### Speaker

### Description

Hafnium (Z = 72) is an element that could be employed in plasma-facing materials in Tokamaks [1,2] and is also produced in neutron-induced transmutation of tungsten (Z = 74) and its alloys that will compose the divertors in these fusion reactors [3]. As a consequence, their sputtering may generate ionic impurities of all possible charge states in the deuterium-tritium plasma. These impurities could contribute to radiation losses in controlled nuclear fusion devices. The radiative properties of these ions have therefore potential important applications in this field [4,5,6]. Many lines of Hf VI in UV range, precisely from 193 A ̊ to 474 A ̊ , have been calculated. As no experimental determination of radiative rates is available in the literature, a multiplaform approach has been adopted to carry out the present calculations so as to estimate the accuracy of the computed rates. From the comparisons of our three independent models based on both the HFR [7] and MCDHF [8,9] methods along with the calculations published by Ryabtsev et al. [5] that they used for line classification purpose, it was found that the uncertainties affecting the theoretical rates range from a few percent (for our HFR model) to ∼40 % (for our MCDHF-RCI-A model) for the strong E1 transitions with S ≥ 1 a.u. With respect to the other lines, they can be highly inaccurate with uncertainties far more than 100 % due to strong cancellation effects and important gauge disagreements that render the rates highly model sensitive. This is essentially caused by the strong mixing affecting most of the Hf VI atomic states. Finally, we recommend our HFR rates except for the two lines at 223.172 Å and at 231.451 A ̊ where the gA-values of Ryabtsev et al. [5] should be used instead with an uncertainty indicator Unc. equal to E (> 50 %), due to strong cancellation effects affecting the former for these two transitions. We have plotted in 3 figures the difference between the level energy calculated in our three independent models and the one determined experimentally by Ryabtsev et al [5]; also plotted in 3 figures the comparison of our transition probabilities, with respect to the calculation of Ryabtsev et al. [5], The ratio, gAHFR/gARYA, is plotted versus our HFR line strength, SHFR, both in logarithmic scale. Similar plots are displayed for our MCDHF-RCI-A and our MCDHF-RCI-B models.

References

[1] Linsmeier C, Rieth M, Aktaa J, Chikada T, Hoffmann A, Houden A, Kurishita H, Jin X, Li M, Litnovsky A, Matsuo S, von Müller A, Nikolic V, Palacios T, Rip- pan R, Qu S, Reiser J, Riesch J, Shikama T, Stieglitz R, Weber T, Wurster S, J-H Y, Zhou Z. Development of advanced high heat flux and plasma-facing materials. Nucl Fusion 2017;57:092007. doi:10.1088/1741-4326/aa6f71.

[2] Pillon M, Angelone M, Forrest RA. Measurements of fusion-induced decay heat in materials and comparison with code predictions. Radiat Phys Chem 2004;71:895. doi:10.1016/j.radphyschem.2004.04.119.

[3] Gilbert MR, J-C S. Neutron-induced transmutation effects in W and W-alloys in a fusion environment. Nucl Fusion 2011;51:043005. doi:10.1088/0029-5515/ 51/4/043005.

4] Ryabtsev AN, Ya KE, Kildiyarova RR, Tchang-Brillet W-Ü L, J-F W. 4f135s25p6 − 4f135s25p56s transitions in the W VIII spectrum and spectra of isoelectronic hafnium, tantalum, and rhenium ions. Opt Spectrosc 2012;113:109. doi:10.1134/S0030400X12080140.

[5] Ryabtsev AN, Ya KE, Kildiyarova RR, Tchang-Brillet W-Ü L, J-F W, Champion N, Blaess C. Spectra of the W VIII isoelectronic sequence:I. hf VI. Phys Scr 2014;89:115402. doi:10.1088/0031-8949/89/11/115402.

[6] Bokamba Motoumba E, Enzonga Yoca S, Quinet P, Palmeri P. Calculations of transition rates in erbium-like ions Lu IV, Hf v and Ta VI using the ab initio MCDHF-RCI and semi-empirical HFR methods. ADNDT 2020;133-134:101340.

[7] Cowan RD. The theory of atomic structure and spectra. Berkeley: University of California Press; 1981.

[8] Froese Fischer C, Gaigalas G, Jönsson P, Bieron ́ J, Grant IP. GRASP2018-a fortran 95 version of the general relativistic atomic structure package. Comput Phys Commun 2019;237:184.

[9] Grant IP. Relativistic quantum theory of atoms and molecules. Theory and computation. New York: Springer; 2007.

Abstract Category | Atomic & Molecular Physics |
---|