PbF分子${{\rm{A}}^2{\text{∑}}^{ +}}$—X2Π1/2跃迁光谱的光谱研究

doi:10.3969/j.issn.1000-5641.2025.03.006

摘要/Abstract

摘要：

通过激光溅射Pb产生的Pb等离子体与SF₆/Ar反应制备了PbF自由基, 利用激光诱导荧光光谱测量了PbF分子${\rm{A}}^2{\text{∑}}^{ +}$—X²Π_1/2跃迁光谱, 并精确测得了其A态振动能级$v=0$和$v =1$的分子常数$ {T}_{0} $、$ B $、$ D $、$ \gamma $和$ p $. 此外, 还精确测量了PbF分子${\rm{A}}^2{\text{∑}}^{ +}$态$v =0$振动态的荧光寿命. 采用Morse势和RKR(Rydberg-Klein-Rees inversion)/LEVEL方法计算了${\rm{A}}^2{\text{∑}}^{ +}$—X²Π_1/2跃迁的Franck-Condon 因子. 计算结果表明, PbF分子不适合进行激光冷却的研究. 这不仅丰富了对PbF分子光谱的深入理解, 而且为进一步精密测量电子电偶极矩 (electronic electric dipole moment, eEDM) 提供了重要参考.

关键词: 电子电偶极矩, PbF分子, 激光诱导荧光光谱技术, 光谱常数, Frank-Condon因子

Abstract:

This study presents the preparation of PbF radicals via the reaction of Pb plasma, generated by the laser ablation of lead, with SF₆/Ar gas mixture. Moreover, the vibrational-rotational bands of the ${\rm{A}}^2{\text{∑}}^{ +}$–X²Π_1/2 transition of PbF molecule were measured using laser induced fluorescence spectroscopy. The molecular constants $ {T}_{0} $, $ B $, $ D $, $ \gamma $ and $ p $ for the vibrational levels $ v $ = 0 and $ v $ = 1 of the PbF molecule in the ${\rm{A}}^2{\text{∑}}^{ +}$ state. The data provide effective information for electronic electric dipole moment(eEDM) measurement. Additionally, the fluorescence lifetime of the PbF molecule in the $v=0$ vibrational state of the ${\rm{A}}^2{\text{∑}}^{ +}$ state was measured. Finally, the Franck-Condon factors for the ${\rm{A}}^2{\text{∑}}^{ +}$–X²Π_1/2 transition were calculated using the Morse potential and Rydberg-Klein-Rees inversion(RKR)/LEVEL methods, indicating that PbF molecules are unsuitable for laser cooling research. The above results enrich the understanding of PbF molecular spectrum and provide key references for future studies on precise eEDM measurements.

Key words: electronic electric dipole moment(eEDM), PbF molecule, laser induced fluorescence spectroscopy technology, spectral constants, Frank-Condon factors

中图分类号:

O433.4

潘佳煖, 朱成成, 汪海玲. PbF分子${{\rm{A}}^2{\text{∑}}^{ +}}$—X²Π_1/2跃迁光谱的光谱研究[J]. 华东师范大学学报（自然科学版）, 2025, 2025(3): 43-50.

Jianuan PAN, Chengcheng ZHU, Hailing WANG. Spectroscopic study on the ${\rm{A}}^2{{\text{∑}}^{ +}}$–X²Π_1/2 transition spectra of PbF molecules[J]. J* E* C* N* U* N* S*, 2025, 2025(3): 43-50.

图/表 6

图1

图2

图3

表1

图4

表2

PbF分子${\rm{A}}^2{\text{∑}}^{ +}$—X2Π1/2跃迁的Frank-Condon因子"

振动态	计算方法	Frank-Condon因子
振动态	计算方法	$v'=0$	$v'=1$	$v'=2$	$v'=3$	$v'=4$	$v'=5$	$v'=6$	$v' =7$
$v''=0$	Morse	3.00 × 10^–1	3.50 × 10^–1	2.15 × 10^–1	9.25 × 10^–2	3.09 × 10^–2	8.50 × 10^–3	2.00 × 10^–3	4.00 × 10^–4
$v''=0$	RKR	2.99 × 10^–1	3.45 × 10^–1	2.14 × 10^–1	9.47 × 10^–2	3.35 × 10^–2	1.00 × 10^–2	2.64 × 10^–3	6.22 × 10^–4
$v''=1$	Morse	3.70 × 10^–1	1.23 × 10^–2	1.01 × 10^–1	2.16 × 10^–1	1.71 × 10^–1	8.57 × 10^–2	3.19 × 10^–2	9.50 × 10^–3
$v''=1$	RKR	3.73 × 10^–1	1.30 × 10^–2	9.50 × 10^–2	2.07 × 10^–1	1.69 × 10^–1	8.96 × 10^–2	3.36 × 10^–2	1.22 × 10^–2
$v''=2$	Morse	2.20 × 10^–1	1.23 × 10^–1	1.38 × 10^–1	2.00 × 10^–4	1.05 × 10^–1	1.77 × 10^–1	1.34 × 10^–1	6.73 × 10^–2
$v''=2$	RKR	2.21 × 10^–1	1.26 × 10^–1	1.41 × 10^–1	6.85 × 10^–7	9.30 × 10^–2	1.66 × 10^–1	1.34 × 10^–1	7.32 × 10^–2
$v''=3$	Morse	8.31 × 10^–2	2.51 × 10^–1	2.50 × 10^–3	1.52 × 10^–1	4.17 × 10^–2	1.86 × 10^–2	1.23 × 10^–1	1.52 × 10^–1
$v''=3$	RKR	8.15 × 10^–2	2.56 × 10^–1	2.66 × 10^–3	1.52 × 10^–1	4.73 × 10^–2	1.21 × 10^–2	1.06 × 10^–1	1.43 × 10^–1
$v''=4$	Morse	2.16 × 10^–2	1.74 × 10^–1	1.54 × 10^–1	3.19 × 10^–2	7.75 × 10^–2	9.94 × 10^–2	1.80 × 10^–3	5.47 × 10^–2
$v''=4$	RKR	2.09 × 10^–2	1.74 × 10^–1	1.59 × 10^–1	3.28 × 10^–2	7.52 × 10^–2	1.05 × 10^–1	5.01 × 10^–3	3.91 × 10^–2
$v''=5$	Morse	4.44 × 10^–3	6.80 × 10^–2	2.12 × 10^–1	5.00 × 10^–2	9.54 × 10^–2	1.38 × 10^–2	1.09 × 10^–1	3.27 × 10^–2
$v''=5$	RKR	3.91 × 10^–3	6.61 × 10^–2	2.16 × 10^–1	5.25 × 10^–2	9.81 × 10^–2	1.16 × 10^–2	1.09 × 10^–1	4.22 × 10^–2
$v''=6$	Morse	5.00 × 10^–4	1.77 × 10^–2	1.23 × 10^–1	1.90 × 10^–1	2.10 × 10^–3	1.20 × 10^–1	1.80 × 10^–3	7.56 × 10^–2
$v''=6$	RKR	5.51 × 10^–4	1.66 × 10^–2	1.22 × 10^–1	1.95 × 10^–1	2.35 × 10^–3	1.23 × 10^–1	3.10 × 10^–3	7.02 × 10^–2
$v''=7$	Morse	1.00 × 10^–4	3.30 × 10^–3	4.21 × 10^–2	1.68 × 10^–1	1.29 × 10^–1	1.19 × 10^–2	9.78 × 10^–2	2.91 × 10^–2
$v''=7$	RKR	5.91 × 10^–5	2.93 × 10^–3	4.03 × 10^–2	1.69 × 10^–1	1.35 × 10^–1	1.21 × 10^–2	9.83 × 10^–2	3.41 × 10^–2

表2

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振动态	相关工作	$ {T}_{0} $	$ B $	$ {10}^{7}D $	$ \gamma $	$ p $
$v=0$	本文工作	22502.06(9)	0.20692(6)	2.16(9)	– 0.2047	0.6185(3)
$v=0$	文献[8]	22502.09(1)	0.20691(4)	2.23(3)	– 0.2047^*	0.6185(3)
$v=1$	本文工作	22897.23(2)	0.20546(1)	2.00(0)	– 0.2038	0.6146(4)
$v=1$	文献[8]	22896.82(1)	0.20546(5)	2.21(5)	– 0.2036^*	0.6146(4)

PbF分子${{\rm{A}}^2{\text{∑}}^{ +}}$—X²Π_1/2跃迁光谱的光谱研究

Spectroscopic study on the ${\rm{A}}^2{{\text{∑}}^{ +}}$–X²Π_1/2 transition spectra of PbF molecules

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