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The Dirac-Hartree-Fock approximation is adopted to calculate the mass shift and the field shift for the 5d 106s 2S 1/2→5d 96s 2 2D 5/2clock transition in Hg +. It is found that the field shift is much larger than the mass shift so that the latter can be neglected in the isotope shift. In addition, we estimate that the isotope shifts of the levels related to the 5d 106s 2S 1/2→5d 96s 2 2D 5/2clock transition of Hg +is on the order of about 10 4GHz, while the hyperfine structure splitting is in a range of 1−10 GHz. However, the isotope shift of the 5d 106s 2S 1/2→5d 96s 2 2D 5/2clock transition is on the same order of magnitude as the hyperfine structure splitting. Therefore, the hyperfine structure splitting must be taken into account for predicting the frequency shifts of the clock transition between different isotopes. On the basis of these results, we perform a multi-configuration Dirac-Hartree-Fock calculation on the field shift of the 5d 106s 2S 1/2→5d 96s 2 2D 5/2clock transition in Hg +and the hyperfine interaction constants of the upper and the lower levels involved. In order to give accurate theoretical results of these physical quantities, we systematically consider the main electron correlations in the atomic system by using the active space method. The restricted single and double (SrD) excitation method is used to capture the correlation between the 5d and the 6s valence electrons, and the correlation between the 3s, 3p, 3d, 4s, 4p, 4d, 5s, 5p, and 5d core and the valence electrons. The isotope shifts and hyperfine structure splitting for this transition of several stable mercury isotopes are given. In particular, the uncertainty of the calculated isotope shift between 199Hg +and 198Hg +is about 2%, compared with the experimental measurement available. Using these results, we predict the absolute frequency values of this transition for seven mercury isotopes, which provides theoretical reference data for experiments. Moreover, the calculated isotope shifts and hyperfine structures are also useful for studying the structure, property and nucleon interaction of mercury nucleus.
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Keywords:
- hyperfine structure/
- isotope shift/
- multi-configuration Dirac-Hartree-Fock method/
- mercury ion clock
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Isotopes’ mass number Relative atomic mass[6] Abundance[7] R/fm[8] I/$\hbar$ $\mu $/nm[9] Q/barn[9] 196 195.9658326 (32) 0.15% 5.4385 0+ – – 198 197.96676860 (52) 10.04% 5.4463 0+ – – 199 198.96828064 (46) 16.94% 5.4474 1/2– +0.5058855(9) – 200 199.96832659 (47) 23.14% 5.4551 0+ – – 201 200.97030284 (69) 13.17% 5.4581 3/2– –0.5602257(14) +0.387(6) 202 201.97064340 (69) 29.74% 5.4648 0+ – – 204 203.97349398 (53) 6.82% 5.4744 0+ – – 
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n Active orbitals Virtual orbitals NCF Energy eigenvalue/104Hartrees DF 1/1 –1.964857825739/–1.964840329639 7 5d6s 7s, 6p, 6d, 5f, 5g 310/1631 –1.964887721767/–1.964870006459 8 5spd6s 8s, 7p, 7d, 6f, 6g 4047/19457 –1.964907829871/–1.964890991924 9 4spdf5spd6s 9s, 8p, 8d, 7f, 7g 29884/151235 –1.964927346267/–1.964910124355 10 3spd4spdf5spd6s 10s, 9p, 9d, 8f, 7g 69579/334460 –1.964929839430/–1.964912598231 11 3spd4spdf5spd6s 11s, 10p, 10d, 9f, 7g 103101/480763 –1.964930723063/–1.964913507368 DownLoad:
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n 196Hg+ 198Hg+ 200Hg+ 201Hg+ 202Hg+ 204Hg+ DF –9.01296 –1.11476 7.80962 10.8553 17.6634 27.4329 7 –9.20985 –1.13911 7.98023 11.0925 18.0493 28.0321 8 –8.81504 –1.09028 7.63813 10.6169 17.2755 26.8305 9 –9.11351 –1.12720 7.89674 10.9764 17.8605 27.7389 10 –9.12483 –1.12860 7.90656 10.9901 17.8827 27.7734 11 –9.14646 –1.13127 7.92530 11.0161 17.9250 27.8392 DownLoad:
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n 199A1/2 199A5/2 201A1/2 201A5/2 201B5/2 DF 36812.0 986.665 –13585.7 –364.216 796.132 7 39090.5 1263.67 –14426.7 –466.447 755.219 8 38761.2 795.021 –14305.1 –293.490 765.173 9 40556.1 951.973 –14967.5 –353.908 936.169 10 40967.0 951.669 –15119.2 –351.307 961.161 11 41133.9 963.552 –15180.8 –355.692 966.809 Ref. [38] 963.5 –355.7 839.4 Ref. [37] 40460 –14960 Ref. [35] 42366 1315 –15527 –482 859 Ref. [36] 41477 –15311 DownLoad:
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[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38]
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