Semi-empirical calculations of radiative rates for parity-forbidden transitionswithin the 4f2 configuration of Ba-like ions La+, Ce2+, Pr3+ and Nd4+and 4f12 configuration of Dy-likeYb4+
Hui Lia, Xiao-YuKuanga,b,[*] , Yau Yuen Yeungc,*,
aInstitute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, PRChina
bInternational Centre for Materials Physics, Academia Sinica, Shenyang 110016, PRChina
cDepartment of Science and Environmental Studies, The Hong Kong Institute of Education, 10 Lo Ping Road, Tai Po, NT, Hong Kong, PR China
Supplementary Material
Table S1.Transition probabilities for forbidden transitions within the 4f2configuration of La IIa.
SLJ / S′L′J′ / λ (nm)b / Type / A′ (s-1) / SLJ / S′L′J′ / λ (nm) / Type / A′ (s-1)3P2 / 3F3 / 1572 / M1+E2 / 5.55×10-3 / 1D2 / 3F3 / 2431 / M1 / 5.61×10-2
3F4 / 1664 / E2 / 1.72×10-3 / 1G4 / 3H4 / 2270 / M1 / 1.54×10-2
1D2 / 4452 / M1 / 2.97×10-2 / 3H5 / 2797 / M1 / 1.68×10-2
3P1 / 17977 / M1 / 2.17×10-3 / 3F3 / 6196 / M1 / 2.08×10-2
3P1 / 3F2 / 1584 / M1+E2 / 1.58×10-3 / 3F4 / 7909 / M1 / 1.30×10-2
3F3 / 1723 / E2 / 2.38×10-3 / 3F4 / 3H4 / 3183 / M1 / 8.28×10-3
1D2 / 5917 / M1 / 7.40×10-3 / 3H5 / 4327 / M1 / 3.01×10-3
3P0 / 38347 / M1 / 3.14×10-4 / 3F3 / 28598 / M1 / 6.57×10-4
3P0 / 3F2 / 1652 / E2 / 3.95×10-3 / 3F3 / 3H4 / 3581 / M1 / 3.07×10-4
1I6 / 3H5 / 1549 / M1 / 2.32×10-2 / 3F2 / 19666 / M1 / 3.32×10-3
3H6 / 1801 / M1 / 2.06×10-2 / 3H6 / 3H5 / 11053 / M1 / 1.67×10-2
1D2 / 3F2 / 2163 / M1 / 4.22×10-2 / 3H5 / 3H4 / 12034 / M1 / 1.50×10-2
aOnly transitions with total vacuum emission ratesA′>1.0×10-4are listed.
bAll wavelengths in our table are vacuum wavelengths derived from our calculated energy levels.
Table S2. Transition probabilities for forbidden lines within the 4f2ground-state configuration of CeIIIa.
SLJ / S′L′J′ / λ (nm)b / Type / A′ (s-1) / SLJ / S′L′J′ / λ (nm) / Type / A′ (s-1)1I6 / 3H4 / 574 / E2 / 4.91×10-4 / 1D2 / 3H4 / 779 / E2 / 1.02×10-4
3H5 / 629 / M1 / 1.97×10-1 / 3F2 / 1102 / M1 / 2.86×10-1
3H6 / 700 / M1 / 2.00×10-1 / 3F3 / 1239 / M1 / 3.86×10-1
3F4 / 806 / E2 / 1.00×10-3 / 3F4 / 1278 / E2 / 1.50×10-3
1G4 / 971 / E2 / 8.49×10-4 / 1G4 / 1749 / E2 / 1.52×10-4
3P2 / 3F2 / 738 / M1+E2 / 3.74×10-3 / 1G4 / 3H4 / 1404 / M1 / 5.81×10-2
3F3 / 797 / M1+E2 / 5.33×10-2 / 3H5 / 1789 / M1 / 6.99×10-2
3F4 / 812 / E2 / 9.75×10-3 / 3F3 / 4245 / M1 / 1.04×10-1
1G4 / 981 / E2 / 6.36×10-3 / 3F4 / 4737 / M1 / 7.94×10-2
1D2 / 2231 / M1 / 2.32×10-1 / 3F4 / 3H4 / 1996 / M1 / 6.44×10-2
3P1 / 12660 / M1 / 6.23×10-3 / 3H5 / 2875 / M1 / 2.20×10-2
3P1 / 3F2 / 784 / M1+E2 / 2.00×10-2 / 3F3 / 40859 / M1 / 1.81×10-4
3F3 / 850 / E2 / 1.81×10-2 / 3F3 / 3H4 / 2099 / M1 / 2.50×10-3
1D2 / 2709 / M1 / 7.57×10-2 / 3F2 / 10005 / M1 / 2.52×10-2
3P0 / 21900 / M1 / 1.70×10-3 / 3H6 / 3H5 / 6256 / M1 / 9.20×10-2
3P0 / 3F2 / 813 / E2 / 3.52×10-2 / 3H5 / 3H4 / 6533 / M1 / 9.27×10-2
aOnly transitions with total vacuum emission ratesA′>1.0×10-4are listed.
bAll wavelengths in our table are vacuum wavelengths derived from our calculated energy levels.
Table S3. Transition probabilities for forbidden lines within the 4f2ground-state configuration of Nd Va.
SLJ / S′L′J′ / λ (nm)b / Type / A′ (s-1) / SLJ / S′L′J′ / λ (nm) / Type / A′ (s-1)3P2 / 3F2 / 463 / M1+E2 / 3.34×10-2 / 1D2 / 3F2 / 682 / M1 / 1.59
3F3 / 508 / M1+E2 / 3.98×10-1 / 3F3 / 783 / M1 / 1.95
3F4 / 522 / E2 / 3.71×10-2 / 3F4 / 817 / E2 / 6.62×10-3
1G4 / 658 / E2 / 2.17×10-2 / 1G4 / 1207 / E2 / 3.91×10-4
1D2 / 1444 / M1 / 1.26 / 1G4 / 3H4 / 815 / M1 / 3.48×10-1
3P1 / 6306 / M1 / 4.86×10-2 / 3H5 / 1060 / M1 / 4.07×10-1
1I6 / 3H4 / 383 / E2 / 1.93×10-3 / 3F3 / 2230 / M1 / 6.66×10-1
3H5 / 430 / M1 / 1.06 / 3F4 / 2527 / M1 / 5.12×10-1
3H6 / 492 / M1 / 9.87×10-1 / 3F4 / 3H4 / 1203 / M1 / 3.57×10-1
3F4 / 563 / E2 / 2.28×10-3 / 3H5 / 1826 / M1 / 9.89×10-2
1G4 / 724 / E2 / 1.77×10-3 / 3F3 / 18981 / M1 / 1.89×10-3
3P1 / 3F2 / 500 / M1+E2 / 1.04×10-1 / 3F3 / 3H4 / 1284 / M1 / 1.56×10-2
3F3 / 552 / E2 / 7.03×10-2 / 3F2 / 5288 / M1 / 1.70×10-1
1D2 / 1872 / M1 / 3.46×10-1 / 3F2 / 3H4 / 1697 / E2 / 1.38×10-4
3P0 / 11872 / M1 / 1.07×10-2 / 3H6 / 3H5 / 3439 / M1 / 5.53×10-1
3P0 / 3F2 / 522 / E2 / 1.45×10-1 / 3H5 / 3H4 / 3527 / M1 / 5.86×10-1
1D2 / 3H4 / 487 / E2 / 4.75×10-4
aOnly transitions with total vacuum emission ratesA′>1.0×10-4are listed.
bAll wavelengths in our table are vacuum wavelengths derived from our calculated energy levels.
Table S4. Transition probabilities for forbidden lines within the 4f12ground-state configuration of Yb Va.
SLJ / S′L′J′ / λ (nm)b / Type / A′ (s-1) / SLJ / S′L′J′ / λ (nm) / Type / A′ (s-1)(3P,1D)2B / 3F4 / 270 / E2 / 1.25×10-1 / (3P,1D)2A / 3H4 / 591 / E2 / 2.55×10-3
3H4 / 348 / E2 / 8.04×10-2 / 3F3 / 669 / M1 / 24.91
3F3 / 374 / M1+E2 / 30.47 / 3F2 / 692 / M1 / 15.65
3F2 / 381 / M1+E2 / 4.24×10-2 / 1G4 / 3H6 / 413 / E2 / 2.97×10-3
1G4 / 528 / E2 / 2.07×10-2 / 3F4 / 553 / M1 / 2.64
(3P,1D)2A / 847 / M1 / 19.83 / 3H5 / 684 / M1 / 35.74
3P1 / 4906 / M1 / 6.58×10-2 / 3H4 / 1022 / M1 / 8.66
3P1 / 3F3 / 405 / E2 / 1.26×10-1 / 3F3 / 1279 / M1 / 9.28×10-1
3F2 / 413 / M1+E2 / 7.23 / 3F2 / 3F4 / 929 / E2 / 6.54×10-4
(3P,1D)2A / 1024 / M1 / 8.49 / 3F3 / 19771 / M1 / 3.51×10-3
3P0 / 7754 / M1 / 3.62×10-2 / 3F3 / 3F4 / 975 / M1 / 17.68
3P0 / 3F2 / 436 / E2 / 1.66×10-1 / 3H4 / 5093 / M1 / 5.50×10-2
1I6 / 3H6 / 256 / M1 / 17.23 / 3H4 / 3H6 / 694 / E2 / 1.18×10-3
3F4 / 304 / E2 / 1.31×10-2 / 3F4 / 1205 / M1 / 6.57
3H5 / 339 / M1 / 5.34 / 3H5 / 2070 / M1 / 2.10
3H4 / 406 / E2 / 3.69×10-3 / 3H5 / 3H6 / 1044 / M1 / 23.23
1G4 / 674 / E2 / 8.19×10-4 / 3F4 / 2885 / M1 / 8.26×10-2
(3P,1D)2A / 3F4 / 397 / E2 / 8.23×10-2
aOnly transitions with total vacuum emission ratesA′>1.0×10-4are listed.
bAll wavelengths in our table are vacuum wavelengths derived from our calculated energy levels.
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[*]Corresponding author: (Xiao-YuKuang), (Yau Yuen Yeung).