Dielectronic recombination in non-LTE plasmas

F. B. Rosmej; V. A. Astapenko; V. S. Lisitsa; L. A. Vainshtein

doi:10.1063/5.0014158

Journals >Matter and Radiation at Extremes >Volume 5 >Issue 6 >Page 064201 > Article

Matter and Radiation at Extremes
Vol. 5, Issue 6, 064201 (2020)

Dielectronic recombination in non-LTE plasmas

F. B. Rosmej^1,2,3,4,a), V. A. Astapenko³, V. S. Lisitsa^3,4,5, and L. A. Vainshtein⁶

Author Affiliations

¹Sorbonne University, Faculty of Science and Engineering, UMR 7605, Case 128, 4 Place Jussieu, F-75252 Paris Cedex 05, France

²LULI, Ecole Polytechnique, CNRS-CEA, Physique Atomique dans les Plasmas Denses (PAPD), Route de Saclay, F-91128 Palaiseau Cedex, France

³Moscow Institute of Physics and Technology MIPT (National Research University), Dolgoprudnyi 141700, Russia

⁴National Research Nuclear University—MEPhI, Department of Plasma Physics, Moscow 115409, Russia

⁵National Research Center “Kurchatov Institute”, Moscow, Russia

⁶P. N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow 119991, Russia

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DOI: 10.1063/5.0014158 Cite this Article

F. B. Rosmej, V. A. Astapenko, V. S. Lisitsa, L. A. Vainshtein. Dielectronic recombination in non-LTE plasmas[J]. Matter and Radiation at Extremes, 2020, 5(6): 064201 Copy Citation Text

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Energy-level diagram of the He-like autoionizing levels 2l2l′ and their associated radiative decays, so-called Lyα satellites. After radiative decay, the singly excited states 1s2l1,3L are formed, from which further radiative decay proceeds (e.g., the resonance and intercombination lines W and Y, respectively). Also indicated are the Li-like autoionizing levels 1s2l2l′.

Fig. 1. Energy-level diagram of the He-like autoionizing levels 2l2l′ and their associated radiative decays, so-called Ly_α satellites. After radiative decay, the singly excited states 1s2l^1,3L are formed, from which further radiative decay proceeds (e.g., the resonance and intercombination lines W and Y, respectively). Also indicated are the Li-like autoionizing levels 1s2l2l′.

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MARIA simulations of dielectronic satellite emission near Lyα of H-like Mg ions for different values of the electron density at kTe = 100 eV. The red arrows indicate the rises in intensity of particular satellite transitions with increasing density. Satellites indicated in blue have effective negative screening due to strong angular-momentum coupling effects.

Fig. 2. MARIA simulations of dielectronic satellite emission near Ly_α of H-like Mg ions for different values of the electron density at kT_e = 100 eV. The red arrows indicate the rises in intensity of particular satellite transitions with increasing density. Satellites indicated in blue have effective negative screening due to strong angular-momentum coupling effects.

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Fig. 3. Comparison of the l-averaged statistical approach with the Burgess and quantum level-by-level calculations for the Ni-like sequence 3s²3p⁶3d¹⁰ of Xe²⁶⁺ and Au⁵¹⁺.

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Fig. 4. Comparison of the l-averaged statistical approach with the Burgess and quantum level-by-level calculations for the Sr-like sequence 4s²4p⁶4d² of W³⁶⁺ and the Zn-like sequence 4s² of tungsten W⁴⁴⁺.

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Element	1s²2lnl′: α₀ = 1s²2s → α = 1s²2p
Element	$B_{d}^{(1 - channel)}$	$B_{d}^{(multichannel)}$	$B_{d}^{(Burgess)}$
Be	8.09 × 10⁻⁵	…	1.34 × 10⁻⁴
C	5.18 × 10⁻⁵	…	7.99 × 10⁻⁵
Mg	1.34 × 10⁻⁵	…	1.94 × 10⁻⁵
Ar	6.87 × 10⁻⁶	…	8.65 × 10⁻⁶
Fe	4.02 × 10⁻⁶	…	4.88 × 10⁻⁶
Mo	3.11 × 10⁻⁶	…	3.87 × 10⁻⁶
	1s²3lnl′: α₀ = 1s²2s → α = 1s²3p
Be	3.44 × 10⁻⁵	1.97 × 10⁻⁶	2.88 × 10⁻⁵
C	6.45 × 10⁻⁵	6.61 × 10⁻⁶	6.98 × 10⁻⁵
Mg	6.43 × 10⁻⁵	2.57 × 10⁻⁵	6.96 × 10⁻⁵
Ar	4.55 × 10⁻⁵	2.42 × 10⁻⁵	5.15 × 10⁻⁵
Fe	2.61 × 10⁻⁵	1.57 × 10⁻⁵	3.54 × 10⁻⁵
Mo	8.61 × 10⁻⁶	6.48 × 10⁻⁶	1.89 × 10⁻⁵
	1s²4lnl′: α₀ = 1s²2s → α = 1s²4p
Be	1.60 × 10⁻⁵	3.47 × 10⁻⁷	1.10 × 10⁻⁵
C	2.52 × 10⁻⁵	3.39 × 10⁻⁷	2.23 × 10⁻⁵
Mg	2.06 × 10⁻⁵	1.30 × 10⁻⁶	1.87 × 10⁻⁵
Ar	1.29 × 10⁻⁵	2.05 × 10⁻⁶	1.27 × 10⁻⁵
Fe	6.54 × 10⁻⁶	2.00 × 10⁻⁶	8.01 × 10⁻⁶
Mo	1.87 × 10⁻⁶	1.17 × 10⁻⁶	3.82 × 10⁻⁶

Table 1. B_d factors according to Eqs. (3.20) and (3.21) for DR into Li-like ions originating from the 1s²nln′l′ autoionizing levels, with Z = Z_n − 2, m = 1, and l₀ = 0. The numerical data show single- and multichannel approximations as well as the corresponding factors according to the Burgess approach (note that the different numerical coefficients and the oscillator strength in the original Burgess formula [Eq. (3.10)] compared with Eq. (3.20) have been included in the value for

B_{d}^{(Burgess)}

to facilitate comparison of the different methods).

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	2lnl′: α₀ = 1s → α = 2p		3lnl′: α₀ = 1s→α = 3p
Element	B_d	χ_d	B_d	χ_d
He	3.12 × 10⁻⁴	0.744	5.48 × 10⁻⁶	0.888
Li	3.72 × 10⁻⁴	0.736	6.41 × 10⁻⁶	0.887
Be	3.67 × 10⁻⁴	0.727	6.53 × 10⁻⁶	0.885
B	3.42 × 10⁻⁴	0.718	6.47 × 10⁻⁶	0.883
C	3.13 × 10⁻⁴	0.709	6.32 × 10⁻⁶	0.881
N	2.85 × 10⁻⁴	0.700	6.31 × 10⁻⁶	0.879
O	2.58 × 10⁻⁴	0.691	5.92 × 10⁻⁶	0.877
F	2.33 × 10⁻⁴	0.682	5.70 × 10⁻⁶	0.874
Ne	2.11 × 10⁻⁴	0.673	5.48 × 10⁻⁶	0.872
Na	1.90 × 10⁻⁴	0.665	5.26 × 10⁻⁶	0.870
Mg	1.72 × 10⁻⁴	0.657	5.04 × 10⁻⁶	0.868
Al	1.56 × 10⁻⁴	0.649	4.84 × 10⁻⁶	0.866
Si	1.41 × 10⁻⁴	0.642	4.63 × 10⁻⁶	0.863
P	1.27 × 10⁻⁴	0.636	4.43 × 10⁻⁶	0.861
S	1.15 × 10⁻⁴	0.630	4.24 × 10⁻⁶	0.859
Cl	1.05 × 10⁻⁴	0.624	4.05 × 10⁻⁶	0.857
Ar	9.50 × 10⁻⁵	0.620	3.87 × 10⁻⁶	0.856
K	8.61 × 10⁻⁵	0.616	3.69 × 10⁻⁶	0.854
C	7.82 × 10⁻⁵	0.612	3.52 × 10⁻⁶	0.852
Sc	7.09 × 10⁻⁵	0.609	3.35 × 10⁻⁶	0.851
Ti	6.45 × 10⁻⁵	0.606	3.19 × 10⁻⁶	0.849
V	5.85 × 10⁻⁵	0.604	3.04 × 10⁻⁶	0.848
Cr	5.33 × 10⁻⁵	0.602	2.89 × 10⁻⁶	0.847
Mn	4.85 × 10⁻⁵	0.601	2.74 × 10⁻⁶	0.846
Fe	4.42 × 10⁻⁵	0.599	2.60 × 10⁻⁶	0.845
Co	4.03 × 10⁻⁵	0.598	2.47 × 10⁻⁶	0.844
Ni	3.68 × 10⁻⁵	0.598	2.34 × 10⁻⁶	0.843
Cu	3.37 × 10⁻⁵	0.597	2.22 × 10⁻⁶	0.842
Zn	3.08 × 10⁻⁵	0.597	2.10 × 10⁻⁶	0.842
Ga	2.83 × 10⁻⁵	0.596	1.99 × 10⁻⁶	0.842
Ge	2.60 × 10⁻⁵	0.596	1.88 × 10⁻⁶	0.841
As	2.39 × 10⁻⁵	0.596	1.78 × 10⁻⁶	0.841
Se	2.20 × 10⁻⁵	0.596	1.68 × 10⁻⁶	0.841
Br	2.03 × 10⁻⁵	0.596	1.59 × 10⁻⁶	0.841
Kr	1.88 × 10⁻⁵	0.596	1.50 × 10⁻⁶	0.841
Rb	1.74 × 10⁻⁵	0.597	1.42 × 10⁻⁶	0.841
Sr	1.61 × 10⁻⁵	0.597	1.34 × 10⁻⁶	0.842
Y	1.50 × 10⁻⁵	0.597	1.27 × 10⁻⁶	0.842
Zr	1.39 × 10⁻⁵	0.598	1.20 × 10⁻⁶	0.842
Nb	1.30 × 10⁻⁵	0.599	1.13 × 10⁻⁶	0.843
Mo	1.21 × 10⁻⁵	0.599	1.07 × 10⁻⁶	0.843

Table 2. Fitting coefficients according to Eqs. (3.20) and (3.21) for DR into H-like ions originating from the 2lnl′ and 3lnl′ autoionizing levels, with Z = Z_n, m = 1, and l₀ = 0. The numerical data include corrections for multiple decay channels (two channels for 2lnl′ and four channels for 3lnl′).

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	1s2lnl′: α₀ = 1s² → α = 1s2p		1s3lnl′: α₀ = 1s² → α = 1s3p
Element	B_d	χ_d	B_d	χ_d
Li	3.39 × 10⁻⁵	1.11	1.57 × 10⁻⁶	1.27
Be	9.94 × 10⁻⁵	0.961	2.12 × 10⁻⁶	1.14
B	1.53 × 10⁻⁴	0.891	2.51 × 10⁻⁶	1.07
C	1.93 × 10⁻⁴	0.848	2.98 × 10⁻⁶	1.03
N	2.17 × 10⁻⁴	0.818	3.40 × 10⁻⁶	1.00
O	2.34 × 10⁻⁴	0.795	3.92 × 10⁻⁶	0.983
F	2.17 × 10⁻⁴	0.775	4.23 × 10⁻⁶	0.967
Ne	2.05 × 10⁻⁴	0.757	4.50 × 10⁻⁶	0.956
Na	1.88 × 10⁻⁴	0.740	4.56 × 10⁻⁶	0.945
Mg	1.72 × 10⁻⁴	0.726	4.54 × 10⁻⁶	0.937
Al	1.57 × 10⁻⁴	0.713	4.47 × 10⁻⁶	0.929
Si	1.43 × 10⁻⁴	0.701	4.36 × 10⁻⁶	0.922
P	1.30 × 10⁻⁴	0.690	4.22 × 10⁻⁶	0.916
S	1.18 × 10⁻⁴	0.681	4.07 × 10⁻⁶	0.910
Cl	1.07 × 10⁻⁴	0.672	3.92 × 10⁻⁶	0.905
Ar	9.72 × 10⁻⁵	0.664	3.76 × 10⁻⁶	0.901
K	8.83 × 10⁻⁵	0.658	3.61 × 10⁻⁶	0.897
C	8.02 × 10⁻⁵	0.652	3.45 × 10⁻⁶	0.893
Sc	7.28 × 10⁻⁵	0.647	3.30 × 10⁻⁶	0.889
Ti	6.62 × 10⁻⁵	0.642	3.15 × 10⁻⁶	0.886
V	6.02 × 10⁻⁵	0.638	3.01 × 10⁻⁶	0.883
Cr	5.47 × 10⁻⁵	0.635	2.87 × 10⁻⁶	0.880
Mn	4.98 × 10⁻⁵	0.632	2.73 × 10⁻⁶	0.877
Fe	4.54 × 10⁻⁵	0.629	2.60 × 10⁻⁶	0.875
Co	4.14 × 10⁻⁵	0.627	2.47 × 10⁻⁶	0.873
Ni	3.78 × 10⁻⁵	0.625	2.35 × 10⁻⁶	0.871
Cu	3.46 × 10⁻⁵	0.623	2.23 × 10⁻⁶	0.869
Zn	3.16 × 10⁻⁵	0.622	2.11 × 10⁻⁶	0.868
Ga	2.90 × 10⁻⁵	0.620	2.00 × 10⁻⁶	0.867
Ge	2.67 × 10⁻⁵	0.619	1.90 × 10⁻⁶	0.865
As	2.45 × 10⁻⁵	0.619	1.80 × 10⁻⁶	0.864
Se	2.26 × 10⁻⁵	0.618	1.70 × 10⁻⁶	0.864
Br	2.08 × 10⁻⁵	0.617	1.61 × 10⁻⁶	0.863
Kr	1.93 × 10⁻⁵	0.617	1.52 × 10⁻⁶	0.862
Rb	1.78 × 10⁻⁵	0.616	1.44 × 10⁻⁶	0.862
Sr	1.65 × 10⁻⁵	0.616	1.36 × 10⁻⁶	0.861
Y	1.53 × 10⁻⁵	0.616	1.29 × 10⁻⁶	0.861
Zr	1.43 × 10⁻⁵	0.616	1.22 × 10⁻⁶	0.861
Nb	1.33 × 10⁻⁵	0.616	1.15 × 10⁻⁶	0.861
Mo	1.24 × 10⁻⁵	0.616	1.09 × 10⁻⁶	0.861

Table 3. Fitting coefficients according to Eqs. (3.20) and (3.21) for DR into He-like ions originating from the 1s2lnl′ and 1s3lnl′ autoionizing levels, with Z = Z_n − 1, m = 2, and l₀ = 0. The numerical data include corrections for multiple decay channels (two channels for 1s2lnl′ and four channels for 1s3lnl′).

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	1s²2lnl′: α₀ = 1s²2s → α = 1s²2p		1s²3lnl′: α₀ = 1s²2s → α = 1s²3p
Element	B_d	χ_d	B_d	χ_d
Be	8.09 × 10⁻⁵	0.057 1	1.97 × 10⁻⁶	0.197
B	6.86 × 10⁻⁵	0.040 0	2.85 × 10⁻⁶	0.173
C	5.18 × 10⁻⁵	0.030 6	6.61 × 10⁻⁶	0.161
N	3.95 × 10⁻⁵	0.024 8	1.06 × 10⁻⁵	0.153
O	3.09 × 10⁻⁵	0.020 7	1.47 × 10⁻⁵	0.149
F	2.47 × 10⁻⁵	0.017 9	1.85 × 10⁻⁵	0.145
Ne	2.02 × 10⁻⁵	0.015 6	2.17 × 10⁻⁵	0.142
Na	1.69 × 10⁻⁵	0.013 9	2.41 × 10⁻⁵	0.140
Mg	1.43 × 10⁻⁵	0.012 6	2.57 × 10⁻⁵	0.138
Al	1.23 × 10⁻⁵	0.011 5	2.67 × 10⁻⁵	0.136
Si	1.07 × 10⁻⁵	0.010 5	2.71 × 10⁻⁵	0.135
P	9.43 × 10⁻⁶	0.009 81	2.69 × 10⁻⁵	0.133
S	8.41 × 10⁻⁶	0.009 14	2.60 × 10⁻⁵	0.131
Cl	7.57 × 10⁻⁶	0.008 58	2.53 × 10⁻⁵	0.130
Ar	6.87 × 10⁻⁶	0.008 09	2.42 × 10⁻⁵	0.128
K	6.25 × 10⁻⁶	0.007 72	2.31 × 10⁻⁵	0.127
C	5.76 × 10⁻⁶	0.007 36	2.19 × 10⁻⁵	0.126
Sc	5.35 × 10⁻⁶	0.007 04	2.09 × 10⁻⁵	0.124
Ti	5.00 × 10⁻⁶	0.006 77	1.97 × 10⁻⁵	0.123
V	4.67 × 10⁻⁶	0.006 58	1.86 × 10⁻⁵	0.122
Cr	4.42 × 10⁻⁶	0.006 37	1.76 × 10⁻⁵	0.120
Mn	4.20 × 10⁻⁶	0.006 20	1.66 × 10⁻⁵	0.119
Fe	4.02 × 10⁻⁶	0.006 05	1.57 × 10⁻⁵	0.118
Co	3.86 × 10⁻⁶	0.005 92	1.48 × 10⁻⁵	0.117
Ni	3.72 × 10⁻⁶	0.005 81	1.40 × 10⁻⁵	0.116
Cu	3.61 × 10⁻⁶	0.005 71	1.32 × 10⁻⁵	0.115
Zn	3.51 × 10⁻⁶	0.005 64	1.25 × 10⁻⁵	0.114
Ga	3.42 × 10⁻⁶	0.005 58	1.18 × 10⁻⁵	0.113
Ge	3.35 × 10⁻⁶	0.005 53	1.11 × 10⁻⁵	0.112
As	3.25 × 10⁻⁶	0.005 56	1.05 × 10⁻⁵	0.111
Se	3.20 × 10⁻⁶	0.005 54	9.96 × 10⁻⁶	0.110
Br	3.20 × 10⁻⁶	0.005 46	9.43 × 10⁻⁶	0.109
Kr	3.17 × 10⁻⁶	0.005 46	8.92 × 10⁻⁶	0.108
Rb	3.15 × 10⁻⁶	0.005 47	8.45 × 10⁻⁶	0.107
Sr	3.13 × 10⁻⁶	0.005 48	8.01 × 10⁻⁶	0.106
Y	3.12 × 10⁻⁶	0.005 51	7.59 × 10⁻⁶	0.105
Zr	3.11 × 10⁻⁶	0.005 54	7.20 × 10⁻⁶	0.105
Nb	3.11 × 10⁻⁶	0.005 58	6.83 × 10⁻⁶	0.104
Mo	3.11 × 10⁻⁶	0.005 63	6.48 × 10⁻⁶	0.103

Table 4. Fitting coefficients according to Eqs. (3.20) and (3.21) for DR into Li-like ions originating from the 1s²2lnl′ and 1s²3lnl′ autoionizing levels, with Z = Z_n − 2, m = 1, and l₀ = 0. The numerical data include corrections for multiple decay channels (one channel for 1s²2lnl′ and four channels for 1s²3lnl′).

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	1s²3lnl′: α₀ = 1s²2p → α = 1s²3d		1s²4lnl′: α₀ = 1s²2p → α = 1s²4d
Element	B_d	χ_d	B_d	χ_d
Be	1.78 × 10⁻⁴	0.140	1.88 × 10⁻⁵	0.190
B	2.99 × 10⁻⁴	0.137	2.01 × 10⁻⁵	0.189
C	3.74 × 10⁻⁴	0.135	2.04 × 10⁻⁵	0.188
N	4.44 × 10⁻⁴	0.133	2.18 × 10⁻⁵	0.187
O	5.15 × 10⁻⁴	0.131	2.35 × 10⁻⁵	0.187
F	5.52 × 10⁻⁴	0.130	2.53 × 10⁻⁵	0.186
Ne	5.65 × 10⁻⁴	0.128	2.67 × 10⁻⁵	0.185
Na	5.76 × 10⁻⁴	0.127	2.88 × 10⁻⁵	0.181
Mg	5.73 × 10⁻⁴	0.125	3.28 × 10⁻⁵	0.174
Al	5.61 × 10⁻⁴	0.124	3.32 × 10⁻⁵	0.172
Si	5.39 × 10⁻⁴	0.122	3.33 × 10⁻⁵	0.171
P	5.19 × 10⁻⁴	0.120	3.48 × 10⁻⁵	0.167
S	4.96 × 10⁻⁴	0.119	3.46 × 10⁻⁵	0.165
Cl	4.71 × 10⁻⁴	0.117	3.44 × 10⁻⁵	0.164
Ar	4.48 × 10⁻⁴	0.115	3.41 × 10⁻⁵	0.163
K	4.25 × 10⁻⁴	0.114	3.38 × 10⁻⁵	0.161
C	4.04 × 10⁻⁴	0.112	3.34 × 10⁻⁵	0.160
Sc	3.83 × 10⁻⁴	0.110	3.30 × 10⁻⁵	0.159
Ti	3.64 × 10⁻⁴	0.109	3.25 × 10⁻⁵	0.158
V	3.45 × 10⁻⁴	0.107	3.20 × 10⁻⁵	0.157
Cr	3.27 × 10⁻⁴	0.105	3.14 × 10⁻⁵	0.156
Mn	3.11 × 10⁻⁴	0.104	3.08 × 10⁻⁵	0.156
Fe	2.95 × 10⁻⁴	0.102	3.02 × 10⁻⁵	0.155
Co	2.80 × 10⁻⁴	0.101	2.95 × 10⁻⁵	0.154
Ni	2.66 × 10⁻⁴	0.0992	2.88 × 10⁻⁵	0.154
Cu	2.53 × 10⁻⁴	0.0978	2.80 × 10⁻⁵	0.153
Zn	2.40 × 10⁻⁴	0.0964	2.72 × 10⁻⁵	0.153
Ga	2.28 × 10⁻⁴	0.0951	2.64 × 10⁻⁵	0.153
Ge	2.17 × 10⁻⁴	0.0939	2.56 × 10⁻⁵	0.152
As	2.06 × 10⁻⁴	0.0927	2.47 × 10⁻⁵	0.152
Se	1.96 × 10⁻⁴	0.0916	2.39 × 10⁻⁵	0.152
Br	1.86 × 10⁻⁴	0.0905	2.30 × 10⁻⁵	0.152
Kr	1.77 × 10⁻⁴	0.0895	2.22 × 10⁻⁵	0.152
Rb	1.68 × 10⁻⁴	0.0885	2.14 × 10⁻⁵	0.152
Sr	1.60 × 10⁻⁴	0.0876	2.05 × 10⁻⁵	0.152
Y	1.52 × 10⁻⁴	0.0867	1.97 × 10⁻⁵	0.152
Zr	1.45 × 10⁻⁴	0.0859	1.89 × 10⁻⁵	0.152
Nb	1.38 × 10⁻⁴	0.0851	1.82 × 10⁻⁵	0.152
Mo	1.31 × 10⁻⁴	0.0844	1.74 × 10⁻⁵	0.152

Table 5. Fitting coefficients according to Eqs. (3.20) and (3.21) for DR into excited states of Li-like ions originating from the 1s²3lnl′ and 1s²4lnl′ autoionizing levels, with Z = Z_n − 2, m = 1, and l₀ = 1. The numerical data include corrections for multiple decay channels (three channels for 1s²3lnl′ and six channels for 1s²4lnl′).

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State	Z_n = 3	Z_n = 6	Z_n = 13	Z_n = 18	Z_n = 26	Z_n = 42
2p²¹S₀	8.4 × 10¹⁰	5.1 × 10¹²	1.3 × 10¹³	1.9 × 10¹³	3.4 × 10¹³	7.0 × 10¹³
2p²¹D₂	1.5 × 10¹⁴	2.5 × 10¹⁴	3.1 × 10¹⁴	3.1 × 10¹⁴	2.3 × 10¹⁴	2.1 × 10¹⁴
2p²³P₀	2.9 × 10⁷	2.3 × 10⁹	2.3 × 10¹¹	1.2 × 10¹²	3.7 × 10¹²	2.8 × 10¹²
2p²³P₁	0	0	0	0	0	0
2p²³P₁ with Breit interaction	2.6 × 10⁷	6.8 × 10⁸	1.9 × 10¹⁰	7.2 × 10¹⁰	3.2 × 10¹¹	2.2 × 10¹²
2p²³P₂	1.1 × 10⁹	3.1 × 10¹⁰	3.0 × 10¹²	2.1 × 10¹³	1.1 × 10¹⁴	1.5 × 10¹⁴

Table 6. Field-free autoionization decay rates (s⁻¹) including intermediate coupling, configuration, and magnetic interaction.

F. B. Rosmej, V. A. Astapenko, V. S. Lisitsa, L. A. Vainshtein. Dielectronic recombination in non-LTE plasmas[J]. Matter and Radiation at Extremes, 2020, 5(6): 064201

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