Low Even Configurations in the First Spectrum of Ruthenium (Ru i)

R. E. Trees

doi:10.1364/JOSA.49.000838

Journal of the Optical Society of America
Vol. 49,
Issue 9,
pp. 838-843
(1959)
•https://doi.org/10.1364/JOSA.49.000838

Low Even Configurations in the First Spectrum of Ruthenium (Ru i)

R. E. Trees

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R. E. Trees, "Low Even Configurations in the First Spectrum of Ruthenium (Ru i)," J. Opt. Soc. Am. 49, 838-843 (1959)

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Abstract

The theory of intermediate coupling with configuration interaction is used to calculate energy levels and g values in the 4d⁶5s², 4d⁷5s, and 4d⁸ configurations of Ru i. By using fifteen parameters, the positions of fifty-seven observed levels are calculated with a mean deviation of ±54 cm⁻¹ between theory and experiment. There are unexplained differences greater than 500 cm⁻¹ for two other levels, one of which is well confirmed by experiment. Over-all agreement between observed and calculated g values is within ±0.006. Linear relations are obtained between similarly defined electrostatic parameters in the three configurations.

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Parameter	Number of observations
Parameter	Forty-two	Fifty-three
A(4d⁸)	15 043±89	14 752±50
A(4d⁷ 5s)	14 576±91	14 518±40
A(4d⁶ 5s²)	20 001±1460	20 874±106
B(4d⁸)	514.7±13	485.7±7
B(4d⁷ 5s)	535.1±7	542.6±3
B(4d⁶ 5s²)	560.4±69	596.7±4
C(4d⁸)	2159.8±205	2412.6±60
C(4d⁷ 5s)	2567.4±25	2578.6±11
C(4d⁶ 5s²)	2801.3±78	2740.4±18
ζ(4d⁸)	880.7±62	837.8±30
ζ(4d⁷ 5s)	906.7±22	915.9±16
ζ(4d⁶ 5s²)	1054.2±78	970.6±23
G₂	1780.6±21	1736.0±11
H₂	334.5±4	329.9±2
α	28.6±3.5	29.41±0.8
Mean error	±126	±63
Mean deviation	±101	±54

Obs. E		9492	11 753	14 828	24 174
Calc. E		9503	11 733	14 904	22 346	27 948	33 411	38 893	41 454	76 048
Diff. E		11	−20	76	−1828
d⁶ s²	4 ⁵D	91.22	6.04	*1.49	*0.01	0.96	0.11	0.00	*0.16	*0.00
(²P)	³P	*2.95	57.20	0.10	*35.28	*3.66	*0.69	*0.03	0.10	0.00
(⁴P)	³P	0.39	0.68	84.38	0.02	10.83	2.20	*0.18	1.32	0.00
d⁸	³P	*1.80	32.72	*0.18	62.41	*0.74	0.21	0.70	1.24	0.00
d⁶ s²	4 ³P	*1.47	0.59	*12.61	*1.17	37.04	17.77	*2.92	26.39	0.05
d⁶ s²	2 ³P	2.10	*2.46	1.05	*0.00	*25.22	*2.26	*0.97	65.64	0.30
d⁶ s²	4 ¹S	0.04	*0.05	0.15	*0.00	*16.26	50.25	*11.70	*4.05	17.49
d⁶ s²	0 ¹S	*0.02	0.04	*0.03	0.02	4.58	*14.27	0.24	0.03	80.77
d⁸	¹S	0.01	*0.23	0.01	*1.09	*0.69	12.25	83.27	1.06	1.39

Obs. E		3105	9073	9620	11 786	13 982	16 713	20 242	22 293	27 561
Calc. E		3102	9165	9619	11 766	14 044	16 723	20 224	22 282	27 538	29 621	36 524	42 236
Diff. E		−3	92	−1	−20	62	10	−18	−11	−23
Obs. g		0.000	1.795	1.985	1.684	1.441	0.676	0.927	1.35
Calc. g		0.009	1.716	2.057	1.690	1.440	0.671	0.928	1.489	1.340	0.662	0.501	1.498
Diff. g		0.009	−0.079	0.072	0.006	−0.001	−0.005	0.001	0.14
(⁴F)	⁵F	98.24	0.02	0.00	*0.09	*0.03	1.30	*0.21	*0.01	0.01	*0.04	*0.04	*0.00
d⁶ s²	4 ⁵D	*0.00	57.24	*35.76	4.72	*1.08	*0.06	*0.02	*0.00	1.01	0.01	0.00	*0.11
(⁴P)	⁵P	*0.00	22.05	55.82	21.17	0.43	0.09	0.00	*0.41	*0.01	*0.01	*0.01	0.00
(²P)	³P	0.02	*11.39	*6.07	40.60	0.90	0.56	0.13	*36.14	*3.23	*0.85	*0.00	0.10
(⁴P)	³P	*0.00	0.29	*0.48	*0.60	75.12	4.10	4.02	*0.18	11.98	1.70	0.07	1.56
(3 ²D)	³D	*1.26	0.23	0.05	*1.56	*1.16	60.28	*16.76	*1.16	0.20	*2.52	14.83	*0.00
(1 ²D)	³D	0.45	*0.02	*0.00	0.33	0.06	*9.19	1.92	0.13	*0.87	4.14	82.90	0.00
(²P)	¹P	*0.02	0.02	0.07	*0.25	*10.27	15.50	73.27	*0.16	0.18	0.25	0.01	0.01
d⁸	³P	0.00	*4.75	* 1.59	26.40	0.19	4.46	*0.00	61.13	*0.47	*0.09	0.00	0.91
d⁶ s²	4 ³P	0.00	*1.59	0.11	1.69	*10.05	*0.61	*1.74	*0.63	43.31	6.86	0.00	33.39
d⁶ s²	2 ³P	*0.00	2.24	*0.02	*2.55	0.71	*0.02	0.32	*0.00	*23.87	*6.57	0.00	63.70
d⁶ s²	4 ³D	*0.02	0.15	*0.03	*0.05	*0.00	3.81	*1.59	*0.13	*14.87	76.96	*2.16	0.22

Obs. E		2713	8044	9058	9184	10 624	11447	13 646	15 054	17 046	20 934	22 343	23 453	24 927		29 352
Calc. E		2703	8227	9047	9167	10 660	11 481	13 670	14 970	17 055	20 934	22 194	23 485	24 887	26 875	29 397	33 905	36 779	42 331	43 019	44 308	60 368
Diff. E		−10	183	−11	−17	36	34	24	−84	9	0	−149	32	−40		45
Obs. g		1.000	1.536	1.232	1.089	1.534	0.764	1.315	1.162	1.175	1.343	0.697	1.162
Calc. g		1.001	1.562	1.474	0.851	1.541	0.762	1.301	1.172.	1.176	1.335	0.693	1.149	1.462	0.677	1.180	1.005	1.162	1.021	0.694	1.451	1.000
Diff. g		0.001	0.026	0.242	−0.237	0.007	−0.002	−0.014	0.010	0.001	−0.008	−0.004	−0.013
(⁴F)	⁵F	98.56	0.01	*0.01	0.14	*0.08	*0.05	0.00	0.07	0.99	*0.02	0.02	0.00	0.00	0.01	*0.02	*0.00	*0.02	*0.00	*0.00	*0.00	0.00
(⁴P)	⁵P	0.00	35.73	*24.45	0.32	35.46	0.84	1.22	*0.82	0.18	*0.67	*0.02	0.20	*0.00	0.00	*0.02	*0.00	*0.05	0.00	0.00	0.00	0.00
d⁶s²	4 ⁵D	*0.00	13.64	59.50	19.36	5.38	0.76	*0.33	0.05	*0.01	0.00	*0.04	*0.08	0.68	0.03	*0.07	*0.01	0.00	0.00	*0.01	*0.04	0.00
(⁴F)	³F	*0.21	*4.55	*11.67	73.34	*2.22	0.00	*1.88	*1.35	0.96	0.12	1.20	0.66	0.03	*1.45	*0.03	0.18	*0.03	*0.01	*0.11	0.00	0.00
(²P)	³P	0.02	*25.44	2.06	*0.01	18.61	1.92	2.11	*7.15	0.20	*25.38	*1.05	13.80	*1.41	0.05	*0.60	0.07	*0.01	*0.00	0.00	0.11	0.00
d⁸	³F	0.00	0.04	*0.09	*0.00	*3.69	77.05	5.97	3.96	*0.14	0.01	7.13	0.60	0.04	0.41	*0.01	0.03	0.01	0.03	0.77	*0.00	0.00
(⁴P)	³P	*0.00	1.64	0.15	0.23	*7.76	*2.26	48.55	*20.92	*0.01	*0.45	*0.05	*0.08	15.85	*0.01	0.36	0.02	0.06	*0.48	0.04	1.08	0.00
(3 ²D)	¹D	0.00	1.27	0.11	*2.17	*0.94	1.45	*10.00	*19.04	1.34	12.56	*0.15	24.09	2.63	1.02	*0.51	0.26	*0.00	19.67	*1.04	1.73	*0.00
(1 ²D)	¹D	*0.00	*0.19	*0.02	0.60	0.06	*0.46	2.54	2.42	*0.00	*2.51	0.68	*2.39	*0.28	*0.06	0.70	*35.34	1.65	44.44	*1.50	2.40	*1.77
(3 ²D)	³D	*0.81	0.69	0.06	*0.22	*0.95	*0.26	0.44	5.12	69.19	*1.09	*0.31	1.03	0.09	*0.10	*2.35	0.36	16.61	*0.30	*0.00	*0.03	0.00
(1 ²D)	³D	0.32	*0.05	*0.06	0.06	0.36	0.18	*0.34	*1.14	*12.00	0.52	*0.08	0.01	*0.23	*0.18	4.53	0.95	78.68	*0.29	0.00	*0.01	*0.00
d⁸	³P	0.00	*9.98	0.44	*0.01	14.78	0.69	5.15	*4.16	6.31	40.50	1.18	*13.35	*2.70	*0.01	*0.01	*0.04	0.00	*0.06	0.01	0.63	*0.00
(²F)	3³F	*0.04	*0.00	0.02	*0.00	0.20	*4.70	*0.37	*0.39	0.12	*1.25	49.37	0.01	0.01	42.58	0.07	0.15	0.36	*0.34	*0.00	*0.02	0.00
d⁸	¹D	*0.00	*0.98	*0.00	0.70	2.52	*6.23	12,36	27.50	*3.14	12.80	0.00	31.40	1.60	0.22	*0.02	0.02	*0.01	0.00	*0.00	*0.01	0.49
d⁶ s²	4 ³P	0.00	*2.49	*0.18	*0.22	3.76	0.69	*6.97	2.48	0.13	*0.23	0.00	*1.25	42.70	*0.07	2.13	*0.90	0.00	*3.38	0.44	31.92	0.05
d⁶ s²	2 ³P	*0.00	2.66	0.11	0.16	*2.62	*0.29	0.38	*0.05	*0.39	0.01	*0.00	1.57	*27.59	0.03	*3.08	*0.30	0.01	*3.95	0.48	56.31	0.02
d⁶ s²	4 ³F	*0.00	*0.24	*0.73	2.15	*0.22	0.58	0.02	0.07	0.01	0.31	*33.02	*1.04	0.00	45.39	*0.01	*1.20	0.08	0.18	14.63	*0.11	0.02
d⁶ s²	2 ³F	*0.00	0.01	0.09	*0.07	0.13	*1.45	*0.14	*0.13	*0.00	*0.07	5.14	0.05	0.02	*7.74	*0.61	0.78	0.02	5.25	78.15	*0.05	0.10
d⁶ s²	4 ³D	*0.01	0.18	0.20	0.02	*0.05	*0.00	0.07	0.04	4.40	*0.03	*0.10	1.47	*4.00	0.00	83.43	2.30	*2.38	0.19	0.49	0.50	*0.13
d⁶ s²	4 ¹D	*0.00	*0.16	*0.03	0.18	0.12	*0.08	0.91	2.31	*0.28	*1.48	*0.35	*6.56	0.00	0.46	*0.60	41.70	*0.00	20.12	*2.31	4.13	18.23
d⁶ s²	2 ¹D	*0.00	0.05	0.01	*0.03	*0.07	0.05	*0.23	*0.83	0.18	0.01	0.13	0.36	*0.15	*0.19	0.83	*15.41	0.02	*1.31	0.02	*0.93	79.18

Obs. E		2092	8084	8575	8771	10 655	13 699	16 191	22 419		26 076	27 517	29 979
Calc. E		2073	8083	8502	8812	10 682	13 697	16 239	22 246	25 210	26 031	27 535	29 397	37 179	39 308	43 571
Diff. E		−19	−1	−73	41	27	−2	48	−173		−45	18	−582
Obs. g		1.249	1.196	1.420	1.624	1.086	0.757	1.333	1.070
Calc. g		1.249	1.200	1.391	1.652	1.084	0.757	1.332	1.076	0.970	0.902	0.975	1.329	1.326	1.015	1.074
Diff. g		0	0.004	−0.029	0.028	−0.002	0	−0.001	0.006
(⁴F)	⁵F	98.77	0.30	0.13	*0.06	*0.03	*0.10	0.53	0.05	0.00	0.00	0.01	*0.01	*0.00	0.00	*0.00
(⁴F)	³F	*0.54	65.77	25.68	*2.08	*0.99	1.01	0.87	1.67	*0.01	*0.24	*0.99	*0.00	*0.01	*0.04	*0.09
d⁶ s²	4 ⁵D	*0.00	*26.68	72.03	*0.22	0.38	0.00	*0.05	*0.22	0.01	0.02	0.12	*0.23	0.00	*0.00	*0.02
(⁴P)	⁵P	0.01	0.89	1.30	96.91	*0.00	*0.00	0.67	0.00	0.00	*0.00	0.00	*0.03	*0.18	0.00	0.00
d⁸	³F	0.00	0.76	*0.00	*0.01	92.03	0.30	*0.00	5.74	0.09	0.19	0.12	*0.00	0.02	0.11	0.62
(²G)	³G	0.15	*0.71	*0.27	0.02	*0.10	94.89	0.02	*0.58	1.24	0.56	*1.44	*0.01	*0.00	*0.02	0.00
(3 ²D)	³D	*0.32	*0.69	*0.15	*0.16	0.02	*0.03	75.81	*0.03	*0.55	0.00	*0.17	*0.95	20.86	*0.25	*0.02
(1² D)	³D	0.14	0.30	0.11	0.47	0.00	0.01	*17.88	*0.25	*0.25	0.00	*0.16	5.92	73.26	*1.2S	*0.00
(²F)	³F	*0.06	*0.23	*0.00	0.00	*4.44	0.17	0.03	45.41	7.16	17.05	24.68	0.09	0.65	*0.00	*0.01
(²F)	¹F	*0.00	*0.05	*0.02	0.00	*0.00	*0.33	0.04	0.15	57.72	*26.65	*0.11	*0.30	0.07	*13.53	1.03
d⁶ s²	4 ³G	*0.00	0.04	0.01	*0.00	0.03	*3.13	0.00	*2.07	16.22	46.44	*31.39	*0.09	*0.01	*0.17	0.42
d⁶ s²	4 ³F	*0.00	3.05	0.16	*0.05	0.37	0.00	0.10	*36.21	4.37	3.89	34.62	*0.47	0.23	2.09	14.38
d⁶ s²	2 ³F	0.00	*0.39	0.01	0.00	*1.58	0.00	*0.03	7.44	*0.81	*2.10	*5.81	*0.31	0.27	9.90	71.33
d⁶ s²	4 ³D	*0.00	*0.13	0.13	*0.01	0.02	*0.00	3.95	*0.17	0.19	*0.00	0.00	91.23	*3.03	*0.05	1.08
d⁶ s²	4 ¹F	*0.00	*0.00	0.00	*0.00	*0.00	*0.04	0.02	*0.00	11.38	*2.86	*0.39	0.35	1.39	72.58	*11.00

Obs. E		1191	6545	7483	9121	12 817	14 700	17 097	21 643	23 005	23 393	25 643	27 289		42 895
Calc. E		1166	6530	7413	9084	12 802	14 691	17 101	21 703	22 997	23 397	25 655	27 311	31 719	42 888	48 417
Diff. E		−25	−15	−70	−37	−15	−9	4	60	−8	4	12	22		−7
Obs. g		1.349	1.284	1.447	1.255	1.033	0.992	0.834	1.08	0.91	0.950
Calc. g		1.347	1.274	1.462	1.254	1.030	0.998	0.835	1.128	0.982	0.971	1.088	1.172	1.010	1.245	1.004
Diff. g		−0.002	−0.010	0.015	−0.001	−0.003	0.006	0.001	−0.05	0.07	0.021
(⁴F)	⁵F	98.38	0.96	0.14	*0.03	*0.36	*0.06	*0.01	*0.03	*0.01	0.00	0.00	0.02	*0.00	*0.00	*0.00
(⁴F)	³F	*0.95	79.24	12.99	*1.11	2.25	*0.50	0.19	* 1.15	*0.67	0.17	*0.05	*0.56	0.04	*0,13	*0.01
d⁶ s²	4 ⁵D	0.00	*11.61	85.24	1.89	0.00	*0.02	0.00	0.64	0.18	*0.01	0.07	0.27	*0.03	*0.03	*0.00
d⁸	³F	0.00	1.34	*0.67	91.91	0.21	0.00	0.04	*3.42	*1.15	*0.06	0.33	0.20	0.01	0.65	0.00
(²G)	³G	0.60	*0.96	*0.15	*0.05	77.63	13.65	2.78	1.26	*0.03	*0.50	0.96	*1.43	0.01	0.00	*0.00
(²G)	¹G	*0.01	1.48	0.31	*0.00	*7.53	61.15	*8.02	*0.62	3.02	*14.54	0.00	0.03	2.38	*0.01	0.90
(²H)	³H	*0.00	0.05	0.01	0.00	*8.59	6.71	77.66	2.29	*4.20	*0.17	*0.23	*0.00	*0.08	*0.00	*0.00
d⁶ s²	4 ³F	*0.01	3.27	*0.12	0.18	0.04	*0.26	0.00	29.49	10.57	*0.67	3.98	26.82	*4.94	18.87	0.80
d⁶ s²	2 ³F	0.00	*0.52	0.33	*1.25	*0.00	0.09	0.00	*7.82	*2.30	0.33	*2.23	*5.32	0.56	78.28	0.96
d⁶ s²	4 ³H	0.00	*0.00	0.00	*0.00	*0.07	0.34	5.74	*12.38	48.56	17.40	12.02	*0.35	*3.01	0.01	*0.10
d⁸	¹G	*0.00	0.13	0.01	0.41	*0.96	13.85	*4.72	8.55	*5.10	60.43	*0.01	*0.98	*4.16	*0.04	0.67
d⁶ s²	4 ³G	*0.01	0.05	*0.00	0.02	*2.20	*1.03	*0.49	7.05	*1.89	*3.45	52.27	*31.01	0.00	0.37	*0.16
(²F)	³F	*0.03	*0.35	0.03	*3.15	0.05	0.85	*0.03	*18.04	*19.53	0.30	27.53	29.28	*0.82	*0.01	0.00
d⁶ s²	4 ¹G	0.00	*0.00	*0.01	0.01	0.08	*1.13	0.01	4.14	*1.90	1.10	0.29	1.81	60.84	*0.18	28.51
d⁶ s²	2 ¹G	0.00	*0.03	0.00	*0.01	0.02	*0.35	0.32	*3.14	0.89	*0.85	0.01	*1.93	*23.13	*1.44	67.88

Obs. E		0	12 207	16 240	20 056	22 519	25 603
Calc. E		−17	12 244	16 270	20 080	22 595	25 562
Diff. E		−17	37	30	24	76	−41
Obs. g		1.397	1.190	1.041	1.007	0.99
Calc. g		1.397	1.191	1.040	1.006	1.058	1.175
Diff. g		0	0.001	−0.001	−0.001	0.07
(⁴F)	⁵F	98.67	* 1.28	*0.03	*0.01	0.01	*0.01
(²G)	³G	1.31	89.16	3.93	1.65	*1.46	2.47
(²H)	³H	*0.01	*5.58	86.65	1.66	*5.93	*0.18
(²H)	¹H	*0.00	*1.18	*3.40	94.55	*0.80	0.06
d⁶ s²	4 ³H	0.00	*0.02	5.28	1.30	78.40	15.00
d⁶ s²	4 ³G	*0.01	*2.78	*0.71	*0.82	*13.40	82.28

Obs. E		15 550	22 162
Calc. E		15 609	22 243	29 788
Diff. E		59	81
Obs. g		1.164	1.160
Calc. g		1.167	1.163	1.004
Diff. g		0.003	0.003
(²H)	³H	94.89	*5.09	0.03
d⁶ s²	4 ³H	5.08	92.50	*2.42
d⁶ s²	4 ¹I	0.04	2.41	97.55

Abstract

Cited By

Tables (8)

Equations (2)

Journal of the Optical Society of America