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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$f_ {n'}$ 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'} $ 时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'} $ 和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.-
Keywords:
- Rb cluster particles /
- resonance spectrum /
- number of 5s electron /
- average magnetic moment
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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 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 
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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.
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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 ${}^2{\Pi _{\rm{u}}}$ 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 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
87Rbnn $\bar \mu {}_n$/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%
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