Energy levels, transition rates, lifetimes of He-like-ions with $Z=72\text{–}76$ deduced from relativistic multiconfiguration Dirac–Hartree–Fock and many body perturbation theory calculations

Abstract

We disclose relativistic multiconfiguration Dirac–Hartree–Fock (MCDHF) spectrum calculations for He-like-ions with $Z=72\text{–}76$. The excitation energy and the oscillator strength values have been computed for the 127 odd- and even-parity states as well as lifetimes and transition rates between different states. To study the accuracy of our results, we have implemented parallel calculations using a Flexible Atomic Code (FAC) by introducing the many body perturbation theory (MBPT). Additionally, the Breit interaction and leading quantum electrodynamics effects (QED) are included as perturbations in the present calculations.

Introduction

It is now well established that tungsten will be the main material covering the divertor, a crucial component of the ITER nuclear fusion reactor (see e.g. [1], [2]). The environment of Tokamak as a magnetic confinement fusion device would be on of the most brutal ever envisioned by material engineers, particularly the plasma-facing materials. The divertor will extract the ash produced by the fusion reaction and will allow some of the heat generated by the irradiation of the particles to be removed. It will therefore be subjected to the most extreme operating conditions. For instance, the divertor in the ITER tokamak project [2] will use tungsten as plasma-facing material due to his specific physical properties especially its fusion temperature in order to support the high heat flux, high-flux irradiation by hard-spectrum neutrons, and the plasma helium ions bombardment. In this case, Tungsten nanotendril would grow due to exposure to the bombardment under tokamak relevant conditions on tungsten plasma-facing materials in a magnetic fusion energy device [3]. Under such reaction conditions, tungsten has been observed to form a thick mat of nanotendrils which vary from few tens of nanometers up to several microns in length [4].

Thus, tungsten will have to cope with neutron bombardment, intense particle flows and very high temperatures. In particular, neutron bombardment will induce the transmutation of tungsten atoms and lead to the creation of atoms such as hafnium (Hf), tantalum (Ta), rhenium (Re) and osmium (Os). The results of recent calculations on transmutation tungsten induced by neutron irradiation during the operational period of the ITER reactor, confirm the presence of these products of primary transmutation [5].

More precisely, these theoretical investigations predicted that, under power-plant conditions, Re, Os, and Ta could reach rather significant concentration of 3.8 × 10${}^4$ appm (3.8 at.%), 1.38 × 10${}^4$ appm (1.4 at.%), and 8.09 × 10${}^3$ appm (0.81 at.%), respectively, after five years of operation. Because of the relatively long reaction pathways required to produce hafnium from the original tungsten isotopes, the contribution from Hf is expected to be somewhat weaker with an estimated concentration of 141 appm. Moreover, Re is usually incorporated as solute into tungsten alloys in order to improve the properties of W for fusion reactor applications. It is indeed known that the addition of $5$–$26$ % Re is expected to increase the low-temperature ductility of W, to improve its high-temperature strength, as well as to enhance its plasticity, its creep strength and its recrystallization temperature [6], [7], [8], [9], [10].

Consequently, Hf, Ta, Re, Os ions, as well as W ions, will constitute impurities in the plasma and will therefore emit electromagnetic radiation, the analysis of which will make it possible to diagnose the physical conditions of the environment. Unfortunately, the radiative parameters related to these ions are still too little known to be used for plasma diagnostics.​ The aim of our work is to fill this gap by reporting a very large number of new atomic data characterizing the electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2) and magnetic quadrupole (M2) transitions in He-like Hf, Ta, W, Re and Os ions. These results were obtained using large-scale calculations within the framework of two independent theoretical approaches, i.e. the multiconfiguration Dirac–Hartree–Fock (MCDHF) method and the multi-body perturbation theory (MBPT) as we mentioned in our previous research [11], [12], [13], each of which being implemented using the most recent versions of the corresponding computer codes (GRASP2018 for the former method and FAC for the latter one).

The present work considerably extends all previous theoretical computations of radiative parameters in He-like ions in the sense that, either the latter studies were often limited to lowly or moderately charged ions along the isoelectronic sequence or they were limited to transitions involving low-lying energy levels. As an example, the very recent relativistic configuration interaction calculations published by Glowacki [14] allowed the author to report excitation energies and oscillator strengths in all He-like ions from Z $=$ 2 to Z - 116 for 1s${}^2$–1s2p, 1s2s–1s2p, and 1s2s–1s3p transitions only.