Relativistic configuration-interaction calculations of then=3-3 transition energies in highly charged tungsten ions

Abstract

A large-scale relativistic configuration-interaction calculation of the n = 3-3 transition energies for Ne-to Ar-like tungsten is carried out. The calculation is based on the relativistic no-pair Hamiltonian and uses finite B-spline orbitals in a cavity as basis functions. Quantum electrodynamic and mass polarization corrections are also included. Results are compared with other theories and with experiment, and are generally found to be more reliable than previous theoretical predictions. PACS number(s): 31.15.am, 31.15.ac, 32.30.Rj I. INTRODUCTIONTungsten is of interest in fusion research as it is a promising material in future magnetic confinement fusion reactors such as the ITER due to its desirable properties with low hydrogen retention, high melting point, and high thermal conductivity. However, since tungsten is a high-Z element, even with 10-20-keV reactor temperature, line emission in the x-ray and vacuum ultraviolet (VUV) regions is a major concern in realizing the magnetically confined fusion reactors. To understand its influence as a plasma impurity, reliable transition energy data are needed for many ionic stages of tungsten which show up in relevant emission spectra.There are not many experimental and theoretical studies in the literature for the n = 3-3 transition energies of highlycharged tungsten ions. Early calculations of the sodium isoelectronic sequence are mostly based on the Dirac-Fock (DF) [1-3] or model potential [4] methods with a relatively crude accuracy of a few electron volts. High-precision relativistic many-body perturbation theory (RMBPT) calculations of the correlation energies for selected Na-like ions were carried out by Johnson et al. [5], but quantum electrodynamic (QED) corrections, which are important for high-Z ions, were not included. Kim et al. [6] later used these RMBPT results to provide accurate relativistic correlation corrections to their DF energies for Na-like ions with 14 Z 92, and calculated the QED corrections with the ad hoc Welton method [7]. Reliable QED corrections from ab initio calculations were first given by Blundell [8], who added them to the RMBPT energies [5] to give accurate transition energies for a few Na-like ions, though tungsten was not included. Theoretical n = 3-3 resonance line energies for Mg-like ions include results from the multiconfiguration Dirac-Fock (MCDF) calculations by Cheng and Johnson [9] and Zou and Froese-Fischer [10], the relativistic random-phase approximation calculations by Shorer et al. [11], the relativistic perturbation calculations with model potentials by Ivanova et al. [12], and the relativistic configuration-interaction (RCI) calculations for low-to mid-Z ions by Chen and Cheng [13]. For the aluminum isoelectronic sequence, transition energies and radiative rates have been * chen7@llnl.gov † ktcheng@llnl.gov

Benchmarking calculations of excitation energies and transition properties with spectroscopic accuracy of highly charged ions used for the fusion plasma and astrophysical plasma

“…On the contrary, their FAC results agree more with the NIST compiled measured values than the GRASP89 results, with the differences by up to 4500 cm −1 (0.1%). Similarly, the excitation energies calculated by Xu et al [104] and Chen and Cheng [106] are lower than the NIST compiled measured values by up to ≃ 5700 cm −1 (0.1%) and 6200 cm −1 (0.1%), respectively. Fig.…”

“…Our theoretical results are in good agreement with experiments and show a clear improvement of accuracy over previous calculations. [5,6,[102][103][104][105][106][107][108][109][110][111][112][113] And our calculations achieve spectroscopic accuracy to assist spectroscopists in their assignment and direct identification. Based on our RMBPT and MCDHF calculations and CRM simulations, we also give suggestions of assignments for all of the unidentified 28 spectral lines (a significant fraction, around sixty percent) of the n = 3 → 3 transitions measured by Lennartsson et al [114] Additionally, the contributions of electron correlation, the Breit interaction, the higher-order frequency-dependent retardation correction, and the leading QED corrections to excitation energies (transition wavelengths, and radiative rates) are also studied in detail.…”

“…Table 7. Comparison of the excitation energies (E, in cm −1 ) from the present RMBPT and MCDHF, from the previous works (GRASP89 and FAC: from Aggarwal and Keenan; [103] MCDHF2: from Xu et al; [104] RCI: from Chen and Cheng [106] ), and from the measurements. [121,122] The NIST compiled values reported in square brackets are determined by semi-empirical parametric calculations using Cowan's code.…”

“…Also using the GRASP89 code, [123] Xu et al [104] studied excitation ener-gies, wavelengths and transition probabilities for W 61+ . The excitation energies and wavelengths for only a few n = 3 levels of W 61+ were provided by Chen and Cheng [106] using the RCI method. Ekman et al [124] also calculated excitation energies and transition probabilities for W 61+ using the RMBPT and MCDHF methods.…”

“…For comparison, the present RMBPT and MCDHF excitation energies for Al-like W 61+ as well as the compiled data from the NIST ASD [125] are listed in Table 7. The two theoretical data sets (GRASP89 and FAC) reported by Aggarwal and Keenan, [104] the theoretical results provided by Xu et al (MCDHF2), [106] and the values (RCI) calculated by Chen and Cheng [107] are also included in Table 7.…”