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激光冷却SH阴离子的理论研究

万明杰 李松 金成国 罗华锋

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激光冷却SH阴离子的理论研究

万明杰, 李松, 金成国, 罗华锋

Theoretical study of laser-cooled SH anion

Wan Ming-Jie, Li Song, Jin Cheng-Guo, Luo Hua-Feng
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  • 本文采用多组态相互作用及Davidson修正方法和全电子基组计算了SH阴离子的${{\rm{X}}^1}{\Sigma ^ + }$, ${{\rm{a}}^3}\Pi $${{\rm{A}}^1}\Pi $态的势能曲线、电偶极矩和跃迁偶极矩. 计算的光谱常数与实验值及已有的理论值符合得很好. 在计算中考虑了自旋-轨道耦合效应. 计算得到${{\rm{a}}^3}{\Pi _1}(\nu ' = 0) \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + (\nu '' = 0)$${{\rm{A}}^1}{\Pi _1}(\nu ' = 0) \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + (\nu '' = 0)$跃迁具有高对角分布的弗兰克-康登因子, 分别为0.9990和0.9999; 计算得到${{\rm{a}}^3}\Pi _1$${{\rm{A}}^1}\Pi _1$态的自发辐射寿命分别为1.472和0.188 ms. ${{\rm{A}}^1}{\Pi _1} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $跃迁存在中间态${{\rm{a}}^3}{\Pi _{{0^ + }}}$${{\rm{a}}^3}{\Pi _1}$, 但中间态对激光冷却SH阴离子的影响可以忽略. 分别利用${{\rm{a}}^3}{\Pi _1}(\nu ' = 0) \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + (\nu '' = 0)$${{\rm{A}}^1}{\Pi _1}(\nu ' = 0) \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + (\nu '' = 0)$跃迁构建了准闭合的能级系统, 冷却所需的激光波长分别为492.27和478.57 nm. 最后预测了激光冷却SH阴离子能达到的多普勒温度和反冲温度. 这些结果为进一步实验提供了理论参数.
    The potential energy curves, dipole moments, and transition dipole moments for the ${{\rm{X}}^1}{\Sigma ^ + }$, ${{\rm{a}}^3}\Pi $, and ${{\rm{A}}^1}\Pi $ electronic state of sulfur hydride anion (SH) are calculated by using the multi-reference configuration interaction method plus Davidson corrections (MRCI+Q) with all-electron basis set. The scalar relativistic corrections and core-valence correlations are also considered. In the CASSCF calculations, H(1s) and S(3s3p4s) shells are chosen as active space, and the rest orbitals S(1s2s2p) as closed-shell. In the MRCI+Q calculations, the S(1s2s2p) shells are used for the core-valence correlation. Spectroscopic parameters, Einstein spontaneous emission coefficient, Franck-Condon factors, and spontaneous radiative lifetimes are obtained by using Le Roy’s LEVEL8.0 program. The calculated spectroscopic parameters are in good agreement with available experimental data and theoretical values. Spin-orbit coupling (SOC) effects are evaluated with Breit-Pauli operators at the MRCI+Q level. Transition dipole moments (TDMs) for the ${{\rm{A}}^1}{\Pi _1} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $, ${{\rm{a}}^3}{\Pi _{{0^ + }}} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $, ${{\rm{a}}^3}{\Pi _1} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $, ${{\rm{A}}^1}{\Pi _1} \leftrightarrow {{\rm{a}}^3}{\Pi _{{0^ + }}}$ and ${{\rm{A}}^1}{\Pi _1} \leftrightarrow {{\rm{a}}^3}{\Pi _1}$ transitions are also calculated. The strength for the ${{\rm{A}}^1}{\Pi _1} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $ is the strongest in these five transitions, the value of TDM at Re is –1.3636 D. We find that the value of TDM for the ${{\rm{a}}^3}{\Pi _1} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $ transition at Re is 0.5269 D. Therefore, this transition must be taken into account to build the scheme of laser-cooled SH anion. Highly diagonally distributed Franck-Condon factor f00 for the ${{\rm{a}}^3}{\Pi _1}(\nu ' = 0) \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $ $ (\nu '' = 0)$ transition is 0.9990 and the value for the ${{\rm{A}}^1}{\Pi _1}(\nu ' = 0) \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + (\nu '' = 0)$ transition is 0.9999. Spontaneous radiative lifetimes of $\tau \left( {{{\rm{a}}^3}{\Pi _1}} \right)= 1.472 \;{\text{μ}}{\rm{s}}$ and $\tau \left( {{{\rm{A}}^1}{\Pi _1}} \right)=0.188 \;{\text{μ}}{\rm{s}}$ are obtained, which can ensure that laser cools SH anion rapidly. To drive the ${{\rm{a}}^3}{\Pi _1} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $ and ${{\rm{A}}^1}{\Pi _1} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $ transitions, just one laser wavelength is required. The wavelengths are 492.27 nm and 478.57 nm for two transitions, respectively. Notably, the influences of the intervening states ${{\rm{a}}^3}{\Pi _1}$ and ${{\rm{a}}^3}{\Pi _{{0^{\rm{ + }}}}}$ on the ${{\rm{A}}^1}{\Pi _1} \leftrightarrow {X^1}\Sigma _{{0^ + }}^ + $ transition are small enough to implement a laser cooling project. A spin-forbidden transition and a three-electronic-level transition optical scheme of laser-cooled SH anion are constructed, respectively. In addition, the Doppler temperatures and recoil temperatures for the ${{\rm{a}}^3}{\Pi _1} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $ and ${{\rm{A}}^1}{\Pi _1} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $ transitions of laser-cooled SH anion are also obtained, respectively.
      通信作者: 万明杰, wanmingjie1983@sina.com
    • 基金项目: 国家自然科学基金理论物理专项(批准号: 11647075, 11747071) 和宜宾学院计算物理四川省高等学校重点实验室开放课题基金(批准号: JSWL2014KF05)资助的课题.
      Corresponding author: Wan Ming-Jie, wanmingjie1983@sina.com
    • Funds: Project supported by the Special Foundation for Theoretical Physics Research Program of China (Grant Nos. 11647075, 11747071) and the Open Research Fund of Computational physics Key Laboratory of Sichuan Province, Yibin University, China (Grant No. JSWL2014KF05).
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    Shuman E S, Barry J F, DeMille D 2010 Nature 467 820Google Scholar

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    Zhelyazkova V, Cournol A, Wall T E, Matsushima A, Hudson J J, Hinds E A, Tarbutt M R, Sauer B E 2014 Phys. Rev. A 89 053416Google Scholar

    [3]

    Hummon M T, Yeo M, Stuhl B K, Collopy A L, Xia Y, Ye J 2013 Phys. Rev. Lett. 110Google Scholar

    [4]

    张云光, 张华, 窦戈, 徐建刚 2017 物理学报 66 233101Google Scholar

    Zhang Y G, Zhang H, Dou G, Xu J G 2017 Acta Phys. Sin. 66 233101Google Scholar

    [5]

    Gao Y, Gao T 2014 Phys. Rev. A 90 052506Google Scholar

    [6]

    Wan M, Shao J, Huang D, Jin C, Yu Y, Wang F 2015 Phys. Chem. Chem. Phys. 17 26731Google Scholar

    [7]

    Wan M, Shao J, Gao Y, Huang D, Yang J, Cao Q, Jin C, Wang F 2015 J. Chem. Phys. 143 024302Google Scholar

    [8]

    Gao Y, Gao T 2015 Phys. Chem. Chem. Phys. 17 10830Google Scholar

    [9]

    李亚超, 孟腾飞, 李传亮等 2017 物理学报 66 163101Google Scholar

    Li Y C, Meng T F, Li C L, et al. 2017 Acta Phys. Sin. 66 163101Google Scholar

    [10]

    Zhang Q, Yang C, Wang M, Ma X, Liu W 2017 Spectrochim. Acta, Part A 182 130Google Scholar

    [11]

    Zhang Q, Yang C, Wang M, Ma X, Liu W 2017 Spectrochim. Acta, Part A 185 365Google Scholar

    [12]

    Wan M, Huang D, Yu Y, Zhang Y 2017 Phys. Chem. Chem. Phys. 19 27360Google Scholar

    [13]

    Steiner B 1968 J. Chem. Phys. 49 5097Google Scholar

    [14]

    Breyer F, Frey P, Hotop H 1981 Z. Phys. 300 7Google Scholar

    [15]

    Janousek B K, Brauman J I 1981 Phys. Rev. A 23 1673Google Scholar

    [16]

    Cade P 1967 J. Chem. Phys. 47 2390Google Scholar

    [17]

    Rosmus P, Meyer W 1978 J. Chem. Phys. 69 2745Google Scholar

    [18]

    Senekowitsch J, Werner H J, Rosmus P, Reinsch E A, Oneil S V 1985 J. Chem. Phys. 83 4661Google Scholar

    [19]

    Vamhindi B S D R, Nsangou M 2016 Mol. Phys. 114 2204Google Scholar

    [20]

    Werner H J, Knowles P J 1988 J. Chem. Phys. 89 5803Google Scholar

    [21]

    Knowles P J, Werner H J 1988 Chem. Phys. Lett. 145 514Google Scholar

    [22]

    Langhoff S R, Davidson E R 1974 Int. J. Quantum Chem. 8 61Google Scholar

    [23]

    Knowles P J, Werner H J 1985 J. Chem. Phys. 82 5053Google Scholar

    [24]

    Knowles P J, Werner H J 1985 Chem. Phys. Lett. 115 259Google Scholar

    [25]

    Douglas M, Kroll N M 1974 Ann. Phys. 82 89Google Scholar

    [26]

    Hess B A 1986 Phys. Rev. A 33 3742Google Scholar

    [27]

    Berning A, Schweizer M, Werner H J, Knowles P J, Palmieri P 2000 Mol. Phys. 98 1823Google Scholar

    [28]

    Werner H J, Knowles P J, Lindh R, et al. MOLPRO, version 2010.1, a package of ab initio programs, 2010, see http://www.molpro.net [2018-11-15]

    [29]

    Peterson K A, Dunning Jr T H 2002 J. Chem. Phys. 117 10548Google Scholar

    [30]

    Dunning Jr T H 1989 J. Chem. Phys. 90 1007Google Scholar

    [31]

    Murrell J N, Sorbie K S. 1974 J Chem. Soc., Faraday Trans. 70 1552Google Scholar

    [32]

    Le Roy R J Level 8.0: A Computer Program for Solving the Radial Schrödinger Equation for Bound and Quasibound Levels (Waterloo: University of Waterloo) Chemical Physics Research Report CP-663

    [33]

    Lykke K R, Murray K K, Lineberger W C 1991 Rhys. Rev. A 43 6104Google Scholar

    [34]

    Hotop H, Lineberger W C 1985 J. Phys. Chem. Ref. Data 14 731Google Scholar

    [35]

    Moore C E 1971 Atomic Energy Levels (Vol. 1) (Washington, DC: National Bureau of Standards Publications) p181

    [36]

    Cohen-Tannoudji C N 1998 Rev. Phys. Mod. 70 707Google Scholar

    [37]

    Kobayashi J, Aikawa K, Oasa K, Inouye S 2014 Phys. Rev. A 89 021401Google Scholar

  • 图 1  SH阴离子的${{\rm{X}}^1}{\Sigma ^ + }$, ${{\rm{a}}^3}\Pi $, ${{\rm{A}}^1}\Pi $, ${1^3}{\Sigma ^ + }$${2^1}{\Sigma ^ + }$态的势能曲线

    Fig. 1.  Potential energy curves for the ${{\rm{X}}^1}{\Sigma ^ + }$, ${{\rm{a}}^3}\Pi $, ${{\rm{A}}^1}\Pi $, and ${2^1}{\Sigma ^ + }$ states of SH anion.

    图 2  SH阴离子的$\Omega$态的势能曲线

    Fig. 2.  Potential energy curves for the $\Omega$ states of SH anion.

    图 3  SH阴离子的跃迁偶极矩 (a) ${{\rm{A}}^{1}}{\Pi _1} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $${{\rm{a}}^3}{\Pi _1} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $跃迁; (b) ${{\rm{a}}^{3}}{\Pi _{{0^ + }}} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $, ${{\rm{A}}^1}{\Pi _1} \!\leftrightarrow\!{{\rm{a}}^3}{\Pi _{{0^ + }}}$${{\rm{A}}^1}{\Pi _1} \leftrightarrow {{\rm{a}}^3}{\Pi _1}$跃迁

    Fig. 3.  Transition dipole moments of SH anion: (a) The ${{\rm{A}}^1}{\Pi _1} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $ and ${{\rm{a}}^{3}}{\Pi _1} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $ transitions; (b) the ${{\rm{a}}^3}{\Pi _{{0^ + }}} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $, ${{\rm{A}}^1}{\Pi _1} \leftrightarrow {{\rm{a}}^3}{\Pi _{{0^ + }}}$ and ${{\rm{A}}^1}{\Pi _1} \leftrightarrow {{\rm{a}}^3}{\Pi _1}$ transitions.

    图 4  采用$\scriptstyle {{{\rm{a}}^3}{\Pi _1}}\leftrightarrow \scriptstyle {{{\rm{X}}^1}\Sigma _{{0^ + }}^ + }$跃迁进行激光冷却SH阴离子的方案, 实线为所需激光, 虚线为自发辐射的弗兰克-康登因子

    Fig. 4.  Proposed laser cooling scheme for the $ \scriptstyle{{{\rm{a}}^3}{\Pi _1}}\leftrightarrow$$\scriptstyle {{{\rm{X}}^1}\Sigma _{{0^ + }}^ + }$ transition (solid line) and spontaneous decay.

    图 5  采用${{\rm{A}}^1}{\Pi _1} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $跃迁进行激光冷却SH阴离子的方案, 其中实线为所需激光, 虚线为自发辐射的弗兰克-康登因子

    Fig. 5.  Proposed laser cooling scheme for the $ {{\rm{A}}^1}{\Pi _1} \leftrightarrow$$ {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $ transition (solid line) and spontaneous decay.

    表 1  SH-阴离子的$\Lambda\text{-}\rm S$态的光谱常数

    Table 1.  Spectroscopic parameters for the $\Lambda\text{-}\rm S $ states of SH anion.

    电子态Re$\omega_{\rm{e}}$/cm–1$\omega_{\rm{e}}\chi_{\rm{e}}$/cm–1Be/cm–1De/eVTe/cm–1RMS/cm–1
    ${{\rm{X}}^1}{\Sigma ^ + }$本文工作1.34352622.0446.669.55903.879304.4107
    实验值[13]1.34—0.022700—3009.46—0.32
    实验值[14]2648—1109.39—0.3
    理论值[17]1.3482642529.493.9020
    理论值[18]1.3462637529.52
    理论值[19]1.34402682.8639.29.5514.19
    ${{\rm{a}}^3}\Pi $本文工作第一势阱1.34662583.6173.229.51480.959820436.920.0604
    理论值[19]1.37461936.16307.5039.1291.3822082.7
    本文工作第二势阱2.1021778.72133.343.90450.435627816.711.1556
    ${{\rm{A}}^1}\Pi $本文工作第一势阱1.34412626.5961.519.55111.184820852.700.0474
    理论值[19]1.34322554.9744.1869.5611.3322225.2
    本文工作第二势阱2.2430424.8036.8103.42960.121730299.280.3277
    下载: 导出CSV

    表 2  SH阴离子的$\Omega$态的光谱常数

    Table 2.  Spectroscopic parameters for the $\Omega$ states of SH anion.

    $\Omega$ stateRe$\omega_{\rm{e}}$/cm–1$\omega_{\rm{e}}\chi_{\rm{e}}$/cm–1Be/cm–1De/eVTe/cm–1RMS/cm–1
    ${{\rm{X}}^1}\Sigma _{{0^ + }}^ + $1.34352618.5344.589.55893.857504.0232
    ${{\rm{a}}^3}{\Pi _2}$第一势阱1.34662584.1372.089.51510.960720247.580.0257
    第二势阱2.1011779.62136.273.90820.442927639.821.1521
    ${{\rm{a}}^{3}}{\Pi _1}$第一势阱1.34632588.5469.879.51960.966520363.640.0537
    第二势阱2.1005773.93135.453.91050.417327802.871.0389
    ${{\rm{a}}^3}{\Pi _{{0^ - }}}$第一势阱1.34662583.8370.949.51490.958920624.880.0203
    第二势阱2.1036776.84132.773.89900.39827989.311.1617
    ${{\rm{a}}^3}{\Pi _{{0^ + }}}$第一势阱1.34662583.8970.929.51490.959420625.010.0195
    第二势阱2.1012780.04136.693.90790.453627999.081.3153
    ${{\rm{A}}^1}{\Pi _1}$第一势阱1.34442621.7061.529.54641.200620924.710.0392
    第二势阱2.2449422.6937.823.42370.102630306.300.2834
    下载: 导出CSV

    表 3  SH阴离子的辐射速率(单位为s–1)、弗兰克-康登因子和自发辐射寿命(单位为s)

    Table 3.  Emission rates ${A_{\nu ' \nu '' }}$ (unit of s–1), Franck-Condon factors ${f_{\nu ' \nu '' }}$ and spontaneous radiative lifetimes $\tau $ (unit of s) of SH anion.

    TransitionA00A01A02A03A0
    f00f01f02f03$\tau $ = 1/A0
    A10A11A12A13
    f10f11f12f13
    ${\operatorname{a} ^3}{\Pi _1} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $6771222184.6925.36762.8984679335
    0.99900.00093.38 × 10–53.46 × 10–61.472 × 10–6
    15577.85610384025.1735.1337
    0.00100.99310.00540.0004
    ${{\rm{A}}^1}{\Pi _1} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $531082033.940430.57460.17365310885
    0.99990.00012.18 × 10–61.07 × 10–81.883 × 10–7
    2970.0552627901089.41217.62
    0.00060.99920.00024.13 × 10–5
    ${{\rm{a}}^3}{\Pi _{{0^ + }}} \leftrightarrow {{\rm{X}}^1}\Sigma _{0^ + }^ + $2229.2498.33840.24560.01262327.84
    0.99890.00113.82 × 10–53.53 × 10–64.295 × 10–4
    102.872852.21284.483.3484
    0.03170.87950.08770.0010
    下载: 导出CSV
  • [1]

    Shuman E S, Barry J F, DeMille D 2010 Nature 467 820Google Scholar

    [2]

    Zhelyazkova V, Cournol A, Wall T E, Matsushima A, Hudson J J, Hinds E A, Tarbutt M R, Sauer B E 2014 Phys. Rev. A 89 053416Google Scholar

    [3]

    Hummon M T, Yeo M, Stuhl B K, Collopy A L, Xia Y, Ye J 2013 Phys. Rev. Lett. 110Google Scholar

    [4]

    张云光, 张华, 窦戈, 徐建刚 2017 物理学报 66 233101Google Scholar

    Zhang Y G, Zhang H, Dou G, Xu J G 2017 Acta Phys. Sin. 66 233101Google Scholar

    [5]

    Gao Y, Gao T 2014 Phys. Rev. A 90 052506Google Scholar

    [6]

    Wan M, Shao J, Huang D, Jin C, Yu Y, Wang F 2015 Phys. Chem. Chem. Phys. 17 26731Google Scholar

    [7]

    Wan M, Shao J, Gao Y, Huang D, Yang J, Cao Q, Jin C, Wang F 2015 J. Chem. Phys. 143 024302Google Scholar

    [8]

    Gao Y, Gao T 2015 Phys. Chem. Chem. Phys. 17 10830Google Scholar

    [9]

    李亚超, 孟腾飞, 李传亮等 2017 物理学报 66 163101Google Scholar

    Li Y C, Meng T F, Li C L, et al. 2017 Acta Phys. Sin. 66 163101Google Scholar

    [10]

    Zhang Q, Yang C, Wang M, Ma X, Liu W 2017 Spectrochim. Acta, Part A 182 130Google Scholar

    [11]

    Zhang Q, Yang C, Wang M, Ma X, Liu W 2017 Spectrochim. Acta, Part A 185 365Google Scholar

    [12]

    Wan M, Huang D, Yu Y, Zhang Y 2017 Phys. Chem. Chem. Phys. 19 27360Google Scholar

    [13]

    Steiner B 1968 J. Chem. Phys. 49 5097Google Scholar

    [14]

    Breyer F, Frey P, Hotop H 1981 Z. Phys. 300 7Google Scholar

    [15]

    Janousek B K, Brauman J I 1981 Phys. Rev. A 23 1673Google Scholar

    [16]

    Cade P 1967 J. Chem. Phys. 47 2390Google Scholar

    [17]

    Rosmus P, Meyer W 1978 J. Chem. Phys. 69 2745Google Scholar

    [18]

    Senekowitsch J, Werner H J, Rosmus P, Reinsch E A, Oneil S V 1985 J. Chem. Phys. 83 4661Google Scholar

    [19]

    Vamhindi B S D R, Nsangou M 2016 Mol. Phys. 114 2204Google Scholar

    [20]

    Werner H J, Knowles P J 1988 J. Chem. Phys. 89 5803Google Scholar

    [21]

    Knowles P J, Werner H J 1988 Chem. Phys. Lett. 145 514Google Scholar

    [22]

    Langhoff S R, Davidson E R 1974 Int. J. Quantum Chem. 8 61Google Scholar

    [23]

    Knowles P J, Werner H J 1985 J. Chem. Phys. 82 5053Google Scholar

    [24]

    Knowles P J, Werner H J 1985 Chem. Phys. Lett. 115 259Google Scholar

    [25]

    Douglas M, Kroll N M 1974 Ann. Phys. 82 89Google Scholar

    [26]

    Hess B A 1986 Phys. Rev. A 33 3742Google Scholar

    [27]

    Berning A, Schweizer M, Werner H J, Knowles P J, Palmieri P 2000 Mol. Phys. 98 1823Google Scholar

    [28]

    Werner H J, Knowles P J, Lindh R, et al. MOLPRO, version 2010.1, a package of ab initio programs, 2010, see http://www.molpro.net [2018-11-15]

    [29]

    Peterson K A, Dunning Jr T H 2002 J. Chem. Phys. 117 10548Google Scholar

    [30]

    Dunning Jr T H 1989 J. Chem. Phys. 90 1007Google Scholar

    [31]

    Murrell J N, Sorbie K S. 1974 J Chem. Soc., Faraday Trans. 70 1552Google Scholar

    [32]

    Le Roy R J Level 8.0: A Computer Program for Solving the Radial Schrödinger Equation for Bound and Quasibound Levels (Waterloo: University of Waterloo) Chemical Physics Research Report CP-663

    [33]

    Lykke K R, Murray K K, Lineberger W C 1991 Rhys. Rev. A 43 6104Google Scholar

    [34]

    Hotop H, Lineberger W C 1985 J. Phys. Chem. Ref. Data 14 731Google Scholar

    [35]

    Moore C E 1971 Atomic Energy Levels (Vol. 1) (Washington, DC: National Bureau of Standards Publications) p181

    [36]

    Cohen-Tannoudji C N 1998 Rev. Phys. Mod. 70 707Google Scholar

    [37]

    Kobayashi J, Aikawa K, Oasa K, Inouye S 2014 Phys. Rev. A 89 021401Google Scholar

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出版历程
  • 收稿日期:  2018-11-16
  • 修回日期:  2019-01-02
  • 上网日期:  2019-03-01
  • 刊出日期:  2019-03-20

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