Theoretical calculations on lifetimes of the low-lying excited states in Lu+

doi:10.1088/1674-1056/ade8e3

中国物理B ›› 2025, Vol. 34 ›› Issue (12): 123101-123101.doi: 10.1088/1674-1056/ade8e3

Theoretical calculations on lifetimes of the low-lying excited states in Lu⁺

Ting Liang(梁婷)^1,2,3, Min Feng(冯敏)^1,2,3, Jin Cao(曹进)^1,2,3, Yi-Ming Wang(王艺铭)^1,2, Ben-Quan Lu(卢本全)^1,2,†, and Hong Chang(常宏)^1,2,3,‡

1 National Time Service Center, Chinese Academy of Sciences, Xi'an 710600, China;
2 School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 100049, China;
3 Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China

收稿日期:2025-05-07 修回日期:2025-06-10 接受日期:2025-06-27 发布日期:2025-12-04
通讯作者: Ben-Quan Lu, Hong Chang E-mail:lubenquan@ntsc.ac.cn;changhong@ntsc.ac.cn
基金资助:
Project supported by the Innovation Program for Quantum Science and Technology (Grant No. 2021ZD0300902), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB35010202), the Operation and Maintenance of Major Scientific and Technological Infrastructure of the Chinese Academy of Sciences (Grant No. 2024000014), and the Natural Science Foundation of Shaanxi Province (Grant No. 2025JC-YBMS-038).

Theoretical calculations on lifetimes of the low-lying excited states in Lu⁺

Ting Liang(梁婷)^1,2,3, Min Feng(冯敏)^1,2,3, Jin Cao(曹进)^1,2,3, Yi-Ming Wang(王艺铭)^1,2, Ben-Quan Lu(卢本全)^1,2,†, and Hong Chang(常宏)^1,2,3,‡

1 National Time Service Center, Chinese Academy of Sciences, Xi'an 710600, China;
2 School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 100049, China;
3 Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China

Received:2025-05-07 Revised:2025-06-10 Accepted:2025-06-27 Published:2025-12-04
Contact: Ben-Quan Lu, Hong Chang E-mail:lubenquan@ntsc.ac.cn;changhong@ntsc.ac.cn
Supported by:
Project supported by the Innovation Program for Quantum Science and Technology (Grant No. 2021ZD0300902), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB35010202), the Operation and Maintenance of Major Scientific and Technological Infrastructure of the Chinese Academy of Sciences (Grant No. 2024000014), and the Natural Science Foundation of Shaanxi Province (Grant No. 2025JC-YBMS-038).

摘要/Abstract

摘要： The lifetime of the 5d6s $^{3}$D$_{1}$ clock state in Lu$^{+}$ exhibits a large discrepancy between experimental and theoretical values. To resolve this discrepancy, we perform calculations of the magnetic dipole transition rate between the 5d6s $^{3}$D$_{1}$ and 6s$^{2}$ $^{1}$S$_0$ states using the multi-configuration Dirac-Hartree-Fock method. The effects of electron correlations, Breit interaction, and quantum electrodynamics (QED) corrections on the transition parameters are analyzed systematically. The calculated 5d6s $^{3}$D$_{1}$-6s$^{2}$ $^{1}$S$_0$ magnetic dipole transition rate, $1.69(7)\times 10^{-6}$ s$^{-1}$, shows excellent agreement with the experimental measurement. To accurately determine the lifetime of the $^{3}$D$_{1}$ clock state, the hyperfine-induced electric quadrupole transition rate between the $^{3}$D$_{1}$ and ground states is also calculated. Furthermore, the rates of various transitions between states in the 5d6s configuration are obtained. The lifetimes of the $^{3}$D$_{2,3}$ and $^{1}$D$_{2}$ states are consistent with previous theoretical calculations.

关键词: Lu⁺ ion, magnetic dipole transition, electric quadrupole transition, hyperfine-induced interaction, lifetime

Abstract: The lifetime of the 5d6s $^{3}$D$_{1}$ clock state in Lu$^{+}$ exhibits a large discrepancy between experimental and theoretical values. To resolve this discrepancy, we perform calculations of the magnetic dipole transition rate between the 5d6s $^{3}$D$_{1}$ and 6s$^{2}$ $^{1}$S$_0$ states using the multi-configuration Dirac-Hartree-Fock method. The effects of electron correlations, Breit interaction, and quantum electrodynamics (QED) corrections on the transition parameters are analyzed systematically. The calculated 5d6s $^{3}$D$_{1}$-6s$^{2}$ $^{1}$S$_0$ magnetic dipole transition rate, $1.69(7)\times 10^{-6}$ s$^{-1}$, shows excellent agreement with the experimental measurement. To accurately determine the lifetime of the $^{3}$D$_{1}$ clock state, the hyperfine-induced electric quadrupole transition rate between the $^{3}$D$_{1}$ and ground states is also calculated. Furthermore, the rates of various transitions between states in the 5d6s configuration are obtained. The lifetimes of the $^{3}$D$_{2,3}$ and $^{1}$D$_{2}$ states are consistent with previous theoretical calculations.

Key words: Lu⁺ ion, magnetic dipole transition, electric quadrupole transition, hyperfine-induced interaction, lifetime

中图分类号: (Ab initio calculations)

31.15.A-

31.15.ag (Excitation energies and lifetimes; oscillator strengths) 31.15.aj (Relativistic corrections, spin-orbit effects, fine structure; hyperfine structure) 31.15.vj (Electron correlation calculations for atoms and ions: excited states)

Ting Liang(梁婷), Min Feng(冯敏), Jin Cao(曹进), Yi-Ming Wang(王艺铭), Ben-Quan Lu(卢本全), and Hong Chang(常宏). Theoretical calculations on lifetimes of the low-lying excited states in Lu⁺[J]. 中国物理B, 2025, 34(12): 123101-123101.

参考文献

[1] Lu X T, Guo F, Liu Y Y, Cao J, Li J A, Xia J J, Xu Q F, Lu B Q, Wang Y B and Chang H 2025 Metrologia 62 035007
[2] Huang Y, Zhang B L, Zeng M Y, Hao Y M, Ma Z X, Zhang H Q, Guan H, Chen Z, Wang M and Gao K L 2022 Phys. Rev. Appl. 17 034041
[3] Hausser H N, Keller J, Nordmann T, et al. 2025 Phys. Rev. Lett. 134 023201
[4] Cui K, Chao S, Sun C, Wang S, Zhang P, Wei Y, Yuan J, Cao J, Shu Hand Huang X 2022 Eur. Phys. J. D 76 140
[5] Tofful A, Baynham C F A, Curtis E A, Parsons A O, Robertson B I, Schioppo M, Tunesi J, Margolis H S, Hendricks R J, Whale J, Thompson R C and Godun R M 2024 Metrologia 61 045001
[6] Li J, Cui X Y, Jia Z P, Kong D Q, Yu H W, Zhu X Q, Liu X Y, Wang D Z, Zhang X, Huang X Y, Zhu M Y, Yang Y M, Hu Y, Liu X P, Zhai X M, Liu P, Jiang X, Xu P, Dai H N, Chen Y A and Pan J W 2024 Metrologia 61 015006
[7] Zhang Z Q, Arnold K J, Kaewuam R and Barrett M D 2023 Sci. Adv. 9 eadg1971
[8] Aeppli A, Kim K, Warfield W, Safronova M S and Ye J 2024 Phys. Rev. Lett. 133 023401
[9] Brewer S M, Chen J S, Hankin A M, Clements E R, Chou C W, Wineland D J, Hume D B and Leibrandt D R 2019 Phys. Rev. Lett. 123 033201
[10] Arnold K, Kaewuam R, Tan T and Barrett M 2018 Nat. Commun. 9 1650
[11] Kaewuam R, Tan T R, Zhang Z Q, Arnold K J, Safronova M S and Barrett M D 2020 Phys. Rev. A 102 042819
[12] Tan T R, Kaewuam R, Arnold K J, Chanu S R, Zhang Z Q, Safronova M S and Barrett M D 2019 Phys. Rev. Lett. 123 063201
[13] Kaewuam R, Tan T R, Arnold K J, Chanu S R, Zhang Z Q and Barrett M D 2020 Phys. Rev. Lett. 124 083202
[14] Takamoto M, Ushijima I, Ohmae N, Yahagi T, Kokado K, Shinkai H and Katori H 2020 Nat. Photonics 14 411
[15] Bothwell T, Kennedy C, Aeppli A, Kedar D, Robinson J, Oelker E, Staron A and Ye J 2022 Nature 602 420
[16] Arvanitaki A, Huang J W and Van Tilburg K 2015 Phys. Rev. D 91 015015
[17] Kalaydzhyan T and Yu N 2017 Phys. Rev. D 96 075007
[18] Yin M J, Wang T, Lu X T, Li T, Wang Y B, Zhang X F, Li W D, Smerzi A and Chang H 2021 Chin. Phys. Lett. 38 073201
[19] Lu X T, Wang T, Li T, Zhou C H, Yin M J, Wang Y B, Zhang X F and Chang H 2021 Phys. Rev. Lett. 127 033601
[20] Arnold K J, Kaewuam R, Roy A, Paez E, Wang S and Barrett M D 2016 Phys. Rev. A 94 052512
[21] Paez E, Arnold K J, Hajiyev E, Porsev S G, Dzuba V A, Safronova U I, Safronova M S and Barrett M D 2016 Phys. Rev. A 93 042112
[22] Grumer J, Brage T, Andersson M, Li J G, Jönsson P, Li W X, Yang Y, Hutton R and Zou Y M 2014 Phys. Scr. 89 114002
[23] Li W X, Grumer J, Brage T and Jönsson P 2020 Comput. Phys. Commun. 253 107211
[24] Johnson W R 2011 Can. J. Phys. 89 429
[25] Andersson M and Jönsson P 2008 Comput. Phys. Commun. 178 156
[26] Zhao G D, Jin C, Ting L, Min F, Ben Quan L and Hong C 2024 Acta. Phys. Sin. 73 093101
[27] Grant I 2007 Relativistic Quantum Theory of Atoms and Molecules vol 40 (New York: Springer)
[28] Jönsson P, Gaigalas G, Fischer C, Bieroń J, Grant I, Brage T, Ekman J, Godefroid M, Grumer J, Li J G and Li W X 2023 Atoms 11 68
[29] Fischer C F, Godefroid M, Brage T, Jönsson P and Gaigalas G 2016 J. Phys. B: At. Mol. Opt. Phys. 49 182004
[30] Verdebout S, Jönsson P, Gaigalas G, GodefroidMand Fischer C F 2010 J. Phys. B: At. Mol. Opt. Phys. 43 074017
[31] Olsen J, Godefroid M R, Jönsson P, Malmqvist P °A and Fischer C F 1995 Phys. Rev. E 52 4499
[32] Olsen J, Roos B O, Jorgensen P and Jensen H J A 1988 J. Chem. Phys. 89 2185
[33] Li J G, Jönsson P, Godefroid M, Dong C Z and Gaigalas G 2012 Phys. Rev. A 86 052523
[34] Fischer C, Brage T and Jönsson P 2019 Computational Atomic Structure: An MCHF Approach (London: Institute of Physics Publishing)
[35] Li J G, GodefroidMandWang J G 2016 J. Phys. B: At. Mol. Opt. Phys. 49 115002
[36] Jönsson P, He X, Froese Fischer C and Grant I P 2007 Comput. Phys. Commun. 177 597
[37] Fischer C F, Gaigalas G, Jönsson P and Bieroń J 2019 Comput. Phys. Commun. 237 184
[38] Dzuba V A 2014 Phys. Rev. A 90 012517
[39] Kahl E V, Berengut J C, Laatiaoui M, Eliav E and Borschevsky A 2019 Phys. Rev. A 100 062505
[40] Kramida A, Ralchenko Yu, Reader J and NIST ASD Team 2024 NIST Atomic Spectra Database (version 5.12) National Institute of Standards and Technology, Gaithersburg, MD
[41] Kozlov A, Dzuba V A and Flambaum V V 2014 Phys. Rev. A 90 042505

Theoretical calculations on lifetimes of the low-lying excited states in Lu⁺

Theoretical calculations on lifetimes of the low-lying excited states in Lu⁺

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Ruijun Zhang(张锐军), Mingkun Zhang(张明昆), Guoliang Zhang(张国良), Yujian Chen(陈雨箭), Jia Liu(刘佳), Ziqian Tian(田自谦), Ye Yu(余烨), Peng Zhao(赵鹏), Jiafa Cai(蔡加法), Xiaping Chen(陈厦平), Dingqu Lin(林鼎渠), Shaoxiong Wu(吴少雄), Yuning Zhang(张宇宁), Xingliang Xu(徐星亮), Rongdun Hong(洪荣墩), and Feng Zhang(张峰). Prolonging carrier lifetime in P-type 4H-SiC epilayer by thermal oxidation and hydrogen annealing[J]. 中国物理B, 2025, 34(6): 67201-067201.
[2]	Kai Wang(王凯), Zhong Liu(刘中), Shuying Wang(王淑英), Chu Qin(秦楚), Zilei Yu(於子雷), and Xiaofang Zhao(赵小芳). Experiment study of energy redistribution during collisions of the excited state H₂(1, 7) with LiH[J]. 中国物理B, 2025, 34(11): 113401-113401.
[3]	Peibo Ding(丁培波), Biao Shan(单标), Yuhang Zhao(赵宇航), Yajing Yang(杨雅婧), Liangchao Chen(陈良超), Zengming Meng(孟增明), Pengjun Wang(王鹏军), and Lianghui Huang(黄良辉). Optimal preparation of Bose and Fermi atomic gas mixtures of ⁸⁷Rb and ⁴⁰K in a crossed optical dipole trap[J]. 中国物理B, 2024, 33(6): 63402-063402.
[4]	Yong-He Deng(邓永和), Bei Chen(陈贝), Qing-Hua Qi(祁清华), Bing-Bing Li(李兵兵), Ming Gao(高明), Da-Dong Wen(文大东), Xiao-Yun Wang(王小云), and Ping Peng(彭平). Research of caged dynamics of clusters center atoms in Pd₈₂Si₁₈ amorphous alloy[J]. 中国物理B, 2024, 33(4): 47102-047102.
[5]	Xin Liu(刘新), Zhi-Long Chen(陈之龙), Hu Wang(王虎), Wen-Qing Zhang(张雯清), Hao Dong(董昊), Peng-Xiang Wang(王鹏祥), and Yu-Chuan Shao(邵宇川). Stable photocurrent—voltage characteristics of perovskite single crystal detectors obtained by pulsed bias[J]. 中国物理B, 2024, 33(4): 48101-048101.
[6]	Huiru Cheng(程慧茹), Yuhuan Li(李钰环), Ziwen Pan(潘子文), Jiandang Liu(刘建党), and Bangjiao Ye(叶邦角). Upconversion photoluminescence of Er-doped Bi₄Ti₃O₁₂ ceramics enhanced by vacancy clusters revealed by positron annihilation spectroscopy[J]. 中国物理B, 2024, 33(12): 126102-126102.
[7]	Hao-Lei Cui(崔浩磊), Zhen Quan(权真), and Shu-Dong Wang(王舒东). Strain tunable excitonic optical properties in monolayer Ga₂O₃[J]. 中国物理B, 2024, 33(10): 107104-107104.
[8]	Peng-Yuan Chen(陈鹏远), Zhen Quan(权真), and Shu-Dong Wang(王舒东). Excitonic optical properties in monolayer SnP₂S₆[J]. 中国物理B, 2024, 33(10): 107105-107105.
[9]	Shuang Li(李双), Jing Zhou(周璟), Liu-Hong Zhu(朱柳红), Xiu-Fei Mei(梅秀菲), and Jun Yan(颜君). Fully relativistic energies, transition properties, and lifetimes of lithium-like germanium[J]. 中国物理B, 2024, 33(10): 103102-103102.
[10]	Ruijun Zhang(张锐军), Rongdun Hong(洪荣墩), Jingrui Han(韩景瑞), Hungkit Ting(丁雄杰), Xiguang Li(李锡光), Jiafa Cai(蔡加法), Xiaping Chen(陈厦平), Deyi Fu(傅德颐), Dingqu Lin(林鼎渠), Mingkun Zhang(张明昆), Shaoxiong Wu(吴少雄),Yuning Zhang(张宇宁), Zhengyun Wu(吴正云), and Feng Zhang(张峰). Impacts of hydrogen annealing on the carrier lifetimes in p-type 4H-SiC after thermal oxidation[J]. 中国物理B, 2023, 32(6): 67205-067205.
[11]	Yuyi Zhang(张钰伊), Yajie Bian(卞亚杰), Wei Zhang(张炜), Yiting Liu(刘易婷), Xiaolei Zhang(张晓磊),Mengdi Chen(陈梦迪), Bingwen Hu(胡炳文), and Qingyuan Jin(金庆原). Molecular fluorescence significantly enhanced by gold nanoparticles@zeolitic imidazolate framework-8[J]. 中国物理B, 2023, 32(5): 54208-054208.
[12]	Shuang Li(李双), Min Zhao(赵敏), Guo-Qing Liu(刘国庆), Chang-Bao Hu(胡昌宝), and Guo-Zhu Pan(潘国柱). Fully relativistic many-body perturbation energies, transition properties, and lifetimes of lithium-like iron Fe XXIV[J]. 中国物理B, 2023, 32(10): 103101-103101.
[13]	Jialin Liu(刘佳林), Yintao Wang(王银涛), Bingsheng Tu(屠秉晟), Liangyu Huang(黄良玉), Ran Si(司然), Jiguang Li(李冀光), Mingwu Zhang(张明武), Yunqing Fu(傅云清), Yaming Zou(邹亚明), and Ke Yao(姚科). Lifetime measurement of the 3d⁹ ²D_3/2 metastable level in Mo¹⁵⁺ at an electron beam ion trap[J]. 中国物理B, 2023, 32(10): 103201-103201.
[14]	Mu-Hong Hu(胡木宏), Nan Wang(王楠), Pin-Jun Ouyang(欧阳品均),Xin-Jie Feng(冯新杰), Yang Yang(杨扬), and Chen-Sheng Wu(武晨晟). Energy levels and magnetic dipole transition parameters for the nitrogen isoelectronic sequence[J]. 中国物理B, 2022, 31(9): 93101-093101.
[15]	Ben Chen(陈犇), Yi-Ni Chen(陈旖旎), Jia-Nuan Pan(潘佳煖), Jian-Ping Yin(印建平), and Hai-Ling Wang(汪海玲)^†. Spectroscopic study of B²Σ⁺–X₁ ²Π_1/2 transition of electron electric dipole moment candidate PbF[J]. 中国物理B, 2022, 31(9): 93301-093301.