Radiative rates for E1, E2, M1, and M2 transitions in F-like ions with 12 $\le$ Z $\le$ 23

Abstract

In this paper, energy levels, radiative rates and lifetimes are reported for 11 F-like ions with 12 $\le$ Z $\le$ 23. Up to 198 levels (depending on the ion) have been considered which include 113 of the 2s${}^2$2p${}^5$, 2s2p${}^6$, 2s${}^2$2p${}^4$3$\ell$, 2s2p${}^5$3$\ell$, and 2p${}^6$3$\ell$ configurations. The general-purpose relativistic atomic structure package (grasp) and the flexible atomic code (fac) have been adopted for calculating the energy levels, but the grasp alone for the remaining parameters. Radiative rates (along with oscillator strengths and line strengths) are listed for all E1, E2, M1, and M2 transitions of the ions. Comparisons are made with earlier available theoretical and experimental energies, for all ions, in order to assess the accuracy of the calculations. Comparisons have also been made for the radiative rates and lifetimes, which have been possible for only those among the lowest 60 levels.

Introduction

F-like ions have been of interest for the diagnostics and modelling of astrophysical and fusion plasmas for which information about atomic data are required, particularly for energy levels, radiative rates and collision strengths. The first major study for these ions was undertaken by Sampson et al. [1], who performed calculations for a wide range of F-like ions with 22 $\le$ Z $\le$ 92 by using their Dirac–Fock–Slater (DFS) code. However, to economise space they reported only limited results, and for only a few ions, for energy levels, oscillator strengths (f-values) and collision strengths ($\Omega$). Since these data are too limited for applications, several workers after them have performed (more accurate) calculations for a variety of atomic parameters, but only for a section of these ions. For example, during the past one decade in a series of papers [[2], [3], [4], [5], [6], [7], [8]], we have reported energy levels, radiative rates (A-values), oscillator strengths (f-values), line strengths (S-values), and lifetimes ($\tau$) for F-like ions with 36 $\le$ Z $\le$ 74. Similarly, Si et al. [9] and Li et al. [10] have reported data for ions with 24 $\le$ Z $\le$ 30 and 31 $\le$ Z $\le$ 35, respectively. Since their data are of comparable high accuracy there is no (real) need to revisit these ions. Therefore, in this paper we list our results for further 11 ions with 12 $\le$ Z $\le$ 23.

As in the past, for our calculations we employ the general-purpose relativistic atomic structure package (grasp) code [11]. However, this original version (referred to as GRASP0) has been extensively modified by (one of the authors) P. H. Norrington, and is available at the website http://amdpp.phys.strath.ac.uk/UK_APAP/codes.html. Since the ions considered in this paper are comparatively lighter, a much larger CI (configuration interaction) has been considered than in the earlier works [[2], [3], [4], [5], [6], [7], [8]]. In fact, for ions towards the neutral end a much (much) larger CI is required to improve accuracy of calculations and to obtain a better match with measurements, particularly for energy levels. To achieve this aim, calculations have also been performed with the flexible atomic code (FAC) of Gu [12].

Earlier work for F-like ions with 12 $\le$ Z $\le$ 23 has mainly been performed by Gu [13] and Jönsson et al. [14]. Gu [13] combined CI with many-body perturbation theory (MBPT) approach in FAC and calculated energies, but only for the lowest three levels. For the same three levels, later on Jönsson et al. [14] reported energies and A-values for which they adopted the revised version of the GRASP code [15], but included a very large CI in the calculations. In spite of the high accuracy of their calculations, the reported data are too limited for applications. Nevertheless, Froese Fischer and Tachiev [16] have already reported a larger amount of data among 60 levels of the 2s${}^2$2p${}^5$, 2s2p${}^6$ and 2s${}^2$2p${}^4$3$\ell$ configurations of F-like ions with 9 $\le$ Z $\le$ 22, for which they adopted the multi-configuration Hartree–Fock (MCHF) code, included relativistic effects through Breit–Pauli Hamiltonian and considered a large CI. Their calculations are (probably) the most accurate available to date because discrepancies with the measured energy levels are insignificant. Therefore, our aim is not to improve upon their work but to extend it to higher levels, particularly those of the 2s2p${}^5$3$\ell$ and 2p${}^6$3$\ell$ configurations.