Extended calculations of energy levels, radiative properties, and lifetimes for P-like Ge XVIII

Highlights

• Energies, transition rates, and lifetimes for the lowest 150 levels of the $3s^{2}3p^3,$ $3s3p^4,$ $3s^{2}3p^{2}3d,$ $3s3p^{3}3d,$ $3p^5,$ and $3s^{2}3p3d^2$ configurations in P-like Ge XVIII are provided.

• The MCDHF and MBPT methods are employed.

• The most accurate and complete atomic data for Ge XVIII are provided.

Abstract

Using the multiconfiguration Dirac-Hartree-Fock (MCDHF) and the relativistic configuration interaction (RCI) methods, a consistent set of transition energies and radiative transition data for the lowest 150 states of the $3s^{2}3p^3,$ $3s3p^4,$ $3s^{2}3p^{2}3d,$ $3s3p^{3}3d,$ $3p^5,$ and $3s^{2}3p3d^2$ configurations in P-like Ge XVIII is provided. To assess the accuracy of the MCDHF transition energies, we have also performed calculations using the many-body perturbation theory (MBPT). Comparisons are made between the present MCDHF and MBPT data sets, as well as with other available experimental and theoretical values. The resulting accurate and consistent MCDHF data set will be useful for line identification and modeling purposes. These data can be considered as a benchmark for other calculations.

Introduction

Because of its applications in fusion plasmas, the phosphorus isoelectronic sequence from Zn XVI to Kr XXII has received great attention [1], [2], [3]. The Zn XVI, Se XX, and Kr XXII spectra were measured in tokamak plasmas [4], [5]. Using the National Institute of Standards and Technology (NIST) electron beam ion trap (EBIT), the extreme-ultraviolet (EUV) spectra of Kr XXII were observed [6]. As regards P-like Ge XVIII, the electric-dipole (E1) transition array $\left(1s^{2}2s^{2}2p^6\right)3s^{2}3p^3$ – $3s^{2}3p^{2}3d$ was observed by  Sugar et al. [7]. The magnetic dipole (M1) transitions within the $3s^{2}3p^3$ configuration of Ge XVIII were measured by Denne et al. [8] in a tokamak discharge.

On the theoretical side, excitation energies and transition rates for the low-lying 41 states of the $3s^{2}3p^3,$ $3s3p^4,$ and $3s^{2}3p^{2}3d$ configurations in Ge XVIII were provided by different calculations [9], [10], [11], [12], [13], [14]. Atomic parameters for higher-lying levels of P-like ions, such as the $3s3p^{3}3d$ levels, are also needed for applications in plasma physics [15], [16], [17], [18], [19].

The present study is a continuation of our recent work [18], [19] on P-like ions, in which a complete accurate data set of excitation energies and radiative rates involving high-lying levels in P-like Ge XVIII is provided. By using a state-of-the-art method, namely, the multi-configuration Dirac-Hartree-Fock (MCDHF) method combined with the relativistic configuration interaction (RCI) approach [20], excitation energies, wavelengths, lifetimes, and radiative transition data including line strengths, oscillator strengths, and transition rates, are provided for the lowest 150 levels of the $3s^{2}3p^3,$ $3s3p^4,$ $3s^{2}3p^{2}3d,$ $3s3p^{3}3d,$ $3p^5,$ and $3s^{2}3p3d^2$ configurations. To assess the accuracy of the MCDHF transition energies, we have also performed calculations and provided excitation energies for Ge XVIII using the many-body perturbation theory (MBPT) [21]. This work extends and complements our long-term theoretical efforts [18], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38], [39], [40], [41], [42] to provide atomic data for L- and M-shells systems with high accuracy.

The paper is organized as follows. The MCDHF and MBPT calculations are outlined in Section 2. In Section 3 we present our numerical results and compare them with measured values and previous calculations. Section 4 is a brief summary.