Energy levels, weighted oscillator strengths, transition rates, lifetimes of He-like-Pt deduced from the relativistic multiconfiguration Dirac–Hartree–Fock and relativistic configuration interaction theory calculations
Introduction
In the design of fusion power plants and experimental fusion devices, such as International Thermonuclear Experimental Reactor (ITER) [1], [2], the tungsten W atomic number = is envisaged for the manufacture of various plasma-facing components because of its properties such as high melting point, high thermal conductivity and high resistance to spraying and erosion [2]. In particular, tungsten will be used in the reactor region, the diverter, undergoing the most extreme conditions. Under neutron irradiation, W will undergo transmutation into adjacent elements of the periodic table [3]. Thus, the transmutation reactions could give the element like Pt [2], [3], which could then penetrate inside the plasma and produce, like the atoms of W, a light radiation that can be analyzed in order to diagnose the plasma. In this framework, we have started calculations of atomic structures and radiative parameters from the Dirac-Hartree–Fock (MCDHF) fully relativistic multiconfigurational method using the latest parallel version of the GRASP2018 [4] program. The calculated atomic data concern the energy levels, the wavelengths, the radiative transition probabilities, the oscillator strengths and the lifetimes characterizing the spectra of He-like-Pt ion belonging to the isoelectronic sequence of helium. The results obtained will not only be very useful for future research directed towards nuclear fusion, but also in other fields.
In the present work, we extend the calculation for = ( fine-structure levels) to improve the precision of the atomic data used in line identification, plasma modeling and diagnostics of astrophysical plasmas. We have used several computing methods: multiconfiguration Dirac-Hartree–Fock (MCDHF) [5] method implemented in GRASP2018 code, to calculate the fine-structure levels for He-like-Pt up to the lowest fine-structure levels, that offer a complete and consistent data sets of high accuracy. We report energy levels, wavelengths, radiative rates and lifetimes for all types of transitions: electric-multipole (dipole (E1) and quadrupole (E2)) and magnetic-multipole (dipole (M1) and quadrupole (M2)), which are required inputs in a complete plasma model. For comparative purpose, the same atomic parameters produced using the flexible atomic code (FAC) [6]. This code employs a fully relativistic approach based on the Dirac equation. Satisfactory agreement is found between our two sets of calculation with both GRASP2018 and FAC.
Our results are the first to be published in the literature and there are no other data sets available for comparison for excited states. A limited number of study has negotiated for providing atomic data for higher levels. In fact, for lifetimes we found only calculations for two states obtained from Indelicato et al. [7] using the multiconfiguration Dirac–Fock (MCDF) method unperturbed and perturbed by hyperfine interaction. Then, Artemyev et al. [8], reported calculations of energy levels only for the and states of He-like ions performed by ab initio including the quantum electrodynamic effects (QED), screened self-energy correction and the two-photon exchange correction.
The configurations 1s2 and 1s (, ) have been included in this calculation together with Breit interactions and quantum electrodynamics (QED) effects such as electron self-energy and vacuum polarization. This computational approach allows us to present a consistent and improved data set of all important transitions of the He-like-Pt spectra, useful for identifying transition lines in further investigations.
Section snippets
Details of calculations
Below we briefly describe our calculations performed with two independent atomic structure codes GRASP2018 [4] and FAC [6].
Generation of configuration expansions MCDHF/RCI
As a starting point, MCDHF/RCI calculations in the scheme were performed for each group of atomic states. Using configuration expansions including all lower states of the same symmetry and parity, and a Dirac–Coulomb version was used. For the optimization of the orbitals, including Breit corrections in a final configuration interaction calculation [9]. To build a CSF expansion, the restrictive active space methods were also used. The idea of the active space methods is to consider only
Energy levels
The 1s2 and 1s (, ) configurations of He-like-Pt give rise to the lowest levels tabulated in Table 1 obtained from valence calculations. We have plotted in Fig. 2 accuracy as function of levels to compare between our energy values obtained from both FAC/RCI and MCDHF/RCI calculations. The accuracy is defined by:
In Fig. 2 we present the accuracy of RCI calculated with FAC code compared to our MCDHF/RCI results using GRASP2018
Outlook and conclusion
The present study has determined energies of the states of He-like-Pt using the ab initio MCDHF and RCI methods implemented in GRASP2018 and FAC codes, respectively. We extend the calculation for = to improve the precision of the atomic data used in line identification, plasma modeling and diagnostics of astrophysical plasmas. The BI + QED effect have been included in the calculations to improve the generated wave functions. We have increased the AS from our MR to AS9 then we add AS10
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
PQ is Research Director of the Belgian National Fund for Scientific Research F.R.S.-FNRS, from which financial support is gratefully appreciated. Also, this work has been realized with the financial support of the Tunisian Ministry of Higher Education and Scientific Research (LR16CNSTN02).
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