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Abstract

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 ⁸⁷Rb ₁and 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 ⁸⁷Rb ₁. 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 nand decreases inverse proportionally with the combined angular momentum Fof 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 nbeing even number, the magnetic moment value becomes 0 and the amplitude is also 0 in the most cases, except for the cluster particles ⁸⁷Rb ₂with 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 _natomic 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 _nare 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:

Authors and contacts

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

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Cited By

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${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

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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KLMN_spd, 其他粒子没有重复标出闭壳层KLMN_spd.

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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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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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[20]	.иCCлEдOBAHиE лPOЦECCA лPOXOЖдEHиЯ ЧACTиЦ ЧEP3 HEлиHEйHYЮ PE3OHAHCHYЮ лиHЮ лиHиЮ (Q_ρ=6/5) B ЦиКлOTPOHE C лPOCTPAHCTBEHHOй BAPиAЦиEй. Acta Physica Sinica, 1964, 20(7): 636-642.doi:10.7498/aps.20.636

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