Theoretical level energies and transition data for ion W28+

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Abstract

The ab initio quasirelativistic approach was used to derive transition data for Pd-like tungsten W28+ ion. This approach was developed specifically for the calculation of spectral parameters for highly charged ions. The relativistic effects were taken into account in the Breit–Pauli approximation. The configuration interaction method was applied to include electron correlation effects. The ground configuration 4p64d10 and the lowest excited 4p64d94f were considered. The calculations for W28+ were performed with different sets of interacting configurations in order to evaluate reliability and accuracy of produced results. Level energies, radiative lifetimes τ, Landé g-factors were determined for the excited configuration 4p64d94f of W28+ levels. The radiative transition wavelengths λ and emission transition probabilities A for the electric and magnetic transitions of various multipole order (up to E5 and M4) among the levels of these two configurations were produced. The uncertainties of computed spectroscopic parameters were evaluated.

Introduction

Over the last few years we have presented theoretical studies of multicharged tungsten ions with an open 4d shell in the ground configuration [1], [2], [3], [4], [5] where we have determined basic spectroscopic parameters for the lowest three configurations of the tungsten ions W33+–W37+. The importance of tungsten and available studies of the tungsten ions is discussed therein. We continue our investigation of tungsten ions in the present paper and present calculation results for two lowest configurations of W28+. The ion W28+ differs from previously studied ions W33+–W37+ as the ground configuration 4p64d10 has closed 4d shell, thus, there is only one level in the ground configuration and only one excited configuration 4p64d94f with n=4.

Since the ground configuration of W28+ has only one level (J=0), the majority of the excited configuration levels are metastable ones. This feature distinguishes W28+ from other tungsten ions previously investigated by us. The electric dipole transitions (E1) are forbidden from the majority of excited configuration levels, and they decay via the radiative transitions of higher multipole orders. A small number of excited levels in the excited configuration 4p64d94f opens for us new possibilities to analyze obtained spectroscopic parameters and their accuracy.

A comprehensive compilation of spectroscopic data for tungsten ions was presented in [6]. Unfortunately, data for multi-charged tungsten ions with an open 4d shell are comparatively scarce, and only few level energies for the W28+ ion are listed in [6]. Some level energies compiled in [6] were derived from measured wavelengths [7], [8], and one energy value was calculated by parametric fitting using Cowan’s codes [9]. Consequently, the compilation [6] presents measured wavelengths of two E1 transitions and one electric quadrupole transition (E2) together with their intensities.

Radiative transitions in W28+ were considered in [10], [11], but their results were presented only in a graphical form with no numerical data to describe separate transitions lines. Thus, it is rather complicated task to use these results for a data comparison or accuracy evaluation. The extensive calculations in [10] have been performed employing the semi-relativistic Hartree–Fock approximation [9] with the configuration interaction. The Dirac–Fock–Slater (DFS) approximation implemented in the FAC code [12] was used in [11] to calculate emission properties of tungsten ions in various ionization stages. The unresolved transition array statistics is further applied to study computed spectroscopic parameters in [10], [11]. We have used their several averaged spectroscopic data values, such as λ¯ and Δλ, to compare with our results in Section 3.

The ion W28+ was theoretically studied in recent work [13] using the DFS potential and the second-order relativistic many-body perturbation theory (RMBPT) approach. A complete set of computed spectroscopic data along the experimental wavelengths were presented in [13]. The most important results from their study of W28+ were also reported in an overview paper on the spectroscopy of tungsten ions [14].

The aim of the present paper is to determine spectroscopic parameters and to assess their uncertainties for the ground and excited configuration in W28+. We utilize a quasirelativistic approach (QR) with a comprehensive inclusion of correlation effects to investigate the spectroscopic properties. The evaluation of our results is mostly based on their comparison with available experimental or theoretical data from other authors. The reliability and convergence of results is demonstrated by performing series of calculations with inclusion of various degrees of the correlation effects by widening the applied CI basis. The uncertainties of determined transition wavelengths λ and transition probabilities A are calculated using available experimental data in the same way as in our previous investigations, e.g. [4], [5].

In Section 2 we provide a brief description of adopted QR approximation. Since this approximation completely matches one applied in our previous calculations of highly-charged tungsten ions, here we present only a short summary of our method. The produced results and the data accuracy assessment are discussed in Section 3.

Section snippets

Calculation method

The calculation method adopted for the W28+ ion is similar to that used in our previous papers [1], [2], [3], [4], [5]. The quasirelativistic approximation is applied in our calculation of level energies and radiative transition parameters, such as transition line strengths S, weighted oscillator strengths gf, radiative multipole transition probabilities A (transition rates). The most complete and consistent description of our QR method utilized to calculate spectroscopic parameters is given in 

Results and discussion

The produced results for tungsten ion W28+ are discussed in this section. We also evaluate the uncertainties of our QR data based on comparison with available experiments. The level energy values E, the total radiative lifetimes τ, the Landé g-factors, and the main contributions in the CI wavefunction expansion (eigenfunctions) for levels of the investigated configurations are listed in Table 1. The level numbers (indexes) N presented in Table 1 are used in the next data table to label the

Summary and conclusions

In the present work we have reported energy levels, Landé g-factors and the total radiative lifetimes τ for the energetically lowest 21 levels of Pd-like tungsten ion W28+. These levels belong to the ground configuration 4p64d10 and the excited 4p64d94f configuration.

We have performed the series of QR calculations within the same RO base but with different CI expansions. These calculations demonstrate that the QR results are stable and reliable. By consistently increasing the CI expansion, we

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