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本文采用多组态相互作用方法计算了KCl–阴离子前两个离解极限K(2Sg) + Cl–(1Sg)和K(2Pu) + Cl–(1Sg)所对应的3个电子态(X2Σ+, A2Π和B2Σ+)的电子结构. 在计算中考虑了Davidson修正, 核-价电子关联效应及自旋轨道耦合效应. 预测了KCl–阴离子的光谱常数和跃迁性质. 计算得到(2)1/2(ν′)↔(1)1/2(ν′′)和(1)3/2(ν′)↔(1)1/2(ν′′) 跃迁具有高对角分布的弗兰克-康登因子, 分别为0.8816和0.8808; 并且(2)1/2和(1)3/2激发态的自发辐射寿命分别为45.7和45.5 ns. 分别利用(2)1/2(ν′)↔(1)1/2(ν′′)和(1)3/2(ν′)↔(1)1/2(ν′′)跃迁构建了准闭合的能级系统, 冷却KCl–阴离子所需的主激光波长分别为1065.77和1064.24 nm. 同时预测了激光冷却KCl–阴离子能达到的多普勒温度和反冲温度. 计算结果为进一步激光冷却KCl–阴离子的实验提供了理论参数.The potential energy curves and transition dipole moments (TDMs) for three Λ-S states (X2Σ+, A2Π, and B2Σ+) of potassium chloride anion (KCl–) are investigated by using multi-reference configuration interaction (MRCI) method. The def2-AQZVPP-JKFI of K atom and AV5Z-DK all-electron basis set of Cl atom are used in all calculations. The Davidson correction, core-valence (CV) correction, and spin-orbit coupling effect (SOC) are also considered. In the complete active self-consistent field (CASSCF) calculations, eight molecular orbitals are selected as active orbitals, which includ K 4s4p and Cl 3s3p shells; K 3p shell is closed orbital, and the remaining shells (K 1s2s3s and Cl 1s2s2p) are frozen orbitals. In the MRCI+Q calculations, K 3p shell is used for the CV correction. There are 15 electrons in the correlation energy calculations. Then, their spectroscopic parameters, Einstein coefficients, Franck-Condon factors, and radiative lifetimes are obtained by solving the radial Schrödinger equation. The spectroscopic properties and transition properties for the Ω states are predicted. Highly diagonally distributed Franck-Condon factor f00 values for the (2)1/2↔(1)1/2 and (1)3/2↔(1)1/2 transition are 0.8816 and 0.8808, respectively. And the short radiative lifetimes for the (2)1/2 and (1)3/2 excited states are also obtained, i.e. τ[(2)1/2] = 45.7 ns and τ[(1)3/2] = 45.5 ns, which can ensure laser cooling of KCl– anion rapidly. The results indicate that the (2)1/2↔(1)1/2 and (1)3/2↔(1)1/2 quasicycling transitions are suitable to the building of laser cooling projects. For driving the (2)1/2↔(1)1/2 transition, a main pump laser (λ00) and two repumping lasers (λ10 and λ21) are required. Their wavelengths are λ00 = 1065.77 nm, λ10 = 1090.13 nm and λ21 = 1087.76 nm. For driving the (1)3/2↔(1)1/2 transition, the wavelengths are λ00 = 1064.24 nm, λ10 = 1088.54 nm, and λ21 = 1086.17 nm. The cooling wavelengths of KCl- anion for two transitions are both deep in the infrared range. Finally, the Doppler temperature and recoil temperature for two transitions are also calculated, respectively. The Doppler temperatures for (2)1/2↔(1)1/2 and (1)3/2(1)1/2 transitions are 83.57 μK and 83.93 μK, and the recoil temperatures for two transitions are 226 nK and 227 nK, respectively. for two transitions are 226 nK and 227 nK, respectively.
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Keywords:
- spin-orbit coupling /
- Franck-Condon factors /
- spontaneous radiative lifetimes /
- laser cooling
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图 1 KCl-阴离子的势能曲线 (a) Λ-S态; (b) Ω态
Fig. 1. Potential energy curves of KCl– anion: (a) Λ-S states; (b) Ω states.
图 4 激光冷却KCl–阴离子的方案 (a) (2)1/2↔(1)1/2准闭合循环跃迁系统; (b) (1)3/2↔(1)1/2准闭合循环跃迁系统
Fig. 4. Proposed laser cooling scheme of KCl– anion: (a) Using (2)1/2↔(1)1/2 transition; (b) using (1)3/2↔(1)1/2 transition.
表 1 KCl–阴离子Ω电子态的离解极限
Table 1. The dissociation relationship for the Ω states of KCl– anion.
原子态 Ω态 ΔE/cm–1 计算值 实验值[33] K(2S1/2) + Cl–(1S0) (1)1/2 0 0 K(2P1/2) + Cl– (1S0) (2)1/2 12997.94 12985.17 K(2P3/2) + Cl– (1S0) (3)1/2, (1)3/2 13046.23 13042.89 
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表 2 KCl– 阴离子的Ω态的光谱常数
Table 2. Spectroscopic parameters for the Ω states of KCl– anion.
Ω态 对应的Λ-S态 Re/Å ωe/cm–1 Be/cm–1 De/eV Te/cm–1 (1)1/2 X2Σ+ 2.8290 212.34 0.1143 1.3483 0 (2)1/2 A2Π 2.7839 229.64 0.1180 1.7976 9375.30 (1)3/2 A2Π 2.7836 229.65 0.1180 1.8018 9388.68 (3)1/2 B2Σ+ 2.7550 235.48 0.1205 1.3865 12746.21
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表 3 (2)1/2↔(1)1/2和(1)3/2↔(1)1/2跃迁的FCFs, Aν′ν′′和τ
Table 3. FCFs, spontaneous emission rates Aν′ν′′ and spontaneous radiative lifetime τ for the (2)1/2↔(1)1/2 and (1)3/2↔(1)1/2 transitions.
跃迁 ν′′ 0 1 2 3 (2)1/2↔(1)1/2 Aν′ν′′/s–1 1.9384(7)a 2.3044(6) 1.7867(5) 1.1906(4) ν′ = 0 fν′ν′′ 0.8816 0.1090 0.0088 0.0006 τ/ns 45.7 Aν′ν′′/s–1 2.5793(6) 1.4757(7) 4.0633(6) 5.0295(5) ν′ = 1 fν′ν′′ 0.1128 0.6687 0.1914 0.0246 τ/ns 45.5 Aν′ν′′/s–1 1.3368(5) 4.7122(6) 1.0816(7) 5.3057(6) ν′ = 2 fν′ν′′ 0.0056 0.2052 0.4883 0.2490 τ/ns 45.4 (1)3/2↔(1)1/2 Aν′ν′′/s–1 1.9451(7) 2.3276(6) 1.8184(5) 1.2242(4) ν′ = 0 fν′ν′′ 0.8808 0.1096 0.0089 0.0006 τ/ns 45.5 Aν′ν′′/s–1 2.6063(6) 1.4777(7) 5.1089(5) 4.7631(4) ν′ = 1 fν′ν′′ 0.1134 0.6668 0.1924 0.0249 τ/ns 45.4 Aν′ν′′/s–1 1.3578(5) 4.7578(6) 1.0803(7) 5.3483(6) ν′ = 2 fν′ν′′ 0.0057 0.2063 0.4857 0.2499 τ/ns 45.2 注: a1.9384(7)表示1.9384 × 107.
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表 4 (3)1/2↔(1)1/2, (3)1/2↔(2)1/2和(3)1/2↔(1)3/2跃迁的FCF, 总辐射速率A0和辐射寿命
Table 4. FCFs, total emission rates A0 and τ for the (3)1/2↔(1)1/2, (3)1/2↔(2)1/2 and (3)1/2↔(1)3/2 transitions.
跃迁 f00 A0/s–1 τ0/s (3)1/2↔(1)1/2 0.7122 2.6535(7) 3.77(–8) (3)1/2↔(2)1/2 0.9484 2.3716(5) 4.22(–6) (3)1/2↔(1)3/2 0.9490 2.3435(5) 4.27(–6) 注: a1.9384(7)表示1.9384 × 107.
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[1] van Veldhoven J, Küpper J, Bethlem H L, Sartakov B, van Roij A J A, Meijer G 2004 Eur. Phys. J. D 31 337
Google Scholar
[2] Micheli A, Brennen G K, Zoller P 2006 Nat. Phys. 2 341
Google Scholar
[3] Willitsch S, Bell M T, Gingell A D, Procter S R, Softley T P 2008 Phys. Rev. Lett. 100 043203
Google Scholar
[4] Shuman E S, Barry J F, de Mille D 2010 Nature 467 820
Google Scholar
[5] Hummon M T, Yeo M, Stuhl B K, Collopy A L, Xia Y, Ye J 2013 Phys. Rev. Lett. 110 143001
Google Scholar
[6] 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 053416
Google Scholar
[7] Gao Y, Gao T 2014 Phys. Rev. A 90 052506
Google Scholar
[8] 张云光, 张华, 窦戈, 徐建刚 2017 66 233101
Google Scholar
Zhang Y G, Zhang H, Dou G, Xu J G 2017 Acta Phys. Sin. 66 233101
Google Scholar
[9] Cui J, Xu J G, Qi J X, Dou G, Zhang Y G 2018 Chin. Phys. B 27 103101
Google Scholar
[10] Yzombard P, Hamamda M, Gerber S, Doser M, Comparat D 2015 Phys. Rev. Lett. 114 213001
Google Scholar
[11] Wan M, Huang D, Yu Y, Zhang Y 2017 Phys. Chem. Chem. Phys. 19 27360
Google Scholar
[12] 万明杰, 李松, 金成国, 罗华锋 2019 68 063103
Google Scholar
Wan M J, Li S, Jin C G, Luo H F 2019 Acta Phys. Sin. 68 063103
Google Scholar
[13] Zhang Q, Yang C, Wang M, Ma X, Liu W 2017 Spectrochim. Acta, Part A 182 130
Google Scholar
[14] Zhang Q, Yang C, Wang M, Ma X, Liu W 2017 Spectrochim. Acta, Part A 185 365
Google Scholar
[15] Huber K P, Herzberg G 1979 Constants of Diatomic Molecules (Vol. IV): Molecular Spectra and Molecular Structure (New York: Van Nostrand Reinhold) p358
[16] Ram R S, Dulick M, Guo B, Zhang K Q, Bernath P F 1997 J. Mol. Spectrosc. 183 360
Google Scholar
[17] Seth M, Pernpointner M, Bowmaker G A, Schwerdtfeger P 1999 Mol. Phys. 96 1767
[18] Wan M J, Shao J X, Huang D H, Jin C G, Yu Y, Wang F H 2015 Phys. Chem. Chem. Phys. 17 26731
Google Scholar
[19] Wan M J, Shao J X, Gao Y F, Huang D H, Yang J S, Cao Q L, Jin C G, Wang F H 2015 J. Chem. Phys. 143 024302
Google Scholar
[20] Fu M K, Ma H T, Cao J W, Bian W S 2016 J. Chem. Phys. 144 184302
Google Scholar
[21] Wan M J, Yuan D, Jin C G, Wang F H, Yang Y J, Yu Y, Shao J X 2016 J. Chem. Phys. 145 024309
Google Scholar
[22] Yuan X, Yin S, Shen Y, Liu Y, Lian Y, Xu H F, Yan B 2018 J. Chem. Phys. 149 094306
Google Scholar
[23] Werner H J, Knowles P J, Lindh R, et al. 2010 MOLPRO, version 2010.1, A Package of ab initio Programs, http://www.molpro.net
[24] Knowles P J, Werner H J 1985 J. Chem. Phys. 82 5053
Google Scholar
[25] Werner H J, Knowles P J 1988 J. Chem. Phys. 89 5803
Google Scholar
[26] Xiao K L, Yang C L, Wang M S, Ma X G, Liu W W 2013 J. Chem. Phys. 139 074305
Google Scholar
[27] Weigend F 2008 J. Comput. Chem. 29 167
Google Scholar
[28] Woon D E, Dunning Jr T H 1993 J. Chem. Phys. 98 1358
Google Scholar
[29] Berning A, Schweizer M, Werner H J, Knowles P J, Palmieri P 2000 Mol. Phys. 98 1823
Google Scholar
[30] Le Roy R J Level 8.0: A Computer Program for Solving the Radial Schrödinger Equation for Bound and Quasibound Levels, University of Waterloo Chemical Physics Research Report CP-663. http://leroy.uwaterloo.ca/programs
[31] Hotop H, Lineberger 1985 J. Phys. Chem. Ref. Data 14 731
Google Scholar
[32] Berzinsh U, Gustafsson M, Hanstorp D, Klinkmueller A E, Ljungblad U, Maartensson-Pendrill A M 1995 Phys. Rev. A 51 231
Google Scholar
[33] Moore C E 1971 Atomic Energy Levels (Vol. 1) Natl. Stand Ref. Data Ser. Natl. Bur. Stand. No. 35 (Washington, DC: U.S. GPO) p228
[34] Kobayashi J, Aikawa K, Oasa K, Inouye S 2014 Phys. Rev. A 89 021401
Google Scholar
[35] Cohen-Tannoudji C N 1998 Rev. Mod. Phys. 70 707
Google Scholar
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