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铷簇同位素效应的量化研究

邸淑红 张阳 杨会静 崔乃忠 李艳坤 刘会媛 李伶利 石凤良 贾玉璇

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铷簇同位素效应的量化研究

邸淑红, 张阳, 杨会静, 崔乃忠, 李艳坤, 刘会媛, 李伶利, 石凤良, 贾玉璇

Quantitative study on isotope effect of rubidium clusters

Di Shu-Hong, Zhang Yang, Yang Hui-Jing, Cui Nai-Zhong, Li Yan-Kun, Liu Hui-Yuan, Li Ling-Li, Shi Feng-Liang, Jia Yu-Xuan
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  • 针对簇类同位素位移难以测定及其产生原因难以鉴别等问题, 本文运用光磁共振和热离解相结合的技术, 获得了气态Rb同位素原子簇87,85Rbn (n = 1, 2, ···, 13)两系列共振离解光谱、等数簇矩移、塞曼能移. 并对每个簇进行基于巨原子概念模型量化计算, 其结果与实测结果严格一致, 表明铷簇可以作为巨原子分析. 进一步运用铷簇塞曼能级间隔公式计算出87,85Rbn (n = 1, 2, 3, ···, 92) 5s电子壳层能级结构, 发现5s单电子壳层结构主要秩序和步距与钠簇的在球状对称势阱下3s单电子壳层结构相似, 证实铷簇5s单电子壳层结构可以由塞曼能级大能隙决定. 共振离解光谱的奇偶交替特性及其在特殊数(如n = 2)处的反常磁矩特征峰均是由价电子的内在性质和分子结构特性引起. 还发现87Rbn85Rbn的5s单电子壳层结构步调严格一致, 量值大小均有3/2比值关系, 且二者光谱中心频率及展宽存在反常差异, 可能与87, 85Rb的核素处于核壳层闭合面附近直接相关.
    Because of the difficulty in measuring the cluster isotope displacement and identifying its cause, the resonance dissociation spectra, the moment shift and Zeeman energy shift of isotope cluster 87,85Rbn (n = 1, 2, 3, ··· , 13) are obtained by the combination of optical magnetic resonance and thermal dissociation techniques in this study. The quantitative calculation is carried out based on the conceptual model of the giant atom, and the results are in excellent agreement with the measured results, which shows that rubidium clusters can be analyzed as giant atoms. Furthermore, 5s electron shell level structures of the rubidium cluster 87,85Rbn (n = 1, 2, 3, ··· , 92) are calculated by using Zeeman level interval model. It is found that the main order and step distance of the 5s electron shell structure are similar to those of 3s single electron shell structure of sodium cluster in spherical symmetry. It is confirmed that the structure of the 5s electron shell of the rubidium cluster is determined by the largest energy gap in total Zeeman levels and the characteristic peaks of odd and even alternating and anomalous magnetic moments of special numbers such as n = 2 are caused by the intrinsic properties of electrons and molecular structures. It is also found that 87Rbn level shell structure and 85Rbn level shell structure strictly conform to the ratio of 3/2 magnitude relationship, and that there are abnormal differences in spectral center frequency and broadening, which may be directly related to the 85,87Rb nuclei close to the shell closure.
      通信作者: 邸淑红, zhudizhe@163.com ; 张阳, 185540891@qq.com ; 杨会静, yanghj619@126.com
      Corresponding author: Di Shu-Hong, zhudizhe@163.com ; Zhang Yang, 185540891@qq.com ; Yang Hui-Jing, yanghj619@126.com
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  • 图 1  (a), (b)实验测得的87Rbn, 85Rbn的8种簇粒子的共振频率$ \bar f $与磁场H0的关系曲线(1 G = 10–4 T)

    Fig. 1.  (a), (b) Relationship between the resonant frequency $ \bar f $ of 8 kinds of 87Rbn, 85Rbn cluster particles and the magnetic field H0

    图 2  (a), (b) 两系列同位素原子簇的87Rbn, 85Rbn (n = 1, 2, ···, 13)的共振离解光谱

    Fig. 2.  (a), (b) Resonance dissociation spectra of two series of isotopic atomic clusters 87Rbn, 85Rbn (n = 1, 2, ···, 13).

    图 3  等数簇矩移随n变化的模型值与实验值比较图(实验值用虚线, 模型值用实线)

    Fig. 3.  Comparison of calculated values and experimental values of magnetic moment shift of equal number cluster with n (dashed lines for experimental value, full lines for model value).

    图 4  等数簇超精细结构塞曼能移随n变化的模型值与实验值比较图(实验值用虚线, 模型值用实线)

    Fig. 4.  Comparison of calculated values and experimental values of Zeeman energy shift of equal-number hyperfine structures with n (dashed lines for experimental value, full lines for model value).

    图 5  (a) 87Rbn 5s电子壳层能级结构; (b) 85Rbn 5s电子壳层能级结构

    Fig. 5.   (a) 5s electron shell level structure of 87Rbn; (b) 5s electron shell level structure of 85Rbn.

    图 6  (a), (b) 87Rbn, 85Rbn同位素原子簇的相对频移图

    Fig. 6.  (a), (b) Diagrams of relative frequency shift of equal-number cluster 87Rbn, 85Rbn.

    表 1  实验测量的87Rbn, 85Rbn等数簇平均矩移和塞曼能移及光谱振幅

    Table 1.  Measured mean magnetic moment shifts, Zeeman energy shifts and spectrum amplitudes of 87Rbn, 85Rbn.

    87,85Rbn 5s
    电子数
    磁矩及矩移/μB 塞曼能移
    $ \Delta {\bar E_n}/{\mu _{\text{B}}}{H_0} $
    磁矩比
    $ {\bar \mu _{{87}n}}/{\bar \mu _{{85}n}} $
    塞曼能比
    $ {\bar E_{87 n}}/{\bar E_{85 n}} $
    光谱平均幅度/mV
    $ {\bar \mu _{87 n}} $ $ {\bar \mu _{85 n}} $ $ \Delta {\bar \mu _n} $ ${{{{\bar A}_{87n}}}} $ ${{{{\bar A}_{85n}}}} $ ${{{{\bar A}_{87n}}}}/ {{{{\bar A}_{85n}}}} $
    87,85Rb1 1 0.494337 0.330120 0.164217 0.164217 1.497446 1.497446 1574.50 1008.71 1.56∶1
    87,85Rb2 2 0.246984 0.164773 0.082211 0.082211 1.498935 1.498935 105.75 70.60 1.50∶1
    87,85Rb3 3 0.164598 0.109974 0.054624 0.054624 1.496699 1.496699 883.07 589.49 1.49∶1
    87,85Rb4 4 0 0 0 0 0 0 无共振
    87,85Rb5 5 0.098789 0.066044 0.032745 0.032745 1.495805 1.495805 383.47 354.10 1.08∶1
    87,85Rb6 6 0 0 0 0 0 0 无共振
    87,85Rb7 7 0.070635 0.047180 0.023455 0.023455 1.497139 1.497139 188.70 170.63 1.10∶1
    87,85Rb8 8 0 0 0 0 0 0 无共振
    87,85Rb9 9 0.054953 0.036718 0.018235 0.018235 1.496623 1.496623 84.92 79.59 1.06∶1
    87,85Rb10 10 0 0 0 0 0 0 无共振
    87,85Rb11 11 0.044975 0.030046 0.014929 0.014929 1.496871 1.496871 48.62 39.90 1.18∶1
    87,85Rb12 12 0 0 0 0 0 0 无共振
    87,85Rb13
    13 0.038060 0.025423 0.012637 0.012637 1.497070 1.497070 31.55 23.07 1.34∶1
    下载: 导出CSV

    表 2  87Rbn, 85Rbn双原子分子基态X和最低激发态A的电子组态和分子态项型表

    Table 2.  Electronic configuration and molecular state item type of 8 pairs of diatomic molecule 87Rbn , 85Rbn ground and lowest excited states.

    团簇分子,
    参考分子
    X组态和分子态及其$ {\lambda }_{合} $和s A组态和分子态及其$ {\lambda }_{合} $和s X与A 稳定性比较$ {p_{\text{a}}} - {p_{\text{b}}}$

    87,85Rb1
    $ \begin{array}{c}{\text{KLMNspd(σ}}_{\text{g}}\text{5s}), \\ {}^{2}\text{Σ}{}_{\text{g}}^{+}, {\lambda }_{合}=0, s=1/2\end{array} $ $ \begin{array}{c} \text{KLMNspd}({\text{π}}_{\text{u}}4\text{d}), \\ {}^{2}\Pi_{\text{u}}, {\lambda }_{合}=1, s=1/2\end{array} $ $ \begin{array}{c} {\text{X:}}\, {p_{\text{a}}} - {p_{\text{b}}} = 1/2; \\ {\text{A:}}\, {p_{\text{a}}} - {p_{\text{b}}} = 1/2 \end{array} $
    87,85Rb2[17] $ \begin{array}{c}({\text{σ}}_{\text{g}}\text{5s})^{2}, {}^{1}\Sigma {}_{\text{g}}^{+}, {\lambda }_{合}=0, s=\text{0;}\\({\text{σ}}_{\text{g}}\text{5s)}{\text{(σ}}_{\text{u}}\text{5s)}, {}^{3}\Sigma {}_{\rm u}^{+}, \\{\lambda }_{合}=0, s=1\end{array} $ $ \begin{array}{c}{\text{(σ}}_{\text{g}}{\text{5s)(π}}_{\text{u}}\text{4d)}, {}^{1}\Pi_{\text{u}}, {\lambda }_{合}=1, s=0;\\或\; ({\text{σ}}_{\text{u}}{\text{5s)(π}}_{\text{u}}\text{4d)}, {}^{3}\Pi_{\text{g}},\\ {\lambda }_{合}=1, s=1\end{array} $ $ \begin{array}{l} {}\quad\;{\text{X:}}\, {p_{\text{a}}} - {p_{\text{b}}} = 1 - 0 = 1; \\ {}\quad\;{\text{A:}}\, {p_{\text{a}}} - {p_{\text{b}}} = 1 - 0 = 1 \\ 或\; {\text{X:}}\, {p_{\text{a}}} - {p_{\text{b}}} = 1/2 - 1/2 = 0; \\ {}\quad\;{\text{A:}}\, {p_{\text{a}}} - {p_{\text{b}}} = 1/2 - 1/2 = 0\, \end{array} $
    87,85Rb3 $ \begin{array}{c}{{\text{(σ}}_{\text{g}}}{\text{5s)}}^2{\text{(σ}}_{\text{u}}\text{5s)}, \\ {}^{2}\Sigma_{\text{u}}^{+}, {\lambda}_{合}=0, s=1/2\end{array} $ $ \begin{array}{c}{\text{(σ}}_{\text{g}}\text{5s)}{\text{(σ}}_{\text{u}}\text{5s)}{\text{(π}}_{\text{u}}\text{4d), }\\ {}^{2}\Pi_{\text{g}}^{}, {\lambda }_{合}=1, s=1/2\end{array} $ $ \begin{array}{c} {\text{X:}}\, {p_{\text{a}}} - {p_{\text{b}}} = 1 - 1/2 = 1/2 \\ {\text{A:}}\, {p_{\text{a}}} - {p_{\text{b}}} = 1 - 1/2 = 1/2 \end{array} $
    87,85Rb5 $ \begin{array}{c}{{\text{(σ}}_{\text{g}}}{\text{5s)}}^2{{\text{(σ}}_{\text{u}}}{\text{5s)}}^2{\text{(σ}}_{\text{g}}\text{4d), }\\ {}^{2}\Sigma_{\text{g}}^{+}, {\lambda }_{合}=0, s=1/2\end{array} $ $ \begin{array}{c}{{\text{(σ}}_{\text{g}}}{\text{5s)}}^2{{\text{(σ}}_{\text{u}}}{\text{5s)}}^2{\text{(π}}_{\text{u}}\text{4d)}, \\ {}^{2}\Pi_{\text{u}}^{}, {\lambda }_{合}=1, s=1/2\end{array} $ $ \begin{array}{c} {\text{X:}}\, {p_{\text{a}}} - {p_{\text{b}}} = 1\dfrac{1}{2} - 1 = 1/2 \\ {\text{A:}}\, {p_{\text{a}}} - {p_{\text{b}}} = 1\dfrac{1}{2} - 1 = 1/2 \end{array} $

    87,85Rb7
    $ \begin{array}{c}{{\text{(σ}}_{\text{g}}}{\text{5s)}}^2{{\text{(σ}}_{\text{u}}}{\text{5s)}}^2{{\text{(σ}}_{\text{g}}}{\text{4d)}}^2{\text{(π}}_{\text{u}}\text{4d)}, \\ {}^{2}\Pi_{\text{u}}, {\lambda }_{合}=1, s=1/2\end{array} $ $ \begin{array}{c}{{\text{(σ}}_{\text{g}}}{\text{5s)}}^2{{\text{(σ}}_{\text{u}}}{\text{5s)}}^2{{\text{(σ}}_{\text{g}}}{\text{4d)}}^1{{\text{(π}}_{\text{u}}}{\text{4d)}}^2, \\{}^{2}\Sigma_{\text{g}}^{+}, {\lambda }_{合}=0, s=1/2;\\ {}^{2}\Delta_{\text{g}}, {\lambda }_{合}=2, s=1/2\end{array} $ $ \begin{array}{c} {\text{X:}}\, {p_{\text{a}}} - {p_{\text{b}}} = 2\dfrac{1}{2} - 1 = 1\dfrac{1}{2} \\ {\text{A:}}\, {p_{\text{a}}} - {p_{\text{b}}} = 2\dfrac{1}{2} - 1 = 1\dfrac{1}{2} \end{array} $

    87,85Rb9
    $ \begin{array}{c}{{\text{(σ}}_{\text{g}}}{\text{5s)}}^2{{\text{(σ}}_{\text{u}}}{\text{5s)}}^2{{\text{(σ}}_{\text{g}}}{\text{4d)}}^2{{\text{(π}}_{\text{u}}}{\text{4d)}}^3, \\ {}^{2}\Pi_{\text{u}}, {\lambda }_{合}=1, s=1/2\end{array} $ $ \begin{array}{c}{{\text{(σ}}_{\text{g}}}{\text{5s)}}^2{{\text{(σ}}_{\text{u}}}{\text{5s)}}^2{{\text{(σ}}_{\text{g}}}{\text{4d)}}^1{{\text{(π}}_{\text{u}}}{\text{4d)}}^4, \\ {}^{2}\Sigma_{\text{g}}^{+}, {\lambda }_{合}=0, s=1/2;\\ {}^{2}\Delta_{\text{g}}, {\lambda }_{合}=2, s=1/2\end{array} $ $ \begin{array}{c} {\text{X:}}\, {p_{\text{a}}} - {p_{\text{b}}} = 3\dfrac{1}{2} - 1 = 2\dfrac{1}{2} \\ {\text{A:}}\, {p_{\text{a}}} - {p_{\text{b}}} = 3\dfrac{1}{2} - 1 = 2\dfrac{1}{2} \end{array} $
    87,85Rb11 $ \begin{array}{c}{{\text{(σ}}_{\text{g}}}{\text{5s)}}^2{{\text{(σ}}_{\text{u}}}{\text{5s)}}^2{{\text{(σ}}_{\text{g}}}{\text{4d)}}^2{{\text{(π}}_{\text{u}}}{\text{4d)}}^4{{\text{(π}}_{\text{g}}}{\text{4d)}}^1, \\ {}^{2}\Pi_{\text{u}}, {\lambda }_{合}=1, s=1/2\end{array} $ $ \begin{array}{c}{{\text{(σ}}_{\text{g}}}{\text{5s)}}^2{{\text{(σ}}_{\text{u}}}{\text{5s)}}^1{{\text{(σ}}_{\text{g}}}{\text{4d)}}^2{{\text{(π}}_{\text{u}}}{\text{4d)}}^4{{\text{(π}}_{\text{g}}}{\text{4d)}}^2, \\ {}^{2}\Sigma_{\text{g}}^{+}, {\lambda }_{合}=0, s=1/2;\\ {}^{2}\Delta_{\text{g}}, {\lambda }_{合}=2, s=1/2\end{array} $ $ \begin{array}{c} {\text{X:}}\, {p_{\text{a}}} - {p_{\text{b}}} = 4 - 1\dfrac{1}{2} = 2\dfrac{1}{2} \\ {\text{A:}}\, {p_{\text{a}}} - {p_{\text{b}}} = 4 - 1\dfrac{1}{2} = 2\dfrac{1}{2} \end{array} $
    87,85Rb13 $ \begin{array}{c}{{\text{(σ}}_{\text{g}}}{\text{5s)}}^2{{\text{(σ}}_{\text{u}}}{\text{5s)}}^2{{\text{(σ}}_{\text{g}}}{\text{4d)}}^2{{\text{(π}}_{\text{u}}}{\text{4d)}}^4{{\text{(π}}_{\text{g}}}{\text{4d)}}^3, \\ {}^{2}\Pi_{\text{g}}, {\lambda }_{合}=1, s=1/2\end{array} $ $ \begin{array}{c}{{\text{(σ}}_{\text{g}}}{\text{5s)}}^2{{\text{(σ}}_{\text{u}}}{\text{5s)}}^1{{\text{(σ}}_{\text{g}}}{\text{4d)}}^2{{\text{(π}}_{\text{u}}}{\text{4d)}}^4{{\text{(π}}_{\text{g}}}{\text{4d)}}^4, \\ {}^{2}\Sigma_{\text{u}}, {\lambda }_{合}=0, s=1/2\end{array} $ $ \begin{array}{c} {\text{X:}}\, {p_{\text{a}}} - {p_{\text{b}}} = 4 - 2\dfrac{1}{2} = 1\dfrac{1}{2} \\ {\text{A:}}\, {p_{\text{a}}} - {p_{\text{b}}} = 4 - 2\dfrac{1}{2} = 1\dfrac{1}{2} \end{array} $
    注: 表2中电子组态仅87,85Rb1的基态和激发态标出了闭壳层KLMNspd, 其他粒子没有重复标出闭壳层KLMNspd.
    下载: 导出CSV

    表 3  原子簇87Rbn磁矩和塞曼能级间隔模型与实验结果比较

    Table 3.  Comparison of experiment values and calculated values of magnetic moment and Zeeman energy level interval of 87Rbn atomic cluster.

    87Rbn 5s
    电子数
    分子态及本
    征值$ {\lambda }_{合} $和s
    模型
    F
    $ {\bar \mu _n}/{\mu _{\text{B}}} $ $ {\bar \mu _n} $相对
    误差/‰
    $ {\bar E_n}/{\mu _{\text{B}}}{H_0} $ $ {\bar E_n} $相对
    误差/‰
    模型 实验 模型 实验
    87Rb1 1 $ {}^{2}\Pi_{\text{u}}, {\lambda }_{合}=1, s=1/2 $ 2 $ 1/2 $ 0.494337 –11.326 $ 1/2 $ 0.494337 –11.326
    87Rb2 2 $ {}^{3}\Pi_{\text{g}}, {\lambda }_{合}=1, s=1 $ 4 $ 1/4 $ 0.246984 –12.064 $ 1/4 $ 0.246984 –12.064
    87Rb3 3 $ {}^{2}\Pi_{\text{g}}, {\lambda }_{合}=1, s=1/2 $ 6 $ 1/6 $ 0.164598 –12.412 $ 1/6 $ 0.164598 –12.412
    87Rb5 5 $ {}^{2}\Pi_{\text{u}}, {\lambda }_{合}=1, s=1/2 $ 10 $ 1/10 $ 0.098789 –12.110 $ 1/10 $ 0.098789 –12.110
    87Rb7 7 $ {}^{2}\Pi_{\text{u}}, {\lambda }_{合}=1, s=1/2 $ 14 $ 1/14 $ 0.070635 –11.110 $ 1/14 $ 0.070635 –11.110
    87Rb9 9 $ {}^{2}\Pi_{\text{u}}, {\lambda }_{合}=1, s=1/2 $ 18 $ 1/18 $ 0.054953 –10.846 $ 1/18 $ 0.054953 –10.846
    87Rb11 11 $ {}^{2}\Pi_{\text{u}}, {\lambda }_{合}=1, s=1/2 $ 22 $ 1/22 $ 0.044975 –10.550 $ 1/22 $ 0.044975 –10.550
    87Rb13 13 $ {}^{2}\Pi_{\text{g}}, {\lambda }_{合}=1, s=1/2 $ 26 $ 1/26 $ 0.038060 –10.440 $ 1/26 $ 0.038060 –10.440
    87Rb4,6,8,10,12 4, 6, 8, 10, 12 [19, 20, 21] 0 0 0 0 0 0
    平均值 –6.989 –6.989
    下载: 导出CSV

    表 4  85Rbn磁矩和塞曼能级间隔模型与实验结果比较

    Table 4.  Comparison of experiment values and calculated values of magnetic moment and Zeeman energy level interval of 85Rbn atomic cluster.

    85Rbn 5s
    电子数
    分子态及本
    征值$ {\lambda }_{合} $和s
    模型
    F
    $ {\bar \mu _n}/{\mu _{\text{B}}} $ $ {\bar \mu _n} $相对
    误差/‰
    $ {\bar E_n}/{\mu _{\text{B}}}{H_0} $ $ {\bar E_n} $相对
    误差/‰
    模型 实验 模型 实验
    85Rb1 1 $ {}^{2}\Pi_{\text{u}}, {\lambda }_{合}=1, s=1/2 $ 3 1/3 0.330120 –9.640 1/3 0.330120 –9.640
    85Rb2 2 $ {}^{3}\Pi_{\text{g}}, {\lambda }_{合}=1, s=1 $ 6 1/6 0.164773 –11.362 1/6 0.164773 –11.362
    85Rb3 3 $ {}^{2}\Pi_{\text{g}}, {\lambda }_{合}=1, s=1/2 $ 9 1/9 0.109974 –10.234 1/9 0.109974 –10.234
    85Rb5 5 $ {}^{2}\Pi_{\text{u}}, {\lambda }_{合}=1, s=1/2 $ 15 1/15 0.066044 –9.340 1/15 0.066044 –9.340
    85Rb7 7 $ {}^{2}\Pi_{\text{u}}, {\lambda }_{合}=1, s=1/2 $ 21 1/21 0.047180 –9.220 1/21 0.047180 –9.220
    85Rb9 9 $ {}^{2}\Pi_{\text{u}}, {\lambda }_{合}=1, s=1/2 $ 27 1/27 0.036718 –8.614 1/27 0.036718 –8.614
    85Rb11 11 $ {}^{2}\Pi_{\text{u}}, {\lambda }_{合}=1, s=1/2 $ 33 1/33 0.030046 –8.482 1/33 0.030046 –8.482
    85Rb13 13 $ {}^{2}\Pi_{\text{g}}, {\lambda }_{合}=1, s=1/2 $ 39 1/39 0.025423 –8.503 1/39 0.025423 –8.503
    85Rb4,6,8,10,12 4, 6, 8, 10, 12 [19, 20, 21] 0 0 0 0 0 0
    平均值 –5.800 –5.800
    下载: 导出CSV

    表 5  87Rbn85Rbn等数簇矩移模型与实验结果对比

    Table 5.  Comparison of experiment values and calculated values of magnetic moment shift interval of 87Rbn and 85Rbn.

    n $ {\bar \mu _n}/{\mu _{\text{B}}} $ 模型矩移
    $ \Delta {\bar \mu _n}/{\mu _{\text{B}}} $
    $ {\bar \mu _n}/{\mu _{\text{B}}} $ 实验矩移
    $ \Delta {\bar \mu _n}/{\mu _{\text{B}}} $
    相对误差/‰
    87Rbn 模型 85Rbn 模型 87Rbn 实验 85Rbn 实验
    1 1/2 1/3 1/6 0.494337 0.330120 0.164217 –14.698
    2 1/4 1/6 1/12 0.246984 0.164773 0.082211 –13.468
    3 1/6 1/9 1/18 0.164598 0.109974 0.054624 –16.768
    4 0 0 0 0 0 0 0
    5 1/10 1/15 1/30 0.098789 0.066044 0.032745 –17.65
    6 0 0 0 0 0 0 0
    7 1/14 1/21 1/42 0.070635 0.047180 0.023455 –14.89
    8 0 0 0 0 0 0 0
    9 1/18 1/27 1/54 0.054953 0.036718 0.018235 –15.31
    10 0 0 0 0 0 0 0
    11 1/22 1/33 1/66 0.044975 0.030046 0.014929 –14.686
    12 0 0 0 0 0 0 0
    13 1/26 1/39 1/78 0.038060 0.025423 0.012637 –14.314
    平均值 –9.368
    下载: 导出CSV

    表 6  87Rbn85Rbn等数簇塞曼能移实验与模型结果比较

    Table 6.  Comparison of experiment values and calculated values of Zeeman energy level shiift interval of 87Rbn and 85Rbn.

    n$ {\bar E_n}/{\mu _{\text{B}}}{H_0} $模型能移
    $\Delta {\bar E_n}/{\mu _{\text{B}}}{H_0} $
    $ {\bar E_n}/{\mu _{\text{B}}}{H_0} $实验能移
    $ \Delta{\bar E_n}/{\mu _{\text{B}}}{H_0} $
    相对误差/‰
    87Rbn 模型85Rbn 模型87Rbn 实验85Rbn 实验
    11/21/31/60.4943370.3301200.164217–14.698
    21/41/61/120.2469840.1647730.082211–13.468
    31/61/91/180.1645980.1099740.054624–16.768
    40000000
    51/101/151/300.0987890.0660440.032745–17.65
    60000000
    71/141/211/420.0706350.0471800.023455–14.89
    80000000
    91/181/271/540.0549530.0367180.018235–15.31
    100000000
    111/221/331/660.0449750.0300460.014929–14.686
    120000000
    131/261/391/780.0380600.0254230.012637–14.314
    平均值–9.368
    下载: 导出CSV

    表 7  实验测量 87Rbn, 85Rbn 光谱中心频率宽度与广泛成分平均宽度BC

    Table 7.  Spectral center frequency width CC and average width BC of 87Rbn, 85Rbn measured by experiments.

    n1579
    1/2 CC87/kHz78.5219.227.928.73
    1/2 CC85/kHz98.3424.8417.0612.41
    CC87/CC850.800.770.460.70
    BC87/kHz812.75167.60116.4089.10
    BC85/kHz510.55113.5174.3558.63
    BC87/BC851.591.471.571.48
    注: 实验测量的1/2 CC是共振峰的半峰高处左半部分对应的中心频率的展宽.
    下载: 导出CSV
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  • 收稿日期:  2023-05-14
  • 修回日期:  2023-07-02
  • 上网日期:  2023-07-18
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