Ga+ 离子4s2 1S0—4s4p 3P0跃迁动态极化率的理论计算

娄宗帅; 王跃飞; 康博溢; 李睿; 张文君; 魏远飞; 布明鹭; 蔡翊宇

doi:10.7498/aps.74.20250125

摘要

利用相对论的组态相互作用加多体微扰理论方法, 对Ga⁺离子的4s² ¹S₀—4s4p ³P₀跃迁的动态极化率进行了理论计算. 并计算出了4s² ¹S₀态和4s4p ³P₀态的“幻零”波长以及跃迁4s² ¹S₀—4s4p ³P₀的“魔幻”波长, 对这些“幻零”波长和“魔幻”波长的精密测量提供了理论指导, 对研究Ga⁺离子的原子结构和4s² ¹S₀, 4s4p ³P₀两量子态静态极化率之差的精确确定, 以及Ga⁺离子的全光囚禁具有重要意义. 同时, 基于“极化率天平”方法, 讨论了静态极化率测量过程中的理论计算误差随波长的变化, 为进一步高精度确定4s² ¹S₀态4s4p ³P₀态的静态极化率提供了理论指导.

关键词:

Abstract

The transition of Ga⁺ ions from 4s² ¹S₀ to 4s4p ³P₀ has advantages such as a high quality factor and a small motional frequency shift, making it suitable as a reference for precision measurement experiments like optical clocks. Calculating the dynamic polarizability of 4s² ¹S₀—4s4p ³P₀ transition for Ga⁺ ion is of great significance for exploring the potential applications of the Ga⁺ ion in the field of quantum precision measurement and for testing atomic and molecular structure theories. In this paper, the dynamic polarizability of the Ga⁺ ion 4s² ¹S₀—4s4p ³P₀ transition is theoretically calculated using the relativistic configuration interaction plus many-body perturbation (RCI+MBPT) method. The “tune-out” wavelengths for the 4s² ¹S₀ state and the 4s4p ³P₀ state, as well as the “magic” wavelength of the 4s² ¹S₀—4s4p ³P₀ transition, are also computed. It is observed that the resonant lines situated near a certain “turn-out” and “magic” wavelength can make dominant contributions to the polarizability, while the remaining resonant lines generally contribute the least. These “tune-out” and “magic” wavelengths provide theoretical guidance for precise measurements, which is important for studying the atomic structure of Ga⁺ ions. The accurate determination of the difference in static polarizability between the 4s² ¹S₀ and 4s4p ³P₀ states is of significant importance. Additionally, based on the “polarizability scaling” method, this work also discusses how the theoretical calculation errors in static polarizability measurements vary with wavelength, which provides theoretical guidance for further determining the static polarizability of the 4s² ¹S₀ and 4s4p ³P₀ states with high precision. This is crucial for minimizing the uncertainty of the blackbody radiation (BBR) frequency shift in Ga⁺ optical clock and suppressing the systematic uncertainty.

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作者及机构信息

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通信作者: 张文君, 20210018@wfu.edu.cn ; 魏远飞, weiyuanfei@must.edu.mo ; 蔡翊宇, yycai@must.edu.mo

基金项目: 国家自然科学基金(批准号: 12304151, 12404421)、澳门科学技术发展基金(批准号: 0024/2024/RIB1)、山东省自然科学基金(批准号: ZR2022QA085)和潍坊学院大学生创新创业训练计划(批准号: S202411067021)资助的课题.

Authors and contacts

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Corresponding author: ZHANG Wenjun, 20210018@wfu.edu.cn ; WEI Yuanfei, weiyuanfei@must.edu.mo ; CAI Yiyu, yycai@must.edu.mo

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12304151, 12404421), the Science and Technology Development Fund, Macao SAR (Grant No. 0024/2024/RIB1), the Natural Science Foundation of Shandong Province, China (Grant No. ZR2022QA085), and the Innovation and Entrepreneurship Training Program for College Students of Weifang University, China (Grant No. S202411067021).

文章全文

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施引文献

下载: 全尺寸图片幻灯片

State	RCI	RCI+MBPT	NIST	Diff./%	Refs.
4s² ¹S₀	396252.81	412181.94	413285.38	–0.27	413285.41^CICP^[5]
4s4p ³P₀	43174.90	47338.76	47367.55	–0.060	47367.57 ^{CICP [5]}; 47032 ^{MCDHF [35]}; 47368^Expt^[36]
4s4p ³P₁	43584.84	47792.83	47814.114	–0.044	47469^{MCDHF [35]}; 47814 ^Expt^[36]
4s4p ¹P₁	68389.17	70709.25	70701.427	0.011	70701.42 ^{CICP [5]}; 70455^MCDHF^[35]; 70701^Expt^[36]
4s5s ³S₁	96653.91	102623.02	102944.595	–0.31	100749.90 ^CICP^[5]; 102665^{MCDHF [35]}; 102945^Expt^[36]
4s4d ³D₁	106905.35	113471.29	113815.885	–0.30	113815.87 ^CICP^[5]; 113305^MCDHF^[35]; 113816^Expt^[36]
4p² ³P₁	109300.03	115272.94	115224.47	–0.042	115224.49 ^{CICP [5]}; 114590^{MCDHF [35]}; 115224^Expt^[36]
4s5p ³P₁	111880.88	118110.59	118518.461	–0.34	118236^MCDHF^[35]; 118518^Expt^[36]
4s5p ¹P₁	114324.78	120211.72	120550.431	–0.28	120715.81 ^CICP^[5]; 120322 ^MCDHF^[35]; 120550 ^{Expt [36]}
4s6s ¹S₀	126011.01	132559.65	133010.30	–0.34	130793.68 ^CICP^[5]; 133517^MCDHF^[35]; 133741^Expt^[36]
4s5d ³D₁	129989.22	136706.55	137157.524	–0.33	137155.79 ^{CICP [5]}; 136759^{MCDHF [35]}; 137157^Expt^[36]
4s6p ³P₁	132039.60	138646.98	—	—	—
4s6p ¹P₁	132671.60	139209.74	—	—	—
4s7s ¹S₀	138282.16	145005.12	145494.205	–0.34	145176^MCDHF^[35]; 145494^Expt^[36]
4s6d ³D₁	140241.35	147033.96	147520.34	–0.33	—
4s8s ¹S₀	144640.75	151383.73	151923.93	–0.36	—
4s7d ³D₁	145733.76	152563.77	153064.92	–0.33	—
4s7p ³P₁	141291.01	148033.38	—	—	—
4s7p ¹P₁	141504.08	148239.62	—	—	—
4s8p ³P₁	146349.69	153163.32	—	—	—
4s8p ¹P₁	146429.38	153251.11	—	—	—
4s9s ¹S₀	148859.67	154959.21	—	—	—
4s8d ³D₁	149030.92	155885.88	156386.7	–0.32	—

下载: 导出CSV

Method	RCI		RCI+MBPT		Recommend	Refs.
Guage	Length	Velocity	Length	Velocity	Recommend	Refs.
4s² ¹S₀—4s4p ³P₁	0.055752	0.059065	0.064832	0.072400	0.065 (17)	0.0744 ^[34]; 0.0895 ^{MCDHF [35]}; 0.0802^{RRPA [38]}
4s² ¹S₀—4s4p ¹P₁	3.0918	3.0507	2.8480	3.0361	2.84 (24)	2.69 ^CICP^[5]; 2.87 ^[34]; 2.68^{MCDHF [35]}; 2.81^{MP [37]}; 2.79^{RRPA [38]}; 2.71^{MCHF [39]}; 2.78 (11)^{Expt [40]}
4s² ¹S₀—4s5p ³P₁	0.000595	0.000455	0.00594	0.000400	0.006 (6)	—
4s² ¹S₀—4s5p ¹P₁	0.28458	0.27302	0.15426	0.23982	0.15 (13)	0.138 ^[34]
4s² ¹S₀—4s6p ³P₁	0.00229	0.00237	0.00815	0.00272	0.0082 (59)	—
4s² ¹S₀—4s6p ¹P₁	0.0741	0.0684	0.0868	0.0594	0.087 (27)	—
4s² ¹S₀—4s7p ¹P₁	0.0264	0.0229	0.0143	0.0205	0.014 (12)	—
4s² ¹S₀—4s7p ³P₁	0.00232	0.00249	0.00803	0.00298	0.008 (6)	—
4s² ¹S₀—4s8p ¹P₁	0.00986	0.00753	0.0183	0.00768	0.02 (1)	—
4s² ¹S₀—4s8p ³P₁	0.00202	0.00233	0.00787	0.003104	0.008 (6)	—
4s4p ³P₀—4s5s ³S₁	0.93304	0.92359	0.92029	0.90827	0.920 (25)	0.974^CICP^[5]; 1.00^{MCDHF [35]}; 0.982^{MP [37]}
4s4p ³P₀—4s4d ³D₁	2.1286	2.0871	2.0181	2.0670	2.02 (11)	2.00^CICP^[5]; 2.08^[34]; 2.02^{MCDHF [35]}; 2.05^{MP [37]}
4s4p ³P₀—4p² ³P₁	1.8133	1.7818	1.6470	1.7695	1.65 (17)	1.64^CICP^[5]; 1.64^{MCDHF [35]}; 1.72^{MP [37]}
4s4p ³P₀—4s6s ³S₁	0.26761	0.26392	0.26890	0.26353	0.269 (5)	0.214^CICP^[5]; 0.205^{MCDHF [35]}; 0.217^{MP [37]}
4s4p ³P₀—4s5d ³D₁	0.66449	0.64536	0.62443	0.65590	0.62 (4)	0.461^CICP^[5]; 0.442^{MCDHF [35]}; 0.479^{MP [37]}
4s4p ³P₀—4s7s ³S₁	0.14979	0.14750	0.15084	0.14798	0.151 (3)	—
4s4p ³P₀—4s6d ³D₁	0.36574	0.35358	0.33986	0.36272	0.340 (26)	—
4s4p ³P₀—4s8s ³S₁	0.10206	0.10042	0.10065	0.098613	0.1021 (34)	—
4s4p ³P₀—4s7d ³D₁	0.24440	0.23567	0.22522	0.24281	0.225 (19)	—
4s4p ³P₀—4s9s ³S₁	0.088839	0.087378	0.078599	0.078310	0.079 (11)	—
4s4p ³P₀—4s8d ³D₁	0.18107	0.17433	0.16616	0.18060	0.181 (14)	—

下载: 导出CSV

Transition	Contributions	Refs.
$ \alpha \left(0\right)( $4s² ¹S₀$ ) $	—	—
4s² ¹S₀—4s4p ³P₁	0.013 (7)	—
4s² ¹S₀—4s4p ¹P₁	16.69 (2.82)	16.601^[5]
4s² ¹S₀—4s5p ³P₁	4.4 (4.4)×10^–5	—
4s² ¹S₀—4s5p ¹P₁	0.027 (27)	0.016^[5]
4s² ¹S₀—4s6p ³P₁	7.1 (7.1)×10^–5	—
4s² ¹S₀-—4s6p ¹P₁	0.008 (5)	—
4s² ¹S₀—4snp ³P₁, n = 7—8	0.00012 (12)	—
4s² ¹S₀—4snp ¹P₁, n = 7—9	0.0006 (4)	—
Core	1.24 (1)^[5]	1.24 (1)^[5]
Total	17.98 (2.82)	17.95 (34)^[5]
$ \alpha \left(0\right)( $4s4p ³P₀$ ) $	—	—
4s4p ³P₀—4s5s ³S₁	2.23 (12)	2.257^[5]
4s4p ³P₀—4s4d ³D₁	8.98 (98)	8.668^[5]
4s4p ³P₀—4p² ³P₁	5.87 (1.21)	5.945^[5]
4s4p ³P₀—4s6s ³S₁	0.124 (5)	—
4s4p ³P₀—4s5d ³D₁	0.62 (8)	—
4s4p ³P₀—4sns ³S₁, n = 7—9	0.057 (13)	—
4s4p ³P₀—4snd ³D₁, n = 6—8	0.283 (29)	—
Core	1.24 (1)^[5]	1.24 (1)^[5]
Total	19.41 (1.56)	19.58 (38)^[5]
$ {{\Delta }}\alpha \left(0\right) $	1.43 (3.2)	1.63 (72)^[5]

下载: 导出CSV

Transition	‘Tune-out’ wavelengths					‘Magic’ wavelengths
Transition	209.101	176.42	148.61	117.197	113.09	209.286	168.1	148.27	116.38	106.7
4s² ¹S₀—4s4p ³P₁	0.025					0.085	<0.1	<0.001	<0.001	<0.1
4s² ¹S₀—4s4p ¹P₁	0.0076					0.049	2.7	0.049	0.16	2.5
4s² ¹S₀—4s5p ¹P₁	<0.001					<0.01	<0.1	<0.001	<0.01	0.11
4s² ¹S₀—4s6p ¹P₁	<0.001					<0.01	<0.1	<0.001	<0.01	<0.1
4s4p ³P₀—4s5s ³S₁		0.17	<0.001	0.0017	0.0073	<0.01	0.27	<0.001	<0.01	<0.1
4s4p ³P₀—4s4d ³D₁		0.19	0.077	0.034	0.0095	0.026	1.6	0.047	0.036	0.68
4s4p ³P₀—4p² ³P₁		0.22	0.15	0.048	0.13	0.030	1.7	0.16	0.047	0.96
4s4p ³P₀—4s6s ³S₁		<0.01	<0.001	<0.001	0.0065	<0.01	<0.1	<0.001	<0.01	<0.1
4s4p ³P₀—4s5d ³D₁		<0.01	<0.001	<0.001	<0.001	<0.01	<0.1	<0.001	<0.01	<0.1
Others	<0.001	<0.01	<0.01	<0.001	<0.01	<0.01	<0.1	<0.01	<0.01	<0.1
Total	0.026	0.34	0.16	0.059	0.16	0.11	3.6	0.17	0.17	2.8

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Transition	‘Tune-out’ wavelengths					‘Magic’ wavelengths
Transition	209.101	176.42	148.61	117.197	113.09	209.286	168.1	148.27	116.38	106.7
4s² ¹S₀—4s4p ³P₁	–32.06	–0.03	–0.01	–0.01	–0.01	9.51	–0.02	–0.01	–0.01	0.00
4s² ¹S₀—4s4p ¹P₁	30.77	46.73	177.29	–36.57	–29.58	30.72	57.11	184.64	–34.99	–22.00
4s² ¹S₀—4s5p ¹P₁	0.03	0.03	0.04	0.05	0.06	0.03	0.04	0.04	0.06	0.06
4s² ¹S₀—4s6p ¹P₁	0.01	0.01	0.01	0.01	0.01	0.01	0.01	0.01	0.01	0.01
Others	0.01	0.01	0.01	0.01	0.01	0.01	0.01	0.01	0.01	0.01
Core	1.24	1.24	1.24	1.24	1.24	1.24	1.24	1.24	1.24	1.24
Total	0.00	47.99	178.58	–35.27	–28.27	41.52	58.39	185.93	–33.68	–20.68
4s4p ³P₀—4s5s ³S₁	8.59	–55.40	–4.78	–1.64	–1.46	8.54	–15.34	–4.71	–1.60	–1.21
4s4p ³P₀—4s4d ³D₁	18.64	33.00	–352.26	–13.85	–11.66	18.61	45.19	–297.43	–13.37	–9.07
4s4p ³P₀—4p² ³P₁	11.66	19.42	353.37	–10.10	–8.41	11.64	25.33	484.39	–9.73	–6.46
4s4p ³P₀—4s6s ³S₁	0.18	0.22	0.32	16.76	–1.87	0.18	0.24	0.33	–18.78	–0.62
4s4p ³P₀—4s5d ³D₁	0.87	1.0	1.43	6.46	20.77	0.87	1.12	1.44	7.43	–6.93
Others	0.44	0.52	0.68	1.13	1.39	0.44	0.61	0.68	1.13	2.37
Core	1.24	1.24	1.24	1.24	1.24	1.24	1.24	1.24	1.24	1.24
Total	41.62	0.00	0.00	0.00	0.00	41.52	58.39	185.93	–33.68	–20.68
Diff.						0.00	0.00	0.00	0.0	0.0

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[16]	高君芳, 程鸿兴, 肖渊, 庞文宁, 龙桂鲁, 尚仁成. 电子与钠原子散射极化参数的计算. 必威体育下载 , 1998, 47(10): 1606-1611. doi: 10.7498/aps.47.1606
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Theoretical calculation of dynamic polarizability of 4s^{2 1}S₀—4s4p³P₀ transition for Ga⁺ ion

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通信作者: 张文君, 20210018@wfu.edu.cn ; 魏远飞, weiyuanfei@must.edu.mo ; 蔡翊宇, yycai@must.edu.mo

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Corresponding author: ZHANG Wenjun, 20210018@wfu.edu.cn ; WEI Yuanfei, weiyuanfei@must.edu.mo ; CAI Yiyu, yycai@must.edu.mo

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Theoretical calculation of dynamic polarizability of 4s2 1S0—4s4p 3P0 transition for Ga+ ion

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Abstract

作者及机构信息

1. 2. 3. 4. 5. 6.

通信作者: 张文君, 20210018@wfu.edu.cn ; 魏远飞, weiyuanfei@must.edu.mo ; 蔡翊宇, yycai@must.edu.mo

Authors and contacts

1. 2. 3. 4. 5. 6.

Corresponding author: ZHANG Wenjun, 20210018@wfu.edu.cn ; WEI Yuanfei, weiyuanfei@must.edu.mo ; CAI Yiyu, yycai@must.edu.mo

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Theoretical calculation of dynamic polarizability of 4s^{2 1}S₀—4s4p³P₀ transition for Ga⁺ ion

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