<trans-title xml:lang="en">Theoretical investigation on hyperfine structure and isotope shift for 5d106s 2S1/2→5d96s2 2D5/2 clock transition in Hg+</trans-title>

Xiang Zhang; Ben-Quan Lu; Ji-Guang Li; Hong-Xin Zou

doi:10.7498/aps.68.20182136

Acta Physica Sinica, Volume. 68, Issue 4, 043101-1(2019)

Theoretical investigation on hyperfine structure and isotope shift for 5d¹⁰6s ²S_1/2→5d⁹6s^{2 2}D_5/2 clock transition in Hg⁺

Xiang Zhang1... Ben-Quan Lu2,3, Ji-Guang Li2,* and Hong-Xin Zou1,* |Show fewer author(s)

Author Affiliations

¹College of Liberal Arts and Science, National University of Defense Technology, Changsha 410073, China

²Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

³National Time Service Center, Chinese Academy of Sciences, Xi’an 710600, China

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Figures & Tables(7)

Fig. 1. Trends of field shift and mass shift for the 5d¹⁰6s ²S_1/2→5d⁹6s^{2 2}D_5/2 transition in mercury isotope ions with respect to ¹⁹⁹Hg⁺ as the increase of mass number. 汞同位素离子5d¹⁰6s ²S_1/2→5d⁹6s^{2 2}D_5/2跃迁相对于¹⁹⁹Hg⁺离子的FS和MS随质量数变化的趋势

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Fig. 2. Hyperfine level structure diagram of ¹⁹⁹Hg⁺ and ¹⁹⁸Hg⁺. ¹⁹⁹Hg⁺和¹⁹⁸Hg⁺离子的超精细能级结构图

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Table 1. Related parameters of seven natural mercury isotopes.

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Table 1. Related parameters of seven natural mercury isotopes.

Isotopes’ mass number	Relative atomic mass^[6]	Abundance^[7]	R/fm^[8]	I/ $\hbar$	$\mu $/nm^[9]	Q/barn^[9]
196	195.9658326 (32)	0.15%	5.4385	0+	–	–
198	197.96676860 (52)	10.04%	5.4463	0+	–	–
199	198.96828064 (46)	16.94%	5.4474	1/2–	+0.5058855(9)	–
200	199.96832659 (47)	23.14%	5.4551	0+	–	–
201	200.97030284 (69)	13.17%	5.4581	3/2–	–0.5602257(14)	+0.387(6)
202	201.97064340 (69)	29.74%	5.4648	0+	–	–
204	203.97349398 (53)	6.82%	5.4744	0+	–	–

Table 2.
Effect of electron correlations on energy eigenvalues.
电子关联对能量本征值的影响

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Table 2.
Effect of electron correlations on energy eigenvalues.
电子关联对能量本征值的影响

n	Active orbitals	Virtual orbitals	NCF	Energy eigenvalue/10⁴ Hartrees
DF			1/1	–1.964857825739/–1.964840329639
7	5d6s	7s, 6p, 6d, 5f, 5g	310/1631	–1.964887721767/–1.964870006459
8	5spd6s	8s, 7p, 7d, 6f, 6g	4047/19457	–1.964907829871/–1.964890991924
9	4spdf5spd6s	9s, 8p, 8d, 7f, 7g	29884/151235	–1.964927346267/–1.964910124355
10	3spd4spdf5spd6s	10s, 9p, 9d, 8f, 7g	69579/334460	–1.964929839430/–1.964912598231
11	3spd4spdf5spd6s	11s, 10p, 10d, 9f, 7g	103101/480763	–1.964930723063/–1.964913507368

Table 3.
Effect of electron correlations on the FS (in GHz) of the 5d¹⁰6s ²S_1/2→5d⁹6s^{2 2}D_5/2 transition in mercury isotope ions (relative to ¹⁹⁹Hg⁺).
汞同位素离子相对¹⁹⁹Hg⁺离子5d¹⁰6s ²S_1/2→5d⁹6s^{2 2}D_5/2钟跃迁的场位移 (单位: GHz)受电子关联的影响

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Table 3.
Effect of electron correlations on the FS (in GHz) of the 5d¹⁰6s ²S_1/2→5d⁹6s^{2 2}D_5/2 transition in mercury isotope ions (relative to ¹⁹⁹Hg⁺).
汞同位素离子相对¹⁹⁹Hg⁺离子5d¹⁰6s ²S_1/2→5d⁹6s^{2 2}D_5/2钟跃迁的场位移 (单位: GHz)受电子关联的影响

n	¹⁹⁶Hg⁺	¹⁹⁸Hg⁺	²⁰⁰Hg⁺	²⁰¹Hg⁺	²⁰²Hg⁺	²⁰⁴Hg⁺
DF	–9.01296	–1.11476	7.80962	10.8553	17.6634	27.4329
7	–9.20985	–1.13911	7.98023	11.0925	18.0493	28.0321
8	–8.81504	–1.09028	7.63813	10.6169	17.2755	26.8305
9	–9.11351	–1.12720	7.89674	10.9764	17.8605	27.7389
10	–9.12483	–1.12860	7.90656	10.9901	17.8827	27.7734
11	–9.14646	–1.13127	7.92530	11.0161	17.9250	27.8392

Table 4.
Magnetic dipole A (in MHz) and electric quadrupole B (in MHz) hyperfine interaction constants for the 5d¹⁰6s ²S_1/2 and 5d⁹6s^{2 2}D_5/2 states of ¹⁹⁹Hg⁺ and ²⁰¹Hg⁺.
¹⁹⁹Hg⁺和²⁰¹Hg⁺离子5d¹⁰6s ²S_1/2和5d⁹6s^{2 2}D_5/2态的磁偶极(A单位: MHz)和电四极(B单位: MHz)超精细结构常数

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Table 4.
Magnetic dipole A (in MHz) and electric quadrupole B (in MHz) hyperfine interaction constants for the 5d¹⁰6s ²S_1/2 and 5d⁹6s^{2 2}D_5/2 states of ¹⁹⁹Hg⁺ and ²⁰¹Hg⁺.
¹⁹⁹Hg⁺和²⁰¹Hg⁺离子5d¹⁰6s ²S_1/2和5d⁹6s^{2 2}D_5/2态的磁偶极(A单位: MHz)和电四极(B单位: MHz)超精细结构常数

n	¹⁹⁹A_1/2	¹⁹⁹A_5/2	²⁰¹A_1/2	²⁰¹A_5/2	²⁰¹B_5/2
DF	36812.0	986.665	–13585.7	–364.216	796.132
7	39090.5	1263.67	–14426.7	–466.447	755.219
8	38761.2	795.021	–14305.1	–293.490	765.173
9	40556.1	951.973	–14967.5	–353.908	936.169
10	40967.0	951.669	–15119.2	–351.307	961.161
11	41133.9	963.552	–15180.8	–355.692	966.809
Ref. [38]		963.5		–355.7	839.4
Ref. [37]	40460		–14960
Ref. [35]	42366	1315	–15527	–482	859
Ref. [36]	41477		–15311

Table 5.
Absolute frequency values of the 5d¹⁰6s ²S_1/2→5d⁹6s^{2 2}D_5/2 transition in mercury isotope ions.
汞同位素离子5d¹⁰6s ²S_1/2→5d⁹6s^{2 2}D_5/2跃迁谱线的绝对频率值
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Table 5.
Absolute frequency values of the 5d¹⁰6s ²S_1/2→5d⁹6s^{2 2}D_5/2 transition in mercury isotope ions.
汞同位素离子5d¹⁰6s ²S_1/2→5d⁹6s^{2 2}D_5/2跃迁谱线的绝对频率值
Ions ¹⁹⁶Hg⁺ ¹⁹⁸Hg⁺ ¹⁹⁹Hg⁺ ²⁰⁰Hg⁺ ²⁰¹Hg⁺ ²⁰²Hg⁺ ²⁰⁴Hg⁺
*Experiment value is 1064691.95 GHz^[15].
ν/GHz 1064683.30 1064691.31* 1064721.61^[14] 1064700.37 1064719.89 1064710.37 1064720.28

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Xiang Zhang, Ben-Quan Lu, Ji-Guang Li, Hong-Xin Zou. Theoretical investigation on hyperfine structure and isotope shift for 5d¹⁰6s ²S_1/2→5d⁹6s^{2 2}D_5/2 clock transition in Hg⁺[J]. Acta Physica Sinica, 2019, 68(4): 043101-1

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Paper Information

Received: Dec. 4, 2018

Accepted: --

Published Online: Sep. 16, 2020

The Author Email: Zou Hong-Xin (hxzou@nudt.edu.cn)

DOI:10.7498/aps.68.20182136

Topics

Nuclear physics

Particles and fields

Particle and nuclear astrophysics and cosmology

Table 1. Related parameters of seven natural mercury isotopes.

Table 1. Related parameters of seven natural mercury isotopes.

Table 2. Effect of electron correlations on energy eigenvalues.电子关联对能量本征值的影响

Table 2. Effect of electron correlations on energy eigenvalues.电子关联对能量本征值的影响

Table 3. Effect of electron correlations on the FS (in GHz) of the 5d106s 2S1/2→5d96s2 2D5/2 transition in mercury isotope ions (relative to 199Hg+). 汞同位素离子相对199Hg+离子5d106s 2S1/2→5d96s2 2D5/2钟跃迁的场位移 (单位: GHz)受电子关联的影响

Table 3. Effect of electron correlations on the FS (in GHz) of the 5d106s 2S1/2→5d96s2 2D5/2 transition in mercury isotope ions (relative to 199Hg+). 汞同位素离子相对199Hg+离子5d106s 2S1/2→5d96s2 2D5/2钟跃迁的场位移 (单位: GHz)受电子关联的影响

Table 4. Magnetic dipole A (in MHz) and electric quadrupole B (in MHz) hyperfine interaction constants for the 5d106s 2S1/2 and 5d96s2 2D5/2 states of 199Hg+ and 201Hg+. 199Hg+和201Hg+离子5d106s 2S1/2和5d96s2 2D5/2态的磁偶极(A单位: MHz)和电四极(B单位: MHz)超精细结构常数

Table 4. Magnetic dipole A (in MHz) and electric quadrupole B (in MHz) hyperfine interaction constants for the 5d106s 2S1/2 and 5d96s2 2D5/2 states of 199Hg+ and 201Hg+. 199Hg+和201Hg+离子5d106s 2S1/2和5d96s2 2D5/2态的磁偶极(A单位: MHz)和电四极(B单位: MHz)超精细结构常数

Table 5. Absolute frequency values of the 5d106s 2S1/2→5d96s2 2D5/2 transition in mercury isotope ions. 汞同位素离子5d106s 2S1/2→5d96s2 2D5/2跃迁谱线的绝对频率值

Table 5. Absolute frequency values of the 5d106s 2S1/2→5d96s2 2D5/2 transition in mercury isotope ions. 汞同位素离子5d106s 2S1/2→5d96s2 2D5/2跃迁谱线的绝对频率值

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Table 2.
Effect of electron correlations on energy eigenvalues.
电子关联对能量本征值的影响

Table 2.
Effect of electron correlations on energy eigenvalues.
电子关联对能量本征值的影响

Table 5.
Absolute frequency values of the 5d¹⁰6s ²S_1/2→5d⁹6s^{2 2}D_5/2 transition in mercury isotope ions.
汞同位素离子5d¹⁰6s ²S_1/2→5d⁹6s^{2 2}D_5/2跃迁谱线的绝对频率值

Table 5.
Absolute frequency values of the 5d¹⁰6s ²S_1/2→5d⁹6s^{2 2}D_5/2 transition in mercury isotope ions.
汞同位素离子5d¹⁰6s ²S_1/2→5d⁹6s^{2 2}D_5/2跃迁谱线的绝对频率值