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类铝离子钟跃迁能级的超精细结构常数和朗德g因子

王霞 贾方石 姚科 颜君 李冀光 吴勇 王建国

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类铝离子钟跃迁能级的超精细结构常数和朗德g因子

王霞, 贾方石, 姚科, 颜君, 李冀光, 吴勇, 王建国

Hyperfine interaction constants and Landé g factors of clock states of Al-like ions

Wang Xia, Jia Fang-Shi, Yao Ke, Yan Jun, Li Ji-Guang, Wu Yong, Wang Jian-Guo
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  • 本文利用多组态Dirac-Hartree-Fock方法计算了类铝等电子序列从Si+到Kr23+离子基组态3s23p 2P1/2, 3/2能级的超精细结构常数和朗德g因子. 通过系统评估电子关联效应对Si+和Co14+离子中所关心原子参数的影响, 尤其是与内壳层电子相关的关联效应, 构建了可靠精确的计算模型, 除Si+离子外, 超精细结构常数和g因子的计算误差分别控制在1%左右和10–5的量级. 此外, 进一步分析了超精细结构常数中电子部分矩阵元和g因子随原子序数Z的变化规律, 并拟合了这些物理量与Z的定量依赖关系, 利用拟合公式可以快速计算类铝离子在14 ≤ Z ≤ 54区间内任意同位素的超精细结构常数和g因子.
    The highly charged Al-like ions are the potential candidates for the next-generation atomic optical clocks, and their atomic parameters are also useful in plasma and nuclear physics. In the present work, the hyperfine interaction constants and Landé g factors of 3s23p 2P1/2, 3/2 states in the ground configuration for Al-like ions in a range between Si+ and Kr23+ ions are calculated by using the multi-configuration Dirac-Hartree-Fock method. Owing to the fact that hyperfine interaction constant is sensitive to electron correlation effects, we systematically investigate its influence on the hyperfine interaction constants, particularly for the high-order correlation related to the 2p electrons. According to this investigation and by taking into account the Breit interaction and QED corrections, we achieve the computational accuracy at a level of 1% and 10–5 for the hyperfine interaction constants and Landé g factors, respectively, except for the Si+ ion. Furthermore, the electronic parts of hyperfine interaction constants and g factors are fitted with functions of atomic number. The deviations between these fitted formulas and the ab initio calculations are less than 2% and 10–5 for the hyperfine interaction constants and the g factors, respectively. As a result, the hyperfine interaction constants and g factors of all isotopes can be determined for Al-like ions with 14 ≤ Z ≤ 54.
      通信作者: 李冀光, li_jiguang@iapcm.ac.cn
    • 基金项目: 国家自然科学基金(批准号: 11874090)资助的课题.
      Corresponding author: Li Ji-Guang, li_jiguang@iapcm.ac.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11874090).
    [1]

    Safronova M S, Budker D, DeMille D, Kimball D F J, Derevianko A, Clark C W 2018 Rev. Mod. Phys. 90 025008Google Scholar

    [2]

    Zhang B L, Huang Y, Zhang H Q, Hao Y M, Zeng M Y, Guan H, Gao K L 2020 Chin. Phys. B 29 074209Google Scholar

    [3]

    Brewer S M, Chen J S, Hankin A M, Clements E R, Chou C W, Wineland D J, Hume D B, Leibrandt D R 2019 Phys. Rev. Lett. 123 033201Google Scholar

    [4]

    Kozlov M G, Safronova M S, López-Urrutia J R C, Schmidt P O 2018 Rev. Mod. Phys. 90 045005Google Scholar

    [5]

    Derevianko A, Dzuba V A, Flambaum V V 2012 Phys. Rev. Lett. 109 180801Google Scholar

    [6]

    Dzuba V A, Derevianko A, Flambaum V V 2012 Phys. Rev. A 86 054501Google Scholar

    [7]

    Dzuba V A, Flambaum V V 2017 Highly Charged Ions for Atomic Clocks and Search for Variation of the Fine Structure Constant (In: Wada M, Schury P, Ichikawa Y (eds) TCP 2014 Springer, Cham.) p79

    [8]

    Yudin V I, Taichenachev A V, Derevianko A 2014 Phys. Rev. Lett. 113 233003Google Scholar

    [9]

    Yu Y, Sahoo B K 2016 Phys. Rev. A 94 062502Google Scholar

    [10]

    Li J G, Godefroid M, Wang J G 2016 J. Phys. B: At. Mol. Opt. Phys. 49 115002Google Scholar

    [11]

    Lu B, Zhang T X, Chang H, Li J G, Wu Y, Wang J G 2019 Phys. Rev. A 100 012504Google Scholar

    [12]

    Goyal A, Khatri I, Singh A K, Mohan M, Sharma R, Singh N 2016 Atoms 4 22Google Scholar

    [13]

    Beiersdorfer P, Träbert E, Pinnington E H 2003 Astrophys. J. 587 836Google Scholar

    [14]

    Schiffmann S, Brage T, Judge P G, Paraschiv A R, Wang K 2021 Astrophys. J 923 186Google Scholar

    [15]

    Booth A J, Blackwell D E 1983 Mon. Not. R. Astro. Soc. 204 777Google Scholar

    [16]

    Roederer I U, Lawler J E 2021 Astrophys. J. 912 119Google Scholar

    [17]

    Grant I P 2007 Relativistic Quantum Theory of Atoms and Molecules-Theory and Computation (New York: Springer) p393

    [18]

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

    [19]

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

    [20]

    Cheng K T, Childs W J 1985 Phys. Rev. A 31 2775Google Scholar

    [21]

    Froese C F, Gaigalas G, Jönsson P, Bierón J 2019 Comput. Phys. Commun. 237 184Google Scholar

    [22]

    Zhang T X, Xie L Y, Li J G, Lu Z H 2017 Phys. Rev. A 96 012514Google Scholar

    [23]

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

    [24]

    Kramida A, Ralchenko Yu, Reader J, NIST ASD Team 2022 NIST Atomic Spectra Database

    [25]

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

    [26]

    Pyykkö P 2008 Mol. Phys. 106 1965Google Scholar

  • 图 1  类铝等电子序列3s23p 2P1/2, 3/2能级的(a)超精细结构常数电子部分矩阵元AelBel以及(b)朗德g因子随原子序数Z的变化关系. 图中实线表示由拟合公式得出的结果, 散点表示用MCDHF方法从头计算的结果

    Fig. 1.  (a) Electronic parts of hyperfine structure constants and (b) Landé g factors of 3s23p 2P1/2, 3/2 states of Al-like isoelectronic sequence ions as functions of atomic number. The solid line represents these results obtained by from numerical fitting formula, and the discrete point represents these results obtained by our ab initio calculation using MCDHF method.

    表 1  Si+和Co14+离子3s23p 2P1/2, 3/2能级的激发能ΔE (cm–1)随组态空间扩大的收敛趋势. DHF代表单组态计算模型. AO和VO分别代表在每个计算模型下允许被激发的占据轨道和新添加的关联轨道. NCSF代表相应的组态波函数数目

    Table 1.  Excitation energies ΔE (in cm–1) of 3s23p 2P1/2, 3/2 states of Si+ and Co14+ ions as functions of various computational models. DHF stands for the single configuration approximation model. AO and VO represent the occupied orbitals allowed to be replaced and the added virtual orbitals in each computational model, respectively. NCSF represents the corresponding numbers of CSFs.

    ModelAOVONCSFΔE
    Si+Co14+
    DHF230523957
    VV + CV1{3s, 3p}{4s, 4p, 3d, 4f, 5g}20429323471
    2{2s, 2p, 3s, 3p}{5s, 5p, 4d, 5f, 6g}857730523588
    3{1s, 2s, 2p, 3s, 3p}{6s, 6p, 5d, 6f, 6g}2049130423598
    4{1s, 2s, 2p, 3s, 3p}{7s, 7p, 6d, 7f, 6g}3350830423605
    5{1s, 2s, 2p, 3s, 3p}{8s, 8p, 7d, 7f, 6g}4450830523609
    6{1s, 2s, 2p, 3s, 3p}{9s, 9p, 8d, 7f, 6g}5721830523610
    7{1s, 2s, 2p, 3s, 3p}{10s, 10p, 9d, 7f, 6g}7163830523611
    8{1s, 2s, 2p, 3s, 3p}{11s, 11p, 10d, 7f, 6g}8776830523611
    9{1s, 2s, 2p, 3s, 3p}{12s, 12p, 11d, 7f, 6g}10560830523611
    10{1s, 2s, 2p, 3s, 3p}{13s, 13p, 12d, 7f, 6g}12515830523611
    下载: 导出CSV

    表 2  Si+和Co14+离子3s23p 2P1/2, 3/2能级超精细结构常数电子部分矩阵元Ael (MHz/μN)和Bel (MHz/b)以及朗德g因子随组态空间扩展的收敛情况. DHF为单组态近似模型

    Table 2.  Electronic parts of hyperfine structure constants Ael (MHz/μN) and Bel (MHz/b) and Landé g factors of 3s23p 2P1/2, 3/2 states in Si+ and Co14+ ions as functions of various computational models. DHF stands for the single configuration approximation model.

    Model Si+ Co14+
    Ael Bel g Ael Bel g
    2P1/2 2P3/2 2P3/2 2P1/2 2P3/2 2P1/2 2P3/2 2P3/2 2P1/2 2P3/2
    DHF 682.2 134.4 248.7 0.6658188 1.3340409 28653 5391 10060 0.6645201 1.3329968
    VV + CV 1 647.7 154.5 237.1 0.6658181 1.3340408 27658 5879 9804 0.6645062 1.3330011
    2 741.9 175.0 289.1 0.6658123 1.3340361 28843 6071 10282 0.6644682 1.3329818
    3 783.5 172.2 296.2 0.6658100 1.3340348 29191 5814 10276 0.6644659 1.3329820
    4 799.1 160.4 298.3 0.6658098 1.3340346 29287 5766 10290 0.6644616 1.3329826
    5 799.8 163.2 299.2 0.6658099 1.3340344 29307 5799 10273 0.6644639 1.3329808
    6 800.9 163.4 297.3 0.6658093 1.3340345 29319 5788 10255 0.6644639 1.3329812
    7 801.1 163.9 297.7 0.6658094 1.3340345 29321 5797 10255 0.6644622 1.3329818
    8 802.7 163.7 295.6 0.6658094 1.3340343 29326 5796 10239 0.6644634 1.3329815
    9 802.8 164.0 295.8 0.6658092 1.3340344 29326 5799 10244 0.6644630 1.3329810
    10 802.6 163.9 295.5 0.6658088 1.3340346 29321 5796 10245 0.6644622 1.3329812
    下载: 导出CSV

    表 3  不同计算模型下Si+与Co14+离子3s23p 2P1/2, 3/2能级的激发能ΔE (cm–1)、超精细结构常数电子部分矩阵元Ael (MHz/μN)和Bel (MHz/b)以及朗德g因子

    Table 3.  Excitation energies ΔE (cm–1), electronic parts of hyperfine structure constants Ael (MHz/μN) and Bel (MHz/b) and Landé g factors of 3s23p 2P1/2, 3/2 states in Si+ and Co14+ ions as functions of various computational models.

    Model Si+ Co14+
    ΔE Ael Bel g ΔE Ael Bel g
    2P1/2 2P3/2 2P1/2 2P3/2 2P3/2 2P1/2 2P3/2 2P1/2 2P3/2 2P1/2 2P3/2 2P3/2 2P1/2 2P3/2
    DHF 305 682 134 249 0.665819 1.334041 23957 28653 5391 10060 0.664520 1.332997
    VV+CV-10 305 803 164 295 0.665809 1.334035 23611 29321 5796 10245 0.664462 1.332981
    +MR1 305 803 164 296 0.665809 1.334035 23611 29319 5797 10245 0.664462 1.332981
    +CC2p 310 785 150 288 0.665811 1.334036 23656 29287 5757 10232 0.664465 1.332983
    +TQ2p 307 785 160 292 0.665810 1.334036 23618 29245 5784 10229 0.664464 1.332983
    +BQ 291 785 160 292 0.665810 1.334036 23044 29230 5788 10211 0.664464 1.332983
    CCSD[9] 22932(13)
    NIST[24] 287 22979
    下载: 导出CSV

    表 4  类铝等电子序列3s23p 2P1/2, 3/2能级的超精细结构常数电子部分矩阵元Ael (MHz/μN), Bel (MHz/b)和朗德g因子. 括号内的数字表示计算结果相应的不确定度

    Table 4.  Electronic parts of hyperfine structure constants Ael (MHz/μN) and Bel (MHz/b) and Landé g factors of 3s23p 2P1/2, 3/2 states of Al-like isoelectronic sequence ions. Numbers in parentheses represent the computational errors.

    IonsAelBelg
    2P1/22P3/22P3/22P1/22P3/2
    Si+785(8)160(8)292(3)0.665811.33404
    P2+1387(14)290(3)512(5)0.665761.33399
    S3+2172(22)457(5)797(8)0.665701.33394
    Cl4+3160(32)664(7)1152(12)0.665621.33389
    Ar5+4372(44)914(9)1585(16)0.665551.33383
    K6+5828(58)1212(12)2104(21)0.665461.33376
    Ca7+7553(76)1561(16)2714(27)0.665361.33368
    Sc8+9569(96)1965(20)3425(34)0.665261.33360
    Ti9+11902(119)2430(24)4243(42)0.665151.33352
    V10+14576(146)2957(30)5175(52)0.665031.33342
    Cr11+17618(176)3553(36)6230(62)0.664901.33332
    Mn12+21055(211)4220(42)7416(74)0.664761.33322
    Fe13+24916(249)4964(50)8740(87)0.664621.33310
    Co14+29230(292)5788(58)10211(102)0.664461.33298
    Ni15+34028(340)6696(67)11836(118)0.664301.33286
    Cu16+39344(393)7693(77)13625(136)0.664131.33273
    Zn17+45209(452)8783(88)15587(156)0.663951.33259
    Ga18+51659(517)9970(100)17729(177)0.663771.33244
    Ge19+58734(587)11259(113)20059(201)0.663571.33229
    As20+66469(665)12654(127)22588(226)0.663371.33214
    Se21+74908(749)14160(142)25326(253)0.663161.33197
    Br22+84092(841)15779(158)28281(283)0.662941.33180
    Kr23+94066(941)17519(175)31462(315)0.662711.33162
    下载: 导出CSV

    表 5  类铝等电子序列3s23p 2P1/2, 3/2能级的超精细结构常数A, B (MHz)和朗德g因子. 所有核参数μ (μN)和Q (mb)均来自于文献[25, 26]. 星号表示用CCSD方法计算的结果[9]. 括号内的数字表示计算结果相应的不确定度

    Table 5.  Hyperfine structure constants and g factors of 3s23p 2P1/2, 3/2 states of Al-like isoelectronic sequence ions. Nuclear parameters μ (μN) and Q (mb) are taken from Ref. [25, 26]. Asterisk represents these results calculated by CCSD method[9]. Numbers in parentheses represent the computational uncertainties.

    Ion I μ Q A B g
    2P1/2 2P3/2 2P3/2 2P1/2 2P3/2
    51V10+ 7/2 5.1464 –52 21433(214) 4349(43) –269(3) 0.66503 1.33342
    21456(146)* 4342(68)* –222(6)* 0.665196* 1.333460*
    53Cr11+ 3/2 –0.4743 –150 –5571(56) –1123(11) –935(9) 0.66490 1.33332
    –5578(30)* –1122(14)* –964(10)* 0.665081* 1.333363*
    55Mn12+ 5/2 3.4669 330 29198(292) 5853(59) 2447(24) 0.66476 1.33322
    29096(3)* 5821(35)* 3162(20)* 0.664957* 1.333258*
    57Fe13+ 1/2 0.09064 160 4517(45) 900(9) 1398(14) 0.66462 1.33310
    4509(39)* 897(2)* 961(10)* 0.664825* 1.333148*
    59Co14+ 7/2 4.615 420 38542(39) 7632(76) 4289(43) 0.66446 1.33298
    5245(42)* 1037(47)* 3603(40)* 0.664684* 1.333032*
    61Ni15+ 3/2 –0.7497 162 –17006(170) –3348(33) 1917(19) 0.66430 1.33286
    –17016(66)* –3345(27)* 1918(20)* 0.664536* 1.332909*
    63Cu16+ 3/2 2.2259 –220 58383(584) 11416(114) –2998(30) 0.66413 1.33273
    58412(254)* 11416(511)* –3012(60)* 0.664379* 1.332779*
    下载: 导出CSV
  • [1]

    Safronova M S, Budker D, DeMille D, Kimball D F J, Derevianko A, Clark C W 2018 Rev. Mod. Phys. 90 025008Google Scholar

    [2]

    Zhang B L, Huang Y, Zhang H Q, Hao Y M, Zeng M Y, Guan H, Gao K L 2020 Chin. Phys. B 29 074209Google Scholar

    [3]

    Brewer S M, Chen J S, Hankin A M, Clements E R, Chou C W, Wineland D J, Hume D B, Leibrandt D R 2019 Phys. Rev. Lett. 123 033201Google Scholar

    [4]

    Kozlov M G, Safronova M S, López-Urrutia J R C, Schmidt P O 2018 Rev. Mod. Phys. 90 045005Google Scholar

    [5]

    Derevianko A, Dzuba V A, Flambaum V V 2012 Phys. Rev. Lett. 109 180801Google Scholar

    [6]

    Dzuba V A, Derevianko A, Flambaum V V 2012 Phys. Rev. A 86 054501Google Scholar

    [7]

    Dzuba V A, Flambaum V V 2017 Highly Charged Ions for Atomic Clocks and Search for Variation of the Fine Structure Constant (In: Wada M, Schury P, Ichikawa Y (eds) TCP 2014 Springer, Cham.) p79

    [8]

    Yudin V I, Taichenachev A V, Derevianko A 2014 Phys. Rev. Lett. 113 233003Google Scholar

    [9]

    Yu Y, Sahoo B K 2016 Phys. Rev. A 94 062502Google Scholar

    [10]

    Li J G, Godefroid M, Wang J G 2016 J. Phys. B: At. Mol. Opt. Phys. 49 115002Google Scholar

    [11]

    Lu B, Zhang T X, Chang H, Li J G, Wu Y, Wang J G 2019 Phys. Rev. A 100 012504Google Scholar

    [12]

    Goyal A, Khatri I, Singh A K, Mohan M, Sharma R, Singh N 2016 Atoms 4 22Google Scholar

    [13]

    Beiersdorfer P, Träbert E, Pinnington E H 2003 Astrophys. J. 587 836Google Scholar

    [14]

    Schiffmann S, Brage T, Judge P G, Paraschiv A R, Wang K 2021 Astrophys. J 923 186Google Scholar

    [15]

    Booth A J, Blackwell D E 1983 Mon. Not. R. Astro. Soc. 204 777Google Scholar

    [16]

    Roederer I U, Lawler J E 2021 Astrophys. J. 912 119Google Scholar

    [17]

    Grant I P 2007 Relativistic Quantum Theory of Atoms and Molecules-Theory and Computation (New York: Springer) p393

    [18]

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

    [19]

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

    [20]

    Cheng K T, Childs W J 1985 Phys. Rev. A 31 2775Google Scholar

    [21]

    Froese C F, Gaigalas G, Jönsson P, Bierón J 2019 Comput. Phys. Commun. 237 184Google Scholar

    [22]

    Zhang T X, Xie L Y, Li J G, Lu Z H 2017 Phys. Rev. A 96 012514Google Scholar

    [23]

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

    [24]

    Kramida A, Ralchenko Yu, Reader J, NIST ASD Team 2022 NIST Atomic Spectra Database

    [25]

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

    [26]

    Pyykkö P 2008 Mol. Phys. 106 1965Google Scholar

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出版历程
  • 收稿日期:  2023-06-05
  • 修回日期:  2023-08-14
  • 上网日期:  2023-09-12
  • 刊出日期:  2023-11-20

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