Extension of the Analysis of Singly Ionized Gadolinium (Gd ii)*

Nissan Spector

doi:10.1364/JOSA.60.000763

Journal of the Optical Society of America
Vol. 60,
Issue 6,
pp. 763-776
(1970)
•https://doi.org/10.1364/JOSA.60.000763

Extension of the Analysis of Singly Ionized Gadolinium (Gd ii)

Nissan Spector

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Nissan Spector, "Extension of the Analysis of Singly Ionized Gadolinium (Gd ii)*," J. Opt. Soc. Am. 60, 763-776 (1970)

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Abstract

Energy levels belonging to a system of three newly identified configurations of singly ionized gadolinium are established. This system is obtained by adding to the ⁷F term of the 4f⁸ core the 6s, 6p, and 5d electrons. The lowest level of this system, designated at ${{}^{8}F}_{6 \frac{1}{2}}$ of 4f⁸(⁷F)6s, lies 7992.31 cm⁻¹ above the $4 f^{7} ({}^{8}S) 5 d 6 s^{10} D_{2 \frac{1}{2}} °$ ground level. Transitions connecting the new system to the ground configuration strictly obey the selection rule ΔS_I = 0, where S_I is the parent spin. Coupling calculations furnish the theoretical basis for this selection rule and explain the unusual intensity relations found experimentally in the infrared. Energy levels for the 4f⁸(⁷F)5d and 4f⁸(⁷F)6p are designated in L–S and J–J coupling, respectively. Best values for the radial parameters of 4f⁸(⁷F)6p are obtained by least-squares calculation, with an rms error of 197 cm⁻¹. About 300 lines are classified.

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Equations (14)

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Configuration	Designation	J	Position (cm⁻¹)
4f⁸(⁷F)6s	⁸F	$6 \frac{1}{2}$	7992.31
	⁸F	$5 \frac{1}{2}$	9092.48
	⁶F	$5 \frac{1}{2}$	9943.78
	⁸F	$4 \frac{1}{2}$	10292.55
	⁸F	$3 \frac{1}{2}$	11084.30
	⁶F	$4 \frac{1}{2}$	11343.51
	⁸F	$2 \frac{1}{2}$	11669.81
	⁸F	$1 \frac{1}{2}$	12071.74
	⁶F	$3 \frac{1}{2}$	12318.25
	⁶F	$2 \frac{1}{2}$	13030.75
	⁶F	$1 \frac{1}{2}$	13515.16
4f⁸(⁷F)5d	⁸G	$7 \frac{1}{2}$	18366.95
	⁸G	$6 \frac{1}{2}$	18389.14
	⁸G	$5 \frac{1}{2}$	18690.14
	⁸G	$4 \frac{1}{2}$	19377.06
	⁸D	$5 \frac{1}{2}$	20093.31
	⁸G	$3 \frac{1}{2}$	20098.35
	⁸D	$4 \frac{1}{2}$	20574.19
	⁸G	$2 \frac{1}{2}$	20631.17
	⁸F	$6 \frac{1}{2}$	21157.54
	⁸D	$3 \frac{1}{2}$	21364.83
	⁸H	$8 \frac{1}{2}$	22531.31
	⁸F	$5 \frac{1}{2}$	22533.14
	⁸D	$1 \frac{1}{2}$	22677.29
	⁸F	$4 \frac{1}{2}$	23025.39
	⁸H	$7 \frac{1}{2}$	23270.49
	⁸F	$3 \frac{1}{2}$	23473.06
	⁸H	$6 \frac{1}{2}$	23970.24

Position (cm⁻¹)	J
32595.30	$5 \frac{1}{2}$
32677.56	$6 \frac{1}{2}$
34108.46	$4 \frac{1}{2}$
34608.10	$5 \frac{1}{2}$
34900.44	$3 \frac{1}{2}$
35111.84	$6 \frac{1}{2}$
35272.58	$7 \frac{1}{2}$
35362.64	$6 \frac{1}{2}$
35404.78	$2 \frac{1}{2}$
35541.15	$4 \frac{1}{2}$
35605.27	$5 \frac{1}{2}$
35991.34	$3 \frac{1}{2}$
36144.60	$2 \frac{1}{2}$
36373.46	$1 \frac{1}{2}$
36398.42	$3 \frac{1}{2}$
36565.62	$4 \frac{1}{2}$
36631.97	$3 \frac{1}{2}$
36687.47	$0 \frac{1}{2}$
36723.69	$5 \frac{1}{2}$
36819.25	$2 \frac{1}{2}$
36821.82	$6 \frac{1}{2}$
37007.20	$1 \frac{1}{2}$
37569.54	$6 \frac{1}{2}$
37642.87	$4 \frac{1}{2}$
37871.70	$5 \frac{1}{2}$
38010.61	$6 \frac{1}{2}$
38230.33	$4 \frac{1}{2}$
38386.52	$3 \frac{1}{2}$
38466.95	$5 \frac{1}{2}$
38555.80	$4 \frac{1}{2}$
38877.15	$3 \frac{1}{2}$
38922.45	$2 \frac{1}{2}$
39237.46	$3 \frac{1}{2}$
39367.27	$1 \frac{1}{2}$
39543.60	$2 \frac{1}{2}$
39635.62	$2 \frac{1}{2}$
39715.18	$2 \frac{1}{2}$
39780.71	$2 \frac{1}{2}$
40086.84	$4 \frac{1}{2}$
41256.36	$3 \frac{1}{2}$
41385.18	$4 \frac{1}{2}$
41439.49	$5 \frac{1}{2}$
41497.42	$6 \frac{1}{2}$
41784.41	$4 \frac{1}{2}$
42574.60	$5 \frac{1}{2}$
42592.44	$3 \frac{1}{2}$
42594.83	$2 \frac{1}{2}$
42626.18	$4 \frac{1}{2}$
43275.56	$2 \frac{1}{2}$
43279.19	$4 \frac{1}{2}$
43372.45	$3 \frac{1}{2}$
43555.62	$1 \frac{1}{2}$
43704.11	$3 \frac{1}{2}$
43744.04	$3 \frac{1}{2}$
43789.30	$1 \frac{1}{2}$
43987.53	$4 \frac{1}{2}$
44890.32	$4 \frac{1}{2}$
45116.23	$2 \frac{1}{2}$
45214.57	$2 \frac{1}{2}$
45394.96	$2 \frac{1}{2}$
46778.99	$1 \frac{1}{2}$

Designation	4f⁷(⁸S)5d6s(1,³D)	4f⁷(⁸S)6s(7,⁹S)5d	4f⁷(⁸S)5d(7,⁹D)6s
a⁸D	65%(³D)⁸D + 35%(¹D)⁸D	96%(⁷S)⁸D + 4%(⁹S)⁸D	96%(⁹D)⁸D + 4%(⁷D)⁸D
b⁸D	65%(¹D)⁸D + 35%(³D)⁸D	96%(⁹S)⁸D + 4%(⁷S)⁸D	96%(⁷D)⁸D + 4%(⁹D)⁸D

	4f⁷(⁸S)5d6s^a
	a⁸D₂	3	4	5	b⁸D₅		4		3		2

4f⁸(⁷F)5d
⁸G₈				⋯	2	0^b
5			⋯	⋯	8	1	5	1
4		⋯	⋯	⋯	15	100	15	100	⋯
3	⋯	⋯	⋯	⋯			10	10	10	60	2	10
2	⋯	⋯							2		10	10
⁸D₅			⋯	⋯	300	80	⋯
4	⋯	⋯	⋯	⋯	80	15	⋯		0	2
3	⋯	⋯	⋯				⋯		30	0	⋯
⁸f₆				⋯	8000	5000
5			⋯	⋯	⋯		100	25
4		⋯	⋯	⋯	15^c		30		150
3	⋯	⋯	⋯						125		150

	F₂	G₂	G₄	${\bar{G}}_{2}$	${\bar{G}}_{4}$
⁸D	−12	−42	−84	−105	−84
F	15	−105	−84	−105	−84
G	−5	−105	−56	−105	−84
⁶D	−12	7	14	14	−28
F	15	35/2	14	35	$\frac{7}{2}$
G	−5	35/2	28/3	−35	77/6

Line (cm⁻¹)	Level (cm⁻¹)	J^a	New level (cm⁻¹)	Wavelength (Å)	Int.	Desig
27119.53	27119.53	6	0.00	3686.330	100
27280.34	27280.34	7	0.00	3664.600	2000
29577.24	29577.23	6	0.01	3380.007	200
24685.25	24685.23	6	0.02	4049.858	2000
30018.33	30018.31	6	0.02	3330.340	800
27612.96	27612.93	5	0.03	3620.456	150
30474.67	30474.64	5	0.03	3280.469	10	${{}^{8}F}_{6 \frac{1}{2}}$
33505.15	33505.11	6	0.04	2983.745	200
34582.30	34582.26	5	0.04	2890.805	20
24603.04	24602.99	5	0.05	4063.390	1500
27370.41	27370.36	6	0.05	3652.540	200
26615.87	26615.77	5	0.10	3756.090	10
33447.33	33447.18	5	0.15	2988.903	60

26448.704	27548.800	4	1100.096	3779.830	20
26512.813	27612.930	5	1100.117	3770.690	300
29463.387	30563.510	4	1100.123	3393.069	30
34186.751	35286.880	4	1100.129	2924.254	200
29374.506	30474.640	5	1100.134	3403.336	40
27631.242	28731.380	5	1100.138	3618.060	15
30994.381	32094.530	4	1100.149	3225.460	600
26019.375	27119.530	6	1100.155	3842.200	400
35797.855	36898.010	4	1100.155	2792.640	15
28477.071	29577.230	6	1100.159	3510.593	10
33482.093	34582.260	5	1100.167	2985.800	8
25515.603	26615.770	5	1100.167	3918.061	150
28918.138	30018.310	6	1100.172	3457.047	300	${{}^{8}F}_{5 \frac{1}{2}}$
32691.927	33792.100	4	1100.173	3057.970	80
32347.005	33447.180	5	1100.175	3090.579	60
23502.815	24602.99	5	1100.175	4253.612	800
32292.684	33392.870	4	1100.186	3095.778	15
32404.923	33505.110	6	1100.187	3085.055	125
23585.042	24685.230	6	1100.188	4238.782	500
29137.838	30238.030	4	1100.192	3430.980	200
28550.393	29650.590	4	1100.197	3501.577	30
26270.160	27370.360	6	1100.200	3805.520	200
33533.664	34633.870	4	1100.206	2981.208	125
25015.947	26116.160	4	1100.213	3996.320	800

34946.582	36898.010	4	1951.428	2860.670	50
26621.890	28573.330	4	1951.440	3755.240	30
27699.147	29650.590	4	1951.443	3609.190	10
24664.325	26615.770	5	1951.445	4053.294	1000
32682.416	34633.870	4	1951.454	3058.860	8
30143.067	32094.530	4	1951.463	3316.558	200
26779.917	28731.380	5	1951.463	3733.080	300
31495.713	33447.180	5	1951.467	3174.117	30
28612.043	30563.510	4	1951.467	3494.032	80
31441.402	33392.870	4	1951.468	3179.600	5
25168.061	27119.530	6	1951.469	3972.166	30	${{}^{6}F}_{5 \frac{1}{2}}$
25661.457	27612.930	5	1951.473	3895.791	400
28286.557	30238.030	4	1951.473	3534.238	40
22733.755	24685.230	6	1951.475	4397.510	300
24164.682	26116.160	4	1951.478	4137.104	500
31553.626	33505.110	6	1951.484	3168.291	60
28066.825	30018.310	6	1951.485	3561.908	8
32630.765	34582.260	5	1951.495	3063.702	10
34043.725	35995.220	4	1951.495	2936.540	40
27625.722	29577.230	6	1951.508	3618.783	6
25418.836	27370.360	6	1951.524	3932.977	50

26105.922	28406.110	3	2300.188	3829.462	4
23815.967	26116.160	4	2300.193	4197.681	800
32299.925	34600.120	3	2300.195	3095.084	8
26273.129	28573.330	4	2300.201	3805.090	80
33411.598	35711.800	3	2300.202	2992.100	4
30963.845	33264.050	3	2300.205	3228.641	15	${{}^{8}F}_{4 \frac{1}{2}}$
28584.654	30884.860	3	2300.206	3497.380	100	${{}^{8}F}_{4 \frac{1}{2}}$
31491.893	33792.100	4	2300.207	3174.502	15
26339.441	28639.650	3	2300.209	3795.510	15
25698.800	27999.010	3	2300.210	3890.130	6
22302.771	24602.99	5	2300.219	4482.49	5
28263.287	30563.510	4	2300.223	3537.148	30
27937.803	30238.030	4	2300.227	3578.358	15
26431.152	28731.380	5	2300.228	3782.340	300
31146.949	33447.180	5	2300.231	3209.660	60
33451.486	35751.720	3	2300.234	2988.532	100
25312.689	27612.930	5	2300.241	3949.470	2
24315.529	26615.770	5	2300.241	4111.438	500
28174.397	30474.640	5	2300.243	3548.308	30	${{}^{8}F}_{4 \frac{1}{2}}$
33079.896	35380.140	3	2300.244	3022.104	150
27350.342	29650.590	4	2300.248	3655.220	2
32282.007	34582.260	5	2300.253	3096.802	50
32986.597	35286.880	4	2300.283	3030.652	150
32333.573	34633.870	4	2300.297	3091.863	40
29794.232	32094.530	4	2300.298	3355.390	3

30300.918	33392.870	4	3091.952	3299.280	8
34310.694	37402.650	2	3091.956	2913.690	3
28551.347	31643.310	2	3091.963	3501.460	15
25734.985	28826.960	2	3091.975	3884.660	15
24320.474	27412.450	2	3091.976	4110.602	150
31510.544	34602.520	2	3091.976	3172.623	5
32903.242	35995.220	4	3091.978	3038.330	15
30700.121	33792.100	4	3091.979	3256.377	80
31541.889	34633.870	4	3091.981	3169.470	80
30172.069	33264.050	3	3091.981	3313.370	80
32288.158	35380.140	3	3091.982	3096.212	50
25314.125	28406.110	3	3091.985	3949.246	25
25481.343	28573.330	4	3091.987	3923.329	80
28696.412	31788.400	2	3091.988	3483.759	25	${{}^{8}F}_{3 \frac{1}{2}}$
27146.040	30238.030	4	3091.990	3682.730	20	${{}^{8}F}_{3 \frac{1}{2}}$
24907.018	27999.010	3	3091.992	4013.798	250
27302.218	30394.210	3	3091.992	3661.663	30
32191.252	35283.250	2	3091.998	3105.533	80
33806.009	36898.010	4	3092.001	2957.190	3
34130.252	37222.260	2	3092.008	2929.095	200
24456.791	27548.800	4	3092.009	4087.690	200
31508.110	34600.120	3	3092.010	3172.868	40
32619.788	35711.800	3	3092.012	3064.733	15
34031.905	37123.920	2	3092.015	2937.560	6
27471.492	30563.510	4	3092.018	3639.100	5
28630.848	31722.900	2	3092.052	3491.737	150
29002.440	32094.530	4	3092.090	3446.998	8
26558.488	29650.590	4	3092.102	3764.205	50

30096.008	33447.180	5	3351.172	3321.744	15
27533.683	30884.860	3	3351.177	3630.880	30
32028.954	35380.140	3	3351.186	3121.270	10
29912.858	33264.050	3	3351.192	3342.083	4
27043.018	30394.210	3	3351.192	3696.760	100
31935.686	35286.880	4	3351.194	3130.386	50
24197.605	27548.800	4	3351.195	4131.475	200
30041.674	33392.870	4	3351.196	3327.752	8
28743.332	32094.530	4	3351.198	3478.072	15
26299.392	29650.590	4	3351.198	3801.290	400
24647.810	27999.010	3	3351.200	4056.010	30	${{}^{6}F}_{4 \frac{1}{2}}$
23264.568	26615.770	5	3351.202	4297.173	400
27123.430	30474.640	5	3351.210	3685.800	5
30440.880	33792.100	4	3351.220	3284.110	4
25380.156	28731.380	5	3351.224	3938.971	50
24261.701	27612.930	5	3351.229	4120.560	2
25054.880	28406.110	3	3351.230	3990.110	2
32400.480	35751.720	3	3351.240	3085.478	20
25222.071	28573.330	4	3351.259	3963.660	150
27212.246	30563.510	4	3351.264	3673.770	8

33446.473	37123.920	2	3677.447	2988.980	4
27252.674	30930.15	2	3677.476	3668.320	25
33544.781	37222.260	2	3677.479	2980.220	10
26716.724	30394.210	3	3677.486	3741.910	30
35109.193	38786.680	1	3677.487	2847.420	5	${{}^{8}F}_{2 \frac{1}{2}}$
32034.311	35711.800	3	3677.489	3120.748	8
33725.155	37402.650	2	3677.495	2964.280	5
27873.790	31551.290	2	3677.500	3586.576	10
24728.609	28406.110	3	3677.501	4042.757	20
29586.549	33264.050	3	3677.501	3378.944	3
27697.459	31374.960	1	3677.501	3609.410	2
27207.358	30884.860	3	3677.502	3674.430	12
31885.808	35563.310	1	3677.502	3135.283	20
32119.487	35796.990	1	3677.503	3112.472	5
24703.629	28381.140	1	3677.511	4046.845	150
25149.447	28826.960	2	3677.513	3975.106	60	${{}^{8}F}_{2 \frac{1}{2}}$
30925.006	34602.520	2	3677.514	3232.696	50
24962.131	28639.650	3	3677.519	4004.936	150
30922.595	34600.120	3	3677.525	3232.948	80
27567.621	31245.150	3	3677.529	3626.410	30
24321.474	27999.010	3	3677.536	4110.433	30
31605.697	35283.250	2	3677.553	3163.071	4
28045.346	31722.900	2	3677.554	3564.636	40

30523.130	34602.520	2	4079.390	3275.260	20
24301.745	28381.140	1	4079.395	4113.770	15
27563.897	31643.310	2	4079.413	3626.900	15
27643.481	31722.900	2	4079.419	3616.458	12
27471.869	31551.290	2	4079.421	3639.050	30
27295.532	31374.960	1	4079.428	3662.560	8
33142.831	37222.260	2	4079.429	3016.365	40	${{}^{8}F}_{1 \frac{1}{2}}$
31483.880	35563.310	1	4079.430	3175.310	6
24747.530	28826.960	2	4079.430	4039.666	100
31717.559	35796.990	1	4079.431	3151.915	20
24935.440	29014.880	1	4079.440	4009.223	80
23333.000	27412.450	2	4079.450	4284.570	5
26850.691	30930.150	2	4079.459	3723.240	8

27462.512	31788.400	2	4325.888	3640.290	5
26068.292	30394.210	3	4325.918	3834.990	150
26919.230	31245.150	3	4325.920	3713.760	5
27225.362	31551.290	2	4325.928	3672.000	15
33076.722	37402.650	2	4325.928	3022.394	5
24313.714	28639.650	3	4325.936	4111.745	100
27396.962	31722.900	2	4325.938	3649.000	10
31669.282	35995.220	4	4325.938	3156.720	10	${{}^{6}F}_{3 \frac{1}{2}}$
30957.306	35283.250	2	4325.944	3229.323	25
21790.216	26116.160	4	4325.944	4587.930	1
32896.313	37222.260	2	4325.947	3038.970	5
30274.171	34600.120	3	4325.949	3302.195	10
30307.918	34633.870	4	4325.952	3298.518	100
24080.158	28406.110	3	4325.952	4151.626	30
23086.495	27412.450	2	4325.955	4330.319	20
26237.549	30563.510	4	4325.961	3810.250	5
32572.049	36898.010	4	4325.961	3069.225	20
23222.838	27548.800	3	4325.962	4304.895	400
31385.831	35711.800	3	4325.969	3185.230	6
26604.179	30930.15	2	4325.971	3757.740	80	${{}^{6}F}_{3 \frac{1}{2}}$
31425.747	35751.720	3	4325.973	3181.184	8
31054.167	35380.140	3	4325.973	3219.250	15
24247.343	28573.330	4	4325.987	4123.000	20
26558.869	30884.860	3	4325.991	3764.151	15

22374.048	27412.450	2	5038.402	4468.210	5
25891.745	30930.15	2	5038.405	3861.140	50
23976.472	29014.880	1	5038.408	4169.580	3
22960.595	27999.010	3	5038.415	4354.064	40
30244.826	35283.250	2	5038.424	3305.399	8
30524.882	35563.310	1	5038.428	3275.072	5
32085.490	37123.920	2	5038.430	3115.770	10
23342.708	28381.140	1	5038.432	4282.788	50
26336.527	31374.960	1	5038.433	3795.930	40
23788.527	28826.960	2	5038.433	4202.523	80
26749.965	31788.400	2	5038.435	3737.260	10	${{}^{6}F}_{2 \frac{1}{2}}$
29561.685	34600.120	3	5038.435	3381.786	40	${{}^{6}F}_{2 \frac{1}{2}}$
33748.243	38786.680	1	5038.437	2962.252	30
25355.766	30394.210	3	5038.444	3942.760	1
29564.072	34602.520	2	5038.448	3381.513	10
23601.194	28639.650	3	5038.456	4235.881	60
23367.653	28406.110	3	5038.457	4278.216	25
26512.813	31551.290	2	5038.477	3770.690	300
26684.421	31722.900	2	5038.479	3746.440	8
26206.668	31245.150	3	5038.482	3814.740	100
26604.817	31643.310	2	5038.493	3757.650	4
32364.137	37402.650	2	5038.513	3088.943	8

30274.171	35796.990	1	5522.819	3302.195	10
26200.075	31722.900	2	5522.825	3815.700	2
30040.465	35563.310	1	5522.845	3327.886	10
26120.463	31643.310	2	5522.847	3827.330	80
29079.671	34602.520	2	5522.849	3437.843	10
23492.024	29014.880	1	5522.856	4255.566	20	${{}^{6}F}_{1 \frac{1}{2}}$
33263.823	38786.680	1	5522.857	3005.393	5
31601.062	37123.920	2	5522.858	3163.535	10
23304.097	28826.960	2	5522.863	4289.884	80
26265.536	31788.400	2	5522.864	3806.190	4
31879.758	37402.650	2	5522.892	3135.878	15

Wavelength (Å)	Intensity in arc	Intensity in E.D.	Wavenumber (cm⁻¹)	Even level (cm⁻¹)	J^a	Odd level (cm⁻¹)	J^a
11153.793	1	0	8963.105	11084	3	20047	3
10974.624	3	0	9109.435	10292	4	19402	4
10919.893	5	2	9155.091	22533	5	13378	5
10627.306	15	2	9407.145	23270	7	32677	6
10571.374	2	3	9456.917	22533	5	13076	4
10469.552	4	1	9548.891	9092	5	18641	5
10430.658	30	10	9584.497	9092	5	18677	6
10271.728	1	0	9732.793	7992	6	17725	5
10268.318	2	2	9736.025	25668	3	35404	2
10195.743	5	1	9805.327	18690	5	8884	4
10161.755	2	0	9838.123	18389	6	8551	5
10048.278	3	0	9949.227	23025	4	13076	4
9860.141	8	1	10139.063	18690	5	8551	5
9829.288	6	0	10170.888	27988	3	17817	4
9697.109	1	4	10309.525	9092	5	19402	4
9397.748	60	80	10637.929	23970	6	34608	5
9387.865	10	50	10649.128	7992	6	18641	5
9380.343	20	100	10657.667	9292	5	19750	5
9356.571	10	100	10684.745	7992	6	18677	6
9290.444	800	20000	10760.796	7992	6	18753	7
9282.987	2	10	10769.440	20098	3	9328	2
9125.412	10	60	10955.402	20098	3	9142	3
9020.227	10	8	11083.153	23025	4	34108	4
8915.391	10	10	11213.479	20098	3	8884	4
8845.355	10	10	11302.265	20631	2	9328	2
				23970	6	35272	7
8748.525	10	3	11427.360	23473	3	34900	3
8745.623	0	2	11431.152	20574	4	9142	3
8718.845	0	2	11466.260	22533	5	11066	4
8702.155	2		11488.251	20631	2	9142	3
8678.163	30	8	11520.012	21157	6	32677	6
8661.477	300	80	11542.205	20093	5	8551	5
8636.697	4	4	11575.321	22533	5	34108	4
8631.136	3	2	11582.779	23025	4	34608	5
8502.604	50	15	11757.872	7992	6	19750	5
8499.807	5	8	11761.741	18366	7	6605	7
8483.829	2	4	11783.893	18389	6	6605	7
8442.617	150	25	11841.415	23270	7	35111	6
8418.650	2	2	11875.126	23025	4	34900	3
8359.947	0	1	11958.512	23025	4	11066	4
8329.556	4	1	12002.143	23270	7	35272	7
8316.415	100	30	12021.108	20574	4	32595	5

8315.030	80	15	12023.110	20574	4	8551	5
8284.083	1	0	12068.025	23473	3	35541	4
8267.532	20	1	12092.184	23270	7	35362	6
8179.770	30	0	12221.923	21364	3	9142	3
7996.459	10	8	12502.097	20093	5	32595	5
7987.664	8	10	12515.862	23025	4	35541	4
7986.123	1	1	12518.277	23473	3	35991	3
7944.233	50	20	12584.286	20093	5	32677	6
7930.241	8000	5000	12606.490	21157	6	8551	5
7913.224	0	6	12633.599	23025	4	10391	3
7889.512	8	4	12671.569	23473	3	36144	2
7854.831	20	15	12727.517	22677	1	35404	2
7844.950	300	300	12743.548	21364	3	34108	4
7838.821	100	80	12753.512	23970	6	36723	5
7814.691	0	2	12792.891	18690	6	5897	6
7778.992	25	15	12851.600	23970	6	36821	6
7734.586	2	2	12925.383	23473	3	36398	3
7710.338	3	6	12966.032	23025	4	35991	3
7685.450	25	20	13008.020	22533	5	35541	4
7660.917	2	4	13049.676	18389	6	5339	5
7635.835	0	2	13092.541	23473	3	36565	4
7597.344	10	10	13158.872	23473	3	36631	3
7490.709	15	8	13346.196	23473	3	36819	2
7475.617	1	2	13373.139	23025	4	36398	3
7432.572	40	20	13450.588	21157	6	34608	5
7386.630	8	4	13534.245	20574	4	34108	4
7379.126	1	2	13548.008	18389	6	4841	5
7377.264	200	30	13551.428	23270	7	36821	6
7347.321	1	1	13606.655	23025	4	36631	3
7324.903	100	25	13648.298	22533	5	8884	4
7299.296	1	0	13696.178	22677	1	36373	1
7201.410	150		13882.343	23025	4	9142	3
7191.490	20		13901.493	23970	6	37871	5
7189.57	800		13905.21	18690	5	32595	5
7164.300	80		13954.251	21157	6	35111	6
7147.310	500		13987.422	18690	5	32677	6
7135.730	250		14010.121	20098	3	34108	4
				22677	1	36687	0
7133.16	100		14015.18	20093	5	34108	4
				22533	5	36565	4
7123.630	2		14033.918	20574	4	34608	5
7120.610	4		14039.870	21364	3	35404	2
7082.700	4		14115.018	21157	6	35272	7
7069.930	80		14140.513	23025	4	8884	4
7069.240	1		14141.893	22677	1	36819	2
7068.090	150		14144.194	23473	3	9328	2
7045.020	80		14190.511	22533	5	36723	5
7037.810	30		14205.048	21157	6	35362	6
7037.260	600		14206.159	18389	6	32595	5
6996.76	1500		14288.40	18389	6	32677	6
6985.890	1500		14310.621	18366	7	32677	6
6978.270	60		14326.248	20574	4	34900	3
6976.350	125		14330.191	23473	3	9142	3
6906.900	15		14474.282	23025	4	8551	5
6887.630	300		14514.778	20093	5	34608	5
6852.94	4		14588.26	23473	3	8884	4
6839.240	3		14617.474	23025	4	37642	4
6835.050	3		14626.435	21364	3	35991	3
6766.920	15		14773.694	20631	2	35404	2

6753.910	200		14802.152	20098	3	34900	3
6679.560	80		14966.914	20574	4	35541	4
6656.620	15		15018.492	20093	5	35111	6
6616.440	10		15109.695	22533	5	37642	4
6547.280	10		15269.300	20093	5	35362	6
6517.740	40		15338.504	22533	5	37871	5
6508.540	15		15360.185	20631	2	35991	3
6483.980	50		15418.366	18690	5	34108	4
6473.680	20		15442.897	20098	3	35541	4
6468.860	12		15454.404	21364	3	36819	2
6444.240	15		15513.446	20631	2	36144	2
6422.420	200		15566.152	21157	6	36723	5
6382.190	150		15664.272	21157	6	36821	6
6368.810	50		15697.181	22533	5	38230	4
6290.310	15		15893.072	20098	3	35991	3
6280.480	10		15917.947	18690	5	34608	5
6247.920	10		16000.900	20631	2	36631	3
6104.780	15		16376.074	20631	2	37007	1
6046.590	5		16533.669	20098	3	36631	3
6011.390	4		16630.482	20093	5	36723	5
5981.320	2		16714.088	21157	6	37871	5
5976.200	30		16728.407	20093	5	36821	6
5970.320	60		16744.882	18366	7	35111	6
5921.350	40		16883.363	18389	6	35272	7
5913.550	800		16905.632	18366	7	35272	7
5882.210	60		16995.703	18366	7	35362	6
5867.650	4		17037.876	22677	1	39715	2
5815.380	3		17191.015	21364	3	38555	4
5722.770	8		17469.209	23970	6	41439	5
5662.180	15		17656.142	20574	4	38230	4
5579.660	60		17917.264	20093	5	38010	6
5513.690	60		18131.637	18690	5	36821	6
5462.080	3		18302.957	20574	4	38877	3
5452.680	50		18334.510	18389	6	36723	5
5423.630	40		18432.712	18389	6	36821	6
5417.120	20		18454.863	18366	4	36821	6
5274.806	20		18952.769	18690	5	37642	4
5211.880	1		19181.594	18690	5	37871	5
5174.420	5		19320.456	18690	5	38010	6
5131.350	1		19482.621	18389	6	37871	5
5095.060	1		19621.385	18389	6	38010	6
4587.930	1		21790.216	12318	3	34108	4
4482.490	5		22302.771	10292	4	32595	5
4468.210	5		22374.048	13030	2	35404	2
4427.033	20		22582.151	12318	3	34900	3
4417.800	1		22629.346	13515	1	36144	2
4397.510	300		22733.755	9943	5	32677	6
4354.064	40		22960.595	13030	2	35991	3
4330.319	20		23086.495	12318	3	35404	2
4314.280	10		23172.321	13515	1	36687	0
4304.895	400		23222.838	12318	3	35541	4
4303.468	25		23230.538	11669	2	34900	3
4297.173	400		23264.568	11343	4	34608	5
4289.884	80		23304.097	13515	1	36819	2
4284.570	5		23333.000	12071	1	35404	2
4282.788	50		23342.708	13030	2	36373	1
4278.216	25		23367.653	13030	2	36398	3
4255.566	20		23492.024	13515	1	37007	1
4253.612	800		23502.815	9092	5	32595	5
4243.839	150		23556.938	11343	4	34900	3
4238.782	500		23585.042	9092	5	32677	6
4235.881	60		23601.194	13030	2	36631	3
4202.523	80		23788.527	13030	2	36819	3
4197.681	800		23815.967	10292	4	34108	4
4195.851	20		23826.354	12318	3	36144	2
4169.580	3		23976.472	13030	2	37007	1
4151.626	30		24080.158	12318	3	36398	3
4137.104	500		24164.682	9943	5	34108	4
4131.475	200		24197.605	11343	4	35541	4
				18377	4	42574	5
4123.000	20		24247.343	12318	3	36565	4
4113.770	15		24301.745	12071	1	36373	1
4111.745	100		24313.714	12318	3	36631	3
4111.438	500		24315.529	10292	4	34608	5
4110.602	150		24320.474	11084	3	35404	2
4110.433	30		24321.474	11609	2	35991	3
4087.690	200		24456.791	11084	3	35541	4
4084.684	30		24474.789	11669	2	36144	2
4080.310	2		24501.024	12318	3	36819	2
4063.390	1500		24603.045	7992	6	32595	5
4062.590	500		24607.890	10292	4	34900	3
4061.296	80		24615.730	12071	1	36687	0
4056.010	30		24647.810	11343	4	35991	3
4053.294	1000		24664.325	9943	5	34608	5
4049.858	2000		24685.251	7992	6	32677	6
4046.845	150		24703.629	11669	2	36373	1
4042.757	20		24728.609	11669	2	36398	3
4039.666	100		24747.530	12071	1	36819	2
4013.798	250		24907.018	11084	3	35991	3
4009.223	80		24935.440	12071	1	37007	1
4004.936	150		24962.131	11669	2	36631	3
3996.320	800		25015.947	9092	5	34108	4
3990.110	2		25054.880	11343	4	36398	3
3989.248	50		25060.294	11084	3	36144	2
3975.106	60		25149.447	11669	2	36819	2
3972.166	30		25168.061	9943	5	35111	6
3963.660	150		25222.071	11343	4	36565	4
3949.246	25		25314.125	11084	3	36398	3
3942.760	1		25355.766	13030	2	38386	3
3938.971	50		25380.156	11343	4	36723	5
3932.977	50		25418.836	9943	5	35362	6
3923.329	80		25481.343	11084	3	36565	4
3918.061	150		25515.603	9092	5	34608	5
3890.130	6		25698.800	10292	4	35991	2
3884.660	15		25734.985	11084	3	36819	3
3861.140	50		25891.745	13030	2	38922	2
3842.200	400		26019.375	9092	5	35111	6
3834.990	150		26068.292	12318	3	38386	3
3829.462	4		26105.922	10292	4	36398	3
3815.700	2		26200.075	13515	1	39715	2
3810.250	5		26237.549	12318	2	38555	4
3805.520	200		26270.160	9092	5	35362	6
3805.090	80		26273.129	10292	4	36565	4
3801.290	400		26299.392	11343	4	37642	4
3795.510	15		26339.441	10292	4	36631	3
3782.340	300		26431.152	10292	4	36723	5
3779.830	20		26448.704	9092	5	35541	4
3770.690	300		26512.813	13030	2	39543	2
3768.500	60		26528.220	11343	4	37871	5
3764.205	50		26558.488	11084	3	37642	4
3764.151	15		26558.869	12318	3	38877	3
3757.740	80		26604.179	12318	3	38922	2
3756.090	10		26615.866	7992	6	34608	5
3755.240	30		26621.890	9943	5	36565	4
3746.440	8		26684.421	13030	2	39715	2
3741.910	30		26716.724	11669	2	38386	3
3733.080	300		26779.917	9943	5	36723	5
3723.240	8		26850.691	12071	1	38922	2
3719.450	800		26878.050	9943	5	36821	6
3696.760	100		27043.018	11343	4	38386	3
3686.330	100		27119.531	7992	6	35111	6
3682.730	20		27146.040	11084	3	38230	4
3674.430	12		27207.358	11669	2	38877	3
3673.770	8		27212.246	11343	4	38555	4
3672.000	15		27225.362	12318	3	39543	2
3668.320	25		27252.674	11669	2	38922	2
3664.600	2000		27280.338	7992	6	35272	7
3661.663	30		27302.218	11084	3	38386	3
3655.220	2		27350.342	10292	4	37642	4
3652.540	200		27370.410	7992	6	35362	6
3649.000	10		27396.962	12318	3	39715	2
3639.100	5		27471.492	11084	3	38555	4
3639.050	30		27471.869	12071	1	39543	2
3638.880	10		27473.153	9092	5	36565	4
3630.880	30		27533.683	11343	4	38877	3
3624.893	80		27579.158	10292	4	37871	5
3618.060	15		27631.242	9092	5	36723	5
3616.458	12		27643.481	12071	1	39715	2
3609.190	10		27699.147	9943	5	37642	4
3605.265	100		27729.302	9092	5	36821	6
3597.014	1		27792.907	11084	3	58877	3
3586.576	10		27873.790	11669	2	39543	2
3578.358	15		27937.803	10292	4	38230	4
3564.636	40		28045.346	11669	2	39715	2
3561.908	8		28066.825	9943	5	38010	6
3537.148	30		28263.287	10292	4	38555	4
3534.238	40		28286.557	9943	5	38230	4
3501.577	30		28550.393	9092	5	37642	4
3497.380	100		28584.654	10292	4	38877	3
3494.032	80		28612.043	9943	5	38555	4
3491.737	150		28630.848	11084	3	39715	2
3478.072	15		28743.332	11343	4	40086	4
3467.664	40		28829.601	7992	6	36821	6
3457.047	300		28918.138	9092	5	38010	6
3446.998	8		29002.440	11084	3	40086	4
3437.843	10		29079.671	13515	1	42594	2
3430.980	200		29137.838	9092	5	38230	4
3393.069	30		29463.387	9092	5	38555	4
3381.786	40		29561.685	13030	2	42592	3
3381.513	10		29564.072	13030	2	42594	2
3355.390	3		29794.232	10292	4	40086	4
3345.825	80		29879.405	7992	6	37871	5
3330.340	800		30018.330	7992	6	38010	6
3327.886	10		30040.465	13515	1	43555	1
3321.744	15		30096.008	11343	4	41439	5
3316.558	200		30143.067	9943	5	40086	4
3302.195	10		30274.171	12318	3	42592	3
3275.260	20		30523.130	12071	1	42594	2
3275.072	5		30524.882	13030	2	43555	1
3232.948	80		30922.595	11669	2	42592	3
3232.696	50		30925.006	11669	2	42594	2
3225.460	600		30994.381	9092	5	40086	4

3209.660	60		31146.949	10292	4	41439	5
3201.019	30		31231.026	11343	4	42574	5
3175.310	6		31483.880	12071	1	43555	1
3174.117	30		31495.713	9943	5	41439	5
3172.868	40		31508.110	11084	3	42592	3
3172.623	5		31510.544	11084	3	42594	2
3135.283	20		31885.808	11669	2	43555	1
3096.802	50		32282.007	10292	4	42574	5
3095.084	8		32299.925	10292	4	42592	3
3090.579	60		32347.005	9092	5	41439	5
3063.702	10		32630.765	9943	5	42574	5
2985.800	8		33482.093	9092	5	42574	5
2890.805	20		34582.301	7992	6	42574	5

Name	Diag. (cm⁻¹)	Least square (cm⁻¹)
F₀	37100	37095 ± 77
F₂	55	48 ± 10
G₂	8	8 ± 1
G₄	eliminated	eliminated
ζ₄_f	1225	1234 ± 31
ζ₆_p	1700	1769 ± 71
rms error (cm⁻¹)		197
(%)		2.7%

J	Percentages in J–j	Percentages in L–S	Observed level (cm⁻¹)	Calculated (cm⁻¹)	O–C cm⁻¹	g_obs.	g_calc.	LS names (Ref. 3)
$5 \frac{1}{2}$	95% (⁷F₆, $\frac{1}{2}$ )	36%⁸D + 38%⁸F + 18%⁶F	32595	32795	−200	1.575	1.55	⁸D
$6 \frac{1}{2}$	90% (⁷F₆, $\frac{1}{2}$ )	100%⁸G	32677	32755	−78	1.475	1.48
$4 \frac{1}{2}$	92% (⁷F₅, $\frac{1}{2}$ )	54%⁸F + 22%⁸D	34108	33911	197	1.571	1.57	⁶D
$5 \frac{1}{2}$	93% (⁷F₅, $\frac{1}{2}$ )	30%⁶F + 26%⁸G + 20%⁶G + 13%⁸F	34608	34215	393	1.46	1.46	⁶F
$3 \frac{1}{2}$	90% (⁷F₄, $\frac{1}{2}$ )	63%⁸F + 14%⁸D + 13%⁸G	34900	34887	13	1.62	1.57	⁶D
$6 \frac{1}{2}$	85% (⁷F₆, $\frac{3}{2}$ )	43%⁸F + 52%⁶G	35111	35198	−87		1.45
$7 \frac{1}{2}$	100% (⁷F₆, $\frac{3}{2}$ )	100%⁸G	35272	35497	−225	1.47	1.47	⁸G
$2 \frac{1}{2}$	89% (⁷F₃, $\frac{1}{2}$ )	67%⁸F + 16%⁸G	35404	35701	−297	1.92	1.65	⁸D
$4 \frac{1}{2}$	95% (⁷F₄, $\frac{1}{2}$ )	42%⁶F + 35%⁸G + 13%⁶G	35541	35316	225	1.45	1.43	⁶F
$5 \frac{1}{2}$	98% (⁷F₆, $\frac{3}{2}$ )	50%⁶F + 38%⁸D	35605	35764	−159	1.51	1.51
$3 \frac{1}{2}$	60% (⁷F₃, $\frac{1}{2}$ ) + 40% (⁷F₅, $\frac{3}{2}$ )	43%⁸G + 41%⁶F	35991	36136	−145	1.55	1.39
$1 \frac{1}{2}$	86% (⁷F₃, $\frac{1}{2}$ )	70%⁸F + 16%⁸G	36373	36340	33	1.79	1.83	⁶D
$4 \frac{1}{2}$	73% (⁷F₆, $\frac{3}{2}$ ) + 20% (⁷F₅, $\frac{3}{2}$ )	61%⁶D + 24%⁶F	36565	36620	−55	1.59	1.51
$0 \frac{1}{2}$	77% (⁷F₁, $\frac{1}{2}$ )	76%⁸F + 13%⁶D	36687	36787	−100	2.81	3.35	⁶D
$5 \frac{1}{2}$	84% (⁷F₅, $\frac{3}{2}$ )	45%⁸F + 33%⁶G + 17%⁸F	36723	36499	224	1.48	1.49	⁶F
$2 \frac{1}{2}$	95% (⁷F₂, $\frac{1}{2}$ )	49%⁸G + 36%⁶F	36819	36709	109	1.39	1.32
$6 \frac{1}{2}$	94% (⁷F₆, $\frac{3}{2}$ )	80%⁸G + 18%⁶G	36821	36735	86	1.44	1.45	⁸G
$1 \frac{1}{2}$	93% (⁷F₁, $\frac{1}{2}$ )	55%⁸G + 30%⁶F	37007	37057	−50	1.19	1.10	⁶F
$0 \frac{1}{2}$	85% (⁷F₀, $\frac{1}{2}$ )	64%⁸G + 25%⁶F	37057^a	37200	−143	−0.28	−0.66	⁶F
$4 \frac{1}{2}$	77% (⁷F₅, $\frac{3}{2}$ ) + 20% (⁷F₆, $\frac{3}{2}$ )	35%⁶D + 25%⁸D + 25%⁶F		37100			1.53
$3 \frac{1}{2}$	41% (⁷F₅, $\frac{3}{2}$ ) + 29% (⁷F₃, $\frac{1}{2}$ ) + 25% (⁷F₄, $\frac{3}{2}$ )	43%⁶D + 37%⁶F	37522^a	37666	−144	1.55	1.46
$4 \frac{1}{2}$	79% (⁷F₄, $\frac{3}{2}$ ) + 16% (⁷F₃, $\frac{3}{2}$ )	39%⁸D + 38%⁸F + 18%⁶G	37642	37627	15	1.42	1.56	⁶F
$5 \frac{1}{2}$	88% (⁷F₄, $\frac{3}{2}$ )	61%⁸G + 33%⁶G	37871	37789	82	1.29	1.41
$3 \frac{1}{2}$	68% (⁷F₄, $\frac{3}{2}$ ) + 16% (⁷F₅, $\frac{3}{2}$ )	49%⁶D + 17%⁸D + 16%⁶F	38386	38183	203	1.39	1.55	⁶F
$2 \frac{1}{2}$	64% (⁷F₄, $\frac{3}{2}$ ) + 28% (⁷F₃, $\frac{3}{2}$ )	49%⁶F + 28%⁶D + 13%⁸G		38510			1.37
$4 \frac{1}{2}$	81% (⁷F₃, $\frac{3}{2}$ ) + 18% (⁷F₄, $\frac{3}{2}$ )	48%⁶G + 45%⁸G	38555	38660	−105	1.16	1.36
$3 \frac{1}{2}$	72% (⁷F₃, $\frac{3}{2}$ ) + 20% (⁷F₂, $\frac{3}{2}$ )	60%⁸D + 28%⁸F	38877	38569	308	1.52	1.68
$2 \frac{1}{2}$	60% (⁷F₃, $\frac{1}{2}$ ) + 24% (⁷F₄, $\frac{3}{2}$ )	60%⁶D + 11%⁸D + 11%⁶F		39020			1.60
$3 \frac{1}{2}$	74% (⁷F₂, $\frac{3}{2}$ ) + 24% (⁷F₃, $\frac{3}{2}$ )	61%⁶G + 31%⁸G	39237	39349	−112	1.25	1.24	⁸G
$1 \frac{1}{2}$	62% (⁷F₃, $\frac{3}{2}$ ) + 30% (⁷F₂, $\frac{3}{2}$ )	60%⁶F + 15%⁶D + 18%³G	39367	39146	221	1.24	1.11	⁶F
$2 \frac{1}{2}$	64% (⁷F₂, $\frac{3}{2}$ ) + 25% (⁷F₁, $\frac{3}{2}$ )	77%⁸D + 16%⁸F	39543	39309	234	1.69	1.94
$0 \frac{1}{2}$	58% (⁷F₂, $\frac{3}{2}$ ) + 41% (⁷F₁, $\frac{3}{2}$ )	71%⁶F + 23%⁸G	39610^a	39557	53	−0.70	−0.63	⁶F
$1 \frac{1}{2}$	51% (⁷F₂, $\frac{3}{2}$ ) + 25% (⁷F₃, $\frac{3}{2}$ )	70%⁶D + 13%⁸F		39610			1.79
$2 \frac{1}{2}$	64% (⁷F₁, $\frac{3}{2}$ ) + 32 (⁷F₂, $\frac{3}{2}$ )	74%⁸G + 18%⁸G	39635	39861	−226	1.03	0.97	⁶G
$1 \frac{1}{2}$	56% (⁷F₁, $\frac{3}{2}$ ) + 30% (⁷F₀, $\frac{3}{2}$ )	91%⁸D		39837			2.71
$1 \frac{1}{2}$	52% (⁷F₀, $\frac{3}{2}$ ) + 41% (⁷F₁, $\frac{3}{2}$ )	88%⁶G	39936^a	40204	−268	0.18	0.12	⁶G
$0 \frac{1}{2}$	50% (⁷F₁, $\frac{3}{2}$ ) + 30% (⁷F₂, $\frac{3}{2}$ )	80%⁶D + 16%⁸F		39949			3.27

Abstract

Cited By

Tables (9)

Equations (14)

Journal of the Optical Society of America