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

doi:10.7498/aps.72.20230778

Abstract

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 ^87,85Rb_n (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 ^87,85Rb_n (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 ⁸⁷Rb_n level shell structure and ⁸⁵Rb_n 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.

Keywords:

Authors and contacts

1.
Institute of Physics Science & Technology, Tangshan Normal University, Tangshan 063000, China
2.
State Key Laboratory of Disastrous Weather, Chinese Academy of Meteorological Sciences, Beijing 100081, China
3.
Department of Chemistry, Tangshan Normal University, Tangshan 063000, China

Corresponding author: Di Shu-Hong, zhudizhe@163.com ; Zhang Yang, 185540891@qq.com ; Yang Hui-Jing, yanghj619@126.com ;

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References

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图 1 (a), (b)实验测得的⁸⁷Rb_n, ⁸⁵Rb_n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)

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

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

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

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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)

Figure 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).

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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)

Figure 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).

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图 5 (a)⁸⁷Rb_n 5s电子壳层能级结构; (b) ⁸⁵Rb_n5s电子壳层能级结构

Figure 5. 　(a) 5s electron shell level structure of ⁸⁷Rb_n; (b) 5s electron shell level structure of ⁸⁵Rb_n.

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

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

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表 1 实验测量的⁸⁷Rb_n, ⁸⁵Rb_n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 ⁸⁷Rb_n, ⁸⁵Rb_n.

^87,85Rb_n	5s 电子数	磁矩及矩移/μ_B			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
^87,85Rb_n	5s 电子数	$ {\bar \mu _{87 n}} $	$ {\bar \mu _{85 n}} $	$ \Delta {\bar \mu _n} $	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}} $	${{{{\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

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表 2 ⁸⁷Rb_n, ⁸⁵Rb_n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 ⁸⁷Rb_n , ⁸⁵Rb_n 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.

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表 3 原子簇⁸⁷Rb_n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 ⁸⁷Rb_n atomic cluster.

⁸⁷Rb_n	5s 电子数	分子态及本征值$ {\lambda }_{合} $和s	模型 F_合	$ {\bar \mu _n}/{\mu _{\text{B}}} $		$ {\bar \mu _n} $相对误差/‰	$ {\bar E_n}/{\mu _{\text{B}}}{H_0} $		$ {\bar E_n} $相对误差/‰
⁸⁷Rb_n	5s 电子数	分子态及本征值$ {\lambda }_{合} $和s	模型 F_合	模型	实验	$ {\bar \mu _n} $相对误差/‰	模型	实验	$ {\bar E_n} $相对误差/‰
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
⁸⁷Rb_4,6,8,10,12	4, 6, 8, 10, 12	[19, 20, 21]		0	0	0	0	0	0
平均值						–6.989			–6.989

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表 4 ⁸⁵Rb_n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 ⁸⁵Rb_n atomic cluster.

⁸⁵Rb_n	5s 电子数	分子态及本征值$ {\lambda }_{合} $和s	模型 F_合	$ {\bar \mu _n}/{\mu _{\text{B}}} $		$ {\bar \mu _n} $相对误差/‰	$ {\bar E_n}/{\mu _{\text{B}}}{H_0} $		$ {\bar E_n} $相对误差/‰
⁸⁵Rb_n	5s 电子数	分子态及本征值$ {\lambda }_{合} $和s	模型 F_合	模型	实验	$ {\bar \mu _n} $相对误差/‰	模型	实验	$ {\bar E_n} $相对误差/‰
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
⁸⁵Rb_4,6,8,10,12	4, 6, 8, 10, 12	[19, 20, 21]		0	0	0	0	0	0
平均值						–5.800			–5.800

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表 5 ⁸⁷Rb_n和⁸⁵Rb_n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 ⁸⁷Rb_n and ⁸⁵Rb_n.

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/‰
n	⁸⁷Rb_n 模型	⁸⁵Rb_n 模型	模型矩移 $ \Delta {\bar \mu _n}/{\mu _{\text{B}}} $	⁸⁷Rb_n 实验	⁸⁵Rb_n 实验	实验矩移 $ \Delta {\bar \mu _n}/{\mu _{\text{B}}} $	相对误差/‰
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

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表 6 ⁸⁷Rb_n和⁸⁵Rb_n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 ⁸⁷Rb_n and ⁸⁵Rb_n.

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/‰
n	⁸⁷Rb_n 模型	⁸⁵Rb_n 模型	模型能移 $\Delta {\bar E_n}/{\mu _{\text{B}}}{H_0} $	⁸⁷Rb_n 实验	⁸⁵Rb_n 实验	实验能移 $ \Delta{\bar E_n}/{\mu _{\text{B}}}{H_0} $	相对误差/‰
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

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表 7 实验测量 ⁸⁷Rb_n, ⁸⁵Rb_n 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 ⁸⁷Rb_n, ⁸⁵Rb_n measured by experiments.

n	1	5	7	9
1/2 CC₈₇/kHz	78.52	19.22	7.92	8.73
1/2 CC₈₅/kHz	98.34	24.84	17.06	12.41
CC₈₇/CC₈₅	0.80	0.77	0.46	0.70
BC₈₇/kHz	812.75	167.60	116.40	89.10
BC₈₅/kHz	510.55	113.51	74.35	58.63
BC₈₇/BC₈₅	1.59	1.47	1.57	1.48
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.

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