Matter and Radiation at Extremes, 2020, 5 (6): 064201, Published Online: Nov. 24, 2020   

Dielectronic recombination in non-LTE plasmas

Author Affiliations
1 Sorbonne University, Faculty of Science and Engineering, UMR 7605, Case 128, 4 Place Jussieu, F-75252 Paris Cedex 05, France
2 LULI, Ecole Polytechnique, CNRS-CEA, Physique Atomique dans les Plasmas Denses (PAPD), Route de Saclay, F-91128 Palaiseau Cedex, France
3 Moscow Institute of Physics and Technology MIPT (National Research University), Dolgoprudnyi 141700, Russia
4 National Research Nuclear University—MEPhI, Department of Plasma Physics, Moscow 115409, Russia
5 National Research Center “Kurchatov Institute”, Moscow, Russia
6 P. N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow 119991, Russia
Figures & Tables

Fig. 1. 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′.

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Fig. 2. 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.

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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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Table1. Bd factors according to Eqs. (3.20) and (3.21) for DR into Li-like ions originating from the 1s2nlnl′ autoionizing levels, with Z = Zn − 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 Bd(Burgess) to facilitate comparison of the different methods).

Element1s22lnl′: α0 = 1s22sα = 1s22p
Bd(1- channel)Bd(multichannel)Bd(Burgess)
Be8.09 × 10−51.34 × 10−4
C5.18 × 10−57.99 × 10−5
Mg1.34 × 10−51.94 × 10−5
Ar6.87 × 10−68.65 × 10−6
Fe4.02 × 10−64.88 × 10−6
Mo3.11 × 10−63.87 × 10−6
1s23lnl′: α0 = 1s22sα = 1s23p
Be3.44 × 10−51.97 × 10−62.88 × 10−5
C6.45 × 10−56.61 × 10−66.98 × 10−5
Mg6.43 × 10−52.57 × 10−56.96 × 10−5
Ar4.55 × 10−52.42 × 10−55.15 × 10−5
Fe2.61 × 10−51.57 × 10−53.54 × 10−5
Mo8.61 × 10−66.48 × 10−61.89 × 10−5
1s24lnl′: α0 = 1s22sα = 1s24p
Be1.60 × 10−53.47 × 10−71.10 × 10−5
C2.52 × 10−53.39 × 10−72.23 × 10−5
Mg2.06 × 10−51.30 × 10−61.87 × 10−5
Ar1.29 × 10−52.05 × 10−61.27 × 10−5
Fe6.54 × 10−62.00 × 10−68.01 × 10−6
Mo1.87 × 10−61.17 × 10−63.82 × 10−6

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Table2. 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 = Zn, m = 1, and l0 = 0. The numerical data include corrections for multiple decay channels (two channels for 2lnl′ and four channels for 3lnl′).

2lnl′: α0 = 1sα = 2p3lnl′: α0 = 1sα = 3p
ElementBdχdBdχd
He3.12 × 10−40.7445.48 × 10−60.888
Li3.72 × 10−40.7366.41 × 10−60.887
Be3.67 × 10−40.7276.53 × 10−60.885
B3.42 × 10−40.7186.47 × 10−60.883
C3.13 × 10−40.7096.32 × 10−60.881
N2.85 × 10−40.7006.31 × 10−60.879
O2.58 × 10−40.6915.92 × 10−60.877
F2.33 × 10−40.6825.70 × 10−60.874
Ne2.11 × 10−40.6735.48 × 10−60.872
Na1.90 × 10−40.6655.26 × 10−60.870
Mg1.72 × 10−40.6575.04 × 10−60.868
Al1.56 × 10−40.6494.84 × 10−60.866
Si1.41 × 10−40.6424.63 × 10−60.863
P1.27 × 10−40.6364.43 × 10−60.861
S1.15 × 10−40.6304.24 × 10−60.859
Cl1.05 × 10−40.6244.05 × 10−60.857
Ar9.50 × 10−50.6203.87 × 10−60.856
K8.61 × 10−50.6163.69 × 10−60.854
C7.82 × 10−50.6123.52 × 10−60.852
Sc7.09 × 10−50.6093.35 × 10−60.851
Ti6.45 × 10−50.6063.19 × 10−60.849
V5.85 × 10−50.6043.04 × 10−60.848
Cr5.33 × 10−50.6022.89 × 10−60.847
Mn4.85 × 10−50.6012.74 × 10−60.846
Fe4.42 × 10−50.5992.60 × 10−60.845
Co4.03 × 10−50.5982.47 × 10−60.844
Ni3.68 × 10−50.5982.34 × 10−60.843
Cu3.37 × 10−50.5972.22 × 10−60.842
Zn3.08 × 10−50.5972.10 × 10−60.842
Ga2.83 × 10−50.5961.99 × 10−60.842
Ge2.60 × 10−50.5961.88 × 10−60.841
As2.39 × 10−50.5961.78 × 10−60.841
Se2.20 × 10−50.5961.68 × 10−60.841
Br2.03 × 10−50.5961.59 × 10−60.841
Kr1.88 × 10−50.5961.50 × 10−60.841
Rb1.74 × 10−50.5971.42 × 10−60.841
Sr1.61 × 10−50.5971.34 × 10−60.842
Y1.50 × 10−50.5971.27 × 10−60.842
Zr1.39 × 10−50.5981.20 × 10−60.842
Nb1.30 × 10−50.5991.13 × 10−60.843
Mo1.21 × 10−50.5991.07 × 10−60.843

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Table3. 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 = Zn − 1, m = 2, and l0 = 0. The numerical data include corrections for multiple decay channels (two channels for 1s2lnl′ and four channels for 1s3lnl′).

1s2lnl′: α0 = 1s2α = 1s2p1s3lnl′: α0 = 1s2α = 1s3p
ElementBdχdBdχd
Li3.39 × 10−51.111.57 × 10−61.27
Be9.94 × 10−50.9612.12 × 10−61.14
B1.53 × 10−40.8912.51 × 10−61.07
C1.93 × 10−40.8482.98 × 10−61.03
N2.17 × 10−40.8183.40 × 10−61.00
O2.34 × 10−40.7953.92 × 10−60.983
F2.17 × 10−40.7754.23 × 10−60.967
Ne2.05 × 10−40.7574.50 × 10−60.956
Na1.88 × 10−40.7404.56 × 10−60.945
Mg1.72 × 10−40.7264.54 × 10−60.937
Al1.57 × 10−40.7134.47 × 10−60.929
Si1.43 × 10−40.7014.36 × 10−60.922
P1.30 × 10−40.6904.22 × 10−60.916
S1.18 × 10−40.6814.07 × 10−60.910
Cl1.07 × 10−40.6723.92 × 10−60.905
Ar9.72 × 10−50.6643.76 × 10−60.901
K8.83 × 10−50.6583.61 × 10−60.897
C8.02 × 10−50.6523.45 × 10−60.893
Sc7.28 × 10−50.6473.30 × 10−60.889
Ti6.62 × 10−50.6423.15 × 10−60.886
V6.02 × 10−50.6383.01 × 10−60.883
Cr5.47 × 10−50.6352.87 × 10−60.880
Mn4.98 × 10−50.6322.73 × 10−60.877
Fe4.54 × 10−50.6292.60 × 10−60.875
Co4.14 × 10−50.6272.47 × 10−60.873
Ni3.78 × 10−50.6252.35 × 10−60.871
Cu3.46 × 10−50.6232.23 × 10−60.869
Zn3.16 × 10−50.6222.11 × 10−60.868
Ga2.90 × 10−50.6202.00 × 10−60.867
Ge2.67 × 10−50.6191.90 × 10−60.865
As2.45 × 10−50.6191.80 × 10−60.864
Se2.26 × 10−50.6181.70 × 10−60.864
Br2.08 × 10−50.6171.61 × 10−60.863
Kr1.93 × 10−50.6171.52 × 10−60.862
Rb1.78 × 10−50.6161.44 × 10−60.862
Sr1.65 × 10−50.6161.36 × 10−60.861
Y1.53 × 10−50.6161.29 × 10−60.861
Zr1.43 × 10−50.6161.22 × 10−60.861
Nb1.33 × 10−50.6161.15 × 10−60.861
Mo1.24 × 10−50.6161.09 × 10−60.861

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Table4. 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 = Zn − 2, m = 1, and l0 = 0. The numerical data include corrections for multiple decay channels (one channel for 1s22lnl′ and four channels for 1s23lnl′).

1s22lnl′: α0 = 1s22sα = 1s22p1s23lnl′: α0 = 1s22sα = 1s23p
ElementBdχdBdχd
Be8.09 × 10−50.057 11.97 × 10−60.197
B6.86 × 10−50.040 02.85 × 10−60.173
C5.18 × 10−50.030 66.61 × 10−60.161
N3.95 × 10−50.024 81.06 × 10−50.153
O3.09 × 10−50.020 71.47 × 10−50.149
F2.47 × 10−50.017 91.85 × 10−50.145
Ne2.02 × 10−50.015 62.17 × 10−50.142
Na1.69 × 10−50.013 92.41 × 10−50.140
Mg1.43 × 10−50.012 62.57 × 10−50.138
Al1.23 × 10−50.011 52.67 × 10−50.136
Si1.07 × 10−50.010 52.71 × 10−50.135
P9.43 × 10−60.009 812.69 × 10−50.133
S8.41 × 10−60.009 142.60 × 10−50.131
Cl7.57 × 10−60.008 582.53 × 10−50.130
Ar6.87 × 10−60.008 092.42 × 10−50.128
K6.25 × 10−60.007 722.31 × 10−50.127
C5.76 × 10−60.007 362.19 × 10−50.126
Sc5.35 × 10−60.007 042.09 × 10−50.124
Ti5.00 × 10−60.006 771.97 × 10−50.123
V4.67 × 10−60.006 581.86 × 10−50.122
Cr4.42 × 10−60.006 371.76 × 10−50.120
Mn4.20 × 10−60.006 201.66 × 10−50.119
Fe4.02 × 10−60.006 051.57 × 10−50.118
Co3.86 × 10−60.005 921.48 × 10−50.117
Ni3.72 × 10−60.005 811.40 × 10−50.116
Cu3.61 × 10−60.005 711.32 × 10−50.115
Zn3.51 × 10−60.005 641.25 × 10−50.114
Ga3.42 × 10−60.005 581.18 × 10−50.113
Ge3.35 × 10−60.005 531.11 × 10−50.112
As3.25 × 10−60.005 561.05 × 10−50.111
Se3.20 × 10−60.005 549.96 × 10−60.110
Br3.20 × 10−60.005 469.43 × 10−60.109
Kr3.17 × 10−60.005 468.92 × 10−60.108
Rb3.15 × 10−60.005 478.45 × 10−60.107
Sr3.13 × 10−60.005 488.01 × 10−60.106
Y3.12 × 10−60.005 517.59 × 10−60.105
Zr3.11 × 10−60.005 547.20 × 10−60.105
Nb3.11 × 10−60.005 586.83 × 10−60.104
Mo3.11 × 10−60.005 636.48 × 10−60.103

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Table5. 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 = Zn − 2, m = 1, and l0 = 1. The numerical data include corrections for multiple decay channels (three channels for 1s23lnl′ and six channels for 1s24lnl′).

1s23lnl′: α0 = 1s22pα = 1s23d1s24lnl′: α0 = 1s22pα = 1s24d
ElementBdχdBdχd
Be1.78 × 10−40.1401.88 × 10−50.190
B2.99 × 10−40.1372.01 × 10−50.189
C3.74 × 10−40.1352.04 × 10−50.188
N4.44 × 10−40.1332.18 × 10−50.187
O5.15 × 10−40.1312.35 × 10−50.187
F5.52 × 10−40.1302.53 × 10−50.186
Ne5.65 × 10−40.1282.67 × 10−50.185
Na5.76 × 10−40.1272.88 × 10−50.181
Mg5.73 × 10−40.1253.28 × 10−50.174
Al5.61 × 10−40.1243.32 × 10−50.172
Si5.39 × 10−40.1223.33 × 10−50.171
P5.19 × 10−40.1203.48 × 10−50.167
S4.96 × 10−40.1193.46 × 10−50.165
Cl4.71 × 10−40.1173.44 × 10−50.164
Ar4.48 × 10−40.1153.41 × 10−50.163
K4.25 × 10−40.1143.38 × 10−50.161
C4.04 × 10−40.1123.34 × 10−50.160
Sc3.83 × 10−40.1103.30 × 10−50.159
Ti3.64 × 10−40.1093.25 × 10−50.158
V3.45 × 10−40.1073.20 × 10−50.157
Cr3.27 × 10−40.1053.14 × 10−50.156
Mn3.11 × 10−40.1043.08 × 10−50.156
Fe2.95 × 10−40.1023.02 × 10−50.155
Co2.80 × 10−40.1012.95 × 10−50.154
Ni2.66 × 10−40.09922.88 × 10−50.154
Cu2.53 × 10−40.09782.80 × 10−50.153
Zn2.40 × 10−40.09642.72 × 10−50.153
Ga2.28 × 10−40.09512.64 × 10−50.153
Ge2.17 × 10−40.09392.56 × 10−50.152
As2.06 × 10−40.09272.47 × 10−50.152
Se1.96 × 10−40.09162.39 × 10−50.152
Br1.86 × 10−40.09052.30 × 10−50.152
Kr1.77 × 10−40.08952.22 × 10−50.152
Rb1.68 × 10−40.08852.14 × 10−50.152
Sr1.60 × 10−40.08762.05 × 10−50.152
Y1.52 × 10−40.08671.97 × 10−50.152
Zr1.45 × 10−40.08591.89 × 10−50.152
Nb1.38 × 10−40.08511.82 × 10−50.152
Mo1.31 × 10−40.08441.74 × 10−50.152

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Table6. Field-free autoionization decay rates (s−1) including intermediate coupling, configuration, and magnetic interaction.

StateZn = 3Zn = 6Zn = 13Zn = 18Zn = 26Zn = 42
2p21S08.4 × 10105.1 × 10121.3 × 10131.9 × 10133.4 × 10137.0 × 1013
2p21D21.5 × 10142.5 × 10143.1 × 10143.1 × 10142.3 × 10142.1 × 1014
2p23P02.9 × 1072.3 × 1092.3 × 10111.2 × 10123.7 × 10122.8 × 1012
2p23P1000000
2p23P1 with Breit interaction2.6 × 1076.8 × 1081.9 × 10107.2 × 10103.2 × 10112.2 × 1012
2p23P21.1 × 1093.1 × 10103.0 × 10122.1 × 10131.1 × 10141.5 × 1014

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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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