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少电子离子束缚态电子g因子的精密测量是借助原子分子体系研究束缚态量子电动力学(QED)理论的有效途径. 特别是在高电荷态重核体系中, 原子核与内壳层电子之间极强的电磁相互作用为研究极端电磁场环境下的QED效应提供了独一无二的条件. 通过精确测量束缚态电子g因子, 还可以分析核效应、测定核结构参数、确定基本物理常数等. 少电子离子束缚态电子g因子的研究已经成为精密谱学方向的前沿课题. 潘宁离子阱(借助稳态电磁场囚禁离子的系统)是进行g因子测量的有效实验装置之一. 本综述将对基于潘宁离子阱开展少电子离子束缚态电子g因子的实验研究进行全面回顾, 介绍基本实验原理与测量方法, 重点论述该领域在近几年中的重要实验成果, 并对未来发展进行简要展望.
The electron g factor is an important fundamental structural parameter in atomic physics, as it reveals various mechanisms of interactions between electrons and external fields. Precise measurements of g factors of bound electrons in simple atomic and molecular systems provide an effective method for investigating the bound-state quantum electrodynamics (QED) theory. Especially in highly-charged heavy ions (HCIs), the strong electromagnetic interactions between the nuclei and inner-shell electrons provide unique opportunities to test QED under extremely strong fields. Accurate measurements of the g factors of the bound-state electrons are also important for determining nuclear effects, nuclear parameters and fundamental constants. The research on g factors of the bound-state electrons has become a frontier topic in fundamental physics. A Penning trap, which uses steady-state electromagnetic fields to confine charged particles, is utilized to precisely measure the g factor. This paper presents a comprehensive review of the experiments on g factors for few-electron simple systems in Penning traps, including experimental principles, experimental setups, measurement methods, and a summary of important research findings. The physical concept of the electron g factor and its historical research background are introduced. The electron g factor is considered as an effective probe to study higher-order QED effects. Through high-precision measurements of the free electron g factor, discrepancies between the fine-structure constants and other experimental results in atomic physics are identified. Notably, the g factor of the 1s electron in HCIs deviates significantly from the value for free electrons as the atomic number increases. Experimental principles, including the principle of the Penning trap and the principle of measuring the bound-state electron g factors are discussed. A double-trap experiment setup and related precision measurement techniques are also introduced. This paper reviews several milestone experiments including (1) the stringent test of bound-state QED by precise measurement of bound-state electron g factor of a 118Sn49+ ion, (2) measurement of the g factors of lithium-like and boron-like ions and their applications, and (3) measurement of the g-factor isotope shift by using an advanced two-ion balance technique in the Penning trap, providing an insight into the QED effects in nuclear recoil. Finally, this paper summarizes the challenges currently faced in measuring the g factors of bound-state electrons in few-electron ion systems and provides the prospects for the future developments of this field. -
Keywords:
- few-electron ions /
- g factor /
- Penning trap /
- precision measurement
1. 引 言
阻变存储器(resistance random access memory, RRAM)可以通过电压调控实现高阻态(high resistance state, HRS)与低阻态(low resistance state, LRS)之间的切换, 进而完成数据“0”或“1”的存储[1,2]. 量子点(quantum dots, QDs)的合成方法简单、能耗低, 可以通过控制它的尺寸、形状、组成和表面等调控其阻变性能[3,4]. Han等[5]将无机QDs引入有机介质层(聚甲基丙烯酸甲酯)中制备了QDs/聚合物复合RRAM. 但由于QDs很难被均匀地分散在聚合物中, QDs、聚合物以及电极之间的界面状态不可控, 致使器件的循环稳定性较差[6]. 采用全无机QDs作为介质层可获得高稳定性的RRAM[7]. Thomas等[8]制备的MoS2 QDs RRAM在运行103 s后仍具有良好的稳定性, 但阻变开关比较低.
研究发现, 铁电材料通过铁电极化可调控其与电极界面间势垒高度来影响器件的电阻大小[1,9,10], 从而实现高低阻态间切换. Fan等[11]在Au/NSTO结构中引入BaTiO3铁电薄膜, 发现BaTiO3铁电薄膜能够通过铁电极化增强对Au/NSTO界面处势垒高度以及耗尽区的宽度的调控, 从而提高RRAM的阻变性能, 并具有更稳定的循环使用寿命.
CuInS2 QDs具有制备成本低、不含有毒元素、带隙可调等特点[12-14], 当QDs尺寸小于8 nm时可观察到显著的量子限域效应[15], 引入介质层可以改变其阻变性能[16]. 铌掺杂锆钛酸铅 (Nb:Pb(Zr0.52Ti0.48)O3, PNZT)具有高介电性、大剩余极化强度、宽禁带宽度和低漏电流等特点[17]. 本文拟利用PNZT可切换的铁电极化调控CuInS2 QDs的阻变性能, 进一步提升CuInS2 QDs基阻变存储器的数据存储能力.
2. 实验方法
2.1 实验过程
以Si/SiO2/Ti/Pt作为基底, 采用磁控溅射法制备Pb[(Zr0.48Ti0.52)0.97Nb0.03]O3 (PZNT)薄膜, 溅射功率为130 W, 溅射气压为0.5 Pa, Ar∶O2为90∶2. 采用电晕极化对PNZT薄膜进行预极化处理, 在室温下向薄膜施加10 V的正负向电压, 并保压10 min, 得到剩余极化方向相反的两种薄膜. 采用热注入法制备CuInS2 QDs, 称量0.75 mmol的醋酸铟(In(ac)3, 纯度99.9%)和0.75 mmol的碘化亚铜(CuI, 纯度99.0%), 加入装有30 mL油胺(C18H37N, 纯度90.0%)的三颈烧瓶内. 在氩气氛围中搅拌加热至140 ℃, 得到淡黄色溶液. 称量1.5 mmol的二苯基硫脲(C13H12N2S, 纯度98.0%)加入2.25 mL二苯醚(C12H10O, 纯度90.0%)溶液中, 在80 ℃下加热溶解, 然后迅速倒入三颈烧瓶, 计时反应5 min. 将反应好后的溶液冷却至室温, 加入甲醇并以9500 r/min的转速离心3 min得到CuInS2 QDs粉末, 将其分散于正己烷中封装等待使用. 将分散于正己烷的CuInS2 QDs溶液分别旋涂在正向极化、负向极化和无极化的PNZT薄膜上, 90 ℃下热处理5 min, 采用磁控溅射法在CuInS2 QDs薄膜上面溅射Au电极, 结构如图1所示.
图 1 CuInS2 QDs/PNZT RRAM结构示意图Fig. 1. Schematic diagram of CuInS2 QDs/PNZT RRAM structure.2.2 测试表征
采用X射线衍射仪(XRD, X′ Pert Pro, PANalytical, Holland)表征PNZT薄膜和CuInS2 QDs的晶体结构. 此外, 采用高分辨率透射电子显微镜(HRTEM, JEM-2010F, Japan)表征CuInS2 QDs的微观形貌. 用场发射扫描电子显微镜(FESEM, Zeiss Ultra Plus, Germany)对PNZT 薄膜以及CuInS2 QDs/PNZT薄膜的表面及断面进行形貌表征. 采用紫外光电子能谱(UPS, AXIS SUPRA, Japan)和紫外可见光吸收光谱(UV-Vis, UV-2550, Japan)对PNZT薄膜的吸收光谱与能带结构进行表征. 采用Keithley 2450测试CuInS2 QDs/PNZT RRAM的阻变性能与循环稳定性, 读取电压为 –0.1 V, 电压脉冲时间保持1 ms.
2.3 阻变机理表征中涉及的物理公式
文中涉及的各导电机制的拟合公式及Tauc公式如下.
欧姆导电机制[18]:
J=nqμE; (1) 热离子发射机制[19]:
J=A∗T2exp{q[ϕB−√qE/(4πεrε0)]kBT}; (2) 空间电荷限制电流 (space charge limit current, SCLC)机制[20]:
J=98μεrθE2d3. (3) 式中, n代表材料导带中所含电子的密度, μ代表电荷的迁移率, q代表电荷量, kB代表玻尔兹曼常数, T代表温度, A*是Richardson常数, ϕB代表界面势垒高度, εr代表相对介电常数, ε0代表真空介电常数, d代表厚度, E代表电场强度, θ代表自由电子密度比率.
Tauc公式[21]为
αhν=A(hν−Eg)m, (4) 其中,
α 表示薄膜的光吸收系数,h 为普朗克常数, A为常数,ν 为频率, Eg为禁带宽度, 不同指数m代表直接带隙和间接带隙半导体.3. 结果与讨论
3.1 CuInS2 QDs/PNZT复合薄膜的制备及结构表征
图2(a)为CuInS2 QDs的TEM图像, 可见CuInS2 QDs呈单分散球状结构, 且球形度良好. 图2(a)中的插图是CuInS2 QDs的尺寸分布直方图, 可见制备的QDs尺寸均一, 约为5 nm. 图2(b)为CuInS2 QDs的HRTEM图像, 清晰明亮的晶格条纹表明制备的CuInS2 QDs具有较高的结晶度, QDs的晶格条纹间距为0.301 nm, 对应于CuInS2 QDs的(112)晶面. CuInS2 QDs的XRD图谱如图2(c)所示, 其在27.58°, 46.81°和55.23°处有较强的衍射峰, XRD衍射结果对应于标准PDF卡片 (ICDD: 01-075-0106), 三个较强衍射峰分别与CuInS2的(112), (204)和(116)晶面相对应. 以上结果表明, 制备的CuInS2 QDs具有四方相黄铜矿结构.
图 2 (a) CuInS2 QDs的TEM图像 (插图为CuInS2 QDs 尺寸分布直方图); (b) CuInS2 QDs的HRTEM图像; (c) CuInS2 QDs的XRD图谱Fig. 2. (a) TEM image of CuInS2 QDs (Inset is the size distribution histogram of CuInS2 QDs); (b) HRTEM image of CuInS2 QDs; (c) XRD pattern of CuInS2 QDs.图3(a)为PNZT 薄膜的XRD图谱, 可见PNZT薄膜具有四方相钙钛矿结构(ICDD 01-089-8266), 其最高峰位于31.05°, 对应于PNZT的(110)晶面. 图3(b)为PNZT的电滞回线. 可见PNZT薄膜拥有较大的剩余极化强度, 即31.0 μC/cm2, 矫顽场强为11.6 kV/mm.
图 3 PNZT薄膜的XRD图谱 (a) 和电滞回线 (b)Fig. 3. XRD pattern (a) and hysteresis loop (b) of PNZT film.图4(a)展示了CuInS2 QDs/PNZT RRAM断面的FESEM图像, 可见CuInS2 QDs层的厚度在81 nm左右, PNZT薄膜约为104 nm. 两者界面结合良好, QDs膜层致密且无明显孔洞. 图4(b)为PNZT薄膜表面的FESEM图像, 可见PNZT薄膜表面均匀致密, 晶粒形状尺寸均一. 图4(c)为旋涂CuInS2 QDs后PNZT表面FESEM图像, QDs在PNZT薄膜表面呈单分散分布, 无明显的团聚. 图4(d)是CuInS2 QDs薄膜的元素分布, 可见Cu, In和S三种元素均匀地分布在PNZT薄膜的表面, 以上结果表明CuInS2 QDs薄膜已经被均匀地覆盖在PNZT薄膜上.
图 4 (a) CuInS2 QDs/PNZT RRAM的断面FESEM图像; (b) PNZT薄膜与(c) CuInS2 QDs薄膜的表面FESEM图像; (d) CuInS2 QDs薄膜表面元素分布图Fig. 4. (a) Cross-sectional FESEM image of CuInS2 QDs/PNZT RRAM; FESEM image of the surface for (b) PNZT film and (c) CuInS2 QDs film; (d) surface element distribution of CuInS2 QDs film.3.2 CuInS2 QDs/PNZT复合薄膜的阻变性能表征
分别在不同极化状态的PNZT薄膜上旋涂CuInS2 QDs制备CuInS2 QDs/PNZT复合薄膜, I-V测试曲线如图5(a)所示, 开关电压的直方图见图5(b), 图5(c)—(f) 分别为CuInS2 QDs RRAM和无极化及正负向极化下CuInS2 QDs/PNZT复合薄膜的循环耐久性测试. 可见CuInS2 QDs/PNZT复合薄膜呈现双极性阻变特征, 在不同极化状态下表现出不同的阻变性能, 相关数据见表1.
图 5 CuInS2 QDs RRAM与正负向和无极化下CuInS2 QDs/PNZT RRAM的 (a) I-V曲线与 (b) 开关电压直方图; (c) CuInS2 QDs RRAM循环稳定性测试; (d) 无极化, (e) 负向极化和 (f) 正向极化的CuInS2 QDs/PNZT RRAM循环稳定性测试(插图为施加的脉冲电压)Fig. 5. (a) I-V curves and (b) SET/RESET voltage histograms of CuInS2 QDs RRAM and CuInS2 QDs/PNZT RRAM with the different polarization orientations; (c) cycling stability test of CuInS2 QDs RRAM; cycling stability test of (d) no polarized, (e) negative polarized and (f) positive polarized CuInS2 QDs/PNZT RRAM (Inset is the applied pulse voltage).表 1 不同器件的阻变性能Table 1. Resistance switching performance of the different devices.测试单元 工作电压/V 阻变开关比 CuInS2 QDs RRAM –4.5/4.5 3.4×103 无极化PNZT/CuInS2 QDs RRAM –5.6/5.0 1.7×105 正向极化PNZT/CuInS2 QDs RRAM –6.4/5.7 1.8×104 负向极化PNZT/CuInS2 QDs RRAM –4.1/3.4 4.8×106 可以看出, PNZT薄膜引入可以明显提高CuInS2 QDs的阻变开关比, 开关电压则有不同的变化. 引入没有极化的PNZT薄膜时, 由于PNZT本身的高绝缘性, CuInS2 QDs/PNZT复合薄膜HRS和LRS状态的电阻不同程度地增加, 开关电压明显增加, 但阻变开关比提高了约102. 正向极化PNZT薄膜使得开关电压进一步提高, 同时提高了LRS状态的电阻, 导致CuInS2 QDs/PNZT复合薄膜阻变开关比反而降低. 负向极化则使得开关电压明显降低, 甚至比CuInS2 QDs薄膜的还低, 同时也降低了CuInS2 QDs/PNZT复合薄膜LRS状态的电阻, 导致阻变开关比进一步提高. 说明引入PNZT铁电薄膜可以改善CuInS2 QDs的阻变性能, 通过改变PNZT的极化方向可以调控复合薄膜的阻变性能.
3.3 CuInS2 QDs/PNZT复合薄膜的阻变机理表征
CuInS2 QDs RRAM的I-V测试曲线取双对数如图6所示. 起初CuInS2 QDs处于HRS状态, 当负向施加电压处于0 V到–0.9 V区间内时 (Slope1), 曲线的斜率是1.04, 即I与V成正比, 属于欧姆导电行为; 当施加电压处于–0.9 V到–2.2 V区间时 (Slope2), 曲线的拟合斜率为1.99, 可认为I与V2成正比, 表明此时电流受SCLC导电机制调控; 继续增加电压至–2.2 V到–4.5 V区间时 (Slope3), 曲线的拟合斜率为3.07, 即I与V 3.07成正比, 表明此时电流仍受SCLC导电机制调控. 达到开关电压 (–4.5 V), CuInS2 QDs进入LRS状态, 继续增加电压或撤掉电压, 状态不变, 曲线 (Slope4) 的拟合斜率为1.05, 完成设置(SET)过程中. 说明当CuInS2 QDs RRAM处于LRS时, 电流由欧姆导电机制控制. 在复位(RESET)过程中, 起初CuInS2 QDs处于LRS状态, 即使正向施加电压也不会改变其状态, 此时曲线 (Slope5) 的斜率为1, 复合薄膜仍由欧姆导电机制主导; 当正向施加电压达到4.5 V时, QDs恢复HRS状态, 继续增加电压或降低电压, 状态不变. 施加电压降低至5.0—3.6 V区间时 (Slope6), 此时I与V2.73成正比, 说明此时电流再次受SCLC导电机制调控; 电压继续降低至3.6—0.5 V区间时 (Slope7), I与V 1.92成正比, 表明此时的电流由SCLC机制主导; 当电压从0.5 V降低至0 V时 (Slope8), 此阶段的曲线斜率为1.12, 符合欧姆导电机制. 说明当CuInS2 QDs处于HRS时, 电流由欧姆导电以及SCLC机制共同主导.
图 6 CuInS2 QDs RRAM在(a) 设置过程及(b) 复位过程的拟合曲线Fig. 6. Fitting curves of CuInS2 QDs RRAM during (a) set process and (b) reset process.图7是不同方向极化下CuInS2 QDs/PNZT复合薄膜在设置及复位过程的拟合曲线. 如图7(a)所示, 负向极化下CuInS2 QDs/PNZT复合薄膜在初始时处于HRS状态, 在0 V到–0.5 V区间时 (Slope9), 属于欧姆导电机制; 当电压升至–0.5 V到–3.0 V区间时 (Slope10), 如图7(b) 所示, 曲线的拟合结果显示lnI与V1/2成正比, 表明此时复合薄膜由热离子发射导电机制主导; 在–3.0 V到–4.1 V区间 (Slope11), 属于SCLC导电机制. 当达到开关电压 (–4.1 V), CuInS2 QDs/PNZT复合薄膜进入LRS状态, 随后增加电压及电压回扫时 (Slope12), 属于欧姆导电机制. 可见当CuInS2 QDs/PNZT RRAM处于LRS时, 电流由欧姆导电机制控制.
图 7 负向极化下CuInS2 QDs/PNZT RRAM (a) 设置过程及(b) Slope10阶段的拟合曲线, (c) 复位过程及(d) Slope15阶段的拟合曲线; 正向极化下CuInS2 QDs/PNZT RRAM (e) 设置过程及(f) Slope18阶段的拟合曲线, (g) 复位过程及(h) Slope23阶段的拟合曲线Fig. 7. Fitting curves of CuInS2 QDs/PNZT RRAM under negative polarization in (a) set process and (b) Slope10 stage, (c) reset process and (d) Slope15 stage; fitting curves of CuInS2 QDs/PNZT RRAM under positive polarization in (e) set process and (f) Slope18 stage, (g) reset process and (h) Slope23 stage.如图7(c)所示, 在复位过程中, 复合薄膜初始处于LRS状态 (Slope13), 此时属于欧姆导电机制. 当施加电压达到开关电压 (3.4 V), 复合薄膜恢复HRS状态. 当施加电压回扫至5.0—3.4 V区间时 (Slope14), 属于SCLC导电机制; 当电压回扫至3.4—0.8 V区间时 (Slope15), 如图7(d) 所示, 此时的lnI与V1/2成正比, 表明此时的电流由热离子发射机制主导; 当电压由0.8 V回扫至0 V时 (Slope16), 属于欧姆导电机制. 说明当CuInS2 QDs/PNZT RRAM处于HRS时, 电流由欧姆导电、热离子发射以及SCLC机制共同主导, 这与单一CuInS2 QDs RRAM在HRS时由欧姆导电和SCLC导电机制主导不同, 表明当CuInS2 QDs复合PNZT铁电薄膜后, 复合薄膜的导电机制发生改变.
图7(e)—(h) 是正向极化下CuInS2 QDs/PNZT复合薄膜在设置及复位过程的拟合曲线, 与负向极化下CuInS2 QDs/PNZT复合薄膜的导电机制相类似, 说明PNZT的极化方向并不会改变复合薄膜的阻变机制. 图8为纯PNZT薄膜的光学性能. 从图8(a) UV-vis光谱看出PNZT的特征吸收边为344 nm, 根据(αhν)2-hν关系曲线(图8(b)), 采用Tauc公式计算得PNZT的光学带隙为3.47 eV, 这与文献[22]报道的结果符合. PNZT薄膜的UPS能谱见图8(c), 对二次电子截止边与费米边进行放大处理见图8(d). 二次电子截止边的截距在15.78 eV处, 表明系统提供的21.20 eV的光子能量最多只能激发结合能为15.78 eV的电子, 因此PNZT的逸出功
Φ = 21.20 eV–15.78 eV = 5.42 eV, 对应于费米能级与真空能级的能量差; 进一步确定其价带顶(valence band maximum, VBM)位置, 费米边的截距在1.10 eV处, 得PNZT的VBM位置与费米能级的能量差为1.10 eV, 因此PNZT的VBM位于EVBM = –(5.42 eV+1.10 eV) = –6.52 eV. 结合图8(b)所示PNZT薄膜的带隙, 得到PNZT薄膜的导带底(conduction band minimum, CBM)位于ECBM = –6.52 eV+3.47 eV = –3.05 eV. 在前期工作中, 我们已经采用相同的方法表征了CuInS2 QDs的能带结构, 其费米能级为–5.04 eV, ECBM = –3.28 eV, EVBM = –5.23 eV[23].
图 8 PNZT薄膜的光学性能 (a) UV-Vis光谱图; (b) 光学带隙图; (c) PNZT薄膜的UPS; (d) 二次电子截止边谱和费米边谱Fig. 8. Optical performance of PNZT films: (a) UV-Vis spectrum; (b) optical band gap; (c) UPS of PNZT film; (d) secondary electron cutoff and Fermi edge intercepts.图9给出了CuInS2 QDs与PNZT等材料的能带结构示意及铁电极化对界面能带结构的影响. 可以看出, CuInS2 QDs的带隙位于PNZT的带隙之间, 且CuInS2 QDs的费米能级高于PNZT薄膜, 当CuInS2 QDs与PNZT薄膜形成CuInS2 QDs/PNZT复合薄膜时, 界面电子将从CuInS2 QDs流向PNZT薄膜, 导致界面处的能带发生弯曲, 并在CuInS2 QDs/PNZT复合薄膜界面处形成耗尽区及界面势垒[24,25]. 界面势垒及耗尽区的形成增加了CuInS2 QDs RRAM在HRS状态时的电阻, 从而提高了器件的阻变开关比. 当PNZT处于负向极化时(图9(c)), 界面处存在的正极化电荷将会在复合薄膜界面形成内建电场将促进界面电子从CuInS2 QDs向PNZT薄膜的流动. 与此同时, 从正到负的偶极子导致PNZT的能带向复合薄膜界面倾斜, 将在复合薄膜界面处聚集更多的缺陷电荷. 这都能有效降低界面的势垒高度和界面耗尽区的宽度(Wd), 有利于降低开关电压阈值以及复合薄膜在LRS时的电阻. 相反地, 当PNZT处于正向极化时(图9(d)), 界面处存在的负极化电荷将排斥CuInS2 QDs中的自由电子, 阻碍界面电子从CuInS2 QDs流向PNZT薄膜, 而且从负到正的偶极子使PNZT的能带向底电极倾斜, 导致缺陷电荷向底电极迁移, 这都将导致界面处的能带弯曲增加, 耗尽区及界面势垒增加, 增加了复合薄膜在LRS状态时的电阻, 反而削弱了PNZT引入增加的阻变开关比, 同时增加了器件的开关电压阈值.
图 9 (a) PNZT与CuInS2 QDs的能带结构. CuInS2 QDs/PNZT复合薄膜界面能带结构示意图 (b) 无极化; (c) 负向极化; (d) 正向极化Fig. 9. (a) Band structures of PNZT and CuInS2 QDs. Schematic diagram of the interfacial band structure of CuInS2 QDs/PNZT film: (b) No polarization; (c) negative polarization; (d) positive polarization.4. 结 论
利用PNZT薄膜可切换的铁电极化调控了CuInS2 QDs的阻变特性. 采用磁控溅射制备PNZT薄膜, 将CuInS2 QDs旋涂在PNZT铁电薄膜上制备CuInS2 QDs/PNZT复合薄膜. 实验结果表明, 纯CuInS2 QDs薄膜的开关电压(–4.5/4.5 V)和阻变开关比为 (103), PNZT引入使HRS状态时的电阻增加明显大于LRS状态电阻, 从而提高了复合薄膜的阻变开关比; 负向极化状态时的PNZT促进了界面电子从CuInS2 QDs向PNZT薄膜的流动, 降低了界面的势垒高度和界面耗尽区(Wd)的宽度, 通过降低复合薄膜处于LRS时的电阻降低开关电压和提升阻变开关比 (–4.1/3.4 V, 106), 并且在103次的循环耐久性测试中始终保持着良好的稳定性; 正向极化状态时的PNZT阻碍了界面电子从CuInS2 QDs向PNZT薄膜的流动, 增加了界面的势垒高度和界面耗尽区(Wd)的宽度, 由于LRS状态电阻的增加, 开关电压提高至–6.4/5.7 V, 阻变开关比为104. 改变极化方向可以调控CuInS2 QDs/PNZT复合薄膜的阻变性能, 是由于PNZT的极化方向改变了界面能带结构, 影响了导电机制.
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图 1 自由电子g因子最低阶QED修正的费曼图描述, 直线代表自由传播的电子, 三角形表示电磁场而曲线表示电子与电磁场作用中的虚光子 (a)自能效应; (b)真空极化效应
Fig. 1. Feynman diagrams of the first-order QED corrections of the free electron g-factor, the straight line represents the electron, curved lines as the photons and the triangle as the magnetic field: (a) The self-energy term; (b) the vacuum-polarization term.
图 2 类氢离子1s电子g因子与平均电场强度随原子序数Z的依赖关系
Fig. 2. g factor of 1s electron and the mean electromagnetic field as a function of atomic number Z.
图 4 潘宁离子阱剖面结构图, 离子运动与镜像电流测量原理示意图(图中部分素材由马克斯普朗克核物理研究所提供)
Fig. 4. Cut model of Penning traps with illustration of ion motion and image current detection system (some of the materials in the image are provided by the Max-Planck-Institute for Nuclear Physics).
图 8 ALPHATRAP实验系统示意图, 高电荷态重离子由Heidelberg EBIT中产生, 离子束团引出后经过电荷态筛选、偏转、减速、聚焦后被潘宁阱俘获, 手动低温阀可以用来隔离室温束线与低温离子阱的真空环境, 保证离子阱内部真空度优于10–17 torr, 图片来自文献[13]
Fig. 8. Schematic diagram of the ALPHATRAP experiment, the highly charged ions are produced in the Heidelberg EBIT, the ions are extracted, with charge-state selection, and injected into the Penning trap, the cryogenic valve can be closed to isolate the trap vacuum from the beamline, resulting in a vacuum better than 10–17 torr, from Ref. [13].
表 1 类氢12C5+, 16O7+, 20Ne9+, 28Si13+和118Sn49+基态g因子计算与实验数据表
Table 1. Experimental and theoretical g factors of 12C5+, 16O7+, 20Ne9+, 28Si13+和118Sn49+.
12C5+ 16O7+ 20Ne9+ 28Si13+ 118Sn49+ gDirac 1.99872135439(1) 1.99772600306(2) 1.99644517090 1.9930235716 1.90807920530 Free QED 0.00231930437(1) 0.00231930437(1) 0.00231930435 0.00231930437(1) 0.00231930435 BS-QED 0.00000084340(3) 0.00000159438(11) 0.00000265069(12) 0.0000058558(17) 0.000148098(298) FNS 0.00000000041 0.00000000155(1) 0.000 00000476(1) 0.000000 205 0.000014489(24) NR 0.00000008762 0.00000011697 0.00000014641 0.0000002051(1) 0.000000726 Hadronic — — — — –0.000000002 gtheo 2.00104159018(3) 2.00004702128(11) 1.99876727711(12) 1.995348958 0(17) 1.910561821(299) gexp 2.0010415964(45) 2.0000470254(46) 1.99876727699(19) 1.99534895910(81) 1.910562058962(914) 注: gDirac 代表Dirac方程计算的g因子值, Free QED代表自由(电子)QED效应贡献, BS-QED代表束缚态(电子)QED效应贡献, FNS代表核尺寸效应贡献, NR代表核反冲效应贡献, Hadronic代表强子效应贡献. 12C5+, 16O7+, 28Si13数据来自于文献[10], 20Ne9+的数据来自于文献[12], 118Sn49+的数据来自于文献[13]. 
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表 2 28Si11+, 40Ca17+和40Ar13+基态g因子计算与实验数据表
Table 2. Theoretical and experimental g factors of 28Si11+, 40Ca17+ and 40Ar13+.
28Si11+ 40Ca17+ 40Ar13 gDirac 1.9982547533 1.9964260253 0.66377545 QED 0.0023202857 (17) 0.0023216601(17) –0.0007682(4) e-e int. 0.000314 8098 (22) 0.0004542910 (24) 0.0006500(2) FNS + NR 0.0000000436 0.0000000662 –0.0000091(2) gtheo 2.000889 8924 (28) 1.9992020426 (29) 0.6636482 (5) gexp 2.00088988845 (14) 1.9992020405 (11) 0.66364845532(93) 注: QED代表经过屏蔽势修正后的束缚态QED效应, e-e int.代表电子-电子关联效应贡献; 28Si11+与40Ca17+数据来自于文献[23], 40Ar13数据来自于文献[24].
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表 3 20Ne9+和22Ne9+基态g因子差以及相关核效应贡献的计算值, 数据来自文献[28]
Table 3. Contributions of the g-factor difference of 20Ne9+ and 22Ne9+ as well as the experimental result, from Ref. [28]
效应贡献 Δg=g(20Ne9+)−g(22Ne9+) (×10−9) FNS 0.166(11) Recoil, non-QED 13.2827 Recoil, QED 0.0435 Recoil, (α/π)(me/M) –0.0103 Recoil, (me/M)2 –0.0077 Nuclear polarization 0.0001(3) Δg total theory 13.474(11) Δg experiment 13.47524(53)stat(99)sys
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[1] Landé A 1921 Z. Für Phys. 5 231
[2] Kusch P, Foley H M 1947 Phys. Rev. 72 1256
[3] Kinoshita T 1990 Advanced Series on Directions in HighEnergy Physics (Singapore: World Scientific) pp218-321
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Google Scholar
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