Radiative rates for E1, E2, M1, and M2 transitions in Ne-like Cu XX, Zn XXI and Ga XXII

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Abstract

Energy levels, radiative rates and lifetimes are reported for the lowest 139 levels of three Ne-like ions, namely Cu XX, Zn XXI and Ga XXII. These levels mostly belong to the 2s22p6, 2s22p53, 2s2p63, 2s22p54, 2s2p64, and 2s22p55 configurations. For the calculations the general-purpose relativistic atomic structure package (GRASP) has been adopted. Comparisons are made with earlier available theoretical and experimental results, particularly among the lowest 27 levels of the 2s22p6 and 2s22p53 configurations. Due to paucity of similar data for higher lying levels, analogous calculations have also been performed with the flexible atomic code (FAC). These calculations help in assessing the accuracy of our calculated results, especially for the energy levels.

Introduction

Ne-like ions occur in a variety of plasmas, such as astrophysical, laser-produced, magnetically confined, and Z-pinch — see for example [1] and references therein. Particularly important among these are the iron group of elements (namely Ti, Cr, Fe and Ni), whose lines are highly useful for the modelling and diagnostics of a range of plasmas, including astrophysical, fusion and laser generated. However, to interpret observations or to model the plasmas, information is required for several atomic parameters, such as energy levels, radiative rates and collision strengths. Therefore, over a period of time we have reported atomic data for a few Ne-like ions, namely Cl VIII [2], Fe XVII [[3], [4]], Ni XIX [[5], [6]], and very recently W LXV [7]. Similarly, many other workers have reported data for Ne-like ions. The most recent works are by Jönsson et al. [8] and Singh and Aggarwal [9], who have also provided references for earlier works.

The majority of calculations available in the literature are confined to the lowest 27 levels of the 2s22p6 and 2s22p53 configurations, for which those by Jönsson et al. [8] are probably the most accurate, because differences between the measured and calculated energy levels are minimal. Moreover, they have covered a wider range of ions with 12Z36. However, very recently Singh and Aggarwal [9] (henceforth to be referred to as SA) have reported energy levels, radiative rates (A-values) and lifetimes (τ) for three Ne-like ions, namely Cu XX, Zn XXI and Ga XXII, among 127 levels of the 2s22p6, 2s22p5 3, 2s2p6 3, 2s22p54, 2s2p6 4, and 2s22p55 ( 3) configurations. We are not aware of any astrophysical importance of these ions, but they are useful for lasing and fusion plasmas [[10], [11], [12]]. For the calculations, they have adopted two independent atomic structure codes, namely the general-purpose relativistic atomic structure package (GRASP) and the flexible atomic code (FAC) of Gu [13]. Both of these codes are freely available on the websites http://amdpp.phys.strath.ac.uk/UK_APAP/codes.html and https://www-amdis.iaea.org/FAC/, respectively. It was mainly done for the assessment of accuracy, particularly for the energy levels, because prior similar data, experimental or theoretical, for most of the levels for these three ions do not exist. Therefore, based on the two calculations they concluded that both codes provide ‘comparable energies’. However, we notice that for many levels of all three ions the differences between the two sets of energies are significant, i.e. up to 1.5 Ryd — see for example, levels 111–127 of Cu XX, 112–119 of Zn XXI and 111–116 of Ga XXII in their tables 1–3. In our long experience for a wide range of ions we have not noticed such large differences between calculations with these two codes, particularly when the same level of CI (configuration interaction) has been used. Additionally, in the absence of any other similar data, it is difficult to know which set of energies is more accurate. Apart from this, there are other reasons to perform yet another calculation, as discussed below.

The 127 levels considered by SA [9] are not the lowest in energy, because some from 2s22p55g intermix. They have included limited CI, among 51 configurations, namely 2s22p6, 2s22p5 n (3 n 7, but 3), 2s2p6 n (3 n 7, but 3), 2s22p433, and 2s22p433. These configurations generate 1016 levels in total, but there is scope for improvement by including additional CI, particularly from the neglected configurations with > 3. More importantly, they have reported A-values only for the resonance transitions, i.e. from the ground level alone, whereas for accurate modelling of plasmas data are required for all transitions. Finally, for the reliability and accuracy of atomic data, which can be confidently applied, multiple calculations are preferred as emphasised by [[14], [15]].

Section snippets

Energy levels

In our calculations we adopt the same GRASP0 version as by SA [9]. It was originally developed by Grant et al. [16] but has been considerably improved and updated by one of the authors, i.e. P.H. Norrington. For the optimisation of the orbitals we use the option of ‘extended average level’ (EAL), in which a weighted (proportional to 2j+1) trace of the Hamiltonian matrix is minimised. The contributions of higher relativistic operators, namely Breit and quantum electrodynamic effects (QED), are

Radiative rates

In Table 4, Table 5, Table 6 we list our calculated results with the GRASP code for transition energies (wavelengths, λji in Å), radiative rates (A-values, in s−1), oscillator strengths (f-values, dimensionless), and line strengths (S-values, in atomic units, 1 a.u. = 6.460 × 10−36 cm2 esu2) for electric dipole (E1) transitions in Ne-like ions Cu XX, Zn XXI and Ga XXII. These results are listed among the same 139 levels given in Table 1, Table 2, Table 3. Although results have been obtained in

Lifetimes

The lifetime τ of a level j can be determined from the A-values as it is equal to 1.0ΣiAji, where the summation runs over all types of transitions, i.e. E1, E2, M1, and M2. It is a measurable quantity but to the best of our knowledge no experiments have yet been performed for transitions/levels of the ions under consideration. However, Jönsson et al. [8] and SA [9] have listed τ and in Table E we make comparisons with their results for the lowest 27 levels of Cu XX, Zn XXI and Ga XXII. As

Conclusions

In this paper, energies for the lowest 139 levels among the 2s22p6, 2s22p5 3, 2s2p6 3, 2s22p54, 2s2p6 4, 2s22p55, and 2s2p6 5 configurations are reported for three Ne-like ions, Cu XX, Zn XXI and Ga XXII. The GRASP code has been adopted for the calculations and a reasonably large CI among 64 configurations (3948 CSF) has been included, which has been found to be sufficient, based on comparisons with other available theoretical and experimental energy levels. Nevertheless, calculations

Acknowledgements

We thank the anonymous referee whose simple observation prompted us to resolve the discrepancy between theory and measurement for one of the levels of Zn XXI and Alexander Kramida who very graciously and promptly confirmed the error in the NIST listing.

References (25)

  • HagelsteinP.L. et al.

    At. Data Nucl. Data Tables

    (1987)
  • AggarwalK.M. et al.

    At. Data Nucl. Data Tables

    (2016)
  • JönssonP.

    At. Data Nucl. Data Tables

    (2014)
  • GrantI.P. et al.

    Comput. Phys. Comm.

    (1980)
  • JönssonP. et al.

    Comput. Phys. Comm.

    (2007)
  • BoikoV.A. et al.

    J. Quant. Spect. Rad. Transf.

    (1978)
  • MohanM. et al.

    Phys. Scr.

    (1994)
  • AggarwalK.M. et al.

    Astrophys. J. Suppl.

    (2003)
  • AggarwalK.M. et al.

    Astron. Astrophys.

    (2004)
  • AggarwalK.M. et al.

    Astron. Astrophys.

    (2006)
  • AggarwalK.M. et al.

    Astron. Astrophys.

    (2008)
  • SinghN. et al.

    Pramana J. Phys.

    (2017)
  • View full text