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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

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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

Experimental observation and theoretical analysis of spontaneous magnetic moment of Rb atom clusters

Di Shu-Hong, Zhang Yang, Yang Hui-Jing, San Xing-Yuan, Liu Hui-Yuan, Zhang Su-Heng, Li Fan-Lin, Tai Jun-Jun, Zhou Chun-Li
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  • 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'}$87Rb1的共振频率f *之间存在$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87Rbn = 87Rbn – 1 + 87Rb联合原子簇构造模式, 给出14种簇粒子87Rbn (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'} $87Rbn的磁矩值与(87Rb)${}_ {n'} $的磁矩值严格吻合(平均相对误差仅为0.6765%), 证实了(87Rb)${}_ {n'} $87Rbn的对应关系.
    For the magnetism of alkali metal clusters, it is difficult to determine the number of atoms and the magnetic moment of isolated atoms cluster. In this paper, we investigate the magnetic moment of single atomic molecule 87Rb1 and 14 kinds of cluster particles (87Rb)${}_{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 87Rbn, 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 87Rbn–1 + 87Rbn 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 87Rbn are in strict consistency (the average relative error is only 0.6765%), confirming the corresponding relationship between (87Rb)${}_{n'} $ and 87Rbn. This research will be of great value in the magnetic research of cluster particles.
      通信作者: 邸淑红, 792423642@qq.com ; 张阳, 185540891@qq.com ; 杨会静, yanghj619@126.com
      Corresponding author: Di Shu-Hong, 792423642@qq.com ; Zhang Yang, 185540891@qq.com ; Yang Hui-Jing, yanghj619@126.com
    [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 953Google 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 3789Google Scholar

    [6]

    Nozue Y, Kodaira T, Ohwashi S, Goto T, Terasaki O 1993 Phys. Rev. B 48 12253Google Scholar

    [7]

    Kodaira T, Ikemoto Y, Nozue Y 2000 Mol. Cryst. Liq. Cryst. 341 461Google Scholar

    [8]

    Kodaira T, IkemotoY, NozueY 1999 Eur. Phys. J. D 9 505Google Scholar

    [9]

    Nakano T, Ikemoto Y, NozueY 2000 Physica B 281-282 688Google Scholar

    [10]

    Nozue Y, Kodaira T, Ohwashi S, Togashi N, Terasaki O 1996 Surf. Rev. Lett. 3 701Google Scholar

    [11]

    Nakano T, Ikemoto Y, NozueY 2001 J. Magn. Magn. Maters. 226-230 238Google Scholar

    [12]

    Duan T C, Nakano T, Nozue Y 2007 J. Magn. Magn. Maters. 310 1013Google 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.

    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.

    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).

    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'}$/μB${\bar A_{n'}}$/mV${n'} $为偶数粒子${n'} $${\bar g_{n'}}$$\bar \mu {}_{n'}$/μB${\bar A_{n'}}$/mV
    87Rb110.4943370.4943371574.50(87Rb)2′20.2469840.246984105.75
    (87Rb)3′30.1645980.164598883.07(87Rb)4′4000
    (87Rb)5′50.0987890.098789383.47(87Rb)6′6000
    (87Rb)7′70.0706350.070635188.70(87Rb)8′8000
    (87Rb)9′90.0549530.05495384.92(87Rb)10′10000
    (87Rb)11′110.0449750.04497548.62(87Rb)12′12000
    (87Rb)13′130.0380600.03806031.55(87Rb)14′14000
    (87Rb)15′150.0329780.03297812.63
    下载: 导出CSV

    表 2  15种原子簇分子87Rbn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 87Rbn.

    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: ${P_{\rm{a} } } - {P_{\rm{b} } } = 1/2$
    87Rb2
    85Rb2[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KLMNspd, 其他粒子没有重复标出闭壳层KLMNspd.
    下载: 导出CSV

    表 3  87Rbn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 clusters87Rbn.

    n为奇数
    的簇分子
    n为奇数的
    分子项
    5s价电子
    个数
    $\bar \mu {}_n$/μB${\bar g_n}$n为偶数
    的簇分子
    n为偶数的
    分子项
    5s价电
    子个数
    $\bar \mu {}_n$/μB${\bar g_n}$
    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$$1/6$87Rb4${}^2{\Pi _{\rm{u}}}$400
    87Rb5${}^2{\Pi _{\rm{u}}}$5$1/10$$1/10$87Rb6${}^2{\Pi _{\rm{u}}}$600
    87Rb7${}^2{\Pi _{\rm{u}}}$7$1/14$$1/14$87Rb8${}^1{\Pi _{\rm{u}}}$800
    87Rb9${}^2{\Pi _{\rm{u}}}$9$1/18$$1/18$87Rb10${}^2{\Pi _{\rm{u}}}$1000
    87Rb11${}^2{\Pi _{\rm{g}}}$11$1/22$$1/22$87Rb12${}^2{\Pi _{\rm{u}}}$1200
    87Rb13${}^2{\Pi _{\rm{g}}}$13$1/26$$1/26$87Rb14${}^2{\Pi _{\rm{u}}}$1400
    87Rb15${}^2{\Pi _{\rm{g}}}$15$1/30$$1/30$
    下载: 导出CSV

    表 4  87Rbn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 87Rbn and (87Rb)${}_{n'} $

    团簇
    87Rbn
    n$\bar \mu {}_n$/μB团簇
    (87Rb)${}_{n'} $
    $n'$$\bar \mu {}_{n'}$/μB磁矩的相对误差%${\bar A_{n'} }$/mV${\bar A_{n'}}$与${\bar A_n}$
    比较
    87Rb11$1/2$87Rb110.4943371.13261574.50一致
    87Rb22$1/4$(87Rb)2′20.2469841.2063105.75线性分子简并态
    87Rb33$1/6$(87Rb)3′30.1645981.2411883.07一致
    87Rb440(87Rb)4′40000
    87Rb55$1/10$(87Rb)5′50.0987891.2110383.47一致
    87Rb660(87Rb)6′60000
    87Rb77$1/14$(87Rb)7′70.0706351.1042188.70一致
    87Rb880(87Rb)8′80000
    87Rb99$1/18$(87Rb)9′90.0549531.084384.92一致
    87Rb10100(87Rb)10′100000
    87Rb1111$1/22$(87Rb)11′110.0449751.055648.62一致
    87Rb12120(87Rb)12′120000
    87Rb1313$1/26$(87Rb)13′130.0380601.046731.55一致
    87Rb14140(87Rb)14′140000
    87Rb1515$1/30$(87Rb)15′150.0329781.065812.63一致
    15种簇粒子(87Rb)${}_{n'} $与87Rbn的磁矩相对误差均值为: 0.6765%
    9种磁矩不为0的簇粒子(87Rb)${}_{n'} $与87Rbn的磁矩相对误差均值为: 1.1275%
    下载: 导出CSV
  • [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 953Google 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 3789Google Scholar

    [6]

    Nozue Y, Kodaira T, Ohwashi S, Goto T, Terasaki O 1993 Phys. Rev. B 48 12253Google Scholar

    [7]

    Kodaira T, Ikemoto Y, Nozue Y 2000 Mol. Cryst. Liq. Cryst. 341 461Google Scholar

    [8]

    Kodaira T, IkemotoY, NozueY 1999 Eur. Phys. J. D 9 505Google Scholar

    [9]

    Nakano T, Ikemoto Y, NozueY 2000 Physica B 281-282 688Google Scholar

    [10]

    Nozue Y, Kodaira T, Ohwashi S, Togashi N, Terasaki O 1996 Surf. Rev. Lett. 3 701Google Scholar

    [11]

    Nakano T, Ikemoto Y, NozueY 2001 J. Magn. Magn. Maters. 226-230 238Google Scholar

    [12]

    Duan T C, Nakano T, Nozue Y 2007 J. Magn. Magn. Maters. 310 1013Google 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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