Ab initio calculation of hyperfine-structure constant A of Fr and evaluation of magnetic dipole moments of Fr isotopes

Bing-Qiong Lou; Fang Li; Pei-Yan Wang; Li-Ming Wang; Yong-Bo Tang

doi:10.7498/aps.68.20190113

Journals >Acta Physica Sinica >Volume 68 >Issue 9 >Page 093101-1 > Article

Acta Physica Sinica
Vol. 68, Issue 9, 093101-1 (2019)

Ab initio calculation of hyperfine-structure constant A of Fr and evaluation of magnetic dipole moments of Fr isotopes

Bing-Qiong Lou¹, Fang Li¹, Pei-Yan Wang¹, Li-Ming Wang¹, and Yong-Bo Tang^1,2,*

Author Affiliations

¹College of Physics and Materials Science, Henan Normal University, Xinxiang 453000, China

²Faculty of Arts and Sciences, Shenzhen Technology University, Shenzhen 518118, China

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DOI: 10.7498/aps.68.20190113 Cite this Article

Bing-Qiong Lou, Fang Li, Pei-Yan Wang, Li-Ming Wang, Yong-Bo Tang. Ab initio calculation of hyperfine-structure constant A of Fr and evaluation of magnetic dipole moments of Fr isotopes [J]. Acta Physica Sinica, 2019, 68(9): 093101-1 Copy Citation Text

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Electron correlation effects in hyperfine-structure constant A for S1/2, P1/2, P3/2, D3/2 and D5/2 states of 212Fr.212Fr原子S1/2, P1/2, P3/2, D3/2和D5/2态磁偶极超精细结构常数中的电子关联效应

Fig. 1. Electron correlation effects in hyperfine-structure constant A for S_1/2, P_1/2, P_3/2, D_3/2 and D_5/2 states of ²¹²Fr. ²¹²Fr原子S_1/2, P_1/2, P_3/2, D_3/2和D_5/2态磁偶极超精细结构常数中的电子关联效应

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Ratios of direct effect ADF, core polarization effect ACP, pair correlation effect APC, and the total of the three effects AT = ADF + APC + ACP to the CCSD, results A for S, P and D states against the principal quantum number n: (a) ADF/A; (b) ACP/A; (c) APC/A; (d) AT/A.直接效应ADF、核极化效应ACP、对关联效应APC, 以及相对于CCSD的3种效应的总和AT = ADF + ACP + APC, 针对主量子数n的S, P和D态的结果A的比率 (a) ADF/A; (b) ACP/A; (c) APC/A; (d) AT/A

Fig. 2. Ratios of direct effect A_DF, core polarization effect A_CP, pair correlation effect A_PC, and the total of the three effects A_T = A_DF + A_PC + A_CP to the CCSD, results A for S, P and D states against the principal quantum number n: (a) A_DF/A; (b) A_CP/A; (c) A_PC/A; (d) A_T/A. 直接效应A_DF、核极化效应A_CP、对关联效应A_PC, 以及相对于CCSD的3种效应的总和A_T = A_DF + A_CP + A_PC, 针对主量子数n的S, P和D态的结果A的比率　(a) A_DF/A; (b) A_CP/A; (c) A_PC/A; (d) A_T/A

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能级	${A_{{\rm{DF}}}}$	${A_{{\rm{CCSD}}}}$	$\varDelta /$%	Ref.[38]	实验值
7S_1/2	6001.76	9403.56	30.93	9124(94)	9064.2(2)^[27]
					9064.4(1.5)^[39]
8S_1/2	1538.03	2014.10	17.37	1986(19)
9S_1/2	631.98	792.19	13.66	784(9)
10S_1/2	321.24	396.86	11.95	419(9)	401(5)^[29]
11S_1/2	185.41	225.71	11.10	212(9)	225(3)^[29]
12S_1/2	116.42	141.25	10.80

Table 1.

Hyperfine-structure constant A for the S states of ²¹²Fr in MHz.

²¹²Fr原子S态的超精细结构常数A (单位: MHz)

能级	${A_{{\rm{DF}}}}$	${A_{{\rm{CCSD}}}}$	$\varDelta /$%	Ref.[38]	实验值
7P_1/2	642.48	1198.10	41.96	1181(9)	1189.1(4.6)^[28]
					1187.1(6.8)^[39]
					1192.0(2)^[32]
8P_1/2	228.04	372.04	33.66	371(5)	373.0(1)^[39]
9P_1/2	106.78	167.21	30.88
10P_1/2	58.35	89.53	29.46
11P_1/2	35.26	53.38	28.51
12P_1/2	22.88	34.24	27.68
7P_3/2	51.05	97.88	43.55	96(3)	97.2(1)^[27]
					97.2(1)^[39]
8P_3/2	18.67	32.51	37.82	32(3)	32.8(1)^[39]
9P_3/2	8.89	15.00	35.83
10P_3/2	4.91	8.15	34.75
11P_3/2	3.00	4.92	34.01
12P_3/2	1.97	3.20	33.33

Table 2.

Hyperfine-structure constant A for the P states of ²¹²Fr in MHz.

²¹²Fr原子P态的超精细结构常数A (单位: MHz)

能级	${A_{{\rm{DF}}}}$	${A_{{\rm{CCSD}}}}$	$\varDelta / $%	Ref.[38]	实验值
6D_3/2	33.25	92.91	61.27	79(5)
7D_3/2	16.82	30.17	39.65	29(3)
8D_3/2	8.65	13.81	32.20	13(1)	13.0(6)^[29]
9D_3/2	4.93	7.50	28.75	7(1)	7.1(7)^[29]
10D_3/2	3.06	4.52	26.64
11D_3/2	2.03	2.93	24.97
6D_5/2	13.14	–53.92	126.38	–54(5)
7D_5/2	6.32	–13.64	150.21	–15(3)
8D_5/2	3.20	–5.67	161.12	–6(1)	–7.1(6)^[29]
9D_5/2	1.81	–2.96	166.96	–3.3(6)	–3.6(4)^[29]
10D_5/2	1.12	–1.72	170.59
11D_5/2	0.74	–1.10	173.16

Table 3.

Hyperfine-structure constant A for the D states of ²¹²Fr in MHz.

²¹²Fr原子D态的超精细结构常数A (单位: MHz)

同位素	核自旋	7P_1/2		7P_3/2		${\mu}$
同位素	核自旋	${A_{{\rm{expt}}.}}$^[33]	${{\mu} _{1/2}}$	${A_{{\rm{expt}}.}}$^[33]	${{\mu} _{3/2}}$	${{\mu} _{{\rm{present}}}}$	${{\mu} _{{\rm{expt}}{\rm{.}}}}$^[33]
²⁰⁷Fr	9/2			90.7(6)	3.85(3)	3.85(3)	3.89(9)
²⁰⁸Fr	7	874.8(3)	4.723(2)	72.4(5)	4.784(33)	4.753(33)	4.75(10)
²⁰⁹Fr	9/2	1127.9(2)	3.914(1)	93.3(5)	3.963(21)	3.939(22)	3.95(8)
²¹⁰Fr	6	946.3(3)	4.379(1)	78.0(2)	4.418(11)	4.399(20)	4.40(9)
²¹¹Fr	9/2	1142.1(2)	3.964(1)	94.9(3)	4.031(13)	3.998(34)	4.00(8)
²¹²Fr	5	1187(7)	4.577(26)	97.2(1)	4.588(5)	4.583(30)	4.62(9)
²¹³Fr	9/2	1150(8)	3.991(28)	95.3(3)	4.047(13)	4.019(30)	4.02(8)
²²⁰Fr	1			–73.2(5)	–0.691(5)	–0.691(5)	–0.67(1)
²²¹Fr	5/2	808(12)	1.558(23)	65.5(6)	1.545(14)	1.552(25)	1.58(3)
²²²Fr	2			33(1)	0.623(19)	0.623(19)	0.63(1)
²²³Fr	3/2			83.3(9)	1.179(13)	1.179(13)	1.17(2)
²²⁴Fr	1			42.1(7)	0.397(7)	0.397(7)	0.40(1)
²²⁵Fr	3/2			77(3)	1.090(42)	1.090(42)	1.07(2)
²²⁶Fr	1			7(1)	0.066(9)	0.066(9)	0.071(2)
²²⁷Fr	1/2			316(2)	1.491(9)	1.491(9)	1.50(3)
²²⁸Fr	2			–41(2)	–0.77(4)	–0.77(4)	–0.76(2)

Table 4. Magnetic dipole moment of Fr isotope. Fr原子同位素的磁偶极矩

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