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The precise measurement of the fine structure and radiative transition properties of highly charged ions (HCI) is essential for testing fundamental physical models, including strong-field quantum electrodynamics (QED) effects, electron correlation effects, relativistic effects, and nuclear effects. These measurements also provide critical atomic physics parameters for astrophysics and fusion plasma physics. Compared with the extensively studied hydrogen-like and lithium-like ion systems, boron-like ions exhibit significant contributions in terms of relativistic and QED effects in their fine structure forbidden transitions. High-precision experimental measurements and theoretical calculations of these systems provide important avenues for further testing fundamental physical models in multi-electron systems. Additionally, boron-like ions are considered promising candidates for HCI optical clocks. This paper presents the latest advancements in experimental and theoretical research on the ground state 2P3/2—2P1/2 transition in boron-like ions, and summarizes the current understanding of their fine and hyperfine structures. It also discusses a proposed experimental setup for measuring the hyperfine splitting of boron-like ions by using an electron beam ion trap combined with high-resolution spectroscopy. This proposal aims to provide a reference for future experimental research on the hyperfine splitting of boron-like ions, to test the QED effects with higher precision, extract the radius of nuclear magnetization distribution, and validate relevant nuclear structure models.
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Keywords:
- highly charged ion /
- hyperfine structure /
- quantum electrodynamics /
- highly charged ion optical clock
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图 1 类硼离子结构示意图(以核自旋为1/2的类硼离子为例)
Figure 1. Schematic structure of boron like ions (Take the example of a boron like ion with a nuclear spin of 1/2).
图 2 (a) 通过QED从头计算的类硼离子2P3/2—2P1/2禁戒跃迁能量的结果与实验结果和MCDF计算结果的对比(QED从头计算[50]; MCDF[54]; 实验结果[6,12,55,56]); (b) Z < 45的放大图
Figure 2. (a) Comparison of the results of the forbidden transition energies of the boron-like ions 2P3/2—2P1/2 calculated by ab initio with experimental and MCDF calculations results (ab initio[50]; MCDF[54]; experimental results[6,12,55,56]); (b) enlarged view of Z < 45.
图 3 兰州重离子储存环示意图, 包括ECR离子源、扇聚焦回旋加速器(SFC)、大型分离扇回旋加速器(SSC)、SSC直线注入器(SSC Linac)、冷却储存环主环(CSRm)和实验环(CSRe)[62]
Figure 3. Schematic diagram of the heavy ion storage ring in Lanzhou, includes the ECR ion source, the sector focusing cyclotron (SFC), the large separating sector cyclotron (SSC), the SSC linear injector (SSC Linac), the CSRm and the CSRe[62].
图 5 (a) 德国马克斯-普朗克研究所的激光精密谱学实验装置[93]. 蓝色激光束通过反射镜从EBIT的收集极进入EBIT的中心漂移管, 与高电荷态离子相互作用; (b) Ar13+离子的激光结合精密谱学实验原理图[19]
Figure 5. (a) Laser Precision Spectroscopy Experimental Setup in Max Planck Institute of Germany[93]. The blue laser beam passes through a reflector from the collection pole of the EBIT into the central drift tube of the EBIT, where it interacts with highly charged state ions; (b) principle Diagram of Laser-Combined Precision Spectroscopy Experiment for Ar13+ ion[19].
图 6 (a) 实验装置示意图, 包括一个作为 HCI 生产场所的 EBIT、一条用于减速和减少 HCI 串能量扩散的光束线、一个具有外部离子注入功能的低温保罗阱(用于存储 HCI 并将其协同冷却至毫开尔文状态)以及一个用于在313 nm处对Be+冷却剂离子进行激光诱导荧光检测的成像系统[94]; (b) 离子引出过程中漂移管电压变化示意图[94]
Figure 6. (a) Illustration of experimental setup consisting of an EBIT as HCI production site, a beamline for deceleration and reduction of energy spread of HCI bunches, a cryogenic Paul trap with external ion injection capabilities for HCI storage and sympathetic cooling to the millikelvin regime, and an imaging system for laser-induced fluorescence detection of the Be+ coolant ions at 313 nm[94]; (b) schematic of the drift tube voltage change during ion elicitation[94].
图 7 制备双离子晶体的时间序列, 从上到下依次为, 由 50—100 个荧光 9Be+ 离子组成的激光冷却库仑晶体被限制在保罗阱中. 单个Ar13+离子沿晶体轴线注入, 共冷却, 最后与9Be+共晶体化. 由于高电荷状态对9Be+的排斥作用, 它呈现为一个巨大的暗空洞. 在没有激光冷却的情况下, 多余的9Be+离子通过调节Paul阱射频电势, 从而减少多余的离子. 最后, 制备出Ar13+-9Be+双离子晶体[20]
Figure 7. Time sequence of HCI recapture and two-ion crystal preparation. In order from top to bottom, a laser-cooled Coulomb crystal of 50–100 fluorescing 9Be+ ions is confined in the Paul trap. A single Ar13+ ion is injected along the crystal axis, sympathetically cooled and finally co-crystallized with 9Be+. It appears as a large dark void owing to the repulsion of the 9Be+ by the high charge state. Excess 9Be+ ions are removed by modulating the Paul trap radio-frequency potential in the absence of laser cooling, resulting in heating and ion losses. Finally, the Ar13+-9Be+ two-ion crystal is prepared[20].
图 8 两个时钟激光器(Ar13+和171Yb+)分别锁定在自己的本地腔体和频率梳上进行预稳定, 并通过数字控制环路最终转向相应的光学转换. 两个频率梳锁定在异常稳定的低温硅腔上. 通过这种方法, 每个光频梳可以获得其时钟激光器与稳定激光器之间的频率比[12]
Figure 8. Each of the two clock lasers (Ar13+ and 171Yb+) is locked for pre-stabilization to its own local cavity and frequency comb, and ultimately steered to the corresponding optical transition by a digital control loop. The two frequency combs are locked to the exceptionally stable cryogenic silicon cavity Si2. This method yields for each comb the frequency ratio between its clock laser and the Si2-stabilized laser. The dedicated laboratories are linked through phase-stabilized optical fibres[12].
图 9 类硼离子16≤Z≤29的计算结果与实验测量结果的比较[55], 图中0处的黑色基线表示Edlén[6]与自己结果的$ \Delta E $, 蓝色
Figure 9. Comparison of calculated results with experimental measurements for the boron-like ions 16 ≤ Z ≤ 29[55], where the black baseline at 0 denotes the ∆E of Edlén[6] versus its own results, the blue box (
图 10 部分适合光学波段测量的类硼离子基态超精细分裂模拟光谱图, 图中给出了模拟光谱的分辨率. 每条线代表F (2P2/3)→F' (2P1/2)跃迁线
Figure 10. Simulation of the ground-state hyperfine splitting spectra of some boron-like ions, with the resolution of the corresponding simulated spectra shown. Each line represents the F (2P2/3)→F' (2P1/2) transition line.
表 1 已有EBIT的主要参数
Table 1. Main parameters of available EBIT.
名称 年份 国家 能量/keV 束流/mA/ 磁场/T 参考文献 Super EBIT 1986 美国 10—200 150 3 [79] EBIT-II 1993 美国 30 200 3 [80] NIST EBIT 1993 美国 33 200 3 [81] Oxford EBIT 1993 英国 0.7—50 200 2.8 [82] Berlin EBIT 1997 德国 40 200 3 [83] Tokyo EBIT 1996 日本 180 330 5 [84] Heidelberg EBIT 2000 德国 100 535 8 [85] Shanghai EBIT 2005 中国 130 160 5 [86] Stockholm EBIT 2007 瑞典 27 150 3 [87] TITAN EBIT 2007 加拿大 27 500 [88] CoBIT 2008 日本 0.1—1 10 0.2 [89] SH-PermEBIT 2012 中国 0.06—5 10.2 0.48 [73] SH-HtscEBIT 2013 中国 0.03—4 10 0.25 [74] HC-EBIT 2018 德国 10 80 0.86 [90] SW-EBIT 2019 中国 0.03—4 9 0.21 [77] 
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表 2 目前已经报道的类硼离子基态精细结构分裂2P3/2—2P1/2实验测量结果, 其中括号中的数字表示跃迁能量的不确定度
Table 2. Experimental measurements of the boron-like ion ground-state fine-structure splitting 2P3/2—2P1/2 that have been reported so far, where the numbers in parentheses indicate the uncertainties in the transition energies.
离子 跃迁能量/eV 参考文献 离子 跃迁能量/eV 参考文献 N2+ 0.02157(13) [6] 40Ar13+ 2.8090135821306312(5) [12] O3+ 0.04786(13) [6] 36Ar13+ 2.8090058148895724(5) [12] F4+ 0.0924(4) [6] K14+ 3.5963(31) [6] Ne5+ 0.1623(5) [6] Ca15+ 4.5397(37) [6] Na6+ 0.2652(8) [6] Sc16+ 5.6583(4) [6] Mg7+ 0.4094(3) [6] Ti17+ 6.9732(4) [56] Al8+ 0.6063(13) [6] V18+ 8.5061(50) [6] Si9+ 0.8665(3) [6] Cr19+ 10.2815(17) [56] P10+ 1.202(2) [6] Mn20+ 12.3100(12) [6] S11+ 1.628860(6) [55] Fe21+ 14.6640(35) [56] Cl12+ 2.158835(10) [55] Ni23+ 20.3286(68) [56] Cu24+ 23.7154(93) [56]
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表 3 已有的高电荷态离子的超精细分裂实验测量结果
Table 3. Existing experimental measurements of hyperfine splitting of highly charged ions.
离子 精度 类型 年份 实验装置 跃迁能级 结果 209Bi82+ 1.6×10–4 类氢 1994 ESR (1s1/2)F=4, 5 243.87(4) nm[21] 165Ho66+ 2.6×10–4 类氢 1996 SuperEBIT (1s1/2) F=3, 4 572.61(15) nm[25] 185Re74+
187Re74+6.6×10–4 类氢 1998 SuperEBIT (1s1/2)F=2, 3 456.05(30) nm[26]
451.69(30) nm[26]209Bi80+ 3.1×10–2 类锂 1998 SuperEBIT (1s22s1/2)F=4, 5 0.820(26) eV[29] 207Pb81+ 1.9×10–4 类氢 1998 ESR (1s1/2)F=0, 1 1019.7(2) nm[27] 203Tl80+ 8.9×10–5 类氢 2001 SuperEBIT (1s1/2)F=0, 1 385.822(30) nm[28] 205Tl80+ 382.184(34) nm[28] Sc18+ 1.3×10–2 类锂 2008 ESR (1s22s1/2)F=3, 4 0.00620(8) eV[30] 141Pr56+ 6.1×10–3 类锂 2014 SuperEBIT (1s22s1/2)F=2, 3 0.1965(12) eV[31] 1.7×10–2 (1s22p1/2)F=2, 3 0.0640(11) eV[31] 141Pr55+ 9.4×10–3 类铍 (1s22s1/22p1/2)F=5/2, 7/2 0.1494(14) eV[31] 1.8×10–2 (1s22s1/22p1/2)F=3/2, 5/2 0.1033(19) eV[31] 7.1×10–3 (1s22s1/22p1/2)F=3/2, 7/2 0.2531(18) eV[31] 209Bi82+ 2.1×10–4 类氢 2014 ESR (1s1/2)F=4, 5 5.0863(11) eV[22] 209Bi80+ 2.3×10–4 类锂 (1s22s1/2)F=4, 5 0.79750(18) eV[22] 209Bi82+ 2.4×10–5 类氢 2015 ESR (1s1/2)F=4, 5 243.821(6) nm[23] 209Bi82+ 1.7×10–5 类氢 2017 ESR (1s1/2)F=4, 5 243.8221(8)(43) nm[24] 209Bi80+ 9.0×10–6 类锂 (1s22s1/2)F=4, 5 1554.377(4)(14) nm[24]
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