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Hg+离子5d106s 2S1/2→5d96s2 2D5/2钟跃迁同位素位移和超精细结构的理论研究

张祥 卢本全 李冀光 邹宏新

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Hg+离子5d106s 2S1/2→5d96s2 2D5/2钟跃迁同位素位移和超精细结构的理论研究

张祥, 卢本全, 李冀光, 邹宏新

Theoretical investigation on hyperfine structure and isotope shift for 5d106s 2S1/2→5d96s2 2D5/2 clock transition in Hg+

Zhang Xiang, Lu Ben-Quan, Li Ji-Guang, Zou Hong-Xin
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  • 本文首先在Dirac-Hartree-Fock近似下理论评估了Hg+离子5d106s 2S1/2→5d96s2 2D5/2钟跃迁的质量位移(mass shift, MS)和场位移(field shift, FS)在其同位素位移(isotope shift, IS)中的相对贡献, 发现MS远小于FS而可以被忽略. 在此基础上, 通过系统地考虑该原子体系中主要的电子关联效应, 计算了这条钟跃迁FS的精确值以及涉及到的上下两个能级的超精细结构常数, 并得到了几种稳定汞同位素离子该跃迁的IS和超精细结构分裂. 其中, 计算的199Hg+198Hg+离子之间的钟跃迁频率偏移与已有实验测量值相比误差为2%左右. 最终, 本文给出了汞离子7种常见同位素该谱线的绝对频率值, 为实验上的谱线测量提供了有效的理论依据.
    The Dirac-Hartree-Fock approximation is adopted to calculate the mass shift and the field shift for the 5d106s 2S1/2→5d96s2 2D5/2 clock 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 5d106s 2S1/2→5d96s2 2D5/2 clock transition of Hg+ is on the order of about 104 GHz, while the hyperfine structure splitting is in a range of 1−10 GHz. However, the isotope shift of the 5d106s 2S1/2→5d96s2 2D5/2 clock 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 5d106s 2S1/2→5d96s2 2D5/2 clock 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.
      通信作者: 李冀光, li_jiguang@iapcm.ac.cn ; 邹宏新, hxzou@nudt.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 11604385, 91536106, 11204374, 11874090)和国防科技大学研究项目(批准号: ZK17-03-11)资助的课题.
      Corresponding author: Li Ji-Guang, li_jiguang@iapcm.ac.cn ; Zou Hong-Xin, hxzou@nudt.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11604385, 91536106, 11204374, 11874090) and the Research Project of National University of Defense Technology, China (Grant No.ZK17-03-11).
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    Prestage J D, Weaver G L 2007 Proc. IEEE 95 2235Google Scholar

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    Tjoelker R L, Prestage J D, Burt E A, Chen P, Chong Y J, Chung S K, Diener W, Ely T, Enzer D G, Mojaradi H, Okino C, Pauken M, Robison D, Swenson B L, Tucker B, Wang R 2016 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 63 1034Google Scholar

    [3]

    Prestage J D, Chung S K, Thompson R J, Neal P M 2009 IEEE International Frequency Control Symposium Joint with the 22nd European Frequency and Time forum Besancon, France, April 20-24, 2009 p54–7

    [4]

    Rosenband T, Hume D B, Schmidt P O, Chou C W, Brusch A, Lorini L, Oskay W H, Drullinger R E, Fortier T M, Stalnaker J E, Diddams S A, Swann W C, Newbury N R, Itano W M, Wineland D J, Bergquist J C 2008 Science 319 1808Google Scholar

    [5]

    Larigani S T, Burt E A, Lea S N, Prestage J D, Tjoelker R L 2009 International Frequency Control Symposium Joint with the 22nd European Frequency and Time forum Besancon, France, April 20-24, 2009 pp774–777

    [6]

    Coursey J S, Schwab D J, Tsai J J, Dragoset R A http://physics.nist.gov/Comp [2018-10-27]

    [7]

    Zucker M A, Kishore A R, Sukumar R, Dragoset R A http://physics.nist.gov/EDI [2018-10-27]

    [8]

    Angeli I, Marinova K P 2013 At. Data Nucl. Data Tables 99 69Google Scholar

    [9]

    Stone N J 2005 At. Data Nucl. Data Tables 90 75Google Scholar

    [10]

    Prestage J D, Janik G R, Dick G J, Maleki L 1991 Conference on Precision Electromagnetic Measurements Ottawa, Ontario, Canada, Canada, June 11-14, 1990 pp270–271

    [11]

    Tjoelker R L, Prestage J D, Maleki L 1996 Telecommun. Data Acquis. Prog. Rep. 126 1

    [12]

    Rafac R J, Young B C, Beall J A, Itano W M, Wineland D J, Bergquist J C 2000 Phys. Rev. Lett. 85 2462Google Scholar

    [13]

    Bergquist J C, Rafac R J, Young B, Beall J A, Itano W M, Wineland D J 2001 Proc. SPIE 4269 1Google Scholar

    [14]

    Oskay W H, Diddams S A, Donley E A, Fortier T M, Heavner T P, Hollberg L, Itano W M, Jefferts S R, Delaney M J, Kim K, Levi F, Parker T E, Bergquist J C 2006 Phys. Rev. Lett. 97 020801Google Scholar

    [15]

    Bergquist J C, Wineland D J, Itano W M, Hemmati H, Daniel H U, Leuchs G 1985 Phys. Rev. Lett. 55 1567Google Scholar

    [16]

    Matveev O I, Smith B W, Winefordner J D 1998 Opt. Lett. 23 304Google Scholar

    [17]

    Zou H X, Wu Y, Chen G Z, Shen Y, Liu Q 2015 Chinese Phys. Lett. 32 054207Google Scholar

    [18]

    Cheal B, Cocolios T E, Fritzsche S 2012 Phys. Rev. A 86 042501Google Scholar

    [19]

    Grant I P 2007 Relativistic Quantum Theory of Atoms and Molecules (New York: Springer) pp259-388

    [20]

    Li J G, Jönsson P, Godefroid M, Dong C Z, Gaigalas G 2012 Phys. Rev. A 86 052523Google Scholar

    [21]

    Fullerton L W, Rinker G A 1976 Phys. Rev. A 13 1283Google Scholar

    [22]

    Dyall K G, Grant I P, Johnson C T, Parpia F A, Plummer E P 1989 Comput. Phys. Commun. 55 425Google Scholar

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    Jönsson P, Gaigalas G, Bieroń J, Fischer C F, Grant I P 2013 Comput. Phys. Commun. 184 2197Google Scholar

    [24]

    McDaniel E W, McDowell M R C 1975 Case Studies in Atomic Physics Ⅳ (Amsterdam: North-Holland) pp197–298

    [25]

    Jönsson P, Parpia F A, Fischer C F 1996 Comput. Phys. Commun. 96 301Google Scholar

    [26]

    Tupitsyn I I, Shabaev V M, Crespo López-Urrutia J R, Draganić I, Orts R S, Ullrich J 2003 Phys. Rev. A 68 022511Google Scholar

    [27]

    Filippin L, Beerwerth R, Ekman J, Fritzsche S, Godefroid M, Jönsson P 2016 Phys. Rev. A 94 062508Google Scholar

    [28]

    Shabaev V M 1985 Theor. Math. Phys. 63 588Google Scholar

    [29]

    Palmer C W P 1987 J. Phys. B At. Mol. Phys. 20 5987Google Scholar

    [30]

    Shabaev V M, Artemyev A N 1994 J. Phys. B At. Mol. Opt. Phys. 27 1307Google Scholar

    [31]

    Jönsson P, Froese C F 1997 Comput. Phys. Commun. 100 81Google Scholar

    [32]

    Nazé C, Gaidamauskas E, Gaigalas G, Godefroid M, Jönsson P 2013 Comput. Phys. Commun. 184 2187Google Scholar

    [33]

    Blundell S A, Baird P E G, Palmer C W P, Stacey D N, Woodgate G K 1987 J. Phys. B: At. Mol. Phys. 20 3663Google Scholar

    [34]

    Fischer C F, Brage T, Jönsson P 1997 Computational Atomic Structure - An MCHF Approach (London: Institute of Physics Publishing) pp67-86

    [35]

    Brage T, Proffitt C, Leckrone D S 1999 Astrophys. J. 513 524Google Scholar

    [36]

    Simmons M, Safronova U I, Safronova M S 2011 Phys. Rev. A 84 052510Google Scholar

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    Guern Y, Méhu A B, Abjean R, Gilles A J 1976 Phys. Scr. 14 273Google Scholar

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    Itano W M 2006 Phys. Rev. A 73 022510Google Scholar

  • 图 1  汞同位素离子5d106s 2S1/2→5d96s2 2D5/2跃迁相对于199Hg+离子的FS和MS随质量数变化的趋势

    Fig. 1.  Trends of field shift and mass shift for the 5d106s 2S1/2→5d96s2 2D5/2 transition in mercury isotope ions with respect to 199Hg+ as the increase of mass number.

    图 2  199Hg+198Hg+离子的超精细能级结构图

    Fig. 2.  Hyperfine level structure diagram of 199Hg+ and 198Hg+.

    表 1  7种天然汞同位素及相关参数

    Table 1.  Related parameters of seven natural mercury isotopes.

    Isotopes’ mass numberRelative atomic mass[6]Abundance[7]R/fm[8]I/$\hbar$$\mu $/nm[9]Q/barn[9]
    196195.9658326 (32)0.15%5.43850+
    198197.96676860 (52)10.04%5.44630+
    199198.96828064 (46)16.94%5.44741/2–+0.5058855(9)
    200199.96832659 (47)23.14%5.45510+
    201200.97030284 (69)13.17%5.45813/2––0.5602257(14)+0.387(6)
    202201.97064340 (69)29.74%5.46480+
    204203.97349398 (53)6.82%5.47440+
    下载: 导出CSV

    表 2  电子关联对能量本征值的影响

    Table 2.  Effect of electron correlations on energy eigenvalues.

    nActive orbitalsVirtual orbitalsNCFEnergy eigenvalue/104 Hartrees
    DF1/1–1.964857825739/–1.964840329639
    75d6s7s, 6p, 6d, 5f, 5g310/1631–1.964887721767/–1.964870006459
    85spd6s8s, 7p, 7d, 6f, 6g4047/19457–1.964907829871/–1.964890991924
    94spdf5spd6s9s, 8p, 8d, 7f, 7g29884/151235–1.964927346267/–1.964910124355
    103spd4spdf5spd6s10s, 9p, 9d, 8f, 7g69579/334460–1.964929839430/–1.964912598231
    113spd4spdf5spd6s11s, 10p, 10d, 9f, 7g103101/480763–1.964930723063/–1.964913507368
    下载: 导出CSV

    表 3  汞同位素离子相对199Hg+离子5d106s 2S1/2→5d96s2 2D5/2钟跃迁的场位移 (单位: GHz)受电子关联的影响

    Table 3.  Effect of electron correlations on the FS (in GHz) of the 5d106s 2S1/2→5d96s2 2D5/2 transition in mercury isotope ions (relative to 199Hg+).

    n196Hg+198Hg+200Hg+201Hg+202Hg+204Hg+
    DF–9.01296–1.114767.8096210.855317.663427.4329
    7–9.20985–1.139117.9802311.092518.049328.0321
    8–8.81504–1.090287.6381310.616917.275526.8305
    9–9.11351–1.127207.8967410.976417.860527.7389
    10–9.12483–1.128607.9065610.990117.882727.7734
    11–9.14646–1.131277.9253011.016117.925027.8392
    下载: 导出CSV

    表 4  199Hg+201Hg+ 离子5d106s 2S1/2和5d96s2 2D5/2态的磁偶极(A单位: MHz)和电四极(B单位: MHz)超精细结构常数

    Table 4.  Magnetic dipole A (in MHz) and electric quadrupole B (in MHz) hyperfine interaction constants for the 5d106s 2S1/2 and 5d96s2 2D5/2 states of 199Hg+ and 201Hg+.

    n199A1/2199A5/2201A1/2201A5/2201B5/2
    DF36812.0986.665–13585.7–364.216796.132
    739090.51263.67–14426.7–466.447755.219
    838761.2795.021–14305.1–293.490765.173
    940556.1951.973–14967.5–353.908936.169
    1040967.0951.669–15119.2–351.307961.161
    1141133.9963.552–15180.8–355.692966.809
    Ref. [38]963.5–355.7839.4
    Ref. [37]40460–14960
    Ref. [35]423661315–15527–482859
    Ref. [36]41477–15311
    下载: 导出CSV

    表 5  汞同位素离子5d106s 2S1/2→5d96s2 2D5/2跃迁谱线的绝对频率值

    Table 5.  Absolute frequency values of the 5d106s 2S1/2→5d96s2 2D5/2 transition in mercury isotope ions.

    Ions196Hg+198Hg+199Hg+200Hg+201Hg+202Hg+204Hg+
    ν/GHz1064683.301064691.31*1064721.61[14]1064700.371064719.891064710.371064720.28
    *Experiment value is 1064691.95 GHz[15].
    下载: 导出CSV
  • [1]

    Prestage J D, Weaver G L 2007 Proc. IEEE 95 2235Google Scholar

    [2]

    Tjoelker R L, Prestage J D, Burt E A, Chen P, Chong Y J, Chung S K, Diener W, Ely T, Enzer D G, Mojaradi H, Okino C, Pauken M, Robison D, Swenson B L, Tucker B, Wang R 2016 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 63 1034Google Scholar

    [3]

    Prestage J D, Chung S K, Thompson R J, Neal P M 2009 IEEE International Frequency Control Symposium Joint with the 22nd European Frequency and Time forum Besancon, France, April 20-24, 2009 p54–7

    [4]

    Rosenband T, Hume D B, Schmidt P O, Chou C W, Brusch A, Lorini L, Oskay W H, Drullinger R E, Fortier T M, Stalnaker J E, Diddams S A, Swann W C, Newbury N R, Itano W M, Wineland D J, Bergquist J C 2008 Science 319 1808Google Scholar

    [5]

    Larigani S T, Burt E A, Lea S N, Prestage J D, Tjoelker R L 2009 International Frequency Control Symposium Joint with the 22nd European Frequency and Time forum Besancon, France, April 20-24, 2009 pp774–777

    [6]

    Coursey J S, Schwab D J, Tsai J J, Dragoset R A http://physics.nist.gov/Comp [2018-10-27]

    [7]

    Zucker M A, Kishore A R, Sukumar R, Dragoset R A http://physics.nist.gov/EDI [2018-10-27]

    [8]

    Angeli I, Marinova K P 2013 At. Data Nucl. Data Tables 99 69Google Scholar

    [9]

    Stone N J 2005 At. Data Nucl. Data Tables 90 75Google Scholar

    [10]

    Prestage J D, Janik G R, Dick G J, Maleki L 1991 Conference on Precision Electromagnetic Measurements Ottawa, Ontario, Canada, Canada, June 11-14, 1990 pp270–271

    [11]

    Tjoelker R L, Prestage J D, Maleki L 1996 Telecommun. Data Acquis. Prog. Rep. 126 1

    [12]

    Rafac R J, Young B C, Beall J A, Itano W M, Wineland D J, Bergquist J C 2000 Phys. Rev. Lett. 85 2462Google Scholar

    [13]

    Bergquist J C, Rafac R J, Young B, Beall J A, Itano W M, Wineland D J 2001 Proc. SPIE 4269 1Google Scholar

    [14]

    Oskay W H, Diddams S A, Donley E A, Fortier T M, Heavner T P, Hollberg L, Itano W M, Jefferts S R, Delaney M J, Kim K, Levi F, Parker T E, Bergquist J C 2006 Phys. Rev. Lett. 97 020801Google Scholar

    [15]

    Bergquist J C, Wineland D J, Itano W M, Hemmati H, Daniel H U, Leuchs G 1985 Phys. Rev. Lett. 55 1567Google Scholar

    [16]

    Matveev O I, Smith B W, Winefordner J D 1998 Opt. Lett. 23 304Google Scholar

    [17]

    Zou H X, Wu Y, Chen G Z, Shen Y, Liu Q 2015 Chinese Phys. Lett. 32 054207Google Scholar

    [18]

    Cheal B, Cocolios T E, Fritzsche S 2012 Phys. Rev. A 86 042501Google Scholar

    [19]

    Grant I P 2007 Relativistic Quantum Theory of Atoms and Molecules (New York: Springer) pp259-388

    [20]

    Li J G, Jönsson P, Godefroid M, Dong C Z, Gaigalas G 2012 Phys. Rev. A 86 052523Google Scholar

    [21]

    Fullerton L W, Rinker G A 1976 Phys. Rev. A 13 1283Google Scholar

    [22]

    Dyall K G, Grant I P, Johnson C T, Parpia F A, Plummer E P 1989 Comput. Phys. Commun. 55 425Google Scholar

    [23]

    Jönsson P, Gaigalas G, Bieroń J, Fischer C F, Grant I P 2013 Comput. Phys. Commun. 184 2197Google Scholar

    [24]

    McDaniel E W, McDowell M R C 1975 Case Studies in Atomic Physics Ⅳ (Amsterdam: North-Holland) pp197–298

    [25]

    Jönsson P, Parpia F A, Fischer C F 1996 Comput. Phys. Commun. 96 301Google Scholar

    [26]

    Tupitsyn I I, Shabaev V M, Crespo López-Urrutia J R, Draganić I, Orts R S, Ullrich J 2003 Phys. Rev. A 68 022511Google Scholar

    [27]

    Filippin L, Beerwerth R, Ekman J, Fritzsche S, Godefroid M, Jönsson P 2016 Phys. Rev. A 94 062508Google Scholar

    [28]

    Shabaev V M 1985 Theor. Math. Phys. 63 588Google Scholar

    [29]

    Palmer C W P 1987 J. Phys. B At. Mol. Phys. 20 5987Google Scholar

    [30]

    Shabaev V M, Artemyev A N 1994 J. Phys. B At. Mol. Opt. Phys. 27 1307Google Scholar

    [31]

    Jönsson P, Froese C F 1997 Comput. Phys. Commun. 100 81Google Scholar

    [32]

    Nazé C, Gaidamauskas E, Gaigalas G, Godefroid M, Jönsson P 2013 Comput. Phys. Commun. 184 2187Google Scholar

    [33]

    Blundell S A, Baird P E G, Palmer C W P, Stacey D N, Woodgate G K 1987 J. Phys. B: At. Mol. Phys. 20 3663Google Scholar

    [34]

    Fischer C F, Brage T, Jönsson P 1997 Computational Atomic Structure - An MCHF Approach (London: Institute of Physics Publishing) pp67-86

    [35]

    Brage T, Proffitt C, Leckrone D S 1999 Astrophys. J. 513 524Google Scholar

    [36]

    Simmons M, Safronova U I, Safronova M S 2011 Phys. Rev. A 84 052510Google Scholar

    [37]

    Guern Y, Méhu A B, Abjean R, Gilles A J 1976 Phys. Scr. 14 273Google Scholar

    [38]

    Itano W M 2006 Phys. Rev. A 73 022510Google Scholar

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出版历程
  • 收稿日期:  2018-12-04
  • 修回日期:  2018-12-22
  • 上网日期:  2019-02-01
  • 刊出日期:  2019-02-20

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