Excitation energies, transition data of SXR, HXR, EUV and far-UV spectral lines with partition function, thermodynamic parameters and level population for W LXVII and W XLIX
Introduction
The spectroscopic properties of tungsten ions has become topic of interest from last few years due to its significant role in the development of magnetic fusion and radiation source. It has been proved that tungsten ions have become the most important impurity ions in plasma fusion reactors [1]. Various atomic properties namely, transition properties, collisional and photoionization data, etc, are urgently required for several ionization stages of tungsten to control the radiation loss and diagnosis of high temperature fusion plasmas. Tungsten ions are also of interest due to their exceptional thermal properties, low hydrogen retention, tensile strength which makes them first choice for plasma facing surfaces [[2], [3], [4], [5], [6]]. Consequently, several spectroscopic observational and theoretical studies on tungsten ions have been performed and some are under process from past few years. Several measurements have been completed and under process on electron beam ion trap (EBIT) at Berlin [[7], [8], [9], [10], [11]], National Institute of Standards and Technology (NIST) [[12], [13], [14], [15]], Lawrence Livermore National Laboratory (LLNL) [[16], [17], [18], [19]] as well as ASDEX upgrade tokomak [[20], [21], [22]]. The radiations emitted from L-shell or n = 2 shell tungsten ions i.e Li-like to Ne-like ions may be useful for the calculation of ion temperature and bulk velocity of plasma.
The atomic physics is an important branch of physics which helps in describing the different states of the plasma as well as in the analysis and diagnosis of plasma properties. Since the plasmas can be in local and non local thermodynamic equilibrium, therefore obtaining atomic properties such as atomic transition properties, energy levels and study of collisional excitation, ionization, and recombination is necessary to properly diagnose and describe high temperature plasmas. Further, O-like ions consist of open 2p subshell in ground state and radiative transition between ground state and excited state will lie in X-ray regime. The SXR transitions have been used in technique of soft X-ray tomography (SXT) for imaging tissues in cell for visualization of internal structure. Therefore, several SXT instruments and soft X-ray sources have been developed and under construction for solving current biological problems [[23], [24], [25], [26], [27], [28], [29], [30]]. Due to the wide range of applications of tungsten ions, including W LXVII and W XLIX, there is urgent demand of atomic data of large number of states of these ions. But till date, a limited experimental and theoretical study on W LXVII and W XLIX is available in the literature. Only limited amount of data of excited states of W LXVII and W XLIX is available in the literature. Therefore, in this work, lowest 200 fin. structure energy levels have been reported and radiative data of soft X-ray spectral lines from ground state have been studied.
The partition function has applications in the calculation of thermodynamic quantities of ions and neutral atoms which are further helpful in the diagnosis and modeling of plasmas. The computation of levels in stellar and inter-stellar plasmas with the help of Saha equation of state also required partition function. So, indirectly partition function and thermodynamic quantities play important roles in the study of plasmas. Due to limitations, it has been very difficult for experimentalists to include large number of excited states in the calculation of partition function specifically at higher temperatures. Therefore, in past few decades, various theoretical methods have been developed and implemented for the study of partition function [[31], [32], [33], [34], [35]]. In some methods cut-off condition has been applied for simplicity and according to availability of data and limitations. Some tables such as NASA, Russian and Drawin-Felenbok available in literature have not included higher excited states in their calculations [[36], [37], [38], [39]]. Physicists have also used Planck-Larkin partition function (PLPF) for the study of high temperature plasmas. This partition function approaches zero at high temperature and hence violates the basic condition that total partition function of the system cannot be less than unity. In last few years, a 3-group model has been presented in the literature [40]. This method divides the levels in three groups, namely, ground state, middle levels and higher excited levels. The limitation of this method is based on the fact that that the contribution of partition function of individual level from this method may provide inaccurate results. We have overcome above difficulties and limitations in our fine structure model.
Section snippets
Available data of W LXVII and W XLIX
In last decade, only limited work is published in literature [[41], [42], [43], [44], [45], [46], [47], [48], [49], [50], [51], [52], [53], [54], [55], [56]]. Most of the work published in last decade is based on theoretical calculation. But in present decade, most of the work is experimental. Clementson et al. [57] have presented overview of results from Livermore WOLFRAM with experimental observations at EBIT-I and superEBIT electron beam ion traps. They have studied spectra of n = 2 to n =
Theoretical method
We have used two different fully relativistic codes GRASP and FAC to perform the calculations. The relativistic corrections, namely, Breit interactions and QED (quantum electrodynamics) corrections are also included in the calculations. For highly ionized ions, the contribution of these effects becomes prominent and therefore, their inclusion is necessary in the calculations. There are several methods have been developed for assessing accuracy of calculations. To check our results from GRASP,
Procedure for W LXVII
By considering single double (SD) excitations from outermost orbitals 2 s and 2p, we have included configurations in our first step in the following manner:
RS1 = {n = 2, l = 0–1}
RS2 = RS1 + {n = 3, l = 0–2}
RS3 = RS2 + {n = 4, l = 0–3}
RS4 = RS3 + {n = 5, l = 0–4}
RS5 = RS4 + {n = 6, l = 0–4}
Finally, in the second step, we have opted out highly contributed configurations having more than 10 % impact on total atomic wave function. So we have omitted less contributed configurations to save
Excitation energies of O-like W
We have reported excitation energies of lowest 200 fin. structure energy levels related to non relativistic configurations 2 s22p4, 2 s2p5, 2p6, 2p53 s, 2p53p, 2 s22p33l (l = s, p, d), 2 s2p43l (l = s,p,d), 2 s22p34l (l = s, p, d, f) from both GRASP and FAC in Table 1 which is provided as supplementary material. In Table 1, we have separately shown the contributions of Dirac-Coulomb and relativistic corrections Breit and QED in total energy. In Table 1, it is clearly visible that contribution
Conclusion
We have listed transition parameters, lifetimes and fine structure energies of first 200 levels from both FAC and GRASP for O-like W and Fe-like W. Matching and discussion of discrepancy of our results from both GRASP and FAC codes with available theoretical and experimental results ensures that our results are trustworthy. We have also predicted SXR, HXR, EUV and far UV transitions from our calculations and also provided their transition data. Further, we have also studied variation of
Declaration of Competing Interest
The authors report no declarations of interest.
Acknowledgement
We are grateful to DTU for providing infrastructure and support for other facilities.
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