Diatomic Hönl–London factor computer program

James O. Hornkohl; Christian G. Parigger; László Nemes

doi:10.1364/AO.44.003686

Applied Optics
Vol. 44,
Issue 18,
pp. 3686-3695
(2005)
•https://doi.org/10.1364/AO.44.003686

Diatomic Hönl–London factor computer program

James O. Hornkohl, Christian G. Parigger, and László Nemes

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James O. Hornkohl, Christian G. Parigger, and László Nemes, "Diatomic Hönl–London factor computer program," Appl. Opt. 44, 3686-3695 (2005)

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Abstract

A new method is presented for computation of diatomic rotational line strengths, or Hönl–London factors. The traditional approach includes separately calculating line positions and Hönl–London factors and assigning parity labels. The present approach shows that one merely computes the line strength for all possible term differences and discards those differences for which the strength vanishes. Numerical diagonalization of the upper and lower Hamiltonians is used, which directly obtains the line positions, Hönl–London factors, total parities, and e/f parities for both heteronuclear and homonuclear diatomic molecules. The fortran computer program discussed is also applicable for calculating n-photon diatomic spectra.

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Hamiltonian Matrix Element	Value of Hamiltonian Matrix Element
〈n υ S Ω Λ Σ\|B_υR²\|n υ S Ω Λ Σ〉	= B_υ[J(J + 1) − Ω² + S(S + 1) − Σ²]
〈n υ S Ω Λ Σ\|B_υJ·S\|n υ S Ω ± 1, Λ, Σ ± 1〉	=B_υ{[J(J + 1) − Ω(Ω ± 1)][S(S + 1) − Σ(Σ ± 1)]}^1/2
〈n υ S Ω Λ Σ\|A_υL·S\|n υS Ω Λ Σ〉	= A_υΛ Σ
〈n υ S Ω Λ Σ\|∊_υ[3S_z′² − S²)\|n υ S Ω Λ Σ〉	= ∊_υ[3Σ² − S(S + 1)]
〈n υ S ΩΛ Σ\|γ_υN·S\|n υ S Ω Λ Σ〉	= γ_υ[Σ Ω − S(S + 1)]
〈n υ S Ω Λ Σ\|γ_υN·S\|n υ S Ω ± 1, Λ, Σ ± 1〉	$= - \frac{1}{2} γ_{υ} {[J (J + 1) - Ω (Ω \pm 1)] [S (S + 1) - Σ (Σ \pm 1)]}^{1 / 2}$

Hamiltonian Matrix Element	Value of Hamiltonian Matrix Element
〈n υ Ω S Λ Σ\|B(r)J·L\|n′ υ′ Ω ± 1, Λ ± 1, Σ〉	= 〈n υ\|B(r)(L₊ + L₋)\|n′υ′〉[J(J + 1) − Ω(Ω ± 1)]^1/2
	= 〈BL〉_{nυ, n′υ′}[J(J + 1) − Ω(Ω ± 1)]^1/2
〈n υ Ω S Λ Σ\|B(r)L·S\|n′υ′ΩΛ ± 1, Σ ∓ 1〉	= 〈n υ \|B(r)(L₊ + L₋)\|n′υ′〉[S(S + 1) − Σ(Σ ∓ 1)]^1/2
	= 〈BL〉_{nυ, n′υ′}[S(S + 1) − Σ(Σ ∓ 1)]^1/2
〈n υ Ω S Λ Σ\|A(r)L·S\|n′ υ′ ΩΛ ∓ 1, Σ ± 1〉	= 〈n υ\|A(r)(L₊ + L₋)/2\|n′υ′〉[S(S + 1) − Σ(Σ ∓ 1)]^1/2
	= 〈AL〉_{nυ, n′υ′}[S(S + 1) − Σ(Σ ∓ 1)]^1/2/2
〈n υ Ω S Σ\|A(r)L·S\|n′ υ′Ω S′ Λ′Σ′〉	= 〈A〉_{nυΛΣ, n′ υ′Λ′Σ′}(−)^Λ′−Λ〈S′Σ′, 1, Λ′ − Λ\|S Σ〉
〈n υ Ω S Λ Σ\|α(r)S²\|n υ Ω S, Λ ± 2 Σ ∓ 2〉	= α_υ[S(+1) − Σ(Σ ± 1)]^1/2 {S(S + 1) − (Σ + 1)[(Σ + 1) ± 1]}^1/2/2

J′	J″	Branch	p′	p″	N′	N″	F_J′	F_J″	$\tilde{υ}$	S_J′J″
0.0	1.0	P₁₂	+e	−e	1	1	20928.963	1555.352	19373.611	0.96178
0.0	1.0	P₁₁	+e	−e	1	0	20928.963	1538.446	19390.517	0.03841
1.0	2.0	P₁₁	+f	−f	0	1	20916.943	1522.542	19394.401	0.06318
1.0	2.0	P₁₂	+f	−f	0	2	20916.943	1544.529	19372.414	1.45812
1.0	2.0	P₁₃	+f	−f	0	3	20916.943	1561.861	19355.082	0.00723
1.0	2.0	P₂₂	−f	−f	1	2	20932.092	1544.529	19387.564	0.03864
1.0	2.0	P₂₃	+f	−f	1	3	20932.092	1561.861	19370.232	1.93368
1.0	1.0	Q₁₂	+f	−e	0	1	20916.943	1555.352	19361.591	0.05431
1.0	1.0	Q₁₁	+f	−e	0	0	20916.943	1538.446	19378.497	1.36140
1.0	1.0	Q₂₂	+f	−f	1	1	20932.092	1555.352	19376.740	0.00325
1.0	1.0	Q₂₁	+f	−e	1	0	20932.092	1538.446	19393.647	0.08105
1.0	0.0	R₁₁	+f	−f	0	1	20916.943	1550.108	19366.834	0.05633
1.0	0.0	R₂₁	+f	−f	1	1	20932.092	1550.108	19381.984	0.94367
2.0	3.0	P33	+e	−e	3	4	20941.675	1574.474	19367.201	2.93372
2.0	3.0	P32	+e	−e	3	3	20941.675	1554.105	19387.570	0.02356
2.0	3.0	P₂₃	+e	−e	2	4	20923.686	1574.474	19349.212	0.00524
2.0	3.0	P₂₂	+e	−e	2	3	20923.686	1554.105	19369.581	2.60804
2.0	3.0	P₂₁	+e	−e	2	2	20923.686	1530.930	19392.756	0.04316
2.0	3.0	P₁₁	+e	−e	1	2	20902.697	1530.930	19371.767	1.71980
2.0	2.0	Q₃₂	+e	−f	3	2	20941.675	1544.529	19397.146	0.09560
2.0	2.0	Q₃₃	+e	−f	3	3	20941.675	1561.861	19379.814	0.01227
2.0	2.0	Q₂₁	+e	−f	2	1	20923.686	1522.542	19401.144	0.05588
2.0	2.0	Q₂₂	+e	−f	2	2	20923.686	1544.529	19379.157	0.71694
2.0	2.0	Q23	+e	−f	2	3	20923.686	1561.861	19361.825	0.08784
2.0	2.0	Q11	+e	−f	1	1	20902.697	1522.542	19380.156	3.17202
2.0	2.0	Q₁₂	+e	−f	1	2	20902.697	1544.529	19358.169	0.02739
2.0	1.0	R₃₂	+e	−e	3	1	20941.675	1555.352	19386.323	1.90991
2.0	1.0	R₃₁	+e	−e	3	0	20941.675	1538.446	19403.229	0.02524
2.0	1.0	R₂₂	+e	−e	2	1	20923.686	1555.352	19368.334	0.07075
2.0	1.0	R₂₁	+e	−e	2	0	20923.686	1538.446	19385.240	1.41308
2.0	1.0	R₁₁	+e	−e	1	0	20902.697	1538.446	19364.252	0.08082

J′	J″	Branch	p′	p″	N^′	N″	F_j′	F_j″	$\tilde{ν}$	S_J′J″
0.0	1.0	P₁₂	−f	+f	1	1	20928.877	1555.122	19373.755	0.96431
0.0	1.0	P₁₁	−f	+f	1	0	20928.877	1538.288	19390.589	0.03569
0.0	1.0	P₁₁	+e	−e	1	0	20927.642	1538.236	19389.406	0.04197
0.0	1.0	P₁₂	+e	−e	1	1	20927.642	1553.830	19373.812	0.95803
1.0	2.0	P₁₁	−e	+e	0	1	20916.771	1522.426	19394.345	0.05996
1.0	2.0	P₁₂	−e	+e	0	2	20916.771	1544.154	19372.616	1.45905
1.0	2.0	P₁₃	−e	+e	0	3	20916.771	1561.294	19355.477	0.00678
1.0	2.0	P₂₃	+f	−f	1	3	20932.965	1562.502	19370.463	1.94471
1.0	2.0	P₂₂	+f	−f	1	2	20932.965	1544.289	19388.676	0.03225
1.0	2.0	P₁₃	+f	−f	0	3	20916.831	1562.502	19354.329	0.00620
1.0	2.0	P₁₂	+f	−f	0	2	20916.831	1544.289	19372.542	1.45653
1.0	2.0	P₁₁	+f	−f	0	1	20916.831	1522.427	19394.404	0.05987
1.0	2.0	P₂₂	−e	+e	1	2	20931.791	1544.154	19387.637	0.03653
1.0	2.0	P₂₃	−e	+e	1	3	20931.791	1561.294	19370.497	1.93627
1.0	1.0	Q₁₂	−e	+f	0	1	20916.771	1555.122	19361.648	0.05079
1.0	1.0	Q₁₁	−e	+f	0	0	20916.771	1538.288	19378.483	1.37072
1.0	1.0	Q₂₁	+f	−e	1	0	20932.965	1538.236	19394.729	0.06513
1.0	1.0	Q₁₁	+f	−e	0	0	20916.831	1538.236	19378.595	1.37216
1.0	1.0	Q₁₂	+f	−e	0	1	20916.831	1553.830	19363.001	0.05984
1.0	1.0	Q₂₁	−e	+f	1	0	20931.791	1538.288	19393.503	0.07649
1.0	0.0	R₁₁	−e	+e	0	1	20916.771	1550.055	19366.716	0.05269
1.0	0.0	R₂₁	+f	−f	1	1	20932.965	1551.399	19381.567	0.95488
1.0	0.0	R₁₁	+f	−f	0	1	20916.831	1551.399	19365.433	0.04540
1.0	0.0	R₂₁	−e	+e	1	1	20931.791	1550.055	19381.736	0.94760
2.0	3.0	P₁₁	+e	−e	1	2	20902.580	1530.514	19372.066	1.71644
2.0	3.0	P₂₁	+e	−e	2	2	20923.118	1530.514	19392.605	0.04137
2.0	3.0	P₂₂	+e	−e	2	3	20923.118	1553.146	19369.972	2.61317
2.0	3.0	P₂₃	+e	−e	2	4	20923.118	1572.320	19350.798	0.00524
2.0	3.0	P₃₃	−f	+f	3	4	20941.038	1573.435	19367.603	2.93627
2.0	3.0	P₃₂	−f	+f	3	3	20941.038	1553.371	19387.668	0.02232
2.0	3.0	P₃₂	+e	−e	3	3	20939.957	1553.146	19386.811	0.02430
2.0	3.0	P₃₃	+e	−e	3	4	20939.957	1572.320	19367.637	2.92741
2.0	3.0	P₂₃	−f	+f	2	4	20923.270	1573.435	19349.834	0.00512
2.0	3.0	P₂₂	−f	+f	2	3	20923.270	1553.371	19369.899	2.60900
2.0	3.0	P₂₁	−f	+f	2	2	20923.270	1530.518	19392.751	0.04125
2.0	3.0	P₁₁	−f	+f	1	2	20902.581	1530.518	19372.063	1.71646
2.0	2.0	Q₁₂	+e	−f	1	2	20902.580	1544.289	19358.291	0.02530
2.0	2.0	Q₁₁	+e	−f	1	1	20902.580	1522.427	19380.153	3.18002
2.0	2.0	Q₂₃	+e	−f	2	3	20923.118	1562.502	19360.616	0.07105
2.0	2.0	Q₂₂	+e	−f	2	2	20923.118	1544.289	19378.829	0.72286
2.0	2.0	Q₂₁	+e	−f	2	1	20923.118	1522.427	19400.692	0.05404
2.0	2.0	Q₃₂	−f	+e	3	2	20941.038	1544.154	19396.884	0.09035
2.0	2.0	Q₃₃	−f	+e	3	3	20941.038	1561.294	19379.744	0.01082
2.0	2.0	Q₃₃	+e	−f	3	3	20939.957	1562.502	19377.455	0.01079
2.0	2.0	Q₃₂	+e	−f	3	2	20939.957	1544.289	19395.668	0.10462
2.0	2.0	Q₂₁	−f	+e	2	1	20923.270	1522.426	19400.844	0.05366
2.0	2.0	Q₂₂	−f	+e	2	2	20923.270	1544.154	19379.115	0.72408
2.0	2.0	Q₂₃	−f	+e	2	3	20923.270	1561.294	19361.976	0.08266
2.0	2.0	Q₁₁	−f	+e	1	1	20902.581	1522.426	19380.156	3.18000
2.0	2.0	Q₁₂	−f	+e	1	2	20902.581	1544.154	19358.427	0.02581
2.0	1.0	R₁₁	+e	−e	1	0	20902.580	1538.236	19364.344	0.07737
2.0	1.0	R₂₁	+e	−e	2	0	20923.118	1538.236	19384.882	1.41799
2.0	1.0	R₂₂	+e	−e	2	1	20923.118	1553.830	19369.288	0.07427
2.0	1.0	R₃₂	−f	+f	3	1	20941.038	1555.122	19385.916	1.91552
2.0	1.0	R₃₁	−f	+f	3	0	20941.038	1538.288	19402.750	0.02418
2.0	1.0	R₃₁	+e	−e	3	0	20939.957	1538.236	19401.721	0.02623
2.0	1.0	R₃₂	+e	−e	3	1	20939.957	1553.830	19386.127	1.90584
2.0	1.0	R₂₂	−f	+f	2	1	20923.270	1555.122	19368.147	0.06738
2.0	1.0	R₂₁	−f	+f	2	0	20923.270	1538.288	19384.982	1.41685
2.0	1.0	R₁₁	−f	+f	1	0	20902.581	1538.288	19364.293	0.07692

J′	J″	Branch	p′	p″	N′	N″	F_J′	F_J″	$\tilde{ν}$	S_J′J″
0.0	1.0	P₁₂	−f	+f	1	1	20896.632	1525.302	19371.330	0.72524
0.0	1.0	P₁₁	−f	+f	1	0	20896.632	1508.563	19388.070	0.02489
0.0	1.0	P₁₁	+e	−e	1	0	20895.409	1508.514	19386.894	0.00973
0.0	1.0	P₁₂	+e	−e	1	1	20895.409	1524.002	19371.407	0.24031
1.0	2.0	P₁₁	−e	+e	0	1	20884.434	1492.711	19391.723	0.04245
1.0	2.0	P₁₂	−e	+e	0	2	20884.434	1514.208	19370.225	1.09618
1.0	2.0	P₁₃	−e	+e	0	3	20884.434	1531.123	19353.311	0.00501
1.0	2.0	P₂₃	+f	−f	1	3	20900.527	1532.345	19368.182	0.48716
1.0	2.0	P₂₂	+f	−f	1	2	20900.527	1514.335	19386.191	0.00765
1.0	2.0	P₁₂	+f	−f	0	2	20884.489	1514.335	19370.154	0.36469
1.0	2.0	P₁₁	+f	−f	0	1	20884.489	1492.712	19391.778	0.01410
1.0	2.0	P₂₂	−e	+e	1	2	20899.359	1514.208	19385.150	0.02597
1.0	2.0	P₂₃	−e	+e	1	3	20899.359	1531.123	19368.236	1.45599
1.0	1.0	Q₁₂	−e	+f	0	1	20884.434	1525.302	19359.131	0.03546
1.0	1.0	Q₁₁	−e	+f	0	0	20884.434	1508.563	19375.871	1.03450
1.0	1.0	Q₂₁	+f	−e	1	0	20900.527	1508.514	19392.013	0.01519
1.0	1.0	Q₁₁	+f	−e	0	0	20884.489	1508.514	19375.975	0.34531
1.0	1.0	Q₁₂	+f	−e	0	1	20884.489	1524.002	19360.487	0.01401
1.0	1.0	Q₂₁	−e	+f	1	0	20899.359	1508.563	19390.796	0.05321
1.0	0.0	R₁₁	−e	+e	0	1	20884.434	1520.403	19364.030	0.03678
1.0	0.0	R₂₁	+f	−f	1	1	20900.527	1521.752	19378.775	0.23947
1.0	0.0	R₁₁	+f	−f	0	1	20884.489	1521.752	19362.737	0.01053
1.0	0.0	R₂₁	−e	+e	1	1	20899.359	1520.403	19378.956	0.71322
2.0	3.0	P₁₁	+e	−e	1	2	20870.198	1500.512	19369.685	0.42868
2.0	3.0	P₂₁	+e	−e	2	2	20890.541	1500.512	19390.029	0.00992
2.0	3.0	P₂₂	+e	−e	2	3	20890.541	1522.849	19367.692	0.65427
2.0	3.0	P₃₃	−f	+f	3	4	20908.228	1542.791	19365.437	2.20554
2.0	3.0	P₃₂	−f	+f	3	3	20908.228	1523.063	19385.165	0.01630
2.0	3.0	P₃₂	+e	−e	3	3	20907.146	1522.849	19384.297	0.00590
2.0	3.0	P₃₃	+e	−e	3	4	20907.146	1541.657	19365.489	0.73356
2.0	3.0	P₂₂	−f	+f	2	3	20890.682	1523.063	19367.619	1.95922
2.0	3.0	P₂₁	−f	+f	2	2	20890.682	1500.517	19390.165	0.02947
2.0	3.0	P₁₁	−f	+f	1	2	20870.199	1500.517	19369.682	1.28580
2.0	2.0	Q₁₂	+e	−f	1	2	20870.198	1514.335	19355.862	0.00600
2.0	2.0	Q₁₁	+e	−f	1	1	20870.198	1492.712	19377.486	0.79708
2.0	2.0	Q₂₃	+e	−f	2	3	20890.541	1532.345	19358.196	0.01672
2.0	2.0	Q₂₂	+e	−f	2	2	20890.541	1514.335	19376.206	0.18230
2.0	2.0	Q₂₁	+e	−f	2	1	20890.541	1492.712	19397.829	0.01272
2.0	2.0	Q₃₂	−f	+e	3	2	20908.228	1514.208	19394.019	0.06407
2.0	2.0	Q₃₃	−f	+e	3	3	20908.228	1531.123	19377.105	0.00717
2.0	2.0	Q₃₂	+e	−f	3	2	20907.146	1514.335	19392.811	0.02456
2.0	2.0	Q₂₁	−f	+e	2	1	20890.682	1492.711	19397.971	0.03774
2.0	2.0	Q₂₂	−f	+e	2	2	20890.682	1514.208	19376.473	0.54827
2.0	2.0	Q₂₃	−f	+e	2	3	20890.682	1531.123	19359.559	0.05889
2.0	2.0	Q₁₁	−f	+e	1	1	20870.199	1492.711	19377.488	2.39150
2.0	2.0	Q₁₂	−f	+e	1	2	20870.199	1514.208	19355.991	0.01825
2.0	1.0	R₁₁	+e	−e	1	0	20870.198	1508.514	19361.683	0.01823
2.0	1.0	R₂₁	+e	−e	2	0	20890.541	1508.514	19382.027	0.35533
2.0	1.0	R₂₂	+e	−e	2	1	20890.541	1524.002	19366.539	0.01760
2.0	1.0	R₃₂	−f	+f	3	1	20908.228	1525.302	19382.926	1.43987
2.0	1.0	R₃₁	−f	+f	3	0	20908.228	1508.563	19399.665	0.01730
2.0	1.0	R₃₁	+e	−e	3	0	20907.146	1508.514	19398.632	0.00622
2.0	1.0	R₃₂	+e	−e	3	1	20907.146	1524.002	19383.145	0.47745
2.0	1.0	R₂₂	−f	+f	2	1	20890.682	1525.302	19365.380	0.04759
2.0	1.0	R₂₁	−f	+f	2	0	20890.682	1508.563	19382.119	1.06565
2.0	1.0	R₁₁	−f	+f	1	0	20870.199	1508.563	19361.636	0.05446

Abstract

Cited By

Figures (2)

Tables (5)

Equations (28)

Applied Optics