铷原子簇自发磁矩的实验观测及理论分析

邸淑红; 张阳; 杨会静; 伞星原; 刘会媛; 张素恒; 李繁麟; 太军君; 周春丽

doi:10.7498/aps.70.20210031

摘要

在碱金属原子簇磁性的研究中, 存在自由原子簇含有的原子个数及其磁矩难以准确确定的问题, 本文采用光磁共振光谱检测手段, 对工作温度约为328 K的饱和铷蒸汽样品中单原子分子⁸⁷Rb₁和14种簇粒子 (⁸⁷Rb)_{${}_ {n'}$} (

${n'}$ = 2, 3, ···, 15)的磁矩进行了深入研究. 实验结果表明: 在同一外磁场下, 14种簇粒子(⁸⁷Rb)

${}_ {n'}$ 的共振频率

$f_ {n'}$ 与⁸⁷Rb₁的共振频率f *之间存在

$f_ {n'} = f^*/{n'}$ 的数值关系, 并且各簇粒子的磁矩值与振幅值均随

$n'$ 的大小和奇、偶性呈现不同性质的变化规律. 运用分子轨态理论通过⁸⁷Rb_n = ⁸⁷Rb_{n – 1} + ⁸⁷Rb联合原子簇构造模式, 给出14种簇粒子⁸⁷Rb_n(n = 2, 3, ···, 15)的基态和最低激发态的电子组态和分子态项型, 分析了各分子态的稳定性和发生可见塞曼效应的可能性. 进一步基于双原子分子磁矩公式计算, 发现当n =

${n'}$ 时⁸⁷Rb_n的磁矩值与(⁸⁷Rb)

${}_ {n'}$ 的磁矩值严格吻合(平均相对误差仅为0.6765%), 证实了(⁸⁷Rb)

${}_ {n'}$ 和⁸⁷Rb_n的对应关系.

关键词:

For the magnetism of alkali metal clusters, it is difficult to determine the number of atoms and the magnetic moment of isolated atoms cluster. In this paper, we investigate the magnetic moment of single atomic molecule ⁸⁷Rb₁ and 14 kinds of cluster particles (⁸⁷Rb)

${}_{n'}$ (

$n'$ = 2, 3, 4, ···, 15) in a saturated rubidium vapor sample at about 328 K, by using optical magnetic resonance spectroscopy. The experimental results show that there is a relationship f

${}_{n'}$ = f */

$n'$ between the resonant frequencies f

${}_{n'}$ of 14 kinds of cluster particles (⁸⁷Rb)

${}_{n'}$ and the resonant frequencies f * of ⁸⁷Rb₁. The magnetic moment and their resonance amplitudes show two different relationships with the

${n'}$ odevity. When the particles have an odd number of 5s electrons, they must have spontaneous magnetic moment, and the value of magnetic moment increases with n and decreases inverse proportionally with the combined angular momentum F of the cluster particles. The amplitude obtained from resonance spectrum complies with the variation law of magnetic moment value. On the other hand, for the cluster particles with n being even number, the magnetic moment value becomes 0 and the amplitude is also 0 in the most cases, except for the cluster particles ⁸⁷Rb₂ with n = 2 i.e. two 5s electrons, which is caused by the Jahn-Teller effect of the linear molecules, and the magnetic moment value is consistent with the calculation results of the odd number particles. When n > 2, the coupling effect between the magnetic moments of the Rb cluster shows a long-range ordered antiferromagnetic property with the increase of the number of 5s valence electrons n. The electron configuration and molecular state of the ground state and the lowest excited state of 14 kinds of 2—15 atoms cluster particles ⁸⁷Rb_n, as well as the stability of each molecular state and the possibility of visible Zeeman effect are obtained by using the molecular orbital-state theory analysis and constructing the ⁸⁷Rb_n–1 + ⁸⁷Rb_n atomic cluster model. Furthermore, based on the magnetic moment of diatomic molecules ruler, it is found that when n =

${n'}$ , the magnetic moment of (⁸⁷Rb)

${}_{n'}$ and ⁸⁷Rb_n are in strict consistency (the average relative error is only 0.6765%), confirming the corresponding relationship between (⁸⁷Rb)

${}_{n'}$ and ⁸⁷Rb_n. This research will be of great value in the magnetic research of cluster particles.

Keywords:

PACS:

作者及机构信息

1.
唐山师范学院物理科学与技术学院, 唐山　063000

2.
中国气象科学研究院, 灾害天气国家重点实验室, 北京　100081

3.
河北大学物理科学与技术学院, 保定　071002

4.
唐山师范学院化学系, 唐山　063000

通信作者: 邸淑红, 792423642@qq.com ; 张阳, 185540891@qq.com ; 杨会静, yanghj619@126.com ;

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.
Institute of Physics Science & Technology, Hebei University, Baoding 071002, China

4.
Department of Chemistry, Tangshan Normal University, Tangshan 063000, China

Corresponding author: Di Shu-Hong, 792423642@qq.com ; Zhang Yang, 185540891@qq.com ; Yang Hui-Jing, yanghj619@126.com ;

文章全文

补充材料

122101-20210031补充材料.rar

参考文献

[1]	Kodaira T, Nozue Y, Ohwashi S, Togashi N, Terasaki O 1994 Stud. Surf. Sci. Catal. 84 837
[2]	Kubo R 1962 J. Phys. Soc. Jpn. 1 7975
[3]	Rao B K, Khanna S N, Jena P 1987 Phys. Rev. B 36 953 Google Scholar
[4]	Khanna S N, Rao B K, Jena P, Martin J L1987 Physics and Chemistry of Small Clusters (New York : New York and London Published in Cooperation with NATO Scientific Affairs Division Plenum Press) p435
[5]	Nozue Y, Kodaira T, Goto T 1992 Phys. Rev. Lett. 68 3789 Google Scholar
[6]	Nozue Y, Kodaira T, Ohwashi S, Goto T, Terasaki O 1993 Phys. Rev. B 48 12253 Google Scholar
[7]	Kodaira T, Ikemoto Y, Nozue Y 2000 Mol. Cryst. Liq. Cryst. 341 461 Google Scholar
[8]	Kodaira T, IkemotoY, NozueY 1999 Eur. Phys. J. D 9 505 Google Scholar
[9]	Nakano T, Ikemoto Y, NozueY 2000 Physica B 281-282 688 Google Scholar
[10]	Nozue Y, Kodaira T, Ohwashi S, Togashi N, Terasaki O 1996 Surf. Rev. Lett. 3 701 Google Scholar
[11]	Nakano T, Ikemoto Y, NozueY 2001 J. Magn. Magn. Maters. 226-230 238 Google Scholar
[12]	Duan T C, Nakano T, Nozue Y 2007 J. Magn. Magn. Maters. 310 1013 Google Scholar
[13]	吴思成, 王祖铨 1999 近代物理实验 (北京: 北京大学出版社) 第348页 Wu S C, Wang Z Q 1999 Modern Physics Experiment (Beijing: BeijingUniversity Press) p348 (in Chinese)
[14]	格哈德 H (王鼎昌译) 1983 分子光谱与分子结构 (第1卷) (北京: 科学出版社) 第4页 Gerhard H (translated by Wang D C) 1983 Molecules Spectroscopy and Molecules Structures (Vol. 1) (Beijing: Science Press) p4 (in Chinese)
[15]	王义遒, 王庆吉, 傅济时, 董太乾 1986 量子频标原理 (北京: 科学出版社) 第366页 Wang Y Q, Wang Q J, Fu J S, Dong T Q 1986 Physics of Quantum Frequency Standards (Beijing: Science Press) p366 (in Chinese)
[16]	徐元植, 姚加 2017 电子磁共振波谱学 (北京: 清华大学出版社) 第136页 Xu Y Z, Yao J 2017 Electron Magnetic Resonance Pectroscopy (Beijing: Qinghua University Press) p136 (in Chinese)
[17]	周公度, 叶宪曾 2012 化学元素综论 (北京: 科学出版社) 第270页 Zhou G D, Ye X Z 2012 Chemical Elements Survey (Beijing: Science Press) p270 (in Chinese)
[18]	鲍林L (卢嘉锡等译) 1981 化学键的本质 (上海: 上海科学技术出版社) 第 330页 Pauling L (translated by Lu J X) 1981 The Nature of the Chemical Bond (ShangHai: Science and Technology Press) p330(in Chinese)
[19]	苏长荣, 李家明 2002 中国科学A辑: 数学 32 103 Su C R, Li J M 2002 Sci. China Mater. 32 103
[20]	周公度, 段连运 2011 结构化学基础 (北京: 北京大学出版社) 第216页 ZhouG D, Duan L Y 2011 Fundamentals of Structural Chemical (Beijing: Beijing University Press) p216 (in Chinese)
[21]	关洪 2000 量子力学基础 (北京: 高等教育出版社) 第168页 Guan H 2000 Basic Quantum Mechanics (Beijing: Higher Education Press) p168 (in Chinese)
[22]	孙汉文 2002 原子光谱分析 (北京: 高等教育出版社) 第172页 Sun H W 2002 Atomic Spectral Analysis (Beijing: Higher Education Press) p172 (in Chinese)
[23]	Jahn H A, Teller E 1937 Proc. Roy. Soc. A 161 220
[24]	Jahn H A 1938 Proc. Roy. Soc. A 164 117

图 1 实验测量的 ${n'}$ = 1—15的铷簇粒子共振光谱振幅及形态示意图

Fig. 1. Schematic illustration of the resonance spectral amplitudes and shape of the 1−15 kinds of Rb cluster particles derived from experiments.

下载: 全尺寸图片幻灯片

图 2 (a), (b)铷簇颗粒的TEM图片; (c), (d)铷元素分布图

Fig. 2. (a), (b) TEM images of the Rb cluster particles; (c), (d) the distribution of rubidium by EDS mappings.

下载: 全尺寸图片幻灯片

图 3 实验测得的 (⁸⁷Rb) ${}_{n'}$ 的9种簇粒子的共振频率 $\bar f$ 与磁场H₀的关系曲线( ${n'}$ = 1, 2, 3, 5, 7, 9, 11, 13, 15)

Fig. 3. Magnetic field strength H₀ dependence of resonance frequency $\bar f$ for the 9 kinds of Rb cluster particles (⁸⁷Rb) ${}_{n'}$ ( ${n'}$ = 1, 2, 3, 5, 7, 9, 11, 13, 15).

下载: 全尺寸图片幻灯片

表 1 实验获得的(⁸⁷Rb) ${}_{n'}$ 各粒子的平均 ${\bar g_{n'}}$ , $\bar \mu {}_{n'}$ , ${\bar A_{n'}}$

Table 1. The ${\bar g_{n'}}$ , $\bar \mu {}_{n'}$ , ${\bar A_{n'}}$ of the 15 kinds of cluster particles (⁸⁷Rb) ${}_{n'}$ .

${n'}$ 为奇数粒子	${n'}$	${\bar g_{n'}}$	$\bar \mu {}_{n'}$ /μ_B	${\bar A_{n'}}$ /mV	${n'}$ 为偶数粒子	${n'}$	${\bar g_{n'}}$	$\bar \mu {}_{n'}$ /μ_B	${\bar A_{n'}}$ /mV
⁸⁷Rb₁	1	0.494337	0.494337	1574.50	(⁸⁷Rb)_2′	2	0.246984	0.246984	105.75
(⁸⁷Rb)_3′	3	0.164598	0.164598	883.07	(⁸⁷Rb)_4′	4	0	0	0
(⁸⁷Rb)_5′	5	0.098789	0.098789	383.47	(⁸⁷Rb)_6′	6	0	0	0
(⁸⁷Rb)_7′	7	0.070635	0.070635	188.70	(⁸⁷Rb)_8′	8	0	0	0
(⁸⁷Rb)_9′	9	0.054953	0.054953	84.92	(⁸⁷Rb)_10′	10	0	0	0
(⁸⁷Rb)_11′	11	0.044975	0.044975	48.62	(⁸⁷Rb)_12′	12	0	0	0
(⁸⁷Rb)_13′	13	0.038060	0.038060	31.55	(⁸⁷Rb)_14′	14	0	0	0
(⁸⁷Rb)_15′	15	0.032978	0.032978	12.63

下载: 导出CSV

表 2 15种原子簇分子⁸⁷Rb_n的基态和最低激发态的电子组态和分子态项型表

Table 2. Electron configuration and molecular state of the ground state and the lowest excited state of 15 kinds of cluster particles ⁸⁷Rb_n.

团簇分子, 参考分子	基态电子组态和分子态及 ${\lambda }_{\text{合}}$ 和S	最低激发电子组态及其 ${\lambda }_{\text{合}}$ 和S (Hund(a) 情形跃迁规则 $\Delta \lambda =0, \pm 1$ , $g\;\, \leftrightarrow u$ , $\Delta n = 0, \;\; \pm 1, ~\Delta S = 0$	基态X与最低激发态A稳定性比较 ${P_{\rm{a}}} - {P_{\rm{b}}}$
⁸⁷Rb₁	${\rm{KLMN}}_{\rm{spd}}(\sigma {}_{\rm{g}}\rm{5}\rm{s})$ ${}^2{\Sigma _{\rm{u} } },$ ${\lambda }_{\text{合} }=0,$ $S = 1/2$	${\rm{KLMN}}_{\rm{spd}}({\text{π}}{}_{\rm{u}}{4}{\rm{d}})$ ${}^2{\Pi _{\rm{u} } },$ ${\lambda }_{\text{合} }=1,$ $S = 1/2$	X: ${P_{\rm{a} } } - {P_{\rm{b} } } = 1/2$ A: ${P_{\rm{a} } } - {P_{\rm{b} } } = 1/2$
⁸⁷Rb₂⁸⁵Rb₂^[14]	${({\rm{\sigma } }{}_{\rm{g} }5{\rm{s} })^2},$ ${}^1{{\Sigma } }_{\rm{g} }^ +,$ ${\lambda }_{\text{合} }=0,$ $S = {{0}}$ 或[ ${\rm{(\sigma } }{}_{\rm{g} }{\rm{5s} })({ {\rm{\sigma } }_{\rm{u} } }{\rm{5 s)} } ,$ ${}^3{ {\Sigma } }_{\rm{u} }^{ + },$ ${\lambda }_{\text{合} }=0 ,$ $S = {{1}}$ ]	${\rm{(\sigma }}{}_{\rm{g}}{\rm{5 s}})({{\text{π}}_{\rm{u}}}{\rm{4 d)}},$ ${}^1{{\Pi}_{\rm{u}}},$ ${\lambda }_{\text{合}}=1,$ $S = {{0}}$ 或[ ${\rm{(\sigma } }{}_{\rm{u} }{\rm{5s} })({ {\text{π} }_{\rm{u} } }{\rm{4 d)} },$ ${}^3{{\Pi}_{\rm{g}}},$ ${\lambda }_{\text{合} }=1,$ $S = {{1}}$ ]	X: ${P_{\rm{a}}} - {P_{\rm{b}}} = 1 - 0 = 1$ A: ${P_{\rm{a}}} - {P_{\rm{b}}} = 1 - 0 = 1$ [X: ${P_{\rm{a} } } - {P_{\rm{b} } } = 1/2 - 1/2 = { {0} }$ A: ${P_{\rm{a} } } - {P_{\rm{b} } } = 1/2 - 1/2 = { {0} }$ ]
⁸⁷Rb₃	${({\rm{\sigma } }{}_{\rm{g} }{\rm{5 s} })^{ {2} } }({ {\rm{\sigma } }_{\rm{u} } }{\rm{5 s)} } ,$ ${}^2{{\Sigma } }_{\rm{u} }^ +,$ ${\lambda }_{\text{合} }=0,$ $S = 1/2$	${\rm{(\sigma } }{}_{\rm{g} }{\rm{5 s)(} }{ {\rm{\sigma } }_{\rm{u} } }{\rm{5 s)(} }{ {\text{π} }_{\rm{u} } }{\rm{4 d)} },$ ${}^2{ {\Pi}_{\rm{g} } },$ ${\lambda }_{\text{合} }=1,$ $S = 1/2$	X: ${P_{\rm{a} } } - {P_{\rm{b} } } = 1 - 1/2 = 1/2$ A: ${P_{\rm{a} } } - {P_{\rm{b} } } = 1 - 1/2 = 1/2$
⁸⁷Rb₄	${({\rm{\sigma } }{}_{\rm{g} }{\rm{5 s)} }^{ {2} } }{({ {\rm{\sigma } }_{\rm{u} } }{\rm{5 s)} }^{ {2} } },$ ${}^1{{\Sigma } }_{\rm{g} }^ +,$ ${\lambda }_{\text{合} }=0,$ $S = {{0}}$	${\rm{(\sigma } }{}_{\rm{g} }{\rm{5 s)(} }{ {\rm{\sigma } }_{\rm{u} } }{\rm{5 s} }{ {\rm{)} }^{ {2} } }{\rm{(\pi } }{}_{\rm{u} }{\rm{4 d)} },$ ${}^1{ {\Pi}_{\rm{u} } },$ ${\lambda }_{\text{合} }=1,$ $S = {{0}}$	X: ${P_{\rm{a}}} - {P_{\rm{b}}} = 1 - 1 = 0$ A: ${P_{\rm{a}}} - {P_{\rm{b}}} = 1 - 1 = 0$
⁸⁷Rb₅	${ {\rm{(\sigma } }{}_{\rm{g} }{\rm{5 s)} }^2}{({ {\rm{\sigma } }_{\rm{u} } }{\rm{5 s)} }^2}({ {\rm{\sigma } }_{\rm{g} } }{\rm{4 d)} } ,$ ${}^2{{\Sigma } }_{\rm{g} }^ + ,$ ${\lambda }_{\text{合} }=0,$ $S = 1/2$	${ {\rm{(\sigma } }{}_{\rm{g} }{\rm{5 s)} }^2}{({ {\rm{\sigma } }_{\rm{u} } }{\rm{5 s)} }^2}{({ {\text{π} }_{\rm{u} } }{\rm{4 d)} }^1},$ ${}^2{ {\Pi}_{\rm{u} } },$ ${\lambda }_{\text{合} }=1,$ $S = 1/2$	X: ${P_{\rm{a} } } - {P_{\rm{b} } } = 1\frac{1}{2} - 1 = 1/2$ A: ${P_{\rm{a} } } - {P_{\rm{b} } } = 1\frac{1}{2} - 1 = 1/2$
⁸⁷Rb₆	${ {\rm{(\sigma } }{}_{\rm{g} }{\rm{5 s)} }^2}{({ {\rm{\sigma } }_{\rm{u} } }{\rm{5 s)} }^2}{({ {\rm{\sigma } }_{\rm{g} } }{\rm{4 d)} }^2},$ ${}^1{{\Sigma } }_{\rm{g} }^ +,$ ${\lambda }_{\text{合} }=0,$ $S = {{0}}$	${ {\rm{(\sigma } }{}_{\rm{g} }{\rm{5 s)} }^2}{({ {\rm{\sigma } }_{\rm{u} } }{\rm{5 s)} }^2}({ {\rm{\sigma } }_{\rm{g} } }{\rm{4 d)(} }{ {\text{π} }_{\rm{u} } }{\rm{4 d)} },$ ${}^1{ {\Pi}_{\rm{u} } } ,$ ${\lambda }_{\text{合} }=1,$ $S = {{0}}$	X: ${P_{\rm{a}}} - {P_{\rm{b}}} = 2 - 1 = 1$ A: ${P_{\rm{a}}} - {P_{\rm{b}}} = 2 - 1 = 1$
⁸⁷Rb₇	${ {\rm{(\sigma } }{}_{\rm{g} }{\rm{5 s)} }^2}{({ {\rm{\sigma } }_{\rm{u} } }{\rm{5 s)} }^2}{({ {\rm{\sigma } }_{\rm{g} } }{\rm{4 d)} }^2}({ {\text{π} }_{\rm{u} } }{\rm{4 d)} },$ ${}^2{ {\Pi}_{\rm{u} } },$ ${\lambda }_{\text{合} }=1,$ $S = 1/2$	${({\rm{\sigma } }{}_{\rm{g} }{\rm{5 s} })^2}{({ {\rm{\sigma } }_{\rm{u} } }{\rm{5 s)} }^2}{({ {\rm{\sigma } }_{\rm{g} } }{\rm{4 d)} }^1}{({ {\text{π} }_{\rm{u} } }{\rm{4 d)} }^2} ,$ ${}^2{ {\Sigma } }_{\rm{g} }^ +,$ ${\lambda }_{\text{合} }=0,$ $S = 1/2$ ; ${}^2{ { {\Delta } }_{\rm{g} } },$ ${\lambda }_{\text{合} }=2, S =1/2$	X: ${P_{\rm{a} } } - {P_{\rm{b} } } = 2\frac{1}{2} - 1 = 1\frac{1}{2}$ A: ${P_{\rm{a} } } - {P_{\rm{b} } } = 2\frac{1}{2} - 1 = 1\frac{1}{2}$
⁸⁷Rb₈	${({\rm{\sigma } }{}_{\rm{g} }{\rm{5 s} })^2}{({ {\rm{\sigma } }_{\rm{u} } }{\rm{5 s)} }^2}{({ {\rm{\sigma } }_{\rm{g} } }{\rm{4 d)} }^2}{({ {\text{π} }_{\rm{u} } }{\rm{4 d)} }^2},$ ${}^1{{\Sigma } }_{\rm{g} }^ +,$ ${\lambda }_{\text{合} }=0,$ $S = {{0}}$	${ {\rm{(\sigma } }{}_{\rm{g} }{\rm{5 s} })^2}{({ {\rm{\sigma } }_{\rm{u} } }{\rm{5 s)} }^2}{({ {\rm{\sigma } }_{\rm{g} } }{\rm{4 d)} }^1}{({ {\text{π} }_{\rm{u} } }{\rm{4 d)} }^3},$ ${}^1{ {\Pi}_{\rm{u} } },$ ${\lambda }_{\text{合} }=1,$ $S = {{0}}$	X: ${P_{\rm{a}}} - {P_{\rm{b}}} = 3 - 1 = 2$ A: ${P_{\rm{a}}} - {P_{\rm{b}}} = 3 - 1 = 2$
⁸⁷Rb₉	${ {\rm{(\sigma } }{}_{\rm{g} }{\rm{5 s} })^2}{({ {\rm{\sigma } }_{\rm{u} } }{\rm{5 s)} }^2}{({ {\rm{\sigma } }_{\rm{g} } }{\rm{4 d)} }^2}{({ {\text{π} }_{\rm{u} } }{\rm{4 d)} }^3},$ ${}^2{ {\Pi}_{\rm{u} } } ,$ ${\lambda }_{\text{合} }=1,$ $S = 1/2$	${ {\rm{(\sigma } }{}_{\rm{g} }{\rm{5 s} })^2}{({ {\rm{\sigma } }_{\rm{u} } }{\rm{5 s)} }^2}{({ {\rm{\sigma } }_{\rm{g} } }{\rm{4 d)} }^1}{({ {\text{π} }_{\rm{u} } }{\rm{4 d)} }^4},$ ${}^2{{\Sigma } }_{\rm{g} }^ + ,$ ${\lambda }_{\text{合} }=0,$ $S = 1/2$ ; ${}^2{ { {\Delta } }_{\rm{g} } },$ ${\lambda }_{\text{合} }=2, S = 1/2$	X: ${P_{\rm{a} } } - {P_{\rm{b} } } = 3\frac{1}{2} - 1 = 2\frac{1}{2}$ A: ${P_{\rm{a} } } - {P_{\rm{b} } } = 3\frac{1}{2} - 1 = 2\frac{1}{2}$
⁸⁷Rb₁₀	${({\rm{\sigma } }{}_{\rm{g} }{\rm{5 s} })^2}{({ {\rm{\sigma } }_{\rm{u} } }{\rm{5 s)} }^2}{({ {\rm{\sigma } }_{\rm{g} } }{\rm{4 d)} }^2}{({ {\text{π} }_{\rm{u} } }{\rm{4 d)} }^4},$ ${}^1{{\Sigma } }_{\rm{g} }^ +,$ ${\lambda }_{\text{合} }=0,$ $S = {{0}}$	${ {\rm{(\sigma } }{}_{\rm{g} }{\rm{5 s} })^2}{({ {\rm{\sigma } }_{\rm{u} } }{\rm{5 s)} }^1}{({ {\rm{\sigma } }_{\rm{g} } }{\rm{4 d)} }^2}{({ {\text{π} }_{\rm{u} } }{\rm{4 d)} }^4}{({ {\text{π} }_{\rm{g} } }{\rm{4 d)} }^1},$ ${}^1{ {\Pi}_{\rm{u} } },$ ${\lambda }_{\text{合} }=1,$ $S = {{0}}$	X: ${P_{\rm{a}}} - {P_{\rm{b}}} = 4 - 1 = 3$ A: ${P_{\rm{a}}} - {P_{\rm{b}}} = {\rm{4 - 1}} = {\rm{3}}$
⁸⁷Rb₁₁	${ {\rm{(\sigma } }{}_{\rm{g} }{\rm{5 s} })^2}{({ {\rm{\sigma } }_{\rm{u} } }{\rm{5 s)} }^2}{({ {\rm{\sigma } }_{\rm{g} } }{\rm{4 d)} }^2}{({ {\text{π} }_{\rm{u} } }{\rm{4 d)} }^4}{({ {\text{π} }_{\rm{g} } }{\rm{4 d)} }^1},$ ${}^2{ {\Pi}_{\rm{g} } },$ ${\lambda }_{\text{合} }=1,$ $S = 1/2$	${ {\rm{(\sigma } }{}_{\rm{g} }{\rm{5 s} })^2}{({ {\rm{\sigma } }_{\rm{u} } }{\rm{5 s)} }^1}{({ {\rm{\sigma } }_{\rm{g} } }{\rm{4 d)} }^2}{({ {\text{π} }_{\rm{u} } }{\rm{4 d)} }^4}{({ {\text{π} }_{\rm{g} } }{\rm{4 d)} }^2},$ ${}^2{{\Sigma } }_{\rm{u} }^ + ,$ ${\lambda }_{\text{合} }=0,$ $S = 1/2$ ; ${}^2{ { {\Delta } }_{\rm{g} } },$ ${\lambda }_{\text{合} }=2,$ $S = 1/2$	X: ${P_{\rm{a} } } - {P_{\rm{b} } } = 4 - 1\frac{1}{2} = 2\frac{1}{2}$ A: ${P_{\rm{a} } } - {P_{\rm{b} } } = 4 - 1\frac{1}{2} = 2\frac{1}{2}$
⁸⁷Rb₁₂	${ {\rm{(\sigma } }{}_{\rm{g} }{\rm{5 s} })^2}{({ {\rm{\sigma } }_{\rm{u} } }{\rm{5 s)} }^2}{({ {\rm{\sigma } }_{\rm{g} } }{\rm{4 d)} }^2}{({ {\text{π} }_{\rm{u} } }{\rm{4 d)} }^4}{({ {\text{π} }_{\rm{g} } }{\rm{4 d)} }^2} ,$ ${}^1{{\Sigma } }_{\rm{g} }^ +,$ ${\lambda }_{\text{合} }=0,$ $S = {{0}}$	${ {\rm{(\sigma } }{}_{\rm{g} }{\rm{5 s} })^2}{({ {\rm{\sigma } }_{\rm{u} } }{\rm{5 s)} }^1}{({ {\rm{\sigma } }_{\rm{g} } }{\rm{4 d)} }^2}{({ {\text{π} }_{\rm{u} } }{\rm{4 d)} }^4}{({ {\text{π} }_{\rm{g} } }{\rm{4 d)} }^3},$ ${}^1{ {\Pi}_{\rm{u} } },$ ${\lambda }_{\text{合} }=1,$ $S = {{0}}$	X: ${P_{\rm{a}}} - {P_{\rm{b}}} = 4 - 2 = 2$ A: ${P_{\rm{a}}} - {P_{\rm{b}}} = {\rm{4 - 2}} = {{2}}$
⁸⁷Rb₁₃	${ {\rm{(\sigma } }{}_{\rm{g} }{\rm{5 s} })^2}{({ {\rm{\sigma } }_{\rm{u} } }{\rm{5 s)} }^2}{({ {\rm{\sigma } }_{\rm{g} } }{\rm{4 d)} }^2}{({ {\text{π} }_{\rm{u} } }{\rm{4 d)} }^4}{({ {\text{π} }_{\rm{g} } }{\rm{4 d)} }^3},$ ${}^2{ {\Pi}_{\rm{g} } },$ ${\lambda }_{\text{合} }=1,$ $S = 1/2$	${ {\rm{(\sigma } }{}_{\rm{g} }{\rm{5 s} })^2}{({ {\rm{\sigma } }_{\rm{u} } }{\rm{5 s)} }^1}{({ {\rm{\sigma } }_{\rm{g} } }{\rm{4 d)} }^2}{({ {\text{π} }_{\rm{u} } }{\rm{4 d)} }^4}{({ {\text{π} }_{\rm{g} } }{\rm{4 d)} }^4},$ ${}^2{ {\Pi}_{\rm{u} } } ,$ ${\lambda }_{\text{合} }=1,$ $S = 1/2$	X: ${P_{\rm{a} } } - {P_{\rm{b} } } = 4 - 2\frac{1}{2} = 1\frac{1}{2}$ A: ${P_{\rm{a} } } - {P_{\rm{b} } } = 4 - 2\frac{1}{2} = 1\frac{1}{2}$
⁸⁷Rb₁₄	${ {\rm{(\sigma } }{}_{\rm{g} }{\rm{5 s} })^2}{({ {\rm{\sigma } }_{\rm{u} } }{\rm{5 s)} }^2}{({ {\rm{\sigma } }_{\rm{g} } }{\rm{4 d)} }^2}{({ {\text{π} }_{\rm{u} } }{\rm{4 d)} }^4}{({ {\text{π} }_{\rm{g} } }{\rm{4 d)} }^4},$ ${}^1{{\Sigma } }_{\rm{g} }^ +,$ ${\lambda }_{\text{合} }=0,$ $S = {{0}}$	${ {\rm{(\sigma } }{}_{\rm{g} }{\rm{5 s} })^2}{({ {\rm{\sigma } }_{\rm{u} } }{\rm{5 s)} }^2}{({ {\rm{\sigma } }_{\rm{g} } }{\rm{4 d)} }^2}{({ {\text{π} }_{\rm{u} } }{\rm{4 d)} }^4}{({ {\text{π} }_{\rm{g} } }{\rm{4 d)} }^3} ({ {\rm{\sigma } }_{\rm{u} } }{\rm{4 d)} },$ ${}^1{ {\Pi}_{\rm{u} } },$ ${\lambda }_{\text{合} }=1,$ $S = {{0}}$	X: ${P_{\rm{a}}} - {P_{\rm{b}}} = 4 - 3 = 1$ A: ${P_{\rm{a}}} - {P_{\rm{b}}} = 4 - 3 = 1$
⁸⁷Rb₁₅	${({\rm{\sigma } }{}_{\rm{g} }{\rm{5 s)} }^2}{({ {\rm{\sigma } }_{\rm{u} } }{\rm{5 s)} }^2}{({ {\rm{\sigma } }_{\rm{g} } }{\rm{4 d)} }^2}{({ {\text{π} }_{\rm{u} } }{\rm{4 d)} }^4}{({ {\text{π} }_{\rm{g} } }{\rm{4 d)} }^4}({ {\rm{\sigma } }_{\rm{u} } }{\rm{4 d)} },$ ${}^2{{\Sigma } }_{\rm{u} }^ +,$ ${\lambda }_{\text{合} }=0,$ $S = 1/2$	${({\rm{\sigma } }{}_{\rm{g} }{\rm{5 s} })^2}{({ {\rm{\sigma } }_{\rm{u} } }{\rm{5 s)} }^2}{({ {\rm{\sigma } }_{\rm{g} } }{\rm{4 d)} }^2}{({ {\text{π} }_{\rm{u} } }{\rm{4 d)} }^4}{({ {\text{π} }_{\rm{g} } }{\rm{4 d)} }^3}{({ {\rm{\sigma } }_{\rm{u} } }{\rm{4 d)} }^2},$ ${}^2{ {\Pi}_{\rm{g} } },$ ${\lambda }_{\text{合} }=1,$ $S = 1/2$	X: ${P_{\rm{a} } } - {P_{\rm{b} } } = 4-3\frac{1}{2} = \frac{1}{2}$ A: ${P_{\rm{a} } } - {P_{\rm{b} } } = 4-3\frac{1}{2} = \frac{1}{2}$
注: 表中电子组态仅⁸⁷Rb₁的基态和激发态标出了闭壳层KLMN_spd, 其他粒子没有重复标出闭壳层KLMN_spd.

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表 3 ⁸⁷Rb_n簇的磁距 ${\bar \mu _n}$ 和朗德因子 ${\bar g_{{n}}}$ 的理论计算结果

Table 3. Theoretical calculation results of $\bar \mu {}_n$ and ${\bar g_n}$ of Rb clusters⁸⁷Rb_n.

n为奇数的簇分子	n为奇数的分子项	5s价电子个数	$\bar \mu {}_n$ /μ_B	${\bar g_n}$	n为偶数的簇分子	n为偶数的分子项	5s价电子个数	$\bar \mu {}_n$ /μ_B	${\bar g_n}$
⁸⁷Rb₁	${}^2{\Pi _{\rm{u}}}$	1	$1/2$	$1/2$	⁸⁷Rb₂	${}^2{\Pi _{\rm{g}}}$	2	$1/4$	$1/4$
⁸⁷Rb₃	${}^2{\Pi _{\rm{g}}}$	3	$1/6$	$1/6$	⁸⁷Rb₄	${}^2{\Pi _{\rm{u}}}$	4	0	0
⁸⁷Rb₅	${}^2{\Pi _{\rm{u}}}$	5	$1/10$	$1/10$	⁸⁷Rb₆	${}^2{\Pi _{\rm{u}}}$	6	0	0
⁸⁷Rb₇	${}^2{\Pi _{\rm{u}}}$	7	$1/14$	$1/14$	⁸⁷Rb₈	${}^1{\Pi _{\rm{u}}}$	8	0	0
⁸⁷Rb₉	${}^2{\Pi _{\rm{u}}}$	9	$1/18$	$1/18$	⁸⁷Rb₁₀	${}^2{\Pi _{\rm{u}}}$	10	0	0
⁸⁷Rb₁₁	${}^2{\Pi _{\rm{g}}}$	11	$1/22$	$1/22$	⁸⁷Rb₁₂	${}^2{\Pi _{\rm{u}}}$	12	0	0
⁸⁷Rb₁₃	${}^2{\Pi _{\rm{g}}}$	13	$1/26$	$1/26$	⁸⁷Rb₁₄	${}^2{\Pi _{\rm{u}}}$	14	0	0
⁸⁷Rb₁₅	${}^2{\Pi _{\rm{g}}}$	15	$1/30$	$1/30$

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表 4 ⁸⁷Rb_n与 (⁸⁷Rb) ${}_{n'}$ 的平均磁矩和振幅值的对比

Table 4. Comparison of average magnetic moment and amplitude of ⁸⁷Rb_n and (⁸⁷Rb) ${}_{n'}$

团簇⁸⁷Rb_n	n	$\bar \mu {}_n$ /μ_B	团簇(⁸⁷Rb) ${}_{n'}$	$n'$	$\bar \mu {}_{n'}$ /μ_B	磁矩的相对误差%	${\bar A_{n'} }$ /mV	${\bar A_{n'}}$ 与 ${\bar A_n}$ 比较
⁸⁷Rb₁	1	$1/2$	⁸⁷Rb₁	1	0.494337	1.1326	1574.50	一致
⁸⁷Rb₂	2	$1/4$	(⁸⁷Rb)_2′	2	0.246984	1.2063	105.75	线性分子简并态
⁸⁷Rb₃	3	$1/6$	(⁸⁷Rb)_3′	3	0.164598	1.2411	883.07	一致
⁸⁷Rb₄	4	0	(⁸⁷Rb)_4′	4	0	0	0	0
⁸⁷Rb₅	5	$1/10$	(⁸⁷Rb)_5′	5	0.098789	1.2110	383.47	一致
⁸⁷Rb₆	6	0	(⁸⁷Rb)_6′	6	0	0	0	0
⁸⁷Rb₇	7	$1/14$	(⁸⁷Rb)_7′	7	0.070635	1.1042	188.70	一致
⁸⁷Rb₈	8	0	(⁸⁷Rb)_8′	8	0	0	0	0
⁸⁷Rb₉	9	$1/18$	(⁸⁷Rb)_9′	9	0.054953	1.0843	84.92	一致
⁸⁷Rb₁₀	10	0	(⁸⁷Rb)_10′	10	0	0	0	0
⁸⁷Rb₁₁	11	$1/22$	(⁸⁷Rb)_11′	11	0.044975	1.0556	48.62	一致
⁸⁷Rb₁₂	12	0	(⁸⁷Rb)_12′	12	0	0	0	0
⁸⁷Rb₁₃	13	$1/26$	(⁸⁷Rb)_13′	13	0.038060	1.0467	31.55	一致
⁸⁷Rb₁₄	14	0	(⁸⁷Rb)_14′	14	0	0	0	0
⁸⁷Rb₁₅	15	$1/30$	(⁸⁷Rb)_15′	15	0.032978	1.0658	12.63	一致
15种簇粒子(⁸⁷Rb) ${}_{n'}$ 与⁸⁷Rb_n的磁矩相对误差均值为: 0.6765%
9种磁矩不为0的簇粒子(⁸⁷Rb) ${}_{n'}$ 与⁸⁷Rb_n的磁矩相对误差均值为: 1.1275%

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[1]	Kodaira T, Nozue Y, Ohwashi S, Togashi N, Terasaki O 1994 Stud. Surf. Sci. Catal. 84 837
[2]	Kubo R 1962 J. Phys. Soc. Jpn. 1 7975
[3]	Rao B K, Khanna S N, Jena P 1987 Phys. Rev. B 36 953 Google Scholar
[4]	Khanna S N, Rao B K, Jena P, Martin J L1987 Physics and Chemistry of Small Clusters (New York : New York and London Published in Cooperation with NATO Scientific Affairs Division Plenum Press) p435
[5]	Nozue Y, Kodaira T, Goto T 1992 Phys. Rev. Lett. 68 3789 Google Scholar
[6]	Nozue Y, Kodaira T, Ohwashi S, Goto T, Terasaki O 1993 Phys. Rev. B 48 12253 Google Scholar
[7]	Kodaira T, Ikemoto Y, Nozue Y 2000 Mol. Cryst. Liq. Cryst. 341 461 Google Scholar
[8]	Kodaira T, IkemotoY, NozueY 1999 Eur. Phys. J. D 9 505 Google Scholar
[9]	Nakano T, Ikemoto Y, NozueY 2000 Physica B 281-282 688 Google Scholar
[10]	Nozue Y, Kodaira T, Ohwashi S, Togashi N, Terasaki O 1996 Surf. Rev. Lett. 3 701 Google Scholar
[11]	Nakano T, Ikemoto Y, NozueY 2001 J. Magn. Magn. Maters. 226-230 238 Google Scholar
[12]	Duan T C, Nakano T, Nozue Y 2007 J. Magn. Magn. Maters. 310 1013 Google Scholar
[13]	吴思成, 王祖铨 1999 近代物理实验 (北京: 北京大学出版社) 第348页 Wu S C, Wang Z Q 1999 Modern Physics Experiment (Beijing: BeijingUniversity Press) p348 (in Chinese)
[14]	格哈德 H (王鼎昌译) 1983 分子光谱与分子结构 (第1卷) (北京: 科学出版社) 第4页 Gerhard H (translated by Wang D C) 1983 Molecules Spectroscopy and Molecules Structures (Vol. 1) (Beijing: Science Press) p4 (in Chinese)
[15]	王义遒, 王庆吉, 傅济时, 董太乾 1986 量子频标原理 (北京: 科学出版社) 第366页 Wang Y Q, Wang Q J, Fu J S, Dong T Q 1986 Physics of Quantum Frequency Standards (Beijing: Science Press) p366 (in Chinese)
[16]	徐元植, 姚加 2017 电子磁共振波谱学 (北京: 清华大学出版社) 第136页 Xu Y Z, Yao J 2017 Electron Magnetic Resonance Pectroscopy (Beijing: Qinghua University Press) p136 (in Chinese)
[17]	周公度, 叶宪曾 2012 化学元素综论 (北京: 科学出版社) 第270页 Zhou G D, Ye X Z 2012 Chemical Elements Survey (Beijing: Science Press) p270 (in Chinese)
[18]	鲍林L (卢嘉锡等译) 1981 化学键的本质 (上海: 上海科学技术出版社) 第 330页 Pauling L (translated by Lu J X) 1981 The Nature of the Chemical Bond (ShangHai: Science and Technology Press) p330(in Chinese)
[19]	苏长荣, 李家明 2002 中国科学A辑: 数学 32 103 Su C R, Li J M 2002 Sci. China Mater. 32 103
[20]	周公度, 段连运 2011 结构化学基础 (北京: 北京大学出版社) 第216页 ZhouG D, Duan L Y 2011 Fundamentals of Structural Chemical (Beijing: Beijing University Press) p216 (in Chinese)
[21]	关洪 2000 量子力学基础 (北京: 高等教育出版社) 第168页 Guan H 2000 Basic Quantum Mechanics (Beijing: Higher Education Press) p168 (in Chinese)
[22]	孙汉文 2002 原子光谱分析 (北京: 高等教育出版社) 第172页 Sun H W 2002 Atomic Spectral Analysis (Beijing: Higher Education Press) p172 (in Chinese)
[23]	Jahn H A, Teller E 1937 Proc. Roy. Soc. A 161 220
[24]	Jahn H A 1938 Proc. Roy. Soc. A 164 117

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