Theoretical study on spectroscopic properties of 10 Λ-S and 26 Ω states for AlH molecule

Xing Wei; Li Sheng-Zhou; Sun Jin-Feng; Cao Xu; Zhu Zun-Lue; Li Wen-Tao; Li Yue-Yi; Bai Chun-Xu

doi:10.7498/aps.72.20230615

Abstract

On the basis of correcting various errors caused by spin-orbit coupling effects, scalar relativity effects, core-valence correlation effects and basis set truncation, the potential energy curves of 10 Λ-S states and 26 Ω states of AlH molecule are calculated by using icMRCI + Q method. The transition dipole moments of 6 pairs of transitions between the ${\rm X}{}^1\Sigma _{{0^ + }}^ + $, $ {\rm a^3}{\Pi _{{0^ + }}} $, ${\rm a^3}{\Pi _1} $, ${\rm a^3}{\Pi _2} $, and ${\rm A^1}{\Pi _1} $ states are calculated by using the icMRCI/AV6Z* theory with the consideration of spin-orbit coupling effects. The spectral and transition data obtained here for AlH molecule are in very good agreement with the available experimental measurements. The findings are below. 1) The transition intensities are relatively strong of the Q(J″) branches for the (0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2), (1, 3), (1, 4) and (1, 5) bands of the A¹Π₁ – ${\rm X}{}^1\Sigma _{{0^ + }}^ + $ transition, with the increase of J″; the Einstein A coefficients and vibrational branching ratio gradually decrease, and the weighted absorption oscillator strength gradually increases of Δυ = 0 band, the Einstein A coefficient, vibrational branching ratio, and weighted absorption oscillator strength gradually increase for the Δυ ≠ 0 bands. 2) The radiation lifetimes of A¹Π₁(υ' = 0, 1) increases slowly as the J' increases. 3) The A¹Π₁(υ' = 0 and 1, J' = 1, +) →${\rm X}{}^1\Sigma _{{0^ + }}^ + $(υ'' = 0–3, J'′ = 1, –) transition of AlH molecule satisfies the criteria for laser cooling of diatomic molecules, that is, the vibrational branching ratio of the highly diagonal distribution, the extremely short radiation lifetimes of the A¹Π₁(υ' = 0 and 1, J' = 1, +) states, and the intermediate electronic states $ {\rm a^3}{\Pi _{{0^ + }}} $, a³Π₁, and a³Π₂ do not interfere with laser cooling. Therefore, based on the cyclic transition A¹Π₁(υ' = 0 and 1, J' = 1, +) ↔ ${\rm X}{}^1\Sigma _{{0^ + }}^ + $(υ'′ = 0–3, J'' = 1, –), we propose a feasible scheme for laser cooling of AlH molecule. When cooled, 2.541 × 10⁴ photons can be scattered by four pump lasers used in the visible range, which are enough to cool AlH to the ultra-cold temperature, and the Doppler temperature and recoil temperature of the main transition are on the order of μK.

Keywords:

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 Nos. 61275132, 11274097, 12074328), the Natural Science Foundation of Henan province, China (Grant No. 212300410233), the Natural Science Foundation of the Henan Higher Education Institutions of China (Grant No. 21A140023), and the Nanhu Scholars Program for Young Scholars of Xinyang Normal University, China.

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图 1 AlH分子10个Λ-S态的势能曲线

Figure 1. Potential energy curves of 10 Λ-S states of the AlH molecule.

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图 2 AlH分子26个Ω态的势能曲线

Figure 2. Potential energy curves of 26 Ω states of the AlH molecule.

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图 3 AlH 分子 6 对跃迁的跃迁偶极矩曲线

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

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图 4 利用A¹Π₁(υ'= 0和1, J' = 1, +) ↔$ {\text{X}}{}^{1}{{\Sigma }}_{{{0}^ + }}^ + $(υ''= 0—3, J'' = 1, –)跃迁进行激光冷却AlH分子的方案. 红色实线表示激光驱动A¹Π₁(υ' = 0和1, +)←$ {\text{X}}{}^{1}{{\Sigma }}_{{{0}^ + }}^ + $(υ'' = 0—3, –)跃迁Q(1)支的激光波长(λ_υ'←υ'')

Figure 4. The proposed laser cooling scheme for the AlH using A¹Π₁ (υ'= 0 and 1, J' = 1, +) ↔$ {\text{X}}{}^{1}{{\Sigma }}_{{{0}^ + }}^ + $(υ''= 0–3, J'' = 1, –) transition. The red solid line indicate the wavelength (λ_υ'←υ'') at which the laser drives the Q(1) branch of the A¹Π₁ (υ' = 0 and 1, +) ←$ {\text{X}}{}^{1}{{\Sigma }}_{{{0}^ + }}^ + $(υ'' = 0–3, –) transition.

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图 5 A¹Π₁态的辐射寿命随转动量子数J'的分布

Figure 5. Distributions of the radiative lifetime varying as the J' of the A¹Π₁ state.

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表 1 AlH分子前3个离解极限产生的10个Λ-S态的离解关系

Table 1. Dissociation relationships of the 10 Λ-S states generated from the first three dissociation asymptotes of the AlH molecule.

离解极限	Λ-S态	能级/cm^–1
离解极限	Λ-S态	本文	实验^[35]	理论^[20]	理论^[24]	理论^[25]
Al(3s²3p²P_u) + H(1s²S_g)	X¹Σ⁺, a³Π, A¹Π, 1³Σ⁺	0	0	0	0	0
Al(3s²4s²S_g) + H(1s²S_g)	C¹Σ⁺, 2³Σ⁺	25217.30	25291.73^a)	25082.40	25533	25306.42
Al(3s3p^{2 4}P_g) + H(1s²S_g)	b³Σ^–, 1⁵Σ^–, 2³Π, 1⁵Π	28790.80	29020.69^b)	28151.60	—	—
a) E(Al, 3s²4s²S_g) = E(Al, 3s²4s²S_1/2) – E(Al, 3s²3p²P_3/2)/2; b) E(Al, 3s3p^{2 4}P_g) = [E(Al, 3s3p^{2 4}P_1/2) +E(Al, 3s3p^{2 4}P_3/2) +E(Al, 3s3p^{2 4}P_5/2)]/3 –E(Al, 3s²3p²P_3/2)/2.

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表 2 AlH分子X¹Σ⁺态的光谱常数

Table 2. Spectroscopic parameters of the X¹Σ⁺ state of AlH molecule.

来源	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
icMRCI + Q/AV6 Z*^a)	0	0.16514	1667.67	25.0119	6.30570	15.7097	3.2353
icMRCI + Q/56^a)	0	0.16510	1668.60	25.0353	6.30871	15.7799	3.2400
∆56^a)	0	–0.00004	0.93	0.0234	0.00301	0.0702	0.0047
icMRCI + Q/56+CV^a)	0	0.16421	1686.55	23.8577	6.35248	14.6527	3.1860
∆CV^a)	0	–0.00089	17.95	–1.1776	0.04377	–1.1272	–0.054
icMRCI + Q/56+SR^a)	0	0.16512	1665.84	24.9979	6.30753	15.7568	3.2365
∆SR^a)	0	0.00002	–2.76	–0.0374	–0.00118	–0.0231	–0.0035
icMRCI + Q/56 + CV + SR^a)	0	0.16423	1683.86	23.8297	6.35184	14.7584	3.1825
∆CV+SR^a)	0	–0.00087	15.26	–1.2056	0.04313	–1.0215	–0.0575
实验^[8]	0	0.16474	1682.44	29.1060	6.3937	18.685	3.16 ± 0.01^b)
实验^[9]	0	0.16454	1682.38	29.0510	6.39378	18.7053	—
实验^[10]	0	—	1682.37	29.0466	6.39377	18.7044	—
实验^[14]	0	—	1682.37	29.0511	6.39379	18.7056	—
实验^[15]	0	0.16474	1682.37	29.0511	6.39379	18.7056	—
实验^[18]	0	—	1682.56	29.9	6.3907	18.58	—
理论^[6]	0	0.16350	—	—	—	—	—
理论^[22]	0	0.16533	1679.60	28.9	6.35	18.25	3.1699
理论^[23]	0	0.16510	1683.37	29.3786	6.3663	18.876	3.1775
理论^[24]	0	0.16540	1675	27	6.35	—	—
理论^[25]	0	0.16500	1665.93	26.99	6.3650	18.61	3.198
理论^[26]	0	0.16399	1690	—	6.45	—	3.19
理论^[27]	0	0.16465	1685.51	29.3786	6.401	18.4	—
理论^[28]	0	0.16490	1690	30	6.378	18.6	3.1738
理论^[29]	0	0.16454	1682.14	28.61	—	18.636	—
理论^[30]	0	0.16470	1683.35	25.80	6.3916	19.18	—
理论^[31]	0	0.16454	—	—	6.31938^c)	—	3.1821
a)本文的结果; b)文献[13]中的值; c) B₀值.

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表 3 AlH分子a³Π, A¹Π, b³Σ^–, 2³Σ⁺, 2³Π, C¹Σ⁺和1⁵Σ^–态的光谱常数

Table 3. Spectroscopic parameters of the a³Π, A¹Π, b³Σ^–, 2³Σ⁺, 2³Π, C¹Σ⁺, and 1⁵Σ^– states of AlH.

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	10²α_e/cm^–1	D_e/eV
a³Π	本文^a)	15445.97	0.15895	1800.73	31.4954	6.65323	2.07076	1.2525
	实验^[20]	x^b)	—	—	—	6.7520^c)	—	—
	理论^[6]	15702.28	0.1585	—	—	—	—	—
	理论^[20]	15223.3^d)	—	—	—	6.648^c)	—	—
	理论^[24]	15115	0.1600	2012	94	6.79	—	—
	理论^[26]	—	0.15868	1811	—	6.89	—	—
A¹Π	本文^a)	23746.94	0.16618	1415.29	186.750	6.87425	136.453	0.2384
	实验^[14]	23638.33	—	1416.50	166.86	6.38642	73.2541	0.24±0.01^e)
	实验^[15]	23638.33	0.16483	1416.50	166.86	6.38642	73.2540	—
	实验^[17]	23763.47^f)	—	1082.77^f)	0^f)	6.38611	73.2282	—
	理论^[6]	23959.82	0.1649	—	—	—	—	—
	理论^[24]	23536	0.1665	1370	125	6.34	—	—
	理论^[25]	23529.19	—	—	—	—	—	—
b³Σ^–	本文^a)	41859.74	0.15876	1741.72	38.5537	6.72229	11.3808	1.5480
	实验^[19]	41445	0.15717	2464	275	7.0759	64.3	—
	实验^[20]	x+26223.71^d)	—	—	—	6.7520^c)	—	—
	理论^[6]	42165.98	0.1582	—	—	—	—	—
	理论^[20]	41370.7^d)	—	—	—	6.602^c)	—	—
2³Σ⁺	本文^a)	43694.99	0.16007	2683.33	503.341	6.78034	66.2526	0.8836
	理论^[6]	43752.71	0.1565	—	—	—	—	—
2³Π	本文^a)	43922.36	0.21642	1119.61	9.70530	3.70365	1.40363	1.2981
	理论^[6]	44202.15	0.2144	—	—	—	—	—
C¹Σ^+势阱一	本文^a)	44744.73	0.16160	1575.90	91.0727	6.69259	44.0337	0.7528
	实验^[15]	44675.37	0.16131	1575.34	125.5	6.66802	55.844	0.7567
	实验^[16]	44675.37	0.16131	1575.34	125.5	6.66804	55.839	0.7567
	理论^[24]	43999	0.1575	1566	100	7.15	—	—
	理论^[25]	44621.50	0.1625	—	—	—	—	—
C¹Σ^+势阱二	本文^a)	43964.50	0.36561	484.710	4.04586	1.29836	0.524053	0.8517
	理论^[6]	44629.05	0.3648	—	—	—	—	—
	理论^[24]	41049	0.3735	491	6	1.24	—	—
	理论^[25]	40595.83	0.3777	—	—	—	—	—
1⁵Σ^–	本文^a)	53899.46	0.24733	294.567	46.1579	2.80395	42.6271	0.0605
a) 利用icMRCI + Q/56 + CV + SR理论获得的结果; b) x表示a³Π态相对于X¹Σ⁺态的T₀值; c) B₀值; d) T₀值; e) 文献[13]中的值; f) ω_ex_e固定为0, 获得的结果.

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表 4 AlH分子26个Ω态的离解关系

Table 4. Dissociation relationships of the 26 Ω states of the AlH molecule.

原子态(Al + H)	Ω态	能级/cm^–1
原子态(Al + H)	Ω态	本文	实验^[35]
Al(3s²3p²P_1/2) + H(1s²S_1/2)	0^–, 0⁺, 1	0	0
Al(3s²3p²P_3/2) + H(1s²S_1/2)	2, 1(2), 0⁺, 0^–	103.93	112.06
Al(3s²4s²S_1/2) + H(1s²S_1/2)	0⁺, 0^–, 1	25281.58	25347.76
Al(3s3p^{2 4}P_1/2) + H(1s²S_1/2)	0^–, 0⁺, 1	28760.86	29020.41
Al(3s3p^{2 4}P_3/2) + H(1s²S_1/2)	2, 1(2), 0⁺, 0^–	28812.66	29066.96
Al(3s3p^{2 4}P_5/2) + H(1s²S_1/2)	3, 2(2), 1(2), 0⁺, 0^–	28893.16	29142.78

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表 5 利用icMRCI + Q/56 + CV + SR + SOC理论获得的19个Ω态的光谱常数

Table 5. Spectroscopic parameters obtained by the icMRCI + Q/56 + CV + SR + SOC calculations for the 19 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}}{}^{1}{{\Sigma }}_{{{0}^ + }}^ + $	0	0.16423	1683.83	23.8232	6.35152	14.7360	3.1732	X¹Σ⁺ (100.00)
${\text{a} }{}^{3}{ { {\Pi } }_{ { {0}^- } }}$	15405.80	0.15895	1778.27	21.8727	6.64964	2.43602	1.2474	a³Π (100.00)
$ {\text{a}}{}^{3}{{{\Pi }}_{{{0}^ + }}} $	15405.93	0.15895	1778.66	22.0650	6.66104	1.34272	1.2618	a³Π (100.00)
a³Π₁	15445.97	0.15895	1777.36	21.4348	6.63386	3.90131	1.2424	a³Π (100.00)
a³Π₂	15486.79	0.15895	1778.71	22.0980	6.65497	1.91466	1.2523	a³Π (100.00)
A¹Π₁	23747.16	0.16618	1414.96	186.498	6.86983	135.891	0.2660^a)	A¹Π (100.00)
(3) 0⁺第一势阱	41859.96	0.15876	1735.05	13.1710	6.71698	21.3299	1.1105	b³Σ^– (100.00)
(3) 0⁺第二势阱	43881.10	0.21643	1114.60	—	3.71441	—	0.8599	2³Π (100.00)
(3) 0⁺第三势阱	43964.94	0.36554	484.319	3.56700	1.29849	0.56879	0.8517	C¹Σ⁺ (100.00)
(3) 1	41859.96	0.15876	—	—	—	—	0.0258	b³Σ^– (100.00)
(4) 1第一势阱	42188.07	0.16787	2943.15	—	5.96262	—	1.2320	1³Σ⁺ (99.96), b³Σ^– (0.04)
(4) 1第二势阱	43922.58	0.21642	1114.52	—	3.71629	—	1.0169	2³Π (100.00)
(3) 0^–第一势阱	43694.98	0.16007	2685.04	—	6.79388	—	1.0452	2³Σ⁺ (100.00)
(3) 0^–第二势阱	43880.88	0.21643	1118.65	9.05865	3.70790	2.61254	1.0221	2³Π (100.00)
(4) 0^–	46017.03	0.18561	3275.38	937.528	5.15024	46.7498	1.0291	2³Π (99.92), 2³Σ⁺(0.08)
(4) 0⁺第一势阱	44744.95	0.16159	1562.41	—	6.66956	—	1.1870	C¹Σ⁺ (100.00)
(4) 0⁺第二势阱	45035.32	0.19346	674.726	161.967	54.9019	2407.50	1.1564	2³Π (97.66), b³Σ^–(2.34)
(4) 0⁺第三势阱	47498.04	0.26377	1589.91	—	2.25963	—	0.8510	C¹Σ⁺ (100.00)
(5) 1第一势阱	43694.98	0.16007	2768.86	—	7.39204	—	1.3227	2³Σ⁺(100.00)
(5) 1第二势阱	45041.46	0.19364	—	—	—	—	1.1556	b³Σ^–(99.42), 2³Π (0.58)
(5) 0⁺	46034.37	0.18560	2898.99	1038.21	5.17322	85.9444	1.0360	2³Π (99.98), b³Σ^–(0.02)
(6) 1	46021.85	0.18577	3308.86	970.712	5.16845	53.5590	1.0375	2³Σ⁺(99.96), 2³Π (0.04)
2³Π₂	43964.28	0.21640	1119.62	9.70272	3.70411	1.40547	1.2892	2³Π (100.00)
${1}{}^{5}{ {\Sigma } }_{ { {0}^- } }^-$	53899.24	0.24737	292.193	40.9254	2.72780	22.1616	0.0568	1⁵Σ^– (99.99), 2³Σ⁺ (0.01)
$1^{5} \Sigma_{1}^-$	53899.46	0.24734	294.957	48.3039	2.85882	57.2987	0.0661	1⁵Σ^– (100.00)
${1}{}^{5}{ {\Sigma } }_{2}^-$	53899.68	0.24733	294.673	46.8641	2.83133	49.9771	0.0661	1⁵Σ^– (100.00)
a) 势阱的深度.

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表 6 A¹Π₁ –$ {\text{X}}{}^{1}{{\Sigma }}_{{{0}^ + }}^ + $系统(0, 0)和(0, 1)带Q支的振转跃迁

Table 6. Rovibrational transitions of the Q branch for the (0, 0) and (0, 1) bands of the A¹Π₁ – $ {\text{X}}{}^{1}{{\Sigma }}_{{{0}^ + }}^ + $system.

	$\tilde{v} $/cm^–1		A_{υ'J'→υ''J''} /s^–1	R_{υ'J'→υ''J''}	gf_{υ'J'←υ''J''}	λ_{υ'J'←υ''J''} /nm	$\tilde{v} $/cm^–1		A_{υ'J'→υ''J''} /s^–1	R_{υ'J'→υ''J''}	gf_{υ'J'←υ''J''}	λ_{υ'J'←υ''J''} /nm
J''	(0, 0)	实验^[17]	A_{υ'J'→υ''J''} /s^–1	R_{υ'J'→υ''J''}	gf_{υ'J'←υ''J''}	λ_{υ'J'←υ''J''} /nm	(0, 1)	实验^[17]	A_{υ'J'→υ''J''} /s^–1	R_{υ'J'→υ''J''}	gf_{υ'J'←υ''J''}	λ_{υ'J'←υ''J''} /nm
1	23529.37	23470.34	1.612×10⁷	0.9906	0.1310	425.30	21881.57	21845.63	9.618×10⁴	0.0059	9.034×10^–4	457.33
2	23528.04	23469.19	1.609×10⁷	0.9904	0.2179	425.33	21880.97	21845.22	9.846×10⁴	0.0061	0.0015	457.34
3	23526.02	23467.45	1.605×10⁷	0.9901	0.3043	425.36	21880.04	21844.58	1.020×10⁵	0.0063	0.0022	457.36
4	23523.31	23465.10	1.599×10⁷	0.9897	0.3898	425.41	21878.78	21843.70	1.067×10⁵	0.0066	0.0030	457.39
5	23519.86	23462.12	1.591×10⁷	0.9892	0.4743	425.48	21877.14	21842.55	1.129×10⁵	0.0070	0.0039	457.42
6	23515.65	23458.47	1.581×10⁷	0.9886	0.5574	425.55	21875.10	21841.10	1.205×10⁵	0.0075	0.0049	457.47
7	23510.63	23454.12	1.570×10⁷	0.9878	0.6388	425.64	21872.61	21839.30	1.299×10⁵	0.0082	0.0061	457.52
8	23504.75	23449.00	1.557×10⁷	0.9869	0.7183	425.75	21869.62	21837.11	1.411×10⁵	0.0089	0.0075	457.58
9	23497.95	23443.07	1.542×10⁷	0.9857	0.7956	425.87	21866.06	21834.46	1.544×10⁵	0.0099	0.0092	457.66
10	23490.15	23436.26	1.525×10⁷	0.9844	0.8702	426.01	21861.87	21831.29	1.701×10⁵	0.0110	0.0112	457.74
11	23481.26	23428.48	1.506×10⁷	0.9827	0.9417	426.17	21856.94	21827.52	1.885×10⁵	0.0123	0.0136	457.85
12	23471.20	23419.66	1.484×10⁷	0.9808	1.010	426.36	21851.19	21823.05	2.100×10⁵	0.0139	0.0165	457.97
13	23459.83	23409.67	1.460×10⁷	0.9784	1.074	426.56	21844.49	21817.77	2.350×10⁵	0.0158	0.0199	458.11
14	23447.03	23398.40	1.433×10⁷	0.9757	1.133	426.80	21836.71	21811.57	2.640×10⁵	0.0180	0.0241	458.27
15	23432.64	23385.70	1.402×10⁷	0.9723	1.187	427.06	21827.68	21804.29	2.975×10⁵	0.0206	0.0290	458.46
16	23416.46	23371.41	1.368×10⁷	0.9683	1.234	427.35	21817.21	21795.75	3.362×10⁵	0.0238	0.0349	458.68
17	23398.26	23355.31	1.329×10⁷	0.9634	1.274	427.69	21805.07	21785.77	3.807×10⁵	0.0276	0.0420	458.94

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表 7 A¹Π₁ –$ {\text{X}}{}^{1}{{\Sigma }}_{{{0}^ + }}^ + $系统(0, 2)和(0, 3)带Q支的振转跃迁

Table 7. Rovibrational transitions of the Q branch for the (0, 2) and (0, 3) bands of the A¹Π₁ –$ {\text{X}}{}^{1}{{\Sigma }}_{{{0}^ + }}^ + $ system.

	$\tilde{v} $/cm^–1		A_{υ'J'→υ''J''} /s^–1	R_{υ'J'→υ''J''}	gf_{υ'J'←υ''J''}	λ_{υ'J'←υ''J''} /nm	$\tilde{v} $/cm^–1	A_{υ'J'→υ''J''} /s^–1	R_{υ'J'→υ''J''}	gf_{υ'J'←υ''J''}	λ_{υ'J'←υ''J''} /nm
J''	(0, 2)	实验^[17]	A_{υ'J'→υ''J''} /s^–1	R_{υ'J'→υ''J''}	gf_{υ'J'←υ''J''}	λ_{υ'J'←υ''J''} /nm	(0,3)	A_{υ'J'→υ''J''} /s^–1	R_{υ'J'→υ''J''}	gf_{υ'J'←υ''J''}	λ_{υ'J'←υ''J''} /nm
1	20290.37	20276.85	5.595×10⁴	0.0034	6.113×10^–4	493.20	18753.82	8.717×10²	5.355×10^–5	1.115×10^–5	533.60
2	20290.47	20277.15	5.637×10⁴	0.0035	0.0010	493.19	18754.62	9.044×10²	5.565×10^–5	1.927×10^–5	533.58
3	20290.61	20277.59	5.700×10⁴	0.0035	0.0015	493.19	18755.79	9.552×10²	5.893×10^–5	2.850×10^–5	533.55
4	20290.76	20278.15	5.787×10⁴	0.0036	0.0019	493.19	18757.33	1.026×10³	6.355×10^–5	3.936×10^–5	533.50
5	20290.89	20278.80	5.898×10⁴	0.0037	0.0024	493.18	18759.19	1.121×10³	6.972×10^–5	5.254×10^–5	533.45
6	20290.97	20279.50	6.037×10⁴	0.0038	0.0029	493.18	18761.34	1.244×10³	7.777×10^–5	6.888×10^–5	533.39
7	20290.95	20280.21	6.206×10⁴	0.0039	0.0034	493.18	18763.74	1.401×10³	8.811×10^–5	8.946×10^–5	533.32
8	20290.78	20280.88	6.411×10⁴	0.0041	0.0040	493.19	18766.33	1.599×10³	1.013×10^–4	1.157×10^–4	533.25
9	20290.39	20281.45	6.655×10⁴	0.0043	0.0046	493.19	18769.05	1.849×10³	1.182×10^–4	1.495×10^–4	533.17
10	20289.71	20281.85	6.945×10⁴	0.0045	0.0053	493.21	18771.81	2.165×10³	1.397×10^–4	1.934×10^–4	533.09
11	20288.65	20282.00	7.289×10⁴	0.0048	0.0061	493.24	18774.53	2.564×10³	1.673×10^–4	2.508×10^–4	533.02
12	20287.11	20281.80	7.697×10⁴	0.0051	0.0070	493.27	18777.10	3.071×10³	2.029×10^–4	3.264×10^–4	532.94
13	20284.96	20281.15	8.181×10⁴	0.0055	0.0080	493.33	18779.41	3.719×10³	2.492×10^–4	4.268×10^–4	532.88
14	20282.08	20279.91	8.759×10⁴	0.0060	0.0093	493.40	18781.31	4.553×10³	3.101×10^–4	5.612×10^–4	532.82
15	20278.28	20277.94	9.450×10⁴	0.0066	0.0107	493.49	18782.63	5.638×10³	3.910×10^–4	7.427×10^–4	532.79
16	20273.39	20275.06	1.028×10⁵	0.0073	0.0124	493.61	18783.19	7.065×10³	5.002×10^–4	9.907×10^–4	532.77
17	20267.15	20271.07	1.129×10⁵	0.0082	0.0144	493.76	18782.72	8.970×10³	6.502×10^–4	0.0013	532.78

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表 8 A¹Π₁ –$ {\text{X}}{}^{1}{{\Sigma }}_{{{0}^ + }}^ + $系统(1, 0)和(1, 1)带Q支的振转跃迁

Table 8. Rovibrational transitions of the Q branch for the (1, 0) and (1, 1) bands of the A¹Π₁ –$ {\text{X}}{}^{1}{{\Sigma }}_{{{0}^ + }}^ + $ system.

	$\tilde{v} $/cm^–1		A_{υ'J'→υ''J ″} /s^–1	R_{υ'J'→υ''J''}	gf_{υ'J'←υ''J''}	λ_{υ'J'←υ''J''} /nm	$\tilde{v} $/cm^–1		A_{υ'J'→υ''J''} /s^–1	R_{υ'J'→υ''J''}	gf_{υ'J'←υ''J''}	λ_{υ'J'←υ''J''} /nm
J''	(1, 0)	实验^[17]	A_{υ'J'→υ''J ″} /s^–1	R_{υ'J'→υ''J''}	gf_{υ'J'←υ''J''}	λ_{υ'J'←υ''J''} /nm	(1, 1)	实验^[17]	A_{υ'J'→υ''J''} /s^–1	R_{υ'J'→υ''J''}	gf_{υ'J'←υ''J''}	λ_{υ'J'←υ''J''} /nm
1	24590.53	24551.64	1.828×10⁶	0.1670	0.0136	406.95	22942.74	22926.94	8.154×10⁶	0.7449	0.0697	436.18
2	24586.03	24547.55	1.837×10⁶	0.1687	0.0228	407.02	22938.96	22923.59	8.079×10⁶	0.7419	0.1151	436.25
3	24579.22	24541.37	1.852×10⁶	0.1714	0.0322	407.14	22933.24	22918.50	7.967×10⁶	0.7373	0.1590	436.36
4	24570.03	24533.04	1.871×10⁶	0.1750	0.0418	407.29	22925.50	22911.64	7.815×10⁶	0.7310	0.2006	436.51
5	24558.36	24522.50	1.894×10⁶	0.1797	0.0518	407.48	22915.64	22902.93	7.623×10⁶	0.7230	0.2394	436.69
6	24544.08	24509.56	1.921×10⁶	0.1854	0.0622	407.72	22903.53	22892.19	7.387×10⁶	0.7130	0.2745	436.92
7	24527.03	24494.16	1.951×10⁶	0.1924	0.0729	408.00	22889.01	22879.35	7.106×10⁶	0.7009	0.3050	437.20

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表 9 A¹Π₁ –$ {\text{X}}{}^{1}{{\Sigma }}_{{{0}^ + }}^ + $系统(1, 2)和(1, 3)带Q支的振转跃迁

Table 9. Rovibrational transitions of the Q branch for the (1, 2) and (1, 3) bands of the A¹Π₁ –$ {\text{X}}{}^{1}{{\Sigma }}_{{{0}^ + }}^ + $system.

	$\tilde{v} $/cm^–1		A_{υ'J'→υ''J ''} /s^–1	R_{υ'J'→υ''J''}	gf_{υ'J'←υ''J''}	λ_{υ'J'←υ''J''} /nm	$\tilde{v} $/cm^–1		A_{υ'J'→υ''J''} /s^–1	R_{υ'J'→υ''J''}	gf_{υ'J'←υ''J''}	λ_{υ'J'←υ''J''} /nm
J''	(1, 2)	实验^[17]	A_{υ'J'→υ''J ''} /s^–1	R_{υ'J'→υ''J''}	gf_{υ'J'←υ''J''}	λ_{υ'J'←υ''J''} /nm	(1, 3)	实验^[17]	A_{υ'J'→υ''J''} /s^–1	R_{υ'J'→υ''J''}	gf_{υ'J'←υ''J''}	λ_{υ'J'←υ''J''} /nm
1	21351.54	21358.16	6.384×10⁵	0.0583	0.0063	468.68	19814.99	19843.91	2.767×10⁵	0.0253	0.0032	505.03
2	21348.47	21355.52	6.437×10⁵	0.0591	0.0106	468.75	19812.61	19841.97	2.790×10⁵	0.0256	0.0053	505.09
3	21343.81	21351.52	6.514×10⁵	0.0603	0.0150	468.85	19808.99	19839.03	2.825×10⁵	0.0261	0.0076	505.18
4	21337.48	21346.09	6.615×10⁵	0.0619	0.0196	468.99	19804.05	19835.01	2.872×10⁵	0.0269	0.0099	505.31
5	21329.39	21339.17	6.739×10⁵	0.0639	0.0244	469.17	19797.69	19829.85	2.931×10⁵	0.0278	0.0123	505.47
6	21319.40	21330.59	6.881×10⁵	0.0664	0.0295	469.39	19789.78	19823.38	3.003×10⁵	0.0290	0.0149	505.67
7	21307.35	21320.25	7.037×10⁵	0.0694	0.0349	469.66	19780.14	19815.51	3.088×10⁵	0.0305	0.0178	505.92

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表 10 A¹Π₁ –$ {\text{X}}{}^{1}{{\Sigma }}_{{{0}^ + }}^ + $系统(1, 4)和(1, 5)带Q支的振转跃迁

Table 10. Rovibrational transitions of the Q branch for the (1, 4) and (1, 5) bands of the A¹Π₁ –$ {\text{X}}{}^{1}{{\Sigma }}_{{{0}^ + }}^ + $ system.

	$\tilde{v} $/cm^–1		A_{υ'J'→υ''J''} /s^–1	R_{υ'J'→υ''J''}	gf_{υ'J'←υ''J''}	λ_{υ'J'←υ''J''} /nm	$\tilde{v} $/cm^–1	A_{υ'J'→υ''J''} /s^–1	R_{υ'J'→υ''J''}	gf_{υ'J'←υ''J''}	λ_{υ'J'←υ''J''} /nm
J''	(1, 4)	实验^[17]	A_{υ'J'→υ''J''} /s^–1	R_{υ'J'→υ''J''}	gf_{υ'J'←υ''J''}	λ_{υ'J'←υ''J''} /nm	(1,5)	A_{υ'J'→υ''J''} /s^–1	R_{υ'J'→υ''J''}	gf_{υ'J'←υ''J''}	λ_{υ'J'←υ''J''} /nm
1	18331.39	18382.88	3.727×10⁴	0.0034	4.988×10^–4	545.90	16899.39	1.003×10⁴	9.167×10^–4	1.580×10^–4	592.16
2	18329.69	18381.64	3.815×10⁴	0.0035	8.512×10^–4	545.95	16898.36	1.031×10⁴	9.469×10^–4	2.707×10^–4	592.19
3	18327.09	18379.73	3.951×10⁴	0.0037	0.0012	546.03	16896.76	1.074×10⁴	9.944×10^–4	3.950×10^–4	592.25
4	18323.51	18377.09	4.140×10⁴	0.0039	0.0017	546.14	16894.52	1.135×10⁴	0.0011	5.368×10^–4	592.33
5	18318.84	18373.66	4.388×10⁴	0.0042	0.0022	546.27	16891.53	1.217×10⁴	0.0012	7.035×10^–4	592.43
6	18312.97	18369.25	4.703×10⁴	0.0045	0.0027	546.45	16887.65	1.324×10⁴	0.0013	9.047×10^–4	592.57
7	18305.71	18363.80	5.096×10⁴	0.0050	0.0034	546.67	16882.73	1.461×10⁴	0.0014	0.0012	592.74

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表 11 $ {{\text{a}}^{3}}{{{\Pi }}_{{{0}^ + }}} $(υ' = 0—3, J' = 0, +) –$ {\text{X}}{}^{1}{{\Sigma }}_{{{0}^ + }}^ + $(υ'' = 0—4, J'' = 1, –)系统的振转跃迁

Table 11. Rovibrational transitions of the $ {{\text{a}}^{3}}{{{\Pi }}_{{{0}^ + }}} $(υ' = 0—3, J' = 0, +) –$ {\text{X}}{}^{1}{{\Sigma }}_{{{0}^ + }}^ + $(υ'' = 0—4, J'' = 1, –) system.

(υ', υ'')	$\tilde{v} $ /cm^–1	A_{υ'J'→υ′′J''} /s^–1	R_{υ'J'→υ′′J''}	gf_{υ'J'←υ′′J''}	λ_{υ'J'←υ′′J''} /nm	(υ', υ'')	$\tilde{v} $ /cm^–1	A_{υ'J'→υ′′J''} /s^–1	R_{υ'J'→υ′′J''}	gf_{υ'J'←υ′′J''}	λ_{υ'J'←υ′′J''} /nm
(0, 0)	15439.35	1.4233	0.4815	8.952×10^–9	648.16	(1, 0)	17153.57	1.1118	0.2666	5.665×10^–9	583.38
(0, 1)	13791.56	1.3715	0.4639	1.081×10^–8	725.60	(1, 1)	15505.78	0.3272	0.0785	2.040×10^–9	645.38
(0, 2)	12200.35	0.1427	0.0483	1.437×10^–9	820.23	(1, 2)	13914.57	2.3636	0.5668	1.830×10^–8	719.18
(0, 3)	10663.80	0.0170	0.0057	2.237×10^–10	938.42	(1, 3)	12378.03	0.3047	0.0731	2.982×10^–9	808.46
(0, 4)	9180.20	0.0017	5.644×10^–4	2.968×10^–11	1090.08	(1, 4)	10894.42	0.0552	0.0132	6.968×10^–10	918.55
(2, 0)	18760.32	0.1534	0.0217	6.534×10^–10	533.42	(3, 0)	20242.83	9.974×10^–4	7.907×10^–5	3.649×10^–12	494.35
(2, 1)	17112.53	3.0626	0.4328	1.568×10^–8	584.78	(3, 1)	18595.04	0.3518	0.0279	1.526×10^–9	538.16
(2, 2)	15521.32	0.0124	0.0018	7.738×10^–11	644.73	(3, 2)	17003.84	5.9524	0.4719	3.086×10^–8	588.52
(2, 3)	13984.78	3.3509	0.4736	2.569×10^–8	715.57	(3, 3)	15467.29	0.8562	0.0679	5.365×10^–9	646.99
(2, 4)	12501.17	0.3662	0.0518	3.513×10^–9	800.49	(3, 4)	13983.68	5.0015	0.3965	3.835×10^–8	715.63

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表 12 a³Π₁(υ' = 0—3, J' = 1, +) –$ {\text{X}}{}^{1}{{\Sigma }}_{{{0}^ + }}^ + $(υ'' = 0 —4, J'' = 1, –)系统的振转跃迁

Table 12. Rovibrational transitions of the a³Π₁(υ' = 0—3, J' = 1, +) –$ {\text{X}}{}^{1}{{\Sigma }}_{{{0}^ + }}^ + $(υ'' = 0—4, J'' = 1, –) system.

(υ', υ'')	$\tilde{v} $ /cm^–1	A_{υ'J'→υ′′J''} /s^–1	R_{υ'J'→υ′′J''}	gf_{υ'J'←υ′′J''}	λ_{υ'J'←υ′′J''} /nm	(υ', υ'')	$\tilde{v} $ /cm^–1	A_{υ'J'→υ′′J''} /s^–1	R_{υ'J'→υ′′J''}	gf_{υ'J'←υ′′J''}	λ_{υ'J'←υ′′J''} /nm
(0, 0)	8076.52	1.0762	0.9466	7.420×10^–8	1239.04	(1, 0)	9138.01	0.5696	0.0665	3.068×10^–8	1095.11
(0, 1)	6362.81	0.0072	0.0493	7.977×10^–10	1572.75	(1, 1)	7424.29	0.2740	0.8481	2.236×10^–8	1347.89
(0, 2)	4756.62	3.940×10^–4	0.0038	7.832×10^–11	2103.83	(1, 2)	5818.10	0.0142	0.0748	1.887×10^–9	1720.00
(0, 3)	3274.75	1.009×10^–5	2.791×10^–4	4.233×10^–12	3055.84	(1, 3)	4336.24	0.0020	0.0096	4.722×10^–10	2307.79
(0, 4)	1943.34	1.047×10^–6	2.303×10^–5	1.246×10^–12	5149.44	(1, 4)	3004.82	1.304×10^–4	8.994×10^–4	6.496×10^–11	3330.35
(2, 0)	18806.49	5.770×10^–4	9.414×10^–6	7.337×10^–12	532.11	(3, 0)	20288.57	0.0063	1.050×10^–4	6.836×10^–11	493.24
(2, 1)	17158.70	6.5353	0.1066	9.983×10^–8	583.21	(3, 1)	18640.77	0.0622	0.0010	8.047×10^–10	536.84
(2, 2)	15567.49	49.009	0.7996	9.095×10^–7	642.82	(3, 2)	17049.57	6.7939	0.1141	1.051×10^–7	586.94
(2, 3)	14030.95	4.6491	0.0759	1.062×10^–7	713.22	(3, 3)	15513.02	47.992	0.8058	8.969×10^–7	645.08
(2, 4)	12547.34	0.9790	0.0160	2.797×10^–8	797.55	(3, 4)	14029.42	3.2035	0.0538	7.320×10^–8	713.29

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