TABLE I
Isotopic constitution of enriched samples of dysprosium, erbium, and ytterbium, in percent.
Sample Isotope 156 158 160 161 162 163 164 160 Dy0.05 0.10 53.70 27.50 9.83 5.19 3.82 164 Dy0.02 0.02 0.02 0.40 1.34 5.55 92.71 162 164 166 167 168 170 166 Er0.01 0.01 99.97 0.02 0.01 0.01 170 Er0.05 0.10 1.03 0.96 1.94 96.07 168 170 171 172 173 174 176 170 Yb0.10 64.10 15.90 9.20 3.90 5.50 1.40 172 Yb0.01 0.15 2.57 91.50 3.46 2.02 0.28 174 Yb0.01 0.03 0.13 0.33 0.78 98.40 0.36 176 Yb0.01 0.05 0.32 0.52 0.56 2.12 96.43
TABLE II
Isotope-shift measurements in Dy i .
Wavelength (Å) Isotope shift Δν (164 − 160) (mK) Energy levels (K) J Even Odd J 7559.78 0 8 20 789 7565 8 7381.57 0 8 23 534 9991 9 7213.27 −86.7 10 26 752 12 892 10 6794.23 −71.0 6 26 387 11673 6 6103.37 0 6 24 899 8519 7
TABLE III
Isotope-shift measurements in Er i .
Wavelength (Å) Isotope shift Δν (170 − 166) (mK) Energy levels (K) J Even Odd J 8472.39 + 99.0 6 0 11 799 6 8312.90 0 8 19 723 7697 7 8181.90 0 7 19 915 7697 7 7847.52 0 7 19 915 7176 6 7355.34 −91.6 6 25 479 11 887 7 7109.60 −92.2 7 25 861 11 799 6 7101.23 −91.6 6 25 479 11 401 5 7001.44 −84.9 7 23 629 9350 8 6989.32 −93.4 7 25 861 11 557 8 6973.03 −85.7 7 26 136 11 799 6 6951.87 −88.7 8 26 268 11 887 7 6874.77 −89.4 9 26 099 11 557 8 6601.11 0 5 32 218 17 073 6 6537.82 −95.4 8 27 178 11 887 7 6432.53 −86.3 9 26 099 10 557 9 6388.18 −61.0 7 31 719 16 070 6 5968.68 −85.2 9 26 099 9350 8 5955.46 −82.5 7 26 136 9350 8 5933.50 −94.7 9 28 406 11 557 8 5906.67 −72.0 5 6958 23 883 4 5850.07 −61.5 4 5035 22 124 5 5784.66 −94.5 9 28 840 11 557 8 5752.53 −57.1 4 10 751 28 129 5 5748.64 −75.8 5 6958 24 348 4 5740.61 −26.9 4 5035 22 450 5 5698.95 −92.3 9 27 198 9655 10 5636.20 −95.3 6 29 138 11 401 5 5324.99 + 99.4 6 0 18 774 7 5297.96 0 6 34 055 15 185 5 5282.66 −90.6 7 30 482 11 557 8 5248.70 −90.6 8 28 397 9350 8 5229.33 0 5211.18 −92.8 9 28 839 9655 10 5203.10 0 6 26 910 7697 7 5180.96 −64.3 6 26 993 7697 7 5065.88 0 6 26 910 7176 6 5004.21 −84.9 10 28 598 8620 9 4973.29 −85.5 8 29 451 9350 8 4966.97 + 66.8 4 5035 25 162 5 4948.70 −86.5 7 32 001 11 799 6 4770.25 0 4738.99 0 5 6958 28 053 6 4735.34 −89.7 4718.69 0 8 38 343 17 157 7 4691.41 0 4 38 657 17 347 5 4691.27 −86.0 8 29 930 8620 9 4676.52 0 4602.06 0 7 38 797 17 073 6 4555.69 + 86.4 4 10 751 32 695 3 4526.42 0 6 38 407 16 321 6 4480.25 + 90.9 5 6958 29 272 5 4473.50 0 4422.51 0 5 6958 29 561 6 4413.74 0 10 31 270 8620 9 4413.51 0 7 32 001 9350 8 4390.23 −86.4 6 30 468 7697 7 4313.67 −87.0 8 32 525 9350 8 4305.91 −97.3 4251.08 −87.6 7 30 693 7176 6 4232.46 0 4220.98 + 70.1 5 6958 30 642 4 4211.87 0 4 38 921 15 185 5 4205.31 0 2 13 097 36 870 2 4197.42 −91.9 6 35 218 11 401 5 4140.38 0 4118.55 0 4 10 751 35 024 4 4024.37 0 4 10 751 35 592 5 3951.48 0 2 13 097 38 397 3 3905.40 0 6 0 25 598 7 3855.90 0 4 5035 30 962 4 3792.79 −108.3 6 34 055 7697 7 3761.99 −89.0 6 33 750 7176 6 3756.05 −87.4 6 34 313 7697 7 3747.43 −101.9 6 33 853 7176 6 3638.68 −95.6
TABLE IV
Isotope–shift measurements in Yb I.
Wavelength (Å) Isotope shift Δν (176 − 172) (mK) Energy levels (K) Configurations J Even Odd J Even Odd 7699.48 + 26.2 1 32 694 19 710 2 4f 14 6s 7s 4f 14 6s 6p 6799.60 + 27.0 1 32 694 17 992 1 4f 14 6s 7s 4f 14 6s 6p 6768.70 0 2 39 838 25 068 1 4f 14 6s 6d 4f 14 6s 6p 6678.17 0 2 27 677 42 647 2 4f 14 5d 6s 6667.82 −15.8 2 40 061 25 068 1 4f 14 6s 6d 4f 14 6s 6p 6643.55 0 2 27 677 42 725 2 4f 14 5d 6s 6489.06 + 27.0 1 32 694 17 288 0 4f 14 6s 7s 4f 14 6s 6p 6417.91 + 33.4 2 27 677 43 254 3 4f 14 5d 6s 6400.35 + 37.8 2 27 677 43 297 3 4f 14 5d 6s 6111.27 + 27.2 0 34 350 17 992 1 4f 14 6s 7s 4f 14 6s 6p 6059.22 −77.7 6 43 814 27 314 6 4f 13 5d 6s 2 6048.44 −82.1 3 44 713 28 184 4 4f 13 5d 6s 2 5803.44 −75.1 5 45 410 28 184 4 4f 13 5d 6s 2 5719.99 −50.8 2 27 677 45 155 2 4f 14 5d 6s 5699.95 −76.4 4 44 984 27 445 3 4f 13 5d 6s 2 5586.36 0 2 24 751 42 647 2 4f 14 5d 6s 5556.47 −64.8 0 0 17 992 1 4f 14 6s 2 4f 14 6s 6p 5539.05 0 5505.49 + 27.8 1 24 489 42 647 2 4f 14 5d 6s 5481.93 0 1 24 489 42 725 2 4f 14 5d 6s 5363.66 −69.9 3 41 827 23 188 2 4f 13 5d 6s 2 5351.29 0 2 24 751 43 433 2 4f 14 5d 6s 4f 14 6s 5f 5277.04 0 1 24 489 43 433 2 4f 14 5d 6s 4f 14 6s 5f 5244.11 + 46.8 2 24 751 43 815 3 4f 14 5d 6s 5211.60 −32.3 3 25 270 44 453 3 4f 14 5d 6s 5196.09 −77.9 6 46 554 27 314 6 4f 13 5d 6s 2 5074.34 0 2 24 751 44 453 3 4f 14 5d 6s 5027.67 −65.9 3 25 270 45 155 2 4f 14 5d 6s 4974.16 0 1 39 808 19 710 2 4f 14 6s 6s 4f 14 6s 6p 4966.90 0 2 39 838 19 710 2 4f 14 6s 6s 4f 14 6s 6p 4935.50 0 3 39 966 19 710 2 4f 14 6s 6s 4f 14 6s 6p 4931.95 0 2 45 338 25 068 1 4f 14 6s 6p 4912.36 0 2 40 061 19 710 2 4f 14 6s 6d 4f 14 6s 6p 4894.60 0 4853.83 −83.1 5 47 911 27 314 6 4f 13 5d 6s 2 4837.46 −65.4 1 24 489 45 155 2 4f 14 5d 6s 4816.43 + 47.3 4781.87 0 4762.59 −77.5 4720.79 −79.9 6 47 036 25 859 5 4f 13 5d 6s 2 4718.56 0 4714.70 0 2 24 751 45 956 2 4f 14 5d 6s 4f 14 6s 6f 4687.59 0 2 24 751 46 078 1 4f 14 5d 6s 4f 14 6s 9p 4684.27 −79.4 4 48 787 27 445 3 4f 13 5d 6s 2 4651.67 −77.0 6 48 806 27 314 6 4f 13 5d 6s 2 4650.05 + 58.1 2 24 751 46 251 3 4f 14 5d 6s 4644.54 −73.5 3 44 713 23 188 2 4f 13 5d 6s 2 4624.41 0 2 24 751 46 370 1 4f 14 5d 6s 4f 14 6s 9p 4590.83 −77.4 5 47 636 25 859 5 4f 13 5d 6s 2 4589.21 0 3 25 270 47 055 2 4f 14 5d 6s 4582.36 0 1 39 808 17 992 1 4f 14 6d 6d 4f 14 6s 6p 4576.21 0 2 39 838 17 992 1 4f 14 6s 6d 4f 14 6s 6p 4568.85 0 1 24 489 46 370 1 4f 14 5d 6s 4f 14 6s 9p 4567.37 + 71.0 2 39 880 17 992 1 4f 14 6s 6p 4563.95 0 1 41 615 19 710 2 4f 14 6s 8s 4f 14 6s 6p 4533.51 −77.0 5 47 911 25 859 5 4f 13 5d 6s 2 4531.33 0 4529.87 0 2 40 061 17 992 1 4f 14 6s 6d 4f 14 6s 6p 4513.40 −107.0 2 45 338 23 188 2 4f 13 5d 6s 2 4503.64 −74.5 5 48 057 25 859 5 4f 13 5d 6s 2 4488.28 −69.2 3 45 462 23 188 2 4f 13 5d 6s 2 4482.42 0 2 24 751 47 055 2 4f 14 5d 6s 4439.19 + 16.0 1 39 808 17 288 0 4f 14 6s 6s 4f 14 6s 6p 4430.21 0 1 24 489 47 055 2 4f 14 5d 6s 4427.39 0 2 24 751 47 332 1 4f 14 5d 6s 4398.96 + 65.1 1 42 436 19 710 2 4f 14 6s 6p 4393.68 −31.8 2 47 821 25 068 1 4f 14 6p 2 4f 14 6s 6p 4309.82 0 4305.97 0 3 25 270 48 488 3 4f 14 5d 6s 4277.74 0 1 24 489 47 859 1 4f 14 5d 6s 4251.52 + 69.3 2 43 224 19 710 2 4f 14 6s 6p 4231.97 0 1 41 615 17 992 1 4f 14 6s 8s 4f 14 6s 6p 4226.15 0 4218.69 0 2 24 751 48 449 2 4f 14 5d 6s 4174.56 0 0 41 939 17 992 1 4f 14 6s 8s 4f 14 6s 6p 4149.07 −53.2 1 43 805 19 710 2 4f 14 6p 2 4f 14 6s 6p 4109.57 0 1 41 615 17 288 0 4f 14 6s 8s 4f 14 6s 6p 4089.68 −37.7 1 42 437 17 992 1 4f 14 6p 2 4f 14 6s 6p 4063.72 0 1 44 311 19 710 2 4f 14 6s 7d 4f 14 6s 6p 4063.45 0 2 44 313 19 710 2 4f 14 6s 7d 4f 14 6s 6p 4052.28 0 3 44 380 19 710 2 4f 14 6s 7d 4f 14 6s 6p 4052.07 0 3 47 860 23 188 2 4f 14 5d 2 4f 13 5d 6s 2 3990.88 0 2 44 760 19 710 2 4f 14 6p 2 4f 14 6s 6p 3987.99 −37.0 0 0 25 068 1 4f 14 6s 2 4f 14 6s 6p 3975.28 + 63.6 1 42 436 17 288 0 4f 14 6s 6p 3872.85 −48.7 1 43 805 17 992 1 4f 14 6p 2 4f 14 6s 6p 3791.74 0 2 44 357 17 992 1 4f 14 6s 7d 4f 14 6s 6p 3770.10 −41.2 1 43 805 17 288 0 4f 14 6p 2 4f 14 6s 6p 3464.36 + 64.4 0 0 28 857 1 4f 14 6s 2 4f 13 5d 6s 2
TABLE V
Average isotope shifts for different electronic configurations in dysprosium, erbium, and ytterbium.
Dy i Δν (164 − 160) n = 10 Er i Δν (170 − 166) n = 12 Yb i Δν (176 − 172) n = 14 Type of transition Configurations Isotope shift (mK) No.a Isotope shift (mK) No. Isotope shift (mK) No. 8s → 6p f n 6s 8s → f n 6s 6p ⋯ ⋯ 0 4 7s → 6p f n 6s 7s → f n 6s 6p ⋯ + 28 ± 13 5 + 27 ± 1 4 6p → 6s f n 6s 6p → f n 6s 2 −65± 5 25 −65 ± 8 23 −65 1 f n −1 5d 6s 6p → f n −1 5d 6s 2 −76 ± 6 7 −89 ± 4 82 −77 ± 3b 15 f n 6p 2 → f n 6s 6p ⋯ ⋯ −48 ± 7 5 6p → 5d f n −1 6s 2 6p → f n −1 5d 6s 2 0 3 0 8 ⋯ f n 6s 9p → f n 5d 6s ⋯ ⋯ 0 3 6d → 6p f n 6s 7d → f n 6s 6p ⋯ ⋯ 0 4 f n 6s 6d → f n 6s 6p ⋯ 0 3 0 10 5d → 4f f n −1 5d 6s 2 → f n 6s 2 + 80 ± 4 19 + 94 ± 3 21 + 64 1 f n −1 5d 6s 6p → f n 6s 6p ⋯ ⋯ + 67 ± 3b 4 4f → 6s f n 5d 6s → f n −1 5d 6s 2 −96 1 −137 ± 10 2 ⋯ 5d 2 → 4f , 6s f n −1 5d 2 6s → f n 6s 2 −23 ± 10 6 −20 ± 10 10 ⋯
a This column gives the number of different lines used in determing the average isotope shift.
b Based on
f 13 5
d 6
s 6
p assignments made in this paper.
TABLE VI
4f 13 5d 6s 6p configuration assignments in Yb i .
Even level (K) J value39 880 2 41 827 3 42 436 1 43 224 2 43 814 6 44 713 3 44 984 4 45 338 2 45 410 5 45 462 3 46 554 6 47 036 6 47 636 5 47 911 5 48 057 5 48 787 4 48 806 6