Breit–Pauli energy levels belonging to 2p⁴, 2s2p⁵, 2p⁶, 2p³3ℓ configurations and all E1 transitions among these levels in Mg V

Abstract

We present accurate oscillator strengths, line strengths and radiative rates for 1073 E1 transitions among the 86 levels belonging to 2s²2p⁴, 2s2p⁵, 2p⁶, and 2s²2p³(⁴S^o, ²D^o, ²P^o)3ℓ configurations in Mg V. We have used 1s and 2s Hartree–Fock orbitals, re-optimized 2p on 2p³(²D^o)3s ³D^o and optimized 3s,3p,3d orbitals on real states. Sixteen additional orbitals up to 8d are optimized either as a correction to n = 3 physical orbitals or as a correlation orbital. A very large set of configurations including up to three electron promotions are used to account for all important correlation effects. All of the main five terms in the Breit–Pauli operator (except the orbit–orbit interaction) are included in order to account for the relativistic effects. Small adjustments to the diagonal elements of the Hamiltonian matrix are made to bring the calculated energies within a few cm⁻¹ of the corresponding NIST recommended data wherever available. The calculated oscillator strengths, line strengths, and radiative rates for almost all of the E1 transitions show excellent agreement with the corresponding MCDF results of Fischer. The recent results of Bhatia et al. are found to be consistently higher by 20–45%. The accuracy of the present calculation is considered to be better than the NIST accuracy ratings for various transitions.

Introduction

Mg V is an important ion in the oxygen-isoelectronic sequence. Its lines are detected in the planetary nebula NGC 7027 [1], [2], [3], [4] and in the wide spectral ranges from soft X-rays to ultraviolet regions. They are also expected to be seen in the solar and astrophysical plasmas. Only a few calculations are available for the atomic structure of Mg V. Fischer and Saha [5] presented multiconfiguration Dirac–Hartree–Fock (MCDHF) energy levels belonging to the ground configuration 2s²2p⁴ (³P, ¹D, ¹S) and E2 and M1 transitions among these levels for some oxygen-like ions including Mg V. Tachiev and Fischer [6] later presented data for E1, E2, M1, M2 transitions from odd levels belonging to 2s2p⁵, 2s²2p³3s, and 2s²2p³3d configurations of Mg V. The MCHF collection of Fischer [7] also presents both ab initio and energy adjusted values for E1 transitions among all but one of the levels belonging to the above configurations and the even configuration 2s²2p³3p, although the level 2s²3p³ (²P^o)3d¹D₂ was missing in these tabulations. Recently, Bhatia et al. [8] reported a calculation of atomic structure and collisional data for Mg V. For the atomic structure part they used the SUPERSTRUCTURE code of Eissner [9] and for the scattering part they used the codes of Eissner and Seaton [10] and Eissner [11] based on the distorted wave approximation. In the present calculation we shall examine only their [8] atomic structure part. Bhatia et al. [8] compared their 6-, 9-, and 24-configuration calculated values of 86 fine-structure levels with the observed values as given by the NIST [12] database. The 9-configuration results were presented only for lowest 46 levels. It might be expected that the 24-configuration results would be more accurate than the two other sets. However, on many occasions, their 6-configuration energy levels show better agreement with the observed values. For example, their 6-configuration results ³P_0,1,2 levels belonging to the configuration 2s²2p³ (²P)3s are some 800 cm⁻¹ lower than corresponding observed values whereas there 24-configuration results are about 14,000 cm⁻¹ lower than corresponding observed values. Similar behavior is manifested for the levels of 2s²2p³ (²P)3d³P configuration. For 2s²2p³ (²P)3p³P the observed values are not available. For this case, too, their 24-configuration energy values differ by amounts similar to their 6-configuration results. Interestingly, their 6-configuration results for the 2p^{6 1}S₀ pushed the level at least six positions down. In short, their energy levels of the 6-configuration or 24-configuration cases show some erratic behavior and in such a case both atomic and scattering data could be in error. It is for this reason we wanted to investigate this ion using our superposition of configuration code CIV3.