Dirac–Fock calculations of forbidden transitions within the 3p^kand 3d^kground configurations of highly charged tungsten ions (W^{47 +}–W^{61 +})

Abstract

Wavelengths and transition probabilities have been computed for forbidden lines within the 3p k and 3d k ground configurations of tungsten ions from W 47+ to W 61+. The fully relativistic multiconfiguration Dirac-Fock method was used for the calculations. They take into account the correlations within the n = 3 complex, some n = 3 → n = 4 single excitations and quantum electrodynamics effects. The present results are compared to and agree very well with experimental wavelengths and theoretical transition probabilities previously published for a few lines.

E1, M1, E2 transition energies and probabilities of W54+ions

“…Notation a(b) for transition probabilities A ij means a × 10 4SD, 5SD(5s-5d), 5SD and 6SD(6s-6d) are given in Table 1. "Other" represents the results from EBIT experiments or other theoretical work, such as RMBPT, MCDF and RCI method [7][8][9][10]. For the M1 transitions, the calculated wavelengths and probabilities are converged with the increase of AS and are in reasonable agreement with available experimental data.…”

“…Then the configuration space was extended by increasing the active orbital set layer by layer to investigate the correlation contributions and only the newly additional orbitals were optimized for the large active set at each step. [7] c From P. Quinet by MCDF method [9] d From X. L. Guo et al by RMBPT and RCI method [10] 3. Results…”

Correlation, Breit and Quantum Electrodynamics effects on energy level and transition properties of W54+ ion

“…The 9 energy levels (in eV) including correlation, Breit interaction and QED effects (C+B+Q) of the ground configuration 3p 6 3d 2 of W 54+ ion were presented in Table 2 to investigate the contribution from the Breit and QED effects. The other available theoretical and experimental results were also listed for comparison [4,5,6,7]. The notation "C+B+Q" and "Coulomb" in the 4 th and 2 th columns of the table represent the results with and without Breit and QED effects which calculated in n=5(5s-5d) model [5] b From P. Quinet by MCDF method [6] c From U. I. Safronova and A. S. Safronova by RMBPT method [4] d From X. L. Guo et al by RMBPT method [7] e From X. L. Guo et al by RCI method [7] and regarding 3s,3p orbital as core and VV+CV+CC correlations were taken into account.…”

“…In recent several decades, several theoretical and experimental work have been performed on the energy level and the E1, E2, M1 transitions properties of W 54+ ion [2,3,4,5,6,7,8,9]. U. I. Safronova et al calculated 9 fine a Email:dingxb@nwnu.edu.cn structure levels belonging to the ground state configuration [Ne]3s 2 3p 6 3d 2 of W 54 ions, and the M1 and E2 transitions between these levels also have been studied by using the relativistic many-body perturbation theory (RMBPT) [4].…”

“…P. Quinet calculated the energy levels and the forbidden transition of the ground configuration for several highly charged tungsten ions (W 47+ − W 61+ ) by using multi-configuration Dirac-Fock (MCDF) method. The correlation within the n = 3 complex and some n = 3 → n ′ = 4 single excitations were considered in their calculations [6]. Furthermore, X. L. Guo et al calculated the energy, transition wavelength and probability for forbidden transition within the 3d k ground configuration of highly charged Hf, Ta, Au and W ions by RMBPT and the relativistic configuration-interaction (RCI) method [7].…”