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单氯化锶分子低激发态的光谱及跃迁特性

伍冬兰 袁金宏 温玉锋 曾学锋 谢安东

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单氯化锶分子低激发态的光谱及跃迁特性

伍冬兰, 袁金宏, 温玉锋, 曾学锋, 谢安东

Spectrum and transition characteristics of low excited state of strontium chloride molecule

Wu Dong-Lan, Yuan Jin-Hong, Wen Yu-Feng, Zeng Xue-Feng, Xie An-Dong
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  • 利用Davidson修正的内收缩多参考组态相互作用(ic-MRCI + Q)方法, 结合相对论有效芯赝势基(aug-cc-pV5Z-PP)作为Sr原子和相关一致五重基aug-cc-pV5Z为Cl原子的计算基组, 优化计算了单氯化锶(Sr35Cl)分子14个低激发电子态的势能曲线和跃迁偶极矩. 为了获得更加精确的光谱参数, 计算中同时引入核价电子相关和相对论效应修正势能曲线. 利用LEVEL 8.0程序拟合修正的势能曲线, 得到相应电子态的光谱常数、振动能级和分子常数等光谱性质, 结果与近来的已获得的理论计算和实验值符合得较好, 同时给出了Franck-Condon因子和辐射寿命等跃迁性质. 这些精确的光谱跃迁特性可为进一步构建Sr35Cl分子激光冷却方案提供理论支持.
    Sr35Cl is a candidate system for laser cooling. The spectrum and transition characteristics are very important for constructing laser cooling schemes. In this paper, the spectral properties are analyzed by using the Davidson's modified internal contraction multi-reference interaction (ic-MRCI + Q) method, in combination with the relativistic effective core pseudopotential group (aug-cc-pV5Z-PP) as the base group for the calculation of the Sr atom and the related consistent quintile aug-cc-pV5Z as the Cl atom. The potential energy curves and dipole moments of 14 low excited electron states of Sr35Cl molecule are optimized. In order to obtain more accurate spectral parameters, nuclear valence electron correlation and relativistic effect correction are introduced into the calculation. Using the LEVEL 8.0 program to fit the modified potential energy curves of 5 bound states, the spectral properties such as spectral constants, vibration energy levels, and molecular constants of the corresponding electron states are obtained. The results show that there is a double potential well in ${\rm B}^2 \Sigma^+$ state and the cross phenomena are avoided in ${\rm A}^2 \Pi$ and ${\rm C}^2 \Pi$, ${\rm B}^2 \Sigma^+$ and $3^2 \Sigma^+$ respectively. The spectrum and molecular constants are in good agreement with the recently obtained theoretical calculations and experimental values except the adiabatic excitation energy. It may be due to the fact that the effect of the interaction of electronic states is taken into account. The transition properties such as Frank-Condon factor and radiation lifetime are also given. It can be seen that the 0-0 band of ${\rm B}^2 \Sigma^+$${\rm X}^2 \Sigma^+$ transition has the largest Franck-Condon factor of 0.861288, and the diagonalization is obvious, which is the condition for laser cooling. The lifetime of ${\rm B}^2 \Sigma^+$${\rm X}^2 \Sigma^+$ transition is 38.89 ns, which is in accordance with the experimental value 39.6 ns ± l.6 ns. These precise spectral transition characteristics may provide theoretical support for further constructing the laser cooling scheme of Sr35Cl molecule.
      通信作者: 伍冬兰, wudonglan1216@sina.com
    • 基金项目: 国家自然科学基金(批准号: 11564019, 11147158)和江西省教育厅科学技术研究项目(批准号: GJJ170654)资助的课题.
      Corresponding author: Wu Dong-Lan, wudonglan1216@sina.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11564019, 11147158) and the Science and Technology Project of Jiangxi Provincial Education Department, China (Grant No. GJJ170654).
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  • 图 1  Sr35Cl分子14个激发态的势能曲线

    Fig. 1.  Potential energy curves of 14 excited states of Sr35Cl.

    图 2  Sr35Cl分子5个束缚态的电偶极矩

    Fig. 2.  Permanent dipole moments of 5 bound states of Sr35Cl.

    图 3  Sr35Cl分子5个束缚态的跃迁偶极矩

    Fig. 3.  Transition dipole moments of 5 bound states of Sr35Cl.

    表 1  5个束缚态的光谱常数

    Table 1.  Spectroscopic constants of the 5 bound states.

    Λ-S态 Te/cm−1 Re/nm $\omega $e/cm−1 $\omega $e$\chi $e/cm−1 Be/cm−1 104αe/cm−1 De/eV Re附近主要电子组态(%)
    $ {{\rm{X}}^{2}}\Sigma^+$ 0.0 0.2575 309.78 0.8682 0.1016 4.131 3.703 6$\text{σ}$ 27$\text{σ}$ 28$\text{σ}$ α9$\text{σ}$ 03$\text{π}$24$\text{π}$2(78.8)
    6${\rm{\sigma }}$ 27$\text{σ}$ 28$\text{σ}$ 09$\text{σ}$ α3$\text{π}$24$\text{π}$2(7.5)
    理论[26] 0.0 0.255 313 0.93 0.1037
    实验[15] 0.0 0.257 302[27] 0.95[27]
    实验[16] 0.0 302.448 −0.9502 0.1016 4.524
    实验[12] 0.0 302.3 0.950
    $ {{\rm{A}}^{2}}\Pi$ 15779.16 0.2518 330.69 0.1061 2.013 1.673 6$\text{σ}$ 27$\text{σ}$ 28$\text{σ}$ 09$\text{σ}$ 03$\text{π}$ααβ 4$\text{π}$2(85.7)
    理论[26] 14730 0.252 323 0.95 0.1055
    实验[15] 14818 0.255 309[27] 0.98[27]
    实验[16] 14966.727 309.625 0.996 0.1030 4.606
    $ {{\rm{B}}^{2}}\Sigma^+$ 16612.74 0.2538 318.67 0.4874 0.1043 2.599 1.937 6$\text{σ}$ 27$\text{σ}$ 28$\text{σ}$ α9$\text{σ}$ 03$\text{π}$24$\text{π}$2(78.8)
    6${\rm{\sigma }}$ 27$\text{σ}$ 28$\text{σ}$ 09$\text{σ}$ α3$\text{π}$24$\text{π}$2(7.6)
    理论[26] 15714 0.253 319 0.99 0.1055
    实验[15] 15719 0.255 306[27] 0.98[27] 0.1030[16]
    实验[12] 15719.5 306.4 0.98
    $ {{\rm{C}}^{2}}\Pi$ 33532.99 0.3477 425.57 15.5691 0.0554 −11.932 1.546 6$\text{σ}$ 27$\text{σ}$ 28$\text{σ}$ 09$\text{σ}$ 03$\text{π}$ααβ 4$\text{π}$2(59.7)
    6$\text{σ}$ 27$\text{σ}$ 28$\text{σ}$ 29$\text{σ}$ 03$\text{π}$24$\text{π}$2(13.4)
    6$\text{σ}$ 27$\text{σ}$ α8$\text{σ}$ β9$\text{σ}$ 03$\text{π}$ααβ2(9.8)
    6$\text{σ}$ 27$\text{σ}$ α8$\text{σ}$ α9$\text{σ}$ 03$\text{π}$αββ 4$\text{π}$2(2.7)
    理论[26] 26688 0.259 278 0.83 0.1095
    实验[27] 26099 270 0.72
    $ {{\rm{3}}^{2}}\Sigma^+$ 36625.55 0.3519 392.49 10.4544 0.0544 −12.567 1.140 6$\text{σ}$ 27$\text{σ}$ α8$\text{σ}$ 29$\text{σ}$ 03$\text{π}$24$\text{π}$2(51.0)
    6$\text{σ}$ 27$\text{σ}$ 28$\text{σ}$ 09$\text{σ}$ α3$\text{π}$24$\text{π}$2(16.4)
    6$\text{σ}$ 27$\text{σ}$ 28$\text{σ}$ α9$\text{σ}$ 03$\text{π}$ααβ 4$\text{π}$2(4.6)
    6$\text{σ}$ 27$\text{σ}$ 28$\text{σ}$ α9$\text{σ}$ 03$\text{π}$β4$\text{π}$ααβ (4.6)
    6$\text{σ}$ 27$\text{σ}$ 28$\text{σ}$ α9$\text{σ}$ 03$\text{π}$24$\text{π}$2(2.5)
    6$\text{σ}$ 27$\text{σ}$ 28$\text{σ}$ α9$\text{σ}$ 03$\text{π}$αββ 4$\text{π}$2(1.6)
    6$\text{σ}$ 27$\text{σ}$ 28$\text{σ}$ 09$\text{σ}$ α3$\text{π}$α4$\text{π}$αββ (1.6)
    6$\text{σ}$ 27$\text{σ}$ α8$\text{σ}$ 09$\text{σ}$ 03$\text{π}$44$\text{π}$2(1.5)
    6$\text{σ}$ 27$\text{σ}$ α8$\text{σ}$ 09$\text{σ}$ 03$\text{π}$24$\text{π}$4(1.5)
    理论[26] 27979 0.248 358 1.01 0.1095
    实验[15] 28822 344[27] 1.04[27] 0.1030[16]
    下载: 导出CSV

    表 2  Sr35Cl分子$ {{\rm{X}}^{2}}\Sigma^+$, $ {{\rm{A}}^{2}}\Pi$, $ {{\rm{B}}^{2}}\Sigma^+$, $ {{\rm{C}}^{2}}\Pi$$ {{\rm{3}}^{2}}\Sigma^+$Gv, BvDv

    Table 2.  The Gv, Bv and Dv of $ {{\rm{X}}^{2}}\Sigma^+$, $ {{\rm{A}}^{2}}\Pi$, $ {{\rm{B}}^{2}}\Sigma^+$, $ {{\rm{C}}^{2}}\Pi$ and $ {{\rm{3}}^{2}}\Sigma^+$ states of Sr35Cl.

    v 0 1 2 3 4 5 6 7 8 9
    $ {{\rm{X}}^{2}}\Sigma^+$ Gv/cm−1 0 308.69 615.44 919.34 1220.80 1520.91 1820.07 2118.05 2414.53 2709.33
    Bv/cm−1 0.101389 0.100964 0.100567 0.100209 0.099815 0.099369 0.098910 0.098467 0.098043 0.097629
    108Dv/cm−1 4.351839 4.364577 4.467493 4.497514 4.362226 4.242542 4.234360 4.286016 4.334124 4.353049
    $ {{\rm{A}}^{2}}\Pi$ Gv/cm−1 15953.74 16281.83 16598.43 16930.62 17269.01 17605.65 17940.04 18272.59 18603.52 18933.04
    Bv/cm−1 0.106234 0.106462 0.106095 0.105137 0.104604 0.104235 0.103859 0.103475 0.103082 0.102679
    108Dv/cm−1 4.461909 5.111509 3.253476 3.332790 4.007870 4.130323 4.085546 4.040997 3.976138 3.938946
    $ {{\rm{B}}^{2}}\Sigma^+$ Gv/cm−1 16777.58 17097.77 17402.46 17705.63 18020.44 18339.16 18656.69 18972.44 19286.60 19599.30
    Bv/cm−1 0.104260 0.104168 0.104392 0.103697 0.102831 0.102297 0.101900 0.101515 0.101130 0.100741
    108Dv/cm−1 4.416717 5.342062 4.947374 3.120903 3.500412 4.129428 4.273733 4.244199 4.206411 4.139361
    $ {{\rm{C}}^{2}}\Pi$ Gv/cm−1 33822.25 34298.68 34607.21 34880.81 35124.57 35352.15 35566.01 35770.85 35971.25 36169.15
    Bv/cm−1 0.056049 0.057354 0.058912 0.059995 0.060974 0.062071 0.063032 0.063843 0.064515 0.065071
    108Dv/cm−1 0.293093 1.069720 1.371596 2.128287 2.433073 3.023576 3.386636 3.382563 3.426546 3.529599
    $ {{\rm{3}}^{2}}\Sigma^+$ Gv/cm−1 36879.56 37294.02 37638.56 37944.07 38221.43 38480.16 38726.99 38965.82 39199.02 39428.18
    Bv/cm−1 0.055079 0.056481 0.057758 0.059028 0.060242 0.061377 0.062432 0.063414 0.064332 0.065193
    108Dv/cm−1 0.363052 0.690909 1.002658 1.373820 1.690530 1.922724 2.122355 2.300506 2.453955 2.583320
    下载: 导出CSV

    表 3  Sr35Cl分子$ {{\rm{A}}^{2}}\Pi$$ {{\rm{X}}^{2}}\Sigma^+ $, $ {{\rm{B}}^{2}}\Sigma^+$$ {{\rm{X}}^{2}}\Sigma^+ $, $ {{\rm{C}}^{2}}\Pi$$ {{\rm{X}}^{2}}\Sigma^+ $$ {{\rm{3}}^{2}}\Sigma^+$$ {{\rm{X}}^{2}}\Sigma^+ $跃迁的Franck-Condon因子

    Table 3.  The Franck-Condon factors of the transitions $ {{\rm{A}}^{2}}\Pi$$ {{\rm{X}}^{2}}\Sigma^+ $, $ {{\rm{B}}^{2}}\Sigma^+$$ {{\rm{X}}^{2}}\Sigma^+ $, $ {{\rm{C}}^{2}}\Pi$$ {{\rm{X}}^{2}}\Sigma^+ $ and $ {{\rm{3}}^{2}}\Sigma^+$$ {{\rm{X}}^{2}}\Sigma^+ $.

    v′′ = 0 1 2 3 4 5 6 7 8 9
    $ {{\rm{A}}^{2}}\Pi$—$ {{\rm{X}}^{2}}\Sigma^+ $
    v′ = 0 0.656888 0.266608 0.062027 0.011563 0.002170 0.000520 0.000163 0.000048 0.000007 0.000000
    1 0.272308 0.192420 0.320947 0.150685 0.466479 0.012567 0.033544 0.008655 0.000174 0.000137
    2 0.061741 0.365100 0.012591 0.236003 0.200935 0.086356 0.027568 0.007557 0.001791 0.000312
    3 0.008378 0.145153 0.330434 0.013476 0.132392 0.200767 0.112395 0.041433 0.012093 0.002903
    4 0.000641 0.027499 0.211170 0.231162 0.064589 0.062086 0.184983 0.134977 0.058263 0.018761
    5 0.000040 0.003015 0.053925 0.25428 0.132467 0.115528 0.018774 0.155878 0.151198 0.077211
    6 0.000004 0.000182 0.008221 0.084623 0.271397 0.058393 0.151118 0.000803 0.117380 0.157174
    7 0.000000 0.000021 0.006253 0.016398 0.117920 0.263055 0.014702 0.164939 0.005113 0.077068
    8 0.000000 0.000000 0.000052 0.001674 0.027547 0.151418 0.233623 0.000068 0.157208 0.024940
    9 0.000000 0.000000 0.000007 0.000118 0.003627 0.041888 0.181283 0.190225 0.008630 0.133109
    $ {{\rm{B}}^{2}}\Sigma^+$—$ {{\rm{X}}^{2}}\Sigma^+ $
    v′ = 0 0.861288 0.125494 0.011927 0.001065 0.000142 0.000047 0.000025 0.000091 0.000000 0.000000
    1 0.129692 0.603795 0.220001 0.038332 0.006251 0.001365 0.000411 0.000120 0.000019 0.000000
    2 0.008650 0.241321 0.360072 0.284163 0.081308 0.018646 0.004456 0.001109 0.000226 0.000018
    3 0.000365 0.027661 0.352567 0.179385 0.288215 0.112584 0.030079 0.007227 0.001600 0.000265
    4 0.000002 0.001707 0.051462 0.411903 0.083378 0.268533 0.131641 0.039281 0.009668 0.002055
    5 0.000001 0.000017 0.003843 0.078423 0.421433 0.034730 0.246976 0.148790 0.049663 0.012870
    6 0.000000 0.000000 0.000117 0.006341 0.108918 0.407382 0.009402 0.221296 0.163711 0.061334
    7 8 0.000000 0.000000 0.000003 0.000002 0.000001 0.000007 0.000333 0.000002 0.009581 0.000763 0.141252 0.014168 0.381199 0.173321 0.000074 0.346687 0.190975 0.003801 0.174597 0.158106
    9 0.000000 0.000000 0.000000 0.000000 0.000000 0.001272 0.020484 0.203605 0.306437 0.017104
    $ {{\rm{C}}^{2}}\Pi$—$ {{\rm{X}}^{2}}\Sigma^+ $
    v′ = 0 0.000002 0.000057 0.000400 0.002491 0.013257 0.048381 0.121107 0.211164 0.245963 0.199742
    1 0.000028 0.000755 0.003923 0.016478 0.054711 0.112499 0.129055 0.063035 0.000478 0.054393
    2 0.000216 0.004536 0.018057 0.052861 0.110648 0.119527 0.040456 0.002385 0.059184 0.058927
    3 0.000894 0.014294 0.042688 0.083192 0.097065 0.033697 0.003920 0.060262 0.039865 0.000817
    $ {{\rm{3}}^{2}}\Sigma^+$—$ {{\rm{X}}^{2}}\Sigma^+ $
    v′ = 0 0.000005 0.000160 0.001014 0.005583 0.025973 0.082035 0.174625 0.263266 0.237744 0.147940
    1 0.000072 0.001726 0.007985 0.028959 0.080861 0.133268 0.106890 0.018946 0.019348 0.137924
    2 0.000444 0.008122 0.028147 0.068699 0.114064 0.085695 0.008341 0.025544 0.075168 0.024261
    3 0.001887 0.025614 0.064048 0.096749 0.076464 0.007949 0.023664 0.062244 0.010184 0.021472
    4 0.005823 0.057375 0.098715 0.079207 0.013459 0.015420 0.056215 0.010480 0.018687 0.044825
    5 0.013104 0.091074 0.099009 0.027450 0.005603 0.051927 0.016773 0.012448 0.040966 0.001448
    6 0.023467 0.109148 0.062336 0.000039 0.043234 0.033313 0.003366 0.042212 0.004752 0.023015
    7 0.036552 0.106016 0.020316 0.019085 0.055807 0.001734 0.035028 0.017051 0.012699 0.031310
    8 0.052050 0.085867 0.000431 0.051861 0.028088 0.011562 0.037256 0.000833 0.036176 0.001957
    9 0.069548 0.057189 0.008529 0.060907 0.001791 0.038489 0.008713 0.024666 0.015229 0.013407
    下载: 导出CSV

    表 4  Sr35Cl分子$ {{\rm{A}}^{2}}\Pi $$ {{\rm{X}}^{2}}\Sigma^+ $, $ {{\rm{B}}^{2}}\Sigma^+ $$ {{\rm{X}}^{2}}\Sigma^+ $$ {{\rm{C}}^{2}}\Pi $$ {{\rm{X}}^{2}}\Sigma^+ $跃迁的辐射寿命

    Table 4.  Radiative lifetimes of the transitions $ {{\rm{A}}^{2}}\Pi $$ {{\rm{X}}^{2}}\Sigma^+ $, $ {{\rm{B}}^{2}}\Sigma^+ $$ {{\rm{X}}^{2}}\Sigma^+ $ and $ {{\rm{C}}^{2}}\Pi $$ {{\rm{X}}^{2}}\Sigma^+ $.

    Transition Radiative lifetimes/ns
    v′ = 0 v′ = 1 v′ = 2
    $ {{\rm{A}}^{2}}\Pi $—$ {{\rm{X}}^{2}}\Sigma^+ $ 31.23 31.35 31.56
    $ {{\rm{B}}^{2}}\Pi $—$ {{\rm{X}}^{2}}\Sigma^+ $ 38.83 38.89 39.12
    $ {{\rm{C}}^{2}}\Pi$—$ {{\rm{X}}^{2}}\Sigma^+ $ 25.92 26.01 26.18
    下载: 导出CSV
  • [1]

    Micheli A, Brennen G, Zoller P 2006 Nat. Phys. 2 341Google Scholar

    [2]

    Baron J, Campbell W C, DeMille D, Doyle J M, Gabrielse G, Gurevich Y V, Hess P W, Hutzler N R, Kirilov E, Kozyryev I, O'Leary B R, Panda C D, Parsons M F, Petrik E S, Spaun B, Vutha A C, West A D 2014 Science 343 269Google Scholar

    [3]

    Krems R V 2008 Phys. Chem. Chem. Phys. 10 4079Google Scholar

    [4]

    Walters O H, Barratt S 1928 Proc. R. Soc. London Ser. A 118 120Google Scholar

    [5]

    Nakagawa J, Domaille P J, Steimle T C, Harris D O 1978 J. Mol. Spectrosc. 70 374Google Scholar

    [6]

    Dulick M, Bernath P F, Field R W 1980 Can. J. Phys. 58 703Google Scholar

    [7]

    Domaille P J, Steimle T C, Wong N B, Harris D O 1977 J. Mol. Spectrosc. 65 354Google Scholar

    [8]

    Berg L E, Klynning L, Martin H 1980 Phys. Scr. 21 173Google Scholar

    [9]

    Bernath P F, Field R W, Pinchemel B, Lefebvre Y, Schamps J 1981 J. Mol. Spectrosc. 88 175Google Scholar

    [10]

    Reisner D E, Bernath P F, Field R W 1981 J. Mol. Spectrosc. 89 107Google Scholar

    [11]

    Zare R N, Schmeltekopf A L, Harrop W J, Albritton D L 1973 J. Mol. Spectrosc. 46 37Google Scholar

    [12]

    Singh J, Nair K P R, Upadhya K N, Rai D K 1970 Opt. Pure Appl. 3 76

    [13]

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出版历程
  • 收稿日期:  2018-09-26
  • 修回日期:  2018-12-11
  • 上网日期:  2019-02-01
  • 刊出日期:  2019-02-05

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