BH分子8个Λ-S态和23个Ω态光谱性质的理论研究

邢伟; 李胜周; 孙金锋; 李文涛; 朱遵略; 刘锋

doi:10.7498/aps.71.20220038

摘要

本文利用内收缩多参考组态相互作用方法计算了BH分子8个低电子态(X¹Σ⁺, a³Π, A¹Π, b³Σ^–, 2³Π, 1³Σ⁺, 1⁵Σ^–和1⁵Π)和在自旋-轨道耦合效应下所产生的23个Ω态的势能曲线、以及${\rm{X}}{}^1\Sigma _{{0^ + }}^ +$, ${{\rm{a}}^3}{\Pi _{{0^ + }}}$, ${{\rm{a}}^3}{\Pi _1}$, ${{\rm{a}}^3}{\Pi _2}$和${{\rm{A}}^1}{\Pi _1}$态之间6对跃迁的跃迁偶极矩. 为了获得精确的势能曲线, 计算中修正了单双电子激发、核价相关效应、相对论效应和基组截断带来的误差. 获得的BH分子的光谱和跃迁数据与现有的理论值和实验值符合得很好. 计算结果表明: BH分子的A¹Π₁(υ' = 0 – 2, J' = 1, +) →$ {\text{X}}{}^1\Sigma _{{0^ + }}^ + $(υ′′ = 0 – 2, J ′′ = 1, –)跃迁具有较大的爱因斯坦A系数和加权的吸收振子强度、高度对角化分布的振动分支比, A¹Π₁态具有较短的辐射寿命. 另外, ${{\rm{a}}^3}{\Pi _{{0^ + }}}$和a³Π₁态对A¹Π₁(υ' = 0) ↔ $ {\rm X}^1\Sigma _{{0^ + }}^ + $(υ′′ = 0)循环跃迁的影响可以忽略. 因此, 基于A¹Π₁(υ'= 0—1, J ′ = 1, +) ↔ $ {\rm X}^1\Sigma _{{0^ + }}^ + $(υ′′= 0—3, J′′ = 1, –)循环跃迁, 我们提出了用一束主冷却激光(λ₀₀ = 432.45 nm)和两束再泵浦激光(λ₁₀ = 479.67 nm和λ₂₁ = 481.40 nm)冷却BH分子的方案, 并评价了冷却效果.

关键词:

Abstract

In this work, the potential energy curves of eight low electronic states (X¹Σ⁺, a³Π, A¹Π, b³Σ^-, 2³Π, 1³Σ⁺, 1⁵Σ^-, and 1⁵Π) and twenty-three Ω states of BH molecule, and the transition dipole moments among the $ {\text{X}}{}^{\text{1}}{\Sigma}_{{{\text{0}}^ + }}^ + $, $ {{\text{a}}^{\text{3}}}{\Pi_{{{\text{0}}^ + }}} $, a³Π₁, a³Π₂, and A¹Π₁ states are calculated by using the internally contracted multireference configuration interaction (icMRCI) method. In order to obtain the accurate potential energy curve, the errors caused by single and double electron excitation, core-valence correlation effects, relativistic effects and basis set truncation are corrected. The spectral and transition data of BH molecule are in good agreement with the available theoretical and experimental data. The calculation results show that the A¹Π₁(υ′ = 0-2, J′ = 1, +) →$ {\text{X}}{}^{\text{1}}{\Sigma}_{{{\text{0}}^ + }}^ + $(υ′′ = 0-2, J′′ = 1, –) transition has large Einstein A-coefficient, weighted absorption oscillator strength, and highly diagonal vibrational branching ratio R_{υ′υ′′}, and the excited state A¹Π₁(υ′ = 0, 1) have short spontaneous radiation lifetimes. Moreover, the effects of $ {{\text{a}}^{\text{3}}}{\Pi_{{{\text{0}}^ + }}} $and a³Π₁ states on A¹Π₁(υ′ = 0) ↔ $ {\text{X}}{}^{\text{1}}{\Sigma}_{{{\text{0}}^ + }}^ + $(υ′′ = 0) cycle transition can be ignored. Therefore, according to the A¹Π₁(υ′= 0-1, J′ = 1, +) ↔ $ {\text{X}}{}^{\text{1}}{\Sigma}_{{{\text{0}}^ + }}^ + $(υ′′= 0-3, J′′ = 1, –) cycle transition, we propose to apply one main cooling laser (λ₀₀ = 432.45 nm) and two repumping lasers (λ₁₀ = 479.67 nm and λ₂₁ = 481.40 nm) to laser cooling BH molecules, and evaluation of the cooling effect.

Keywords:

作者及机构信息

1.
信阳师范学院物理电子工程学院, 信阳　464000

2.
河南师范大学物理学院, 新乡　453000

3.
潍坊科技学院, 寿光　262700

通信作者: 邢伟, wei19820403@163.com

基金项目: 国家自然科学基金(批准号: 61275132, 11274097)、河南省自然科学基金(批准号: 212300410233)、河南省高等学校重点科研项目(批准号: 21A140023)和信阳师范学院南湖学者奖励计划青年项目资助的课题.

Authors and contacts

1.
College of Physics and Electronic Engineering, Xinyang Normal University, Xinyang 464000, China

2.
School of Physics, Henan Normal University, Xinxiang 453000, China

3.
Weifang University of Science and Technology, Shouguang 262700, China

Corresponding author: Xing Wei, wei19820403@163.com

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61275132, 11274097), the Natural Science Foundation of Henan Province, China (Grant No. 212300410233), the Key Scientific Research Prgoram of Higher Education of Henan Province, China (Grant No. 21A140023), and the Nanhu Scholars Program for Young Scholars of XYNU, China.

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参考文献

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施引文献

图 1 BH分子8个Λ-S态的势能曲线

Fig. 1. Potential energy curves of 8Λ-S states of the BH molecule.

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图 2 BH分子23个Ω态的势能曲线

Fig. 2. Potential energy curves of 23 Ω states of the BH molecule.

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图 3 BH分子6对跃迁的跃迁偶极矩曲线

Fig. 3. Curves of the transition dipole moments versus internuclear separation of six-pair states of the BH molecule.

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图 4 利用A¹Π₁(υ′) ↔$ {\text{X}}{}^{\text{1}}{\Sigma}_{{{\text{0}}^ + }}^ + $(υ′′)跃迁进行激光冷却BH分子的方案. 虚线表示A¹Π₁(υ′ = 0, 1) →$ {\text{X}}{}^{\text{1}}{\Sigma}_{{{\text{0}}^ + }}^ + $(υ′′ = 0 –3)跃迁的自发辐射振动分支比(R_{υ′υ′′}). 红色实线表示激光驱动$ {\text{X}}{}^{\text{1}}{\Sigma}_{{{\text{0}}^ + }}^ + $(υ′′) → A¹Π₁ (υ′)跃迁

Fig. 4. The proposed laser cooling scheme for the BH using A¹Π₁(υ′) ↔$ {\text{X}}{}^{\text{1}}{\Sigma}_{{{\text{0}}^ + }}^ + $(υ′′) transition. The dotted line indicate the spontaneous radiation vibrational branching ratio (R_{υ′υ′′}) of A¹Π₁(υ′ = 0, 1) →$ {\text{X}}{}^{\text{1}}{\Sigma}_{{{\text{0}}^ + }}^ + $(υ′′ = 0 – 3) transition. The red solid line indicate the wavelength (λ_{υ′′υ′}) at which the laser drives the $ {\text{X}}{}^{\text{1}}{\Sigma}_{{{\text{0}}^ + }}^ + $(υ′′) →A¹Π₁ (υ′). transition.

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表 1 BH分子前两个离解极限产生的8个Λ-S态的离解关系

Table 1. Dissociation relationships of the 8 Λ –S states generated from the first two dissociation asymptotes of the BH molecule

离解极限	Λ-S态	能级^a/cm^–1
离解极限	Λ-S态	本文	实验^[30]	理论^[31]
B(²P_u) + H(²S_g)	X¹Σ⁺, a³Π, A¹Π, 1³Σ⁺	0.00	0.00	0.00
B(⁴P_g) + H(²S_g)	b³Σ^–, 1⁵Σ^–, 2³Π, 1⁵Π	28907.66	28644.99+x^b	28932.70
a, ⁴P_g态能级为⁴P_1/2, ⁴P_3/2和⁴P_5/2能级的算术平均值减去²P_3/2与²P_1/2能级的算术平均值; b, ⁴P_5/2能级外推值的不确定度.

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表 2 icMRCI + Q/56 + CV + SR理论水平上BH分子7个Λ-S态的光谱常数

Table 2. Spectroscopic parameters of the 7 Λ-S states of BH at level of icMRCI + Q/56 + CV + SR.

Λ-S态	来源	T_e/cm^–1	R_e/nm	ω_e/cm^–1	ω_ex_e/cm^–1	B_e/cm^–1	α_e/(10²cm^–1)	D_e/eV
X¹Σ⁺	本文	0	0.12295	2367.28	48.7782	12.0395	37.0985	3.7137
	实验^[8]	0	0.12322	2366.73	49.3384	12.0255	42.1516
	实验^[10]	0	—	2366.73	49.3398	12.0258	42.1565
	实验^[12]	0	—	2364.66	47.7098	12.0257	42.1591	3.6476±0.0037^a
	实验^[13]	0	0.12322	2366.73	49.3405	12.0255	42.1450
	理论^[5]	0	0.12290	2352.0	44.0	12.086	—	3.6863
	理论^[15]	0	0.12301	2379	46.79	12.07	—	3.70
	理论^[16]	0	0.12312	2378		12.055		3.578^b
	理论^[17]	0	0.1230	2359	48.8	—	41.8	3.6773
	理论^[18]	0	0.12327	2368.48	50.6957	12.110	43.05	3.6580
	理论^[19]	0	0.12300	—	—	—	—	3.6751
	理论^[20]	0	0.12293	2365.69	47.2310	12.0801	41.6	3.6851
a³Π	本文	10944.32	0.11899	2625.97	59.4177	12.8919	41.6404	2.3507
	实验^[14]	x^c	0.11900	2625.14	55.7840	12.8931	41.5610	2.3867
	理论^[5]	10645.0	0.11900	2961.0	109.6	12.904	—	2.3806
	理论^[15]		0.11913	2653	62.70	12.87	—	2.38
	理论^[17]	10583	0.11900	2625	60.4	—	45.5	2.3677
	理论^[18]	9557.67	0.11925	2598.98	46.6300	12.9400	42.53	2.3135
A¹Π	本文	23203.52	0.12223	2253.28	36.8310	11.8343	11.6254	0.8368
	实验^[10]	23135.44	0.12195^d	2251.46	56.5725	12.20035	53.7670	0.697^d
	实验^[12]	23105.10	—	2342.41	127.7618	12.19986	53.6736	0.7786±0.0037^a
	理论^[5]	22997.90	0.12210	2404.60	147.3	12.2795	—	0.9098
	理论^[15]		0.12213	2320	136.5	12.24	—	0.71
	理论^[16]	23061	0.12235	2290	—	12.20	—	0.73^b
	理论^[17]	23144	0.1222	2341	129.6	—	85.1	0.8109
	理论^[18]	22260.89	0.12267	2280.26	93.6233	12.229	60.83	0.7536
	理论^[19]	23099.84	0.12212	2343.96	128.178	12.2836	74.0	0.8938
b³Σ^–	本文	38238.63	0.12164	2440.89	54.4477	12.2508	33.6712	2.5959
	实验^[14]	x^c+27152.75	0.121625	2438.10	55.562	12.3426	43.087	2.5987
	理论^[15]		0.12256	2345	48.45	12.16	—	2.54
	理论^[17]	37708	0.1217	2430	57.3	—	45.9	2.5845
	理论^[18]	36859.52	0.12199	2428.33	55.409	12.284	44.31	2.5403
2³Π	本文	50730.46	0.19215	1273.89	20.7896	4.94471	3.0957	1.0467
	理论^[15]		0.19338	1425	57.04	4.88	—	1.04
	理论^[17]	50216	0.1931	1295	38.6	—	9.9	1.0321
1³Σ⁺	本文	51738.07	0.12592	—	—	—	—	0.0031
	理论^[17]	51688	0.123
1⁵Σ^–	本文	58295.54	0.16981	634.868	167.676	6.51936	192.641	0.1093
	理论^[17]	57674	0.1701	528	87.3	—	153.2	0.1084
a, 文献[11]中的值; b, D₀值; c, x表示a³Π态相对于X¹Σ⁺态的T_e值; d, 文献[7]中的值.

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表 3 BH分子23个Ω态的离解关系

Table 3. Dissociation relationships of the 23 Ω states of the BH molecule.

原子态(B + H)	Ω态	能级/cm^–1
原子态(B + H)	Ω态	本文	实验^[30]
B(²P_1/2) + H(²S_1/2)	0^–, 0⁺, 1	0.00	0.00
B(²P_3/2) + H(²S_1/2)	2, 1(2), 0⁺, 0^–	14.572	15.287
B(⁴P_1/2) + H(²S_1/2)	0^–, 0⁺, 1	28910.63	28647.43+x ^a
B(⁴P_3/2) + H(²S_1/2)	2, 1(2), 0⁺, 0^–	28914.67	28652.07+x ^a
B(⁴P_5/2) + H(²S_1/2)	3, 2(2), 1(2), 0⁺, 0^–	28921.41	28658.40+x ^a
a, ⁴P_5/2能级外推值的不确定度.

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表 4 利用icMRCI + Q/56 + CV + SR + SOC理论计算获得的17个Ω态的光谱常数

Table 4. Spectroscopic parameters obtained by the icMRCI + Q/56 + CV + SR + SOC calculations for the 17 Ω states.

Ω态	T_e/cm^–1	R_e/nm	ω_e/cm^–1	ω_ex_e/cm^–1	B_e/cm^–1	10²α_e/cm^–1	D_e/eV	在R_e附近主要的Λ–S态/%
$ {\text{X}}{}^{\text{1}}{\Sigma}_{{{\text{0}}^ + }}^ + $	0	0.12295	2367.28	48.7783	12.0395	37.0985	3.7138	X¹Σ⁺ (100.00)
${\text{a} }{}^{\text{3} }{\Pi_{ { {\text{0} }^{{ - } } } }}$	10940.36	0.11899	2625.93	59.4165	12.8918	41.6426	2.3506	a³Π (100.00)
$ {\text{a}}{}^{\text{3}}{\Pi_{{{\text{0}}^ + }}} $	10940.37	0.11899	2625.93	59.4192	12.8918	41.6424	2.3506	a³Π (100.00)
a³Π₁	10944.32	0.11899	2625.97	59.4140	12.8919	41.6403	2.3513	a³Π (100.00)
a³Π₂	10948.49	0.11899	2626.01	59.4131	12.8919	41.6384	2.3509	a³Π (100.00)
A¹Π₁	23203.52	0.12223	2253.28	36.8317	11.8338	11.7034	0.9051	A¹Π (100.00)
(3)0⁺第一势阱	38244.33	0.12163	2438.08	44.7281	12.2925	38.3041	1.5501	b³Σ^– (100.00)
(3)0⁺第二势阱	50725.86	0.19213	—	—	—	—	0.0026	2³Π (100.00)
(3)1	38244.35	0.12163	2447.69	54.2934	12.3167	37.6149	0.8995	b³Σ^– (100.00)
(4)1	45758.49	0.16496	4850.09	1293.00	6.73952	4.02168	1.6629	1³Σ⁺ (100.00)
${\text{2} }{}^{\text{3} }{\Pi_{ { {\text{0} }^{ { - } } } } }$	50726.07	0.19214	1274.00	20.8450	4.94470	3.09611	1.0466	2³Π (100.00)
(4)0⁺	50726.51	0.18860	2344.54	77.7976	16.5616	29.6976	1.0478	b³Σ^– (99.82), 2³Π (0.18)
(5)1	50728.05	0.18863	2531.33	412.671	5.20415	61.4752	1.0476	b³Σ^– (99.92), 2³Π (0.08)
2³Π₂	50734.85	0.19215	1273.86	20.7903	4.94471	3.09520	1.0467	2³Π (100.00)
${\text{1} }{}^{\text{3} }{\Sigma}_{ { {\text{0} }^{{ - } } } }^ +$	51738.08	0.12592	—	—	—	—	0.0031	1³Σ⁺ (100.00)
${\text{1} }{}^{\text{5} }{\Sigma}_{ { {\text{0} }^{{ - } } } }^{{ - } }$	58295.53	0.16981	634.857	167.653	6.51872	192.471	0.1096	1⁵Σ^– (100.00)
${\text{1} }{}^{\text{5} }{\Sigma}_{\text{2} }^{{ - } }$	58295.55	0.16981	634.862	167.660	6.51884	192.502	0.1096	1⁵Σ^– (100.00)
${\text{1} }{}^{\text{5} }{\Sigma}_{\text{2} }^{{ - } }$	58295.57	0.16981	634.867	167.669	6.51902	192.550	0.1095	1⁵Σ^– (100.00)

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表 5 A¹Π₁(υ′, J′ = 1, +) → $ {\text{X}}{}^{\text{1}}{\Sigma}_{{{\text{0}}^ + }}^ + $(υ′′, J′′ = 1, –)跃迁的跃迁波数(${\tilde v} $)、爱因斯坦A系数(A_{υ′υ′′})、振动分支比(R_{υ′υ′′})、波长(λ_{υ′υ′′})、加权的吸收振子强度(gf_{υ′υ′′})

Table 5. The transition wavenumber (${\tilde v} $), Einstein A-coefficients (A_{υ′υ′′}), vibrational branching ratios (R_{υ′υ′′}), wavelength (λ_υ_′υ′′), and weighted absorption oscillator strengths (gf_υ_′υ′′) for the A¹Π₁(υ′, J′ = 1, +) → $ {\text{X}}{}^{\text{1}}{\Sigma}_{{{\text{0}}^ + }}^ + $(υ′′, J′′ = 1, –) transitions.

υ′–υ″	${\tilde v}/$cm^–1	A_{υ′υ′′/s}	R_{υ′υ′′}	λ_{υ′υ′′}/nm	gf_{υ′υ′′}	υ′–υ″	${\tilde v} $/cm^–1	A_{υ′υ′′/s}	R_{υ′υ′′}	λ_{υ′υ′′}/nm	gf_{υ′υ′′}
0-0	23140.44	7.98×10⁶	0.9912	432.45	0.0067	1-0	25243.77	9.61×10⁴	0.0138	396.42	6.78×10^–4
0-1	20862.55	6.67×10⁴	0.0083	479.67	6.89×10^–4	1-1	22965.88	6.80×10⁶	0.9777	435.74	0.0580
0-2	18684.36	3.86×10³	4.79×10^–4	535.59	4.97×10^–5	1-2	20787.69	4.72×10⁴	0.0068	481.40	4.91×10^–4
0-3	16602.97	4.43×10¹	5.50×10^–6	602.73	7.22×10^–7	1-3	18706.30	1.13×10⁴	0.0016	534.96	1.45×10^–4
0-4	14612.08	1.75	2.17×10^–7	684.85	3.69×10^–8	1-4	16715.40	7.15×10¹	1.03×10^–5	598.68	1.15×10^–6
2-0	27090.98	1.76×10³	3.10×10^–4	369.39	1.08×10^–5	3-0	28588.60	1.08×10³	2.66×10^–4	350.04	5.95×10^–6
2-1	24813.09	4.31×10⁵	0.0759	403.30	0.0032	3-1	26310.72	1.89×10³	4.66×10^–4	380.34	1.23×10^–5
2-2	22634.90	5.22×10⁶	0.9192	442.11	0.0458	3-2	24132.53	1.16×10⁶	0.2858	414.67	0.0090
2-3	20553.51	1.38×10³	2.43×10^–4	486.88	1.47×10^–5	3-3	22051.13	2.80×10⁶	0.6887	453.81	0.0259
2-4	18562.62	2.46×10⁴	0.0043	539.10	3.21×10^–4	3-4	20060.24	4.31×10⁴	0.0106	498.85	4.82×10^–4
2-5	16658.64	1.50×10¹	2.64×10^–6	600.72	2.43×10^–7	3-5	18156.26	5.40×10⁴	0.1330	551.17	7.37×10^–4

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表 7 a³Π₁(υ′, J′ = 1, +) →$ {\text{X}}{}^{\text{1}}{\Sigma}_{{{\text{0}}^ + }}^ + $(υ′′, J′′ = 1, –)跃迁的跃迁波数(${\tilde v} $)、爱因斯坦A系数(A_{υ′υ′′})、振动分支比(R_{υ′υ′′})、波长(λ_{υ′υ′′})、加权的吸收振子强度(gf_{υ′υ′′})

Table 7. The transition wavenumber (${\tilde v} $), Einstein A-coefficients(A_{υ′υ′′}), vibrational branching ratios (R_{υ′υ′′}), wavelength (λ_{υ′υ′′}), and weighted absorption oscillator strengths (gf_{υ′υ′′}) for the a³Π₁(υ′, J′ = 1, +) →$ {\text{X}}{}^{\text{1}}{\Sigma}_{{{\text{0}}^ + }}^ + $(υ′′, J′′ = 1, –).

υ′–υ″	${\tilde v} $/cm^–1	A_{υ′υ′′/s}	R_{υ′υ′′}	λ_{υ′υ′′}/nm	gf_{υ′υ′′}	υ′–υ″	${\tilde v} $/cm^–1	A_{υ′υ′′/s}	R_{υ′υ′′}	λ_{υ′υ′′}/nm	gf_{υ′υ′′}
0-0	11039.58	0.1278	0.9615	906.48	4.72×10^–9	1-0	13546.43	0.0081	0.0607	738.73	1.98×10^–10
0-1	8761.69	0.0050	0.0374	1142.14	2.91×10^–10	1-1	11268.54	0.1148	0.8613	888.06	4.07×10^–9
0-2	6583.50	1.48×10^–4	0.0011	1520.03	1.54×10^–11	1-2	9090.35	0.0099	0.0739	1100.85	5.36×10^–10
0-3	4502.11	3.00×10^–6	2.25×10^–5	2222.76	6.65×10^–13	1-3	7008.96	5.33×10^–4	0.0040	1427.76	4.88×10^–11
0-4	2511.21	3.32×10^–8	2.50×10^–7	3984.98	2.37×10^–14	1-4	5018.07	1.86×10^–5	1.39×10^–4	1994.22	3.32×10^–12
2-0	15928.88	2.81×10^–5	2.12×10^–4	628.24	4.98×10^–13	3-0	18182.60	1.94×10^–6	1.47×10^–5	550.37	2.63×10^–14
2-1	13651.00	0.0152	0.1142	733.07	3.66×10^–10	3-1	15904.71	5.54×10^–5	4.22×10^–4	629.19	9.84×10^–13
2-2	11472.81	0.1023	0.7703	872.25	3.49×10^–9	3-2	13726.52	0.0211	0.1607	729.04	5.04×10^–10
2-3	9391.41	0.0141	0.1059	1065.56	7.17×10^–10	3-3	11645.13	0.0912	0.6945	859.34	3.03×10^–9
2-4	7400.52	0.0012	0.0089	1352.22	9.71×10^–11	3-4	9654.23	0.0168	0.1277	1036.55	8.09×10^–10

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表 6 $ {{\text{a}}^{\text{3}}}{\Pi_{{{\text{0}}^ + }}} $(υ′, J′ = 0, + ) →$ {\text{X}}{}^{\text{1}}{\Sigma}_{{{\text{0}}^ + }}^ + $(υ′′, J′′ = 1, –)跃迁的跃迁波数(${\tilde v} $)、爱因斯坦A系数(A_{υ′υ′′})、振动分支比(R_{υ′υ′′})、波长(λ_{υ′υ′′})、加权的吸收振子强度(gf_{υ′υ′′})

Table 6. The transition wavenumber(${\tilde v} $), Einstein A-coefficients(A_{υ′υ′′}), vibrational branching ratios (R_{υ′υ′′}), wavelength (λ_{υ′υ′′}), and weighted absorption oscillator strengths (gf_{υ′υ′′}) for the $ {{\text{a}}^{\text{3}}}{\Pi_{{{\text{0}}^ + }}} $(υ′, J′ = 0, + ) →$ {\text{X}}{}^{\text{1}}{\Sigma}_{{{\text{0}}^ + }}^ + $(υ′′, J′′ = 1, –) transitions.

υ′–υ″	${\tilde v} $/cm^–1	A_{υ′υ′′/s}	R_{υ′υ′′}	λ_{υ′υ′′}/nm	gf_{υ′υ′′}	υ′–υ″	${\tilde v} $/cm^–1	A_{υ′υ′′/s}	R_{υ′υ′′}	λ_{υ′υ′′}/nm	gf_{υ′υ′′}
0-0	11039.10	0.1878	0.8913	906.52	2.31×10^–9	1-0	13546.35	5.67×10^–4	0.0030	738.73	4.63×10^–12
0-1	8761.22	0.0216	0.1027	1142.21	4.22×10^–10	1-1	11268.46	0.1441	0.7666	888.06	1.70×10^–9
0-2	6583.03	0.0012	0.0058	1520.14	4.24×10^–11	1-2	9090.27	0.0391	0.2082	1100.86	7.10×10^–10
0-3	4501.63	4.60×10^–5	2.18×10^–4	2223.00	3.40×10^–12	1-3	7008.88	0.0039	0.0209	1427.78	1.20×10^–10
0-4	2510.74	9.71×10^–7	4.61×10^–6	3985.72	2.31×10^–13	1-4	5017.98	2.33×10^–4	0.0012	1994.25	1.39×10^–11
2-0	15929.21	3.36×10^–4	0.0020	628.22	1.98×10^–12	3-0	18183.37	1.76×10^–6	1.12×10^–5	550.34	7.97×10^–15
2-1	13651.32	0.0023	0.0142	733.05	1.84×10^–11	3-1	15905.48	9.50×10^–4	0.0061	629.16	5.63×10^–12
2-2	11473.13	0.1081	0.6354	872.22	1.23×10^–9	3-2	13727.29	0.0050	0.0320	728.99	3.99×10^–11
2-3	9391.74	0.0507	0.2982	1065.52	8.62×10^–10	3-3	11645.90	0.0817	0.5216	859.28	9.03×10^–10
2-4	7400.84	0.0080	0.0468	1352.16	2.18×10^–10	3-4	9655.01	0.0542	0.3464	1036.47	8.72×10^–10

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表 8 A¹Π₁(υ′, J′ = 1, +), $ {{\text{a}}^{\text{3}}}{\Pi _{{0^ + }}} $(υ′, J′ = 0, + )和a³Π₁(υ′, J′ = 1, +)态的辐射寿命(τ_υ’)

Table 8. Spontaneous radiative lifetimes(τ_υ′) for the A¹Π₁(υ′, J′ = 1, +), $ {{\text{a}}^{\text{3}}}{\Pi _{{0^ + }}} $(υ′, J′ = 0, +)和a³Π₁(υ′, J′ = 1, +) transitions

υ′	$ {\text{a}}{}^{\text{3}}{\Pi_{{{\text{0}}^ + }}} $/s	a³Π₁/s	A¹Π₁/ns
υ′			总和/ns	$ {\text{A}}{}^{\text{1}}{\Pi_{\text{1}}}{\text{ - }}{{\text{X}}^{\text{1}}}{\Sigma}_{{{\text{0}}^ + }}^ + $/ns	$ {\text{A}}{}^{\text{1}}{\Pi_{\text{1}}} $-$ {\text{a}}{}^{\text{3}}{\Pi_{{{\text{0}}^ + }}} $/s	A¹Π₁– a³Π₁/s	A¹Π₁– a³Π₂/s
0	4.75	7.52	124.18	124.18	2.71	111.48	177.04
1	5.32	7.50	143.86	143.86	3.03	90.08	116.30
2	5.88	7.53	176.12	176.12	3.58	83.05	192.36
3	6.39	7.61	246.20	246.20	4.77	93.55	255.19
4	6.85	7.78
5	7.27	8.09

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