( F) F o / ( P)3d ( P) D o / -0.23( 93)-0.43( 98)-0.12( 33)+0.14(409)-0.11(177)+0.14(187)+0.24(416)-0.15( 89)-0.12(143)+0.28(134)+0.15(290)-0.27(351)-0.11( 25)-0.41( 26)+0.41(359)-0.12(378)-0.11( 44)27 3s ( P)3d F / -0.57( 27)+0.57( 2)+0.19( 12)+0.36(137)+0.31( 45)-0.27( 40)28 3s ( D)3d ( G) I o / ( P)3d ( P) D o / ( P)3d F / ( D)3d G / ( S)3d ( G) G o / ( S)3d ( P) P o / ( P)3d ( D) P o / ( S)3d ( G) G o / ( P)3d ( P) D o / ( P)3d ( G) F o / -0.24(478)+0.13( 33)-0.39(110)+0.13( 16)-0.11( 68)-0.12(409)-0.15( 84)-0.14(177)-0.15(416)-0.19(104)-0.33(147)+0.13(154)-0.13( 78)+0.18( 25)+0.26( 54)+0.15( 26)+0.14(378)-0.52( 37)-0.17( 44)38 3s ( P)3d ( P) P o / -0.15( 71)-0.29(145)-0.30(434)+0.21(415)-0.44(126)-0.10(196)+0.19( 51)+0.14(131)-0.18( 15)-0.29( 95)+0.22(118)+0.47( 38)+0.30(368)39 3s ( D)3d F / ( D)3d P / -0.24( 27)-0.15( 2)+0.47( 12)-0.10( 56)+0.40(137)-0.50( 45)+0.52( 40)41 3s ( D)3d S / ( P)3d F / ( P)3d ( F) G o / ( P)3d ( D) D o / ( D)3d D / -0.15( 27)-0.36( 2)-0.45( 12)+0.21( 56)+0.54(137)-0.33( 45)-0.45( 40)46 3s ( P)3d ( D) F o / -0.20(160)+0.32(352)-0.17( 32)+0.28(144)-0.13( 53)-0.12(453)-0.20( 99)+0.17(124)+0.13(130)+0.11(149)-0.30(289)-0.12(180)-0.13(108)+0.19(170)+0.19(360)+0.39( 29)+0.18(374)-0.14(139)+0.41( 46)47 3s ( P)3d F / -0.21( 30)+0.38( 3)+0.47(165)+0.66( 47)-0.16( 13)+0.17( 39)+0.31( 50)48 3s ( D)3d G / ( P)3d ( F) F o / -0.32( 92)+0.30(116)+0.21( 35)-0.18( 20)-0.34(102)-0.21(423)+0.12( 73)+0.20(176)+0.18(133)+0.50( 49)+0.37(168)+0.15(127)-0.23(381)50 3s ( D)3d D / -0.15( 30)+0.52(165)+0.11( 47)+0.35( 13)-0.36( 39)-0.65( 50)10 able B. Comparison of excitation energies (in Ryd) for the lowest 50 levels of W LVIII.Index Configuration Level GRASP FAC1 FAC2 FAC31 3s P o / ( P)3d D / ( P)3d D / ( P)3d P / ( P)3d F / ( S)3d D / ( P)3d D / ( P)3d F / ( P)3d P / P o / ( S)3d D / ( P)3d P / ( P)3d D / ( D)3d ( F) D o / ( P)3d ( F) D o / ( S)3d ( D) D o / ( D)3d ( F) H o / ( D)3d ( P) F o / S / ( D)3d ( F) H o / ( P)3d ( F) F o / ( P)3d D / ( P)3d ( F) D o / ( P)3d ( P) S o / ( P)3d ( F) F o / ( P)3d ( P) D o / ( P)3d F / ( D)3d ( G) I o / ( P)3d ( P) D o / ( P)3d F / ( D)3d G / ( S)3d ( G) G o / ( S)3d ( P) P o / ( P)3d ( D) P o / ( S)3d ( G) G o / ( P)3d ( P) D o / ( P)3d ( G) F o / ( P)3d ( P) P o / ( D)3d F / ( D)3d P / ( D)3d S / ( P)3d F / ( P)3d ( F) G o / ( P)3d ( D) D o / ( D)3d D / ( P)3d ( D) F o / ( P)3d F / ( D)3d G / ( P)3d ( F) F o / ( D)3d D / GRASP: present calculations from the
GRASP code with 4978 levelsFAC1: present calculations from the
FAC code with 5821 levelsFAC2: present calculations from the
FAC code with 9160 levelsFAC3: present calculations from the
FAC code with 18,459 levels able C. Comparison of oscillator strengths (f- values) for some transitions of W LVIII. See Table 2 for level indices. a ± b ≡ a × ± b .I J GRASP FAC1 FAC2 Ratio I J GRASP FAC1 FAC2 Ratio1 2 1.0882-3 1.081-3 1.077-3 1.0-0 3 18 2.6720-3 2.639-3 2.636-3 9.7-11 3 2.4344-3 2.430-3 2.430-3 1.1-0 3 21 2.3411-5 2.132-5 2.138-5 8.7-11 4 3.8991-3 3.868-3 3.859-3 1.1-0 3 23 4.3433-3 4.284-3 4.277-3 1.0-01 6 5.9768-4 5.986-4 6.004-4 1.1-0 3 25 3.6256-3 3.617-3 3.611-3 9.8-11 9 9.0692-3 8.975-3 8.963-3 1.1-0 3 26 4.2007-4 3.789-4 3.689-4 1.0-01 11 4.4697-5 6.737-5 9.514-5 1.1-0 3 29 5.2679-4 5.322-4 5.282-4 1.1-01 12 9.3168-2 9.295-2 9.274-2 1.0-0 3 32 1.2444-1 1.242-1 1.238-1 1.1-01 13 1.8842-1 1.880-1 1.876-1 1.1-0 3 33 4.4983-2 4.489-2 4.471-2 1.0-01 19 4.8822-2 5.232-2 5.211-2 9.9-1 3 34 7.6192-5 7.642-5 7.771-5 1.4-01 22 2.5003-3 2.304-3 2.302-3 9.8-1 3 36 8.5831-3 8.615-3 8.565-3 9.4-11 27 2.1816-5 2.009-5 2.024-5 1.0-0 3 37 2.1401-4 2.079-4 2.058-4 1.1-01 30 1.1023-2 1.090-2 1.085-2 1.1-0 3 44 2.6467-5 2.670-5 2.632-5 8.4-11 39 2.8342-1 2.832-1 2.826-1 1.1-0 3 46 5.6125-4 5.520-4 5.487-4 1.0-01 40 1.8851-1 1.884-1 1.880-1 1.0-0 4 10 1.2802-4 1.337-4 1.335-4 1.3-01 41 1.9575-1 1.920-1 1.919-1 1.0-0 4 14 3.5475-3 3.523-3 3.520-3 1.0-01 45 5.2287-4 5.113-4 5.087-4 1.1-0 4 15 1.0169-2 1.007-2 1.006-2 1.0-01 47 3.1041-6 3.707-6 3.526-6 1.1-0 4 18 8.3105-4 8.490-4 8.475-4 1.0-01 50 2.1506-4 2.176-4 2.148-4 1.0-0 4 23 1.4887-2 1.488-2 1.489-2 1.1-02 10 1.5585-5 1.633-5 1.625-5 1.3-0 4 24 1.5940-2 1.587-2 1.584-2 1.0-02 14 2.3239-3 2.317-3 2.313-3 9.6-1 4 34 9.2343-2 9.225-2 9.199-2 1.0-02 15 1.1027-3 1.085-3 1.083-3 1.0-0 4 36 6.2968-2 6.287-2 6.244-2 1.0-02 16 3.6626-4 3.652-4 3.630-4 1.0-0 4 38 3.3164-3 3.390-3 3.361-3 9.3-12 18 9.5118-5 9.609-5 9.746-5 1.1-0 5 16 4.6102-3 4.580-3 4.558-3 8.8-12 23 1.8987-2 1.889-2 1.882-2 1.0-0 5 17 6.2113-4 6.121-4 6.125-4 1.0-02 24 6.9418-3 6.891-3 6.883-3 1.0-0 5 20 6.3760-5 6.604-5 6.564-5 1.0-02 25 5.0532-2 5.065-2 5.067-2 1.1-0 5 21 6.4773-3 6.474-3 6.469-3 1.0-02 26 2.6290-3 2.336-3 2.251-3 1.0-0 5 25 4.5108-3 4.516-3 4.491-3 9.4-12 33 6.1696-2 6.168-2 6.140-2 1.0-0 5 26 3.3682-5 2.362-5 2.123-5 1.2-02 34 3.7762-2 3.774-2 3.754-2 1.0-0 5 29 2.6977-2 2.684-2 2.680-2 1.0-02 36 1.1263-3 1.113-3 1.110-3 1.0-0 5 32 2.1229-3 2.145-3 2.134-3 1.1-02 37 5.0808-3 5.130-3 5.145-3 1.0-0 5 33 2.9199-3 2.880-3 2.853-3 8.7-12 38 1.6200-5 2.086-5 2.258-5 6.9-1 5 35 1.4637-1 1.461-1 1.457-1 1.1-02 44 1.1047-4 1.066-4 1.063-4 1.1-0 5 37 7.7067-3 7.776-3 7.709-3 8.8-13 14 1.2620-3 1.260-3 1.251-3 8.8-1 5 44 7.4564-5 7.122-5 7.361-5 1.7-03 16 1.6292-4 1.670-4 1.644-4 7.4-1 5 46 3.7162-5 3.540-5 3.698-5 1.6-03 17 3.4001-3 3.409-3 3.404-3 1.1-0 5 49 2.1782-3 2.129-3 2.112-3 1.1-0 GRASP: present calculations from the
GRASP code with 4978 levelsFAC1: present calculations from the
FAC code with 5821 levelsFAC2: present calculations from the
FAC code with 9160 levelsRatio: ratio of velocity and length forms of f- values from the
GRASP code xplanation of Tables Table 1. Configurations and levels of W LVIII.Index Configuration IndexConfiguration The configuration included in the calculationNo. of Levels The number of levels the configuration generates. Odd parity levels are designated with a superscript “o”Energy Range Energy range of the levels in Ryd unitGRASP1 Calculations of Mohan et al. [8] from the
GRASP code with 1163 levelsGRASP2 Present calculations from the
GRASP code with 4978 levelsY If a configuration is included under a calculationTable 2. Energies (Ryd) for the lowest 400 levels of W LVIII and their lifetimes ( τ , s).Index Level IndexConfiguration The configuration to which the level belongsLevel The LSJ designation of the levelEnergy Present energies from the
GRASP code with 4978 level calculations τ (s) Lifetime of the level in sTable 3. Transition wavelengths ( λ ij in ˚ A ), radiative rates (A ji in s − ), oscillator strengths (f ij , dimensionless), and linestrengths (S, in atomic units) for electric dipole (E1), and A ji for electric quadrupole (E2), magnetic dipole (M1), and magneticquadrupole (M2) transitions of W LVIII. i and j The lower ( i ) and upper ( j ) levels of a transition as defined in Table 2. λ ij Transition wavelength (in ˚ A )A E ji Radiative transition probability (in s − ) for the E1 transitionsf E ij Absorption oscillator strength (dimensionless) for the E1 transitionsS E Line strength in atomic unit (a.u.), 1 a.u. = 6.460 × − cm esu for the E1 transitionsA E ji Radiative transition probability (in s − ) for the E2 transitionsA M ji Radiative transition probability (in s − ) for the M1 transitionsA M ji Radiative transition probability (in s − ) for the M2 transitions a ± b ≡ a × ± b
3d 28 17-75 Y Y2 3s3p
261 55-130 Y Y4 3s3p
211 73-143 Y Y5 3p
3d 2 100-106 Y Y6 3s3p
858 113-196 Y7 3s
4s 8 182-209 Y Y8 3s
4d 28 205-261 Y Y9 3s
4p 18 227-265 Y12 3s3p
4f 24 253-283 Y13 3s
5s 8 276-329 Y14 3s
5d 28 288-342 Y15 3s
5g 30 295-348 Y16 3p
4s 1 267 Y17 3p
4d 2 290-293 Y18 3s3p
5s 7 316-345 Y19 3s3p
5p 18 320-353 Y20 3s3p
5f 24 332-361 Y21 3s
37 157-179 Y22 3p
513 180-258 Y23 3s3d
63 219-244 Y24 3d
19 285-303 Yii) odd25 3s o o
3d 23 o o o o
4p 21 o
4f 30 o o o
4s 7 o
4d 23 o
5p 21 o
5f 30 o
4p 2 o
4f 2 o
5d 23 o
5g 24 o o o o o GRASP1: earlier calculations of Mohan et al. [8] from the
GRASP code with 1163 levelsGRASP2: present calculations from the
GRASP code with 4978 levelsY: configuration included under a calculation τ , s). a ± b ≡ a × ± b .Index Configuration Level Energy τ (s)1 3s P o / ( P)3d D / ( P)3d D / ( P)3d P / ( P)3d F / ( S)3d D / ( P)3d D / ( P)3d F / ( P)3d P / P o / ( S)3d D / ( P)3d P / ( P)3d D / ( D)3d ( F) D o / ( P)3d ( F) D o / ( S)3d ( D) D o / ( D)3d ( F) H o / ( D)3d ( P) F o / S / ( D)3d ( F) H o / ( P)3d ( F) F o / ( P)3d D / ( P)3d ( F) D o / ( P)3d ( P) S o / ( P)3d ( F) F o / ( P)3d ( P) D o / ( P)3d F / ( D)3d ( G) I o / ( P)3d ( P) D o / ( P)3d F / ( D)3d G / ( S)3d ( G) G o / ( S)3d ( P) P o / ( P)3d ( D) P o / ( S)3d ( G) G o / ( P)3d ( P) D o / ( P)3d ( G) F o / ( P)3d ( P) P o / ( D)3d F / ( D)3d P / ( D)3d S / ( P)3d F / ( P)3d ( F) G o / ( P)3d ( D) D o / ( D)3d D / ( P)3d ( D) F o / ( P)3d F / ( D)3d G / ( P)3d ( F) F o / ( D)3d D / τ (s)51 3s ( D)3d ( D) P o / ( D)3d F / ( D)3d ( F) F o / ( P)3d ( F) D o / ( P)3d ( S) P o / ( P)3d D / ( D)3d ( S) D o / ( D)3d P / ( P)3d ( F) G / ( P)3d P o / ( P)3d P o / ( P)3d F o / ( P)3d D o / ( P)3d P o / ( P)3d D o / ( P)3d F o / ( S)3d ( F) F o / ( D)3d ( F) G o / ( S)3d ( F) F / ( D)3d ( F) G o / ( S)3d ( F) F o / ( P)3d ( P) P / ( D)3d ( F) H o / ( P)3d ( P) D / ( P)3d F o / ( S)3d ( G) G / ( S)3d ( H) H / ( P)3d ( F) G o / ( P)3d D o / ( P)3d D o / ( S)3d ( P) P o / ( P)3d D o / ( S)3d ( P) P / ( D)3d ( F) D o / ( D)3d ( F) P o / ( P)3d F o / ( S)3d ( F) F o / ( D)3d ( F) D o / ( D)3d ( P) D o / ( P)3d D o / ( D)3d ( P) P o / ( S)3d ( F) F o / ( S)3d ( F) F o / ( S)3d ( F) F o / ( P)3d ( P) D o / ( P)3d P o / ( P)3d ( D) D o / ( S)3d ( P) P o / ( D)3d ( P) F o / ( P)3d P o / τ (s)101 3s ( D)3d ( F) H o / ( D)3d ( F) G o / ( D)3d ( F) F o / ( D)3d ( G) F o / ( D)3d ( F) H o / ( S)3d ( F) F / ( D)3d ( G) I o / ( P)3d ( F) G o / ( S)3d ( F) F / ( S)3d ( G) G o / ( S)3d ( F) F o / ( P)3d ( P) D / ( D)3d ( F) D o / ( P)3d ( P) D / ( S)3d ( D) D / ( S)3d ( F) F o / ( P)3d ( P) D o / ( P)3d ( P) P o / ( D)3d ( P) F o / ( D)3d ( F) G o / ( S)3d ( F) F o / ( D)3d ( F) G o / ( S)3d ( H) H / ( D)3d ( P) F o / ( P)3d ( D) D / ( D)3d ( P) D o / ( P)3d ( G) H o / ( S)3d ( F) F / ( D)3d ( P) P o / ( D)3d ( G) G o / ( D)3d ( D) S o / ( D)3d ( G) D o / ( D)3d ( G) H o / ( D)3d ( P) D o / ( D)3d ( P) D o / ( D)3d ( P) D o / ( P)3d P / ( P)3d ( D) F / ( P)3d ( G) F o / ( S)3d ( F) F o / ( D)3d ( F) F o / ( P)3d ( P) P o / ( D)3d ( P) F o / ( S)3d ( D) D o / ( S)3d ( P) P o / ( D)3d ( D) P o / ( D)3d ( G) D o / ( P)3d ( F) D / ( D)3d ( G) F o / ( D)3d ( F) H o / τ (s)151 3s ( D)3d ( F) P o / ( D)3d ( D) G o / ( D)3d ( P) P o / ( D)3d ( D) F o / ( P)3d ( F) D / ( D)3d ( G) G o / ( P)3d ( F) F / ( D)3d ( D) D o / ( P)3d ( F) G / ( S)3d ( F) F o / ( D)3d ( G) H o / ( P)3d ( F) G / ( D)3d ( F) F o / ( S)3d ( G) G / ( P)3d P / ( S)3d ( S) S o / ( P)3d ( P) D / ( P)3d ( F) G o / ( D)3d ( P) P o / ( P)3d ( F) D o / ( P)3d ( D) F o / ( P)3d ( F) D / ( S)3d ( F) F / ( D)3d ( D) D o / ( P)3d ( D) F / ( D)3d ( F) G o / ( D)3d ( F) P o / ( S)3d ( P) P o / ( S)3d ( D) D / ( D)3d ( D) F o / ( S)3d ( F) F / ( P)3d ( S) P o / ( P)3d ( F) D / ( D)3d ( S) D o / ( D)3d ( D) G / ( D)3d ( F) H / ( D)3d ( F) D o / ( D)3d ( F) P o / ( S)3d ( P) P / ( P)3d ( F) F / ( P)3d ( P) S / ( P)3d ( F) G / ( P)3d ( P) S / ( P)3d ( F) F / ( P)3d ( P) D / ( D)3d ( P) P o / ( P)3d ( P) D / ( P)3d ( G) H / ( P)3d ( G) G / ( P)3d ( F) D / τ (s)201 3s3p ( P)3d ( F) F / ( D)3d ( F) D / ( P)3d ( F) G / ( D)3d ( F) P / ( P)3d ( F) F / ( P)3d ( F) D / ( D)3d ( G) G / ( P)3d ( F) F / ( P)3d ( G) F / ( P)3d ( G) F / ( S)3d ( F) F / ( P)3d ( F) G / ( P)3d ( F) F / ( P)3d ( D) P / ( P)3d ( P) P / ( P)3d ( F) G / ( P)3d F o / ( P)3d ( P) D / ( D)3d ( F) P / ( P)3d ( G) G / ( P)3d ( F) D / ( S)3d ( P) P / ( P)3d ( P) D / ( S)3d ( F) F / ( P)3d ( P) S / ( P)3d ( G) H / ( S)3d ( G) G / ( D)3d ( F) G / ( P)3d ( G) F / ( D)3d ( F) D / ( P)3d F o / ( P)3d ( G) G / ( P)3d ( P) D / ( P)3d ( F) D / ( P)3d ( P) D / ( S)3d ( F) G / ( S)3d ( D) D / ( P)3d ( G) F / ( S)3d ( P) P / ( P)3d ( F) G / ( P)3d ( D) D / ( P)3d ( F) G / ( P)3d ( F) G / ( P)3d ( P) D / ( P)3d D o / ( P)3d ( P) D / ( P)3d ( F) F / ( P)3d ( P) P / ( P)3d P o / ( P)3d ( G) H / τ (s)251 3s3p ( P)3d ( G) G / ( P)3d ( D) F / ( D)3d ( F) D / ( P)3d ( F) F / ( D)3d ( G) I / ( D)3d ( G) D / ( P)3d ( G) G / ( P)3d ( G) H / ( P)3d ( F) G / ( P)3d ( P) P / ( P)3d ( F) G / ( D)3d ( F) H / ( P)3d ( F) F / ( P)3d ( F) D / ( P)3d P o / ( D)3d ( F) H / ( P)3d ( P) D / ( P)3d ( P) P / ( P)3d ( P) P / ( P)3d ( D) F / ( P)3d ( H) I / ( P)3d ( F) F / ( P)3d ( G) G / ( D)3d ( G) H / ( D)3d ( P) D / ( P)3d ( H) H / ( P)3d ( F) G / ( P)3d ( F) D / ( P)3d ( F) F / ( P)3d ( F) D / ( D)3d ( F) P / ( S)3d ( F) F / ( P)3d ( G) G / ( P)3d ( F) D / ( P)3d ( S) P / ( D)3d ( F) P / ( D)3d ( G) F / ( D)3d ( H) G / ( D)3d ( D) G o / ( P)3d ( F) F o / ( P)3d ( D) P / ( P)3d ( F) F / ( P)3d ( F) G o / ( P)3d ( F) F o / ( P)3d ( P) P / ( D)3d ( D) G / ( P)3d ( D) F / ( S)3d ( P) P / ( D)3d ( F) P o / ( D)3d ( P) P / τ (s)301 3s3p ( P)3d D o / ( S)3d ( F) F / ( P)3d F o / ( S)3d ( P) P / ( D)3d ( G) F / ( P)3d ( D) P / ( D)3d ( F) G / ( D)3d ( P) D / ( P)3d ( P) P / ( P)3d ( F) G / ( P)3d ( P) S / ( P)3d ( G) H / ( D)3d ( F) D / ( P)3d ( H) G / ( P)3d ( P) P / ( P)3d ( F) D / ( S)3d ( S) S / ( P)3d ( F) D / ( P)3d ( D) D / ( P)3d ( P) D / ( P)3d ( H) I / ( P)3d ( P) P o / ( P)3d ( F) D o / ( P)3d ( G) F / ( P)3d ( D) F / ( D)3d ( G) D / ( P)3d ( S) P / ( P)3d ( F) G / ( P)3d ( F) G / ( P)3d ( F) F / ( D)3d ( H) F / ( P)3d ( F) G / ( P)3d ( D) P / ( P)3d ( S) P / ( P)3d ( F) G / ( S)3d ( F) F o / ( P)3d ( F) G / ( P)3d ( P) S / ( D)3d ( F) P / ( S)3d ( F) F o / ( P)3d ( H) G / ( D)3d ( H) K / ( P)3d ( P) D o / ( D)3d ( F) H / ( D)3d ( P) P / ( D)3d ( F) G / ( P)3d ( H) I / ( P)3d ( F) F / ( P)3d ( F) G o / ( P)3d ( D) D / τ (s)351 3s ( P)3d ( F) D o / ( S)3d ( P) P o / ( P)3d ( G) H o / ( P)3d ( D) F / ( P)3d ( F) D / ( P)3d ( H) H / ( S)3d ( P) P o / ( D)3d ( P) F / ( P)3d ( P) P o / ( P)3d ( F) F o / ( P)3d ( F) F o / ( D)3d ( F) H / ( P)3d ( F) F / ( D)3d ( F) G / ( D)3d ( F) G / ( P)3d ( P) D / ( P)3d ( P) S / ( P)3d ( D) P o / ( D)3d ( H) F / ( D)3d ( F) P / ( D)3d ( F) F / ( P)3d ( D) D / ( D)3d ( P) P / ( P)3d ( G) G o / ( D)3d ( F) F / ( P)3d ( H) I / ( D)3d ( D) G / ( P)3d ( P) D o / ( D)3d ( D) F / ( D)3d ( P) P / ( P)3d ( G) G o / ( D)3d ( D) P / ( D)3d ( H) H / ( D)3d ( P) F / ( P)3d ( P) S o / ( D)3d ( P) P / ( D)3d ( F) H o / ( D)3d ( F) G / ( D)3d ( D) G / ( D)3d ( F) D / ( P)3d ( D) D / ( P)3d ( F) F o / ( D)3d ( P) D / ( D)3d ( F) F / ( D)3d ( F) D / ( D)3d ( D) F / ( S)3d ( F) F o / ( P)3d ( F) D o / ( P)3d ( P) P / ( D)3d ( D) F / λ ij in ˚ A ), radiative rates (A ji in s − ), oscillator strengths (f ij , dimensionless), and line strengths(S, in atomic units) for electric dipole (E1), and A ji for E2, M1, and M2 transitions in W LVIII. ( a ± b ≡ a × ± b ). i j λ ij A E1 ji f E1 ij S E1 A E2 ji A M1 ji A M2 ji +
01 2.647 +
09 1.088 −
03 7.505 −
04 0.000 +
00 0.000 +
00 3.430 +
001 3 5.103 +
01 4.157 +
09 2.434 −
03 1.636 −
03 0.000 +
00 0.000 +
00 1.466 +
011 4 5.085 +
01 2.011 +
10 3.899 −
03 2.611 −
03 0.000 +
00 0.000 +
00 3.636 +
011 5 5.027 +
01 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 3.598 +
011 6 4.659 +
01 1.836 +
09 5.977 −
04 3.667 −
04 0.000 +
00 0.000 +
00 1.470 +
021 7 3.909 +
01 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 3.608 +
041 9 3.801 +
01 8.374 +
10 9.069 −
03 4.539 −
03 0.000 +
00 0.000 +
00 9.836 +
041 10 3.569 +
01 0.000 +
00 0.000 +
00 0.000 +
00 1.060 +
07 3.825 +
08 0.000 +
001 11 3.556 +
01 1.571 +
08 4.470 −
05 2.093 −
05 0.000 +
00 0.000 +
00 2.548 +
041 12 3.491 +
01 5.100 +
11 9.317 −
02 4.283 −
02 0.000 +
00 0.000 +
00 3.215 +
041 13 3.450 +
01 7.041 +
11 1.884 −
01 8.559 −
02 0.000 +
00 0.000 +
00 2.317 +
031 14 2.539 +
01 0.000 +
00 0.000 +
00 0.000 +
00 5.673 +
03 2.339 +
04 0.000 +
001 15 2.506 +
01 0.000 +
00 0.000 +
00 0.000 +
00 2.123 +
05 1.885 +
05 0.000 +
001 16 2.507 +
01 0.000 +
00 0.000 +
00 0.000 +
00 4.322 +
04 1.634 +
04 0.000 +
001 17 2.497 +
01 0.000 +
00 0.000 +
00 0.000 +
00 9.337 +
03 0.000 +
00 0.000 +
001 18 2.388 +
01 0.000 +
00 0.000 +
00 0.000 +
00 1.737 +
05 3.978 +
02 0.000 +
001 19 2.286 +
01 1.247 +
12 4.882 −
02 1.469 −
02 0.000 +
00 0.000 +
00 5.761 +
051 21 2.174 +
01 0.000 +
00 0.000 +
00 0.000 +
00 9.287 +
03 0.000 +
00 0.000 +
001 22 2.165 +
01 7.114 +
10 2.500 −
03 7.130 −
04 0.000 +
00 0.000 +
00 1.126 +
051 23 2.141 +
01 0.000 +
00 0.000 +
00 0.000 +
00 3.967 +
04 1.096 +
03 0.000 +
001 24 2.139 +
01 0.000 +
00 0.000 +
00 0.000 +
00 3.230 +
05 4.706 +
03 0.000 +
001 25 2.135 +
01 0.000 +
00 0.000 +
00 0.000 +
00 1.607 +
05 1.732 +
04 0.000 +
001 26 2.131 +
01 0.000 +
00 0.000 +
00 0.000 +
00 6.497 +
02 7.465 +
03 0.000 +
001 27 2.126 +
01 3.221 +
08 2.182 −
05 6.107 −
06 0.000 +
00 0.000 +
00 1.158 +
041 29 2.111 +
01 0.000 +
00 0.000 +
00 0.000 +
00 5.895 +
05 0.000 +
00 0.000 +
001 30 2.097 +
01 1.115 +
11 1.102 −
02 3.043 −
03 0.000 +
00 0.000 +
00 1.675 +
041 31 2.092 +
01 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 1.740 +
041 32 2.069 +
01 0.000 +
00 0.000 +
00 0.000 +
00 2.231 +
05 0.000 +
00 0.000 +
001 33 2.064 +
01 0.000 +
00 0.000 +
00 0.000 +
00 3.543 +
05 3.891 +
00 0.000 +
001 34 2.053 +
01 0.000 +
00 0.000 +
00 0.000 +
00 5.266 +
03 2.289 +
04 0.000 +
001 36 2.024 +
01 0.000 +
00 0.000 +
00 0.000 +
00 3.596 +
04 2.112 +
04 0.000 +
001 37 2.000 +
01 0.000 +
00 0.000 +
00 0.000 +
00 9.447 +
04 1.254 +
03 0.000 +
001 38 1.993 +
01 0.000 +
00 0.000 +
00 0.000 +
00 9.423 +
05 1.949 +
05 0.000 +
001 39 1.985 +
01 3.200 +
12 2.834 −
01 7.407 −
02 0.000 +
00 0.000 +
00 7.563 +
001 40 1.977 +
01 3.218 +
12 1.885 −
01 4.907 −
02 0.000 +
00 0.000 +
00 1.342 +
041 41 1.954 +
01 6.838 +
12 1.957 −
01 5.037 −
02 0.000 +
00 0.000 +
00 2.099 +
051 42 1.886 +
01 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 2.173 +
051 44 1.866 +
01 0.000 +
00 0.000 +
00 0.000 +
00 1.058 +
06 5.099 +
03 0.000 +
001 45 1.860 +
01 1.009 +
10 5.229 −
04 1.280 −
04 0.000 +
00 0.000 +
00 2.296 +
051 46 1.853 +
01 0.000 +
00 0.000 +
00 0.000 +
00 6.441 +
05 0.000 +
00 0.000 +
001 47 1.848 +
01 4.041 +
07 3.104 −
06 7.555 −
07 0.000 +
00 0.000 +
00 5.126 +
031 50 1.829 +
01 2.858 +
09 2.151 −
04 5.180 −
05 0.000 +
00 0.000 +
00 2.832 +
051 51 1.813 +
01 0.000 +
00 0.000 +
00 0.000 +
00 2.603 +
06 1.560 +
03 0.000 +
001 52 1.807 +
01 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 2.662 +
041 53 1.772 +
01 0.000 +
00 0.000 +
00 0.000 +
00 2.258 +
04 0.000 +
00 0.000 +
001 54 1.763 +
01 0.000 +
00 0.000 +
00 0.000 +
00 1.274 +
05 1.380 +
03 0.000 +
001 55 1.760 +
01 0.000 +
00 0.000 +
00 0.000 +
00 2.223 +
06 3.962 +
03 0.000 +
001 56 1.746 +
01 4.351 +
10 1.989 −
03 4.573 −
04 0.000 +
00 0.000 +
00 8.998 +
041 57 1.729 +
01 0.000 +
00 0.000 +
00 0.000 +
00 1.484 +
06 3.608 +
03 0.000 +
001 58 1.722 +
01 4.522 +
10 1.005 −
03 2.281 −
04 0.000 +
00 0.000 +
00 4.986 + λ ij in ˚ A ), radiative rates (A ji in s − ), oscillator strengths (f ij , dimensionless), and line strengths(S, in atomic units) for electric dipole (E1), and A ji for E2, M1, and M2 transitions in W LVIII. ( a ± b ≡ a × ± b ). i j λ ij A E1 ji f E1 ij S E1 A E2 ji A M1 ji A M2 ji +
01 2.522 +
08 1.017 −
05 2.195 −
06 0.000 +
00 0.000 +
00 2.296 +
011 60 1.632 +
01 0.000 +
00 0.000 +
00 0.000 +
00 1.017 +
07 1.952 +
03 0.000 +
001 61 1.598 +
01 0.000 +
00 0.000 +
00 0.000 +
00 2.893 +
07 3.837 +
03 0.000 +
001 62 1.582 +
01 0.000 +
00 0.000 +
00 0.000 +
00 1.280 +
08 0.000 +
00 0.000 +
001 63 1.578 +
01 0.000 +
00 0.000 +
00 0.000 +
00 5.520 +
07 4.160 +
04 0.000 +
001 64 1.553 +
01 0.000 +
00 0.000 +
00 0.000 +
00 1.099 +
08 1.317 +
06 0.000 +
001 65 1.540 +
01 0.000 +
00 0.000 +
00 0.000 +
00 5.818 +
07 1.734 +
03 0.000 +
001 66 1.534 +
01 0.000 +
00 0.000 +
00 0.000 +
00 6.564 +
07 1.983 +
04 0.000 +
001 67 1.490 +
01 0.000 +
00 0.000 +
00 0.000 +
00 1.652 +
07 1.055 +
04 0.000 +
001 68 1.490 +
01 0.000 +
00 0.000 +
00 0.000 +
00 2.104 +
06 2.993 +
02 0.000 +
001 69 1.482 +
01 5.342 +
05 2.638 −
08 5.147 −
09 0.000 +
00 0.000 +
00 1.070 +
011 70 1.483 +
01 0.000 +
00 0.000 +
00 0.000 +
00 6.949 +
06 0.000 +
00 0.000 +
001 71 1.479 +
01 0.000 +
00 0.000 +
00 0.000 +
00 1.579 +
08 8.731 +
05 0.000 +
001 72 1.470 +
01 5.013 +
06 1.624 −
07 3.142 −
08 0.000 +
00 0.000 +
00 3.575 +
011 74 1.459 +
01 4.001 +
05 6.386 −
09 1.227 −
09 0.000 +
00 0.000 +
00 2.999 +
001 76 1.459 +
01 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 3.754 +
001 78 1.448 +
01 0.000 +
00 0.000 +
00 0.000 +
00 4.996 +
06 8.886 +
03 0.000 +
001 79 1.437 +
01 0.000 +
00 0.000 +
00 0.000 +
00 1.596 +
08 1.335 +
03 0.000 +
001 80 1.430 +
01 0.000 +
00 0.000 +
00 0.000 +
00 1.796 +
08 0.000 +
00 0.000 +
001 81 1.425 +
01 0.000 +
00 0.000 +
00 0.000 +
00 5.868 +
06 7.724 +
05 0.000 +
001 82 1.421 +
01 0.000 +
00 0.000 +
00 0.000 +
00 4.428 +
08 8.390 +
04 0.000 +
001 83 1.415 +
01 2.980 +
05 1.343 −
08 2.503 −
09 0.000 +
00 0.000 +
00 1.431 −
021 84 1.409 +
01 0.000 +
00 0.000 +
00 0.000 +
00 3.750 +
05 8.121 +
04 0.000 +
001 85 1.407 +
01 0.000 +
00 0.000 +
00 0.000 +
00 4.532 +
06 2.158 +
02 0.000 +
001 86 1.410 +
01 0.000 +
00 0.000 +
00 0.000 +
00 2.076 +
08 0.000 +
00 0.000 +
001 87 1.404 +
01 0.000 +
00 0.000 +
00 0.000 +
00 5.679 +
05 0.000 +
00 0.000 +
001 88 1.402 +
01 0.000 +
00 0.000 +
00 0.000 +
00 4.253 +
07 3.457 +
04 0.000 +
001 89 1.392 +
01 0.000 +
00 0.000 +
00 0.000 +
00 3.152 +
07 4.926 +
04 0.000 +
001 90 1.391 +
01 0.000 +
00 0.000 +
00 0.000 +
00 2.465 +
08 2.164 +
04 0.000 +
001 91 1.380 +
01 0.000 +
00 0.000 +
00 0.000 +
00 2.482 +
07 2.056 +
04 0.000 +
001 93 1.379 +
01 0.000 +
00 0.000 +
00 0.000 +
00 1.284 +
07 2.095 +
03 0.000 +
001 94 1.378 +
01 0.000 +
00 0.000 +
00 0.000 +
00 7.806 +
07 0.000 +
00 0.000 +
001 95 1.373 +
01 0.000 +
00 0.000 +
00 0.000 +
00 4.939 +
05 7.736 +
04 0.000 +
001 96 1.373 +
01 0.000 +
00 0.000 +
00 0.000 +
00 4.843 +
08 2.642 +
05 0.000 +
001 97 1.368 +
01 0.000 +
00 0.000 +
00 0.000 +
00 2.895 +
07 6.798 +
03 0.000 +
001 98 1.368 +
01 0.000 +
00 0.000 +
00 0.000 +
00 8.273 +
07 6.575 +
03 0.000 +
001 99 1.369 +
01 0.000 +
00 0.000 +
00 0.000 +
00 1.993 +
06 0.000 +
00 0.000 +
001 100 1.366 +
01 0.000 +
00 0.000 +
00 0.000 +
00 3.908 +
07 6.577 +
03 0.000 +
001 103 1.351 +
01 0.000 +
00 0.000 +
00 0.000 +
00 2.464 +
06 8.932 +
01 0.000 +
001 104 1.351 +
01 0.000 +
00 0.000 +
00 0.000 +
00 4.122 +
06 6.528 +
03 0.000 +
001 106 1.337 +
01 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 7.415 +
001 108 1.331 +
01 0.000 +
00 0.000 +
00 0.000 +
00 4.266 +
05 0.000 +
00 0.000 +
001 110 1.325 +
01 0.000 +
00 0.000 +
00 0.000 +
00 1.150 +
07 7.483 +
03 0.000 +
001 111 1.322 +
01 0.000 +
00 0.000 +
00 0.000 +
00 1.358 +
06 5.286 +
04 0.000 +
001 112 1.321 +
01 1.280 +
07 3.347 −
07 5.821 −
08 0.000 +
00 0.000 +
00 2.046 +
011 113 1.319 +
01 0.000 +
00 0.000 +
00 0.000 +
00 6.593 +
06 4.450 +
03 0.000 +
001 114 1.316 +
01 1.272 +
06 1.652 −
08 2.863 −
09 0.000 +
00 0.000 +
00 1.412 −
011 115 1.315 +
01 9.268 +
06 3.606 −
07 6.246 −
08 0.000 +
00 0.000 +
00 4.153 −
011 117 1.315 +
01 0.000 +
00 0.000 +
00 0.000 +
00 1.495 +
07 1.135 +
00 0.000 +
001 118 1.312 +
01 0.000 +
00 0.000 +
00 0.000 +
00 1.380 +
06 3.700 +
02 0.000 + λ ij in ˚ A ), radiative rates (A ji in s − ), oscillator strengths (f ij , dimensionless), and line strengths(S, in atomic units) for electric dipole (E1), and A ji for E2, M1, and M2 transitions in W LVIII. ( a ± b ≡ a × ± b ). i j λ ij A E1 ji f E1 ij S E1 A E2 ji A M1 ji A M2 ji +
01 0.000 +
00 0.000 +
00 0.000 +
00 2.888 +
06 2.309 +
03 0.000 +
001 122 1.312 +
01 0.000 +
00 0.000 +
00 0.000 +
00 3.699 +
07 0.000 +
00 0.000 +
001 124 1.302 +
01 0.000 +
00 0.000 +
00 0.000 +
00 2.512 +
07 0.000 +
00 0.000 +
001 125 1.299 +
01 5.245 +
07 1.990 −
06 3.403 −
07 0.000 +
00 0.000 +
00 5.658 −
051 126 1.298 +
01 0.000 +
00 0.000 +
00 0.000 +
00 2.466 +
07 1.712 +
04 0.000 +
001 128 1.298 +
01 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 1.344 +
011 129 1.297 +
01 0.000 +
00 0.000 +
00 0.000 +
00 7.440 +
04 1.133 +
04 0.000 +
001 130 1.298 +
01 0.000 +
00 0.000 +
00 0.000 +
00 5.942 +
06 0.000 +
00 0.000 +
001 131 1.293 +
01 0.000 +
00 0.000 +
00 0.000 +
00 1.626 +
06 1.381 +
04 0.000 +
001 132 1.293 +
01 0.000 +
00 0.000 +
00 0.000 +
00 8.060 +
07 3.979 +
03 0.000 +
001 134 1.289 +
01 0.000 +
00 0.000 +
00 0.000 +
00 1.267 +
06 1.002 +
04 0.000 +
001 135 1.289 +
01 0.000 +
00 0.000 +
00 0.000 +
00 1.546 +
07 0.000 +
00 0.000 +
001 136 1.286 +
01 0.000 +
00 0.000 +
00 0.000 +
00 3.665 +
06 4.884 +
04 0.000 +
001 137 1.284 +
01 9.157 +
08 2.262 −
05 3.823 −
06 0.000 +
00 0.000 +
00 1.563 +
031 138 1.269 +
01 4.199 +
07 1.013 −
06 1.693 −
07 0.000 +
00 0.000 +
00 1.567 +
001 139 1.270 +
01 0.000 +
00 0.000 +
00 0.000 +
00 3.661 +
06 0.000 +
00 0.000 +
001 141 1.268 +
01 0.000 +
00 0.000 +
00 0.000 +
00 1.533 +
07 1.271 +
02 0.000 +
001 142 1.260 +
01 0.000 +
00 0.000 +
00 0.000 +
00 7.421 +
05 1.141 +
04 0.000 +
001 143 1.258 +
01 0.000 +
00 0.000 +
00 0.000 +
00 1.764 +
07 7.903 +
04 0.000 +
001 144 1.260 +
01 0.000 +
00 0.000 +
00 0.000 +
00 1.341 +
04 0.000 +
00 0.000 +
001 145 1.256 +
01 0.000 +
00 0.000 +
00 0.000 +
00 4.035 +
07 1.104 +
04 0.000 +
001 146 1.255 +
01 0.000 +
00 0.000 +
00 0.000 +
00 3.735 +
07 2.166 +
03 0.000 +
001 147 1.247 +
01 0.000 +
00 0.000 +
00 0.000 +
00 1.553 +
08 4.352 +
03 0.000 +
001 148 1.243 +
01 1.166 +
08 1.350 −
06 2.209 −
07 0.000 +
00 0.000 +
00 2.365 +
021 149 1.247 +
01 0.000 +
00 0.000 +
00 0.000 +
00 1.701 +
08 0.000 +
00 0.000 +
001 151 1.244 +
01 0.000 +
00 0.000 +
00 0.000 +
00 9.893 +
06 1.770 +
04 0.000 +
001 153 1.239 +
01 0.000 +
00 0.000 +
00 0.000 +
00 1.086 +
07 2.037 +
04 0.000 +
001 154 1.239 +
01 0.000 +
00 0.000 +
00 0.000 +
00 2.615 +
07 2.285 +
04 0.000 +
001 155 1.232 +
01 3.196 +
08 7.267 −
06 1.179 −
06 0.000 +
00 0.000 +
00 2.869 +
021 157 1.226 +
01 3.203 +
08 1.083 −
05 1.748 −
06 0.000 +
00 0.000 +
00 1.941 +
021 158 1.227 +
01 0.000 +
00 0.000 +
00 0.000 +
00 3.366 +
06 1.350 +
05 0.000 +
001 159 1.223 +
01 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 7.644 +
011 160 1.223 +
01 0.000 +
00 0.000 +
00 0.000 +
00 3.273 +
06 0.000 +
00 0.000 +
001 163 1.212 +
01 0.000 +
00 0.000 +
00 0.000 +
00 5.908 +
06 0.000 +
00 0.000 +
001 165 1.209 +
01 1.055 +
09 3.465 −
05 5.514 −
06 0.000 +
00 0.000 +
00 5.250 +
021 166 1.205 +
01 0.000 +
00 0.000 +
00 0.000 +
00 1.266 +
05 2.550 +
05 0.000 +
001 167 1.201 +
01 7.663 +
06 2.484 −
07 3.928 −
08 0.000 +
00 0.000 +
00 7.362 +
021 169 1.202 +
01 0.000 +
00 0.000 +
00 0.000 +
00 1.899 +
04 2.255 +
05 0.000 +
001 170 1.200 +
01 0.000 +
00 0.000 +
00 0.000 +
00 2.004 +
07 0.000 +
00 0.000 +
001 171 1.197 +
01 0.000 +
00 0.000 +
00 0.000 +
00 8.548 +
04 1.354 +
04 0.000 +
001 172 1.190 +
01 1.302 +
08 1.384 −
06 2.169 −
07 0.000 +
00 0.000 +
00 6.725 +
021 173 1.190 +
01 2.347 +
08 4.984 −
06 7.811 −
07 0.000 +
00 0.000 +
00 1.229 +
021 174 1.194 +
01 0.000 +
00 0.000 +
00 0.000 +
00 2.660 +
06 9.626 +
05 0.000 +
001 175 1.193 +
01 2.732 +
07 5.829 −
07 9.157 −
08 0.000 +
00 0.000 +
00 2.578 +
011 177 1.190 +
01 0.000 +
00 0.000 +
00 0.000 +
00 8.047 +
06 3.528 +
05 0.000 +
001 178 1.187 +
01 0.000 +
00 0.000 +
00 0.000 +
00 5.032 +
06 5.429 +
05 0.000 +
001 179 1.181 +
01 6.555 +
07 2.054 −
06 3.193 −
07 0.000 +
00 0.000 +
00 4.407 −
011 180 1.181 +
01 0.000 +
00 0.000 +
00 0.000 +
00 5.752 +
06 0.000 +
00 0.000 +
001 181 1.173 +
01 7.699 +
06 2.380 −
07 3.675 −
08 0.000 +
00 0.000 +
00 9.389 +
021 182 1.175 +
01 0.000 +
00 0.000 +
00 0.000 +
00 5.618 +
05 5.354 +
04 0.000 + λ ij in ˚ A ), radiative rates (A ji in s − ), oscillator strengths (f ij , dimensionless), and line strengths(S, in atomic units) for electric dipole (E1), and A ji for E2, M1, and M2 transitions in W LVIII. ( a ± b ≡ a × ± b ). i j λ ij A E1 ji f E1 ij S E1 A E2 ji A M1 ji A M2 ji +
01 6.671 +
08 1.371 −
05 2.114 −
06 0.000 +
00 0.000 +
00 5.396 +
021 184 1.174 +
01 0.000 +
00 0.000 +
00 0.000 +
00 1.343 +
07 1.228 +
05 0.000 +
001 185 1.169 +
01 9.837 +
08 3.024 −
05 4.655 −
06 0.000 +
00 0.000 +
00 8.775 +
011 186 1.169 +
01 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 7.370 +
021 187 1.171 +
01 0.000 +
00 0.000 +
00 0.000 +
00 1.143 +
07 1.215 +
04 0.000 +
001 188 1.162 +
01 0.000 +
00 0.000 +
00 0.000 +
00 3.743 +
07 2.831 +
04 0.000 +
001 189 1.148 +
01 5.389 +
08 5.320 −
06 8.040 −
07 0.000 +
00 0.000 +
00 9.710 +
021 191 1.144 +
01 1.627 +
08 3.191 −
06 4.805 −
07 0.000 +
00 0.000 +
00 8.457 +
011 193 1.139 +
01 2.412 +
07 7.033 −
07 1.054 −
07 0.000 +
00 0.000 +
00 3.713 +
011 194 1.139 +
01 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 7.393 +
001 195 1.138 +
01 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 4.585 +
021 196 1.139 +
01 0.000 +
00 0.000 +
00 0.000 +
00 9.416 +
06 1.549 +
06 0.000 +
001 200 1.120 +
01 1.738 +
08 1.633 −
06 2.408 −
07 0.000 +
00 0.000 +
00 2.031 +
021 201 1.120 +
01 3.852 +
07 7.240 −
07 1.068 −
07 0.000 +
00 0.000 +
00 3.351 +
011 202 1.116 +
01 3.598 +
07 6.716 −
07 9.868 −
08 0.000 +
00 0.000 +
00 4.455 +
021 203 1.115 +
01 4.328 +
07 1.211 −
06 1.779 −
07 0.000 +
00 0.000 +
00 2.418 +
001 204 1.114 +
01 4.694 +
06 4.363 −
08 6.397 −
09 0.000 +
00 0.000 +
00 5.471 +
021 205 1.112 +
01 5.313 +
07 1.479 −
06 2.167 −
07 0.000 +
00 0.000 +
00 1.678 +
011 206 1.111 +
01 3.912 +
07 7.240 −
07 1.059 −
07 0.000 +
00 0.000 +
00 8.138 −
011 207 1.111 +
01 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 1.865 +
021 208 1.107 +
01 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 3.210 +
011 209 1.104 +
01 5.912 +
07 1.080 −
06 1.569 −
07 0.000 +
00 0.000 +
00 1.047 +
031 210 1.103 +
01 4.058 +
06 1.110 −
07 1.613 −
08 0.000 +
00 0.000 +
00 5.915 +
021 211 1.102 +
01 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 1.108 +
021 213 1.099 +
01 2.057 +
07 5.585 −
07 8.080 −
08 0.000 +
00 0.000 +
00 6.250 +
011 214 1.097 +
01 5.749 +
08 5.183 −
06 7.486 −
07 0.000 +
00 0.000 +
00 8.210 +
011 215 1.094 +
01 8.769 +
07 1.573 −
06 2.265 −
07 0.000 +
00 0.000 +
00 4.197 +
001 217 1.094 +
01 0.000 +
00 0.000 +
00 0.000 +
00 1.514 +
06 1.023 +
04 0.000 +
001 218 1.093 +
01 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 1.491 +
031 219 1.090 +
01 3.690 +
07 9.863 −
07 1.416 −
07 0.000 +
00 0.000 +
00 4.688 +
001 220 1.088 +
01 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 6.662 +
021 221 1.085 +
01 2.181 +
07 1.927 −
07 2.754 −
08 0.000 +
00 0.000 +
00 1.405 +
001 222 1.085 +
01 2.501 +
07 4.416 −
07 6.310 −
08 0.000 +
00 0.000 +
00 1.233 +
031 223 1.085 +
01 4.440 +
07 1.176 −
06 1.680 −
07 0.000 +
00 0.000 +
00 1.611 +
031 224 1.083 +
01 1.014 +
07 2.672 −
07 3.810 −
08 0.000 +
00 0.000 +
00 3.777 +
011 225 1.082 +
01 6.047 +
07 1.061 −
06 1.511 −
07 0.000 +
00 0.000 +
00 8.982 +
011 228 1.078 +
01 3.983 +
07 1.041 −
06 1.477 −
07 0.000 +
00 0.000 +
00 2.788 +
011 229 1.079 +
01 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 7.267 +
001 230 1.078 +
01 7.530 +
07 1.311 −
06 1.861 −
07 0.000 +
00 0.000 +
00 2.632 +
021 231 1.076 +
01 0.000 +
00 0.000 +
00 0.000 +
00 3.058 +
06 8.084 +
01 0.000 +
001 233 1.073 +
01 7.853 +
07 6.779 −
07 9.580 −
08 0.000 +
00 0.000 +
00 3.225 +
021 234 1.072 +
01 7.116 +
07 1.226 −
06 1.730 −
07 0.000 +
00 0.000 +
00 7.601 +
021 235 1.072 +
01 2.597 +
06 6.709 −
08 9.468 −
09 0.000 +
00 0.000 +
00 1.109 +
031 236 1.072 +
01 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 2.467 +
011 237 1.069 +
01 2.495 +
08 4.275 −
06 6.018 −
07 0.000 +
00 0.000 +
00 2.114 +
021 238 1.070 +
01 3.402 +
07 8.755 −
07 1.233 −
07 0.000 +
00 0.000 +
00 2.941 +
011 239 1.067 +
01 1.014 +
08 8.657 −
07 1.217 −
07 0.000 +
00 0.000 +
00 1.535 +
031 241 1.063 +
01 1.463 +
08 3.719 −
06 5.206 −
07 0.000 +
00 0.000 +
00 5.409 +
011 242 1.063 +
01 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 1.453 +
021 244 1.059 +
01 3.198 +
06 8.060 −
08 1.124 −
08 0.000 +
00 0.000 +
00 1.598 + λ ij in ˚ A ), radiative rates (A ji in s − ), oscillator strengths (f ij , dimensionless), and line strengths(S, in atomic units) for electric dipole (E1), and A ji for E2, M1, and M2 transitions in W LVIII. ( a ± b ≡ a × ± b ). i j λ ij A E1 ji f E1 ij S E1 A E2 ji A M1 ji A M2 ji +
01 0.000 +
00 0.000 +
00 0.000 +
00 7.150 +
04 1.634 +
06 0.000 +
001 246 1.057 +
01 9.831 +
03 1.648 −
10 2.294 −
11 0.000 +
00 0.000 +
00 1.966 +
031 247 1.057 +
01 2.819 +
07 2.360 −
07 3.285 −
08 0.000 +
00 0.000 +
00 7.562 +
011 248 1.056 +
01 7.985 +
04 1.334 −
09 1.855 −
10 0.000 +
00 0.000 +
00 6.440 +
011 249 1.056 +
01 0.000 +
00 0.000 +
00 0.000 +
00 3.403 +
06 4.015 +
03 0.000 +
001 251 1.056 +
01 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 7.641 +
001 253 1.051 +
01 4.325 +
06 3.578 −
08 4.951 −
09 0.000 +
00 0.000 +
00 2.231 +
021 254 1.050 +
01 1.640 +
07 2.713 −
07 3.752 −
08 0.000 +
00 0.000 +
00 2.660 +
031 256 1.049 +
01 4.374 +
07 1.083 −
06 1.496 −
07 0.000 +
00 0.000 +
00 2.167 +
011 257 1.049 +
01 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 1.826 +
001 260 1.041 +
01 4.847 +
06 1.182 −
07 1.621 −
08 0.000 +
00 0.000 +
00 1.426 +
031 261 1.038 +
01 3.120 +
07 7.553 −
07 1.032 −
07 0.000 +
00 0.000 +
00 1.095 +
031 262 1.034 +
01 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 9.207 +
001 263 1.032 +
01 4.383 +
05 6.999 −
09 9.511 −
10 0.000 +
00 0.000 +
00 1.244 +
031 264 1.034 +
01 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 5.103 +
021 265 1.032 +
01 0.000 +
00 0.000 +
00 0.000 +
00 6.808 +
05 1.388 +
05 0.000 +
001 267 1.029 +
01 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 4.517 +
011 268 1.027 +
01 7.582 +
04 5.996 −
10 8.110 −
11 0.000 +
00 0.000 +
00 5.622 +
011 269 1.028 +
01 2.784 +
08 4.411 −
06 5.973 −
07 0.000 +
00 0.000 +
00 7.741 +
031 270 1.028 +
01 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 4.368 +
021 273 1.024 +
01 2.817 +
06 6.647 −
08 8.967 −
09 0.000 +
00 0.000 +
00 8.110 +
011 275 1.022 +
01 3.425 +
06 5.363 −
08 7.219 −
09 0.000 +
00 0.000 +
00 3.585 +
021 276 1.023 +
01 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 6.717 +
011 278 1.019 +
01 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 3.701 +
011 279 1.019 +
01 1.807 +
07 4.216 −
07 5.655 −
08 0.000 +
00 0.000 +
00 2.553 +
021 280 1.017 +
01 3.929 +
05 6.095 −
09 8.165 −
10 0.000 +
00 0.000 +
00 5.437 +
011 281 1.015 +
01 1.376 +
08 1.064 −
06 1.423 −
07 0.000 +
00 0.000 +
00 4.606 +
001 284 1.014 +
01 3.973 +
08 9.190 −
06 1.227 −
06 0.000 +
00 0.000 +
00 4.344 +
021 285 1.012 +
01 2.270 +
09 5.228 −
05 6.967 −
06 0.000 +
00 0.000 +
00 5.333 +
031 286 1.010 +
01 6.975 +
07 1.067 −
06 1.420 −
07 0.000 +
00 0.000 +
00 6.474 +
021 287 1.009 +
01 9.430 +
07 2.159 −
06 2.869 −
07 0.000 +
00 0.000 +
00 1.174 +
031 288 1.009 +
01 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 2.611 +
021 289 1.010 +
01 0.000 +
00 0.000 +
00 0.000 +
00 4.191 +
06 0.000 +
00 0.000 +
001 290 1.009 +
01 0.000 +
00 0.000 +
00 0.000 +
00 4.627 +
05 1.524 +
02 0.000 +
001 291 1.007 +
01 2.551 +
09 3.880 −
05 5.147 −
06 0.000 +
00 0.000 +
00 1.912 +
011 293 1.007 +
01 0.000 +
00 0.000 +
00 0.000 +
00 7.603 +
04 0.000 +
00 0.000 +
001 294 1.006 +
01 0.000 +
00 0.000 +
00 0.000 +
00 2.667 +
06 1.121 +
02 0.000 +
001 295 1.006 +
01 1.423 +
08 3.240 −
06 4.294 −
07 0.000 +
00 0.000 +
00 3.102 +
001 297 1.006 +
01 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 4.037 +
031 298 1.005 +
01 3.089 +
09 7.018 −
05 9.289 −
06 0.000 +
00 0.000 +
00 1.370 +
021 299 1.004 +
01 0.000 +
00 0.000 +
00 0.000 +
00 2.125 +
06 6.647 +
05 0.000 +
001 300 1.004 +
01 6.270 +
09 4.734 −
05 6.256 −
06 0.000 +
00 0.000 +
00 6.018 +
031 301 1.003 +
01 0.000 +
00 0.000 +
00 0.000 +
00 9.769 +
05 2.543 +
03 0.000 +
001 302 1.003 +
01 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 1.975 +
021 303 1.003 +
01 0.000 +
00 0.000 +
00 0.000 +
00 7.390 +
06 1.920 +
04 0.000 +
001 304 9.997 +
00 3.126 +
08 4.685 −
06 6.167 −
07 0.000 +
00 0.000 +
00 2.070 +
031 305 9.985 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 4.546 +
021 306 9.971 +
00 2.977 +
08 6.656 −
06 8.740 −
07 0.000 +
00 0.000 +
00 1.747 +
001 307 9.974 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 2.516 +
031 308 9.960 +
00 5.798 +
07 8.622 −
07 1.131 −
07 0.000 +
00 0.000 +
00 3.261 + λ ij in ˚ A ), radiative rates (A ji in s − ), oscillator strengths (f ij , dimensionless), and line strengths(S, in atomic units) for electric dipole (E1), and A ji for E2, M1, and M2 transitions in W LVIII. ( a ± b ≡ a × ± b ). i j λ ij A E1 ji f E1 ij S E1 A E2 ji A M1 ji A M2 ji +
00 3.454 +
09 7.708 −
05 1.011 −
05 0.000 +
00 0.000 +
00 4.329 +
031 311 9.949 +
00 2.511 +
08 1.863 −
06 2.441 −
07 0.000 +
00 0.000 +
00 1.522 +
021 313 9.941 +
00 1.242 +
08 2.760 −
06 3.613 −
07 0.000 +
00 0.000 +
00 2.891 +
011 315 9.920 +
00 3.129 +
07 4.616 −
07 6.030 −
08 0.000 +
00 0.000 +
00 7.674 +
011 316 9.910 +
00 4.007 +
07 8.848 −
07 1.155 −
07 0.000 +
00 0.000 +
00 1.616 +
021 317 9.888 +
00 3.693 +
08 2.707 −
06 3.524 −
07 0.000 +
00 0.000 +
00 1.998 +
021 318 9.902 +
00 9.157 +
08 1.346 −
05 1.755 −
06 0.000 +
00 0.000 +
00 1.064 +
031 319 9.892 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 3.383 +
021 320 9.876 +
00 1.122 +
09 1.641 −
05 2.134 −
06 0.000 +
00 0.000 +
00 4.364 +
031 322 9.870 +
00 0.000 +
00 0.000 +
00 0.000 +
00 9.057 +
04 3.063 +
02 0.000 +
001 323 9.842 +
00 0.000 +
00 0.000 +
00 0.000 +
00 1.595 +
03 2.989 +
02 0.000 +
001 324 9.858 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 6.852 +
001 325 9.866 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 4.129 +
021 326 9.844 +
00 1.365 +
09 1.982 −
05 2.570 −
06 0.000 +
00 0.000 +
00 1.406 +
021 327 9.834 +
00 7.261 +
09 5.264 −
05 6.817 −
06 0.000 +
00 0.000 +
00 9.599 +
031 328 9.845 +
00 3.897 +
07 8.494 −
07 1.101 −
07 0.000 +
00 0.000 +
00 1.102 +
001 330 9.819 +
00 8.354 +
08 1.208 −
05 1.561 −
06 0.000 +
00 0.000 +
00 1.622 +
021 331 9.819 +
00 3.985 +
08 8.639 −
06 1.117 −
06 0.000 +
00 0.000 +
00 4.496 +
021 332 9.821 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 4.064 +
021 333 9.807 +
00 1.250 +
09 2.703 −
05 3.491 −
06 0.000 +
00 0.000 +
00 8.861 +
021 334 9.794 +
00 1.957 +
10 2.814 −
04 3.629 −
05 0.000 +
00 0.000 +
00 3.698 +
031 336 9.771 +
00 0.000 +
00 0.000 +
00 0.000 +
00 9.193 +
02 1.982 +
02 0.000 +
001 337 9.800 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 5.376 +
021 338 9.784 +
00 1.258 +
09 2.708 −
05 3.489 −
06 0.000 +
00 0.000 +
00 1.639 +
021 339 9.768 +
00 6.266 +
08 4.481 −
06 5.764 −
07 0.000 +
00 0.000 +
00 5.170 +
021 340 9.734 +
00 0.000 +
00 0.000 +
00 0.000 +
00 7.009 +
01 3.405 +
02 0.000 +
001 343 9.711 +
00 0.000 +
00 0.000 +
00 0.000 +
00 1.035 +
03 0.000 +
00 0.000 +
001 345 9.704 +
00 1.063 +
10 7.501 −
05 9.584 −
06 0.000 +
00 0.000 +
00 6.773 +
001 348 9.696 +
00 3.459 +
08 7.313 −
06 9.338 −
07 0.000 +
00 0.000 +
00 2.356 +
011 350 9.672 +
00 6.988 +
06 9.801 −
08 1.248 −
08 0.000 +
00 0.000 +
00 2.890 +
011 351 9.634 +
00 0.000 +
00 0.000 +
00 0.000 +
00 1.036 +
05 8.526 +
04 0.000 +
001 352 9.636 +
00 0.000 +
00 0.000 +
00 0.000 +
00 1.659 +
03 0.000 +
00 0.000 +
001 354 9.610 +
00 7.122 +
06 1.479 −
07 1.872 −
08 0.000 +
00 0.000 +
00 1.612 +
011 355 9.609 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 2.938 +
021 357 9.601 +
00 0.000 +
00 0.000 +
00 0.000 +
00 9.275 +
02 3.678 +
04 0.000 +
001 358 9.595 +
00 5.430 +
07 7.494 −
07 9.469 −
08 0.000 +
00 0.000 +
00 1.032 +
001 359 9.597 +
00 0.000 +
00 0.000 +
00 0.000 +
00 1.575 +
06 8.226 +
04 0.000 +
001 360 9.603 +
00 0.000 +
00 0.000 +
00 0.000 +
00 2.248 +
04 0.000 +
00 0.000 +
001 361 9.556 +
00 0.000 +
00 0.000 +
00 0.000 +
00 1.880 +
03 1.029 +
03 0.000 +
001 363 9.575 +
00 5.014 +
07 1.034 −
06 1.304 −
07 0.000 +
00 0.000 +
00 5.160 +
011 364 9.575 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 1.054 +
021 366 9.558 +
00 2.667 +
08 1.826 −
06 2.298 −
07 0.000 +
00 0.000 +
00 1.497 +
011 367 9.552 +
00 1.293 +
09 1.769 −
05 2.224 −
06 0.000 +
00 0.000 +
00 5.305 +
021 368 9.554 +
00 0.000 +
00 0.000 +
00 0.000 +
00 1.304 +
04 8.169 +
04 0.000 +
001 369 9.555 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 5.990 −
011 370 9.536 +
00 5.524 +
07 1.130 −
06 1.419 −
07 0.000 +
00 0.000 +
00 7.883 +
011 372 9.516 +
00 4.440 +
07 3.014 −
07 3.776 −
08 0.000 +
00 0.000 +
00 1.048 +
011 373 9.516 +
00 1.320 +
09 1.793 −
05 2.246 −
06 0.000 +
00 0.000 +
00 9.936 +
011 374 9.521 +
00 0.000 +
00 0.000 +
00 0.000 +
00 1.980 +
05 0.000 +
00 0.000 +
001 375 9.508 +
00 3.143 +
08 6.390 −
06 8.000 −
07 0.000 +
00 0.000 +
00 1.783 + λ ij in ˚ A ), radiative rates (A ji in s − ), oscillator strengths (f ij , dimensionless), and line strengths(S, in atomic units) for electric dipole (E1), and A ji for E2, M1, and M2 transitions in W LVIII. ( a ± b ≡ a × ± b ). i j λ ij A E1 ji f E1 ij S E1 A E2 ji A M1 ji A M2 ji +
00 0.000 +
00 0.000 +
00 0.000 +
00 6.038 +
03 5.464 +
04 0.000 +
001 379 9.495 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 8.014 +
021 380 9.483 +
00 1.264 +
08 8.522 −
07 1.064 −
07 0.000 +
00 0.000 +
00 1.310 +
021 382 9.474 +
00 3.308 +
05 4.452 −
09 5.554 −
10 0.000 +
00 0.000 +
00 1.309 +
011 385 9.467 +
00 0.000 +
00 0.000 +
00 0.000 +
00 2.151 +
04 9.692 +
04 0.000 +
001 386 9.461 +
00 4.538 +
08 9.134 −
06 1.138 −
06 0.000 +
00 0.000 +
00 6.463 +
011 387 9.427 +
00 0.000 +
00 0.000 +
00 0.000 +
00 1.288 +
03 1.039 +
02 0.000 +
001 389 9.441 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 1.037 +
021 390 9.420 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 4.891 +
011 391 9.408 +
00 8.166 +
06 1.084 −
07 1.342 −
08 0.000 +
00 0.000 +
00 7.346 +
001 392 9.374 +
00 0.000 +
00 0.000 +
00 0.000 +
00 2.811 +
02 4.138 +
02 0.000 +
001 393 9.403 +
00 2.090 +
09 1.385 −
05 1.715 −
06 0.000 +
00 0.000 +
00 1.550 +
031 394 9.384 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 0.000 +
00 1.479 +
021 395 9.365 +
00 6.290 +
07 8.272 −
07 1.020 −
07 0.000 +
00 0.000 +
00 3.447 +
031 396 9.363 +
00 2.751 +
07 5.424 −
07 6.688 −
08 0.000 +
00 0.000 +
00 6.306 +
001 398 9.305 +
00 0.000 +
00 0.000 +
00 0.000 +
00 1.306 +
03 1.286 +
04 0.000 +
001 399 9.295 +
00 2.727 +
08 3.532 −
06 4.323 −
07 0.000 +
00 0.000 +
00 8.545 +
011 400 9.296 +
00 3.005 +
07 5.840 −
07 7.150 −
08 0.000 +
00 0.000 +
00 5.495 ++