Experimental and Theoretical Hyperfine Structure of Low-Lying Levels of Terbium 4f85d6s2 Configuration; Quadrupole Moment of 159Tb

Claire Arnoult; Simon Gerstenkorn

doi:10.1364/JOSA.56.000177

Journal of the Optical Society of America
Vol. 56,
Issue 2,
pp. 177-181
(1966)
•https://doi.org/10.1364/JOSA.56.000177

Experimental and Theoretical Hyperfine Structure of Low-Lying Levels of Terbium 4f⁸5d6s² Configuration; Quadrupole Moment of ¹⁵⁹Tb

Claire Arnoult and Simon Gerstenkorn

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Claire Arnoult and Simon Gerstenkorn, "Experimental and Theoretical Hyperfine Structure of Low-Lying Levels of Terbium 4f⁸5d6s² Configuration; Quadrupole Moment of ¹⁵⁹Tb," J. Opt. Soc. Am. 56, 177-181 (1966)

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Abstract

The hyperfine-structure splitting of the lowest levels ⁸G_13/2, ⁸G_15/2, ⁸G_11/2 belonging to 4f⁸5d6s² configuration of TbI have been investigated with a Fabry–Perot spectrometer.

Calculations of eigenfunctions have been carried out on the basis of recent work by Klinkenberg on the Tb classification. Using the magnetic-moment value given by Baker, Chadwick, Garton, and Hurrell, we obtained for the parameters belonging to the 4f⁸5d6s² configuration

{〈 {a_{0}}^{3} / r^{3} 〉}_{4 f} = 7.91 \pm 0.08 au {〈 {a_{0}}^{3} / r^{3} 〉}_{5 d} = 2.7 \pm 0.4 au

and for the quadrupole moment of Tb

Q = + 1.32 \pm 0.13 b .

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⁸G_13/2	⁸G_15/2	⁸G_11/2
ΔW₇⁸=161.5 mK	ΔW₈⁹=164.8 mK	ΔW₆⁷=156.8 mK
ΔW₆⁷=119.2 mK	ΔW₇⁸=121.3 mK	ΔW₅⁶=109.5 mK
ΔW₅⁶=86.0 mK	ΔW₆⁷=86.0 mK	ΔW₄⁵=73.7 mK

⁸G_13/2	⁸G_15/2	⁸G_11/2
A=17.7 mK	A=15.7 mK	A=19.1 mK
B=33 mK	B=39 mK	B=35 mK

Calculated energy levels		Proposed label	Observed energy levels		g_cal	g_obs	g_LS
cm⁻¹	J	Proposed label	cm⁻¹	J	g_cal	g_obs	g_LS
0	13/2	⁸G	0	13/2	1.476	1.464	1.456
172	15/2	⁸G	176	15/2	1.461	1.455	1.467
139	11/2	⁸G	224	11/2	1.529	1.517	1.440
961	9/2	⁸D	1085	9/2	1.554	1.537	1.697
2073	11/2	⁸D	2024	11/2	1.529	1.535	1.636
2065	7/2	⁸G	2133	7/2	1.515	1.48	1.365
2569	9/2	⁸G	2554	9/2	1.545	1.57	1.414
2782	5/2	⁸G	2889	5/2	1.385	1.35	1.257
3354	3/2	⁸G	3420	3/2	1.052	1.015	0.933
3255	13/2	⁸F	3434	13/2	1.506	1.515	1.538
3592	7/2	⁸D	3535	7/2	1.621	1.610	1.809
3695	1/2	⁸G			−1.181		−1.333
4284	17/2	⁸H			1.412		1.412
4352	5/2	⁸D	4410	5/2	1.784	1.80	2.057
4997	15/2	⁸H			1.382		1.388
5004	11/2	⁸F	5067	11/2	1.543	1.54	1.552
5083	3/2	⁸F	5198	3/2	2.195	2.305	2.000
5421	9/2	⁸F	5544	9/2	1.588	1.58	1.576
5707	1/2	⁸F			3.843		4.000
5883	13/2	⁸H	6066	13/2	1.357		1.354
6184	7/2	⁸F	6202	7/2	1.665	1.63	1.619
6494	5/2	⁸F			1.838		1.714
6497	11/2	⁸H	6388	11/2	1.316		1.301
6579	3/2	⁸D			2.463		2.800
6938	9/2	⁸H			1.233		1.212
7131	7/2	⁸H			1.045		1.048
7534	5/2	⁸H			0.707		0.686
7708	3/2	⁸H			−0.382		−0.400
7725	11/2	⁶F			1.450		1.454
7817	9/2	⁸P			1.740		1.778
7850	15/2	⁶H	7904	15/2	1.345	1.385	1.333
8524	13/2	⁶G			1.372		1.385
8995	9/2	⁶F			1.444		1.434
10 013	13/2	⁶H			1.305		1.282
10 130	7/2	⁸P			1.861		1.936
10 285	7/2	⁶F			1.467		1.397
10 413	11/2	⁶G			1.315		1.343
11 265	5/2	⁶F			1.323		1.314
11 420	9/2	⁶D			1.511		1.555
11 467	11/2	⁶H			1.247		1.203
11 725	9/2	⁶G			1.244		1.273
11 747	5/2	⁸P			2.273		2.286
11 948	3/2	⁶F			1.074		1.067
12 309	7/2	⁶D			1.572		1.587
12 362	1/2	⁶F			−0.644		−0.667
12 582	9/2	⁶H			1.149		1.071
12 728	7/2	⁶G			1.063		1.143
13 378	7/2	⁶H			0.956		0.825
13 466	5/2	⁶G			0.750		0.857
13 645	5/2	⁶D			1.507		1.657
13 962	5/2	⁶H			0.567		0.286
14 050	7/2	⁶P			1.679		1.714
14 162	3/2	⁶G			0.052		0
14 388	3/2	⁶D			1.825		1.867
14 829	1/2	⁶D			3.315		3.333
15 619	5/2	⁶P			1.867		1.886
16 582	3/2	⁶P			2.387		2.400

Calculated energy levels cm⁻¹	Eigenfunctions
Calculated energy levels cm⁻¹	J	⁶P	⁶D	⁶F	⁶G	⁶H	⁸P	⁸D	⁸F	⁸G	⁸H
0	13/2				−0.126	−0.064			0.544	0.808	0.174
139	11/2			−0.090	−0.093	−0.033		0.513	0.598	0.591	0.110
172	15/2					−0.094				0.968	0.231
961	9/2		−0.022	−0.066	−0.075	−0.023	0.179	0.523	0.579	0.582	0.099
2065	7/2	0.009	0.005	−0.023	−0.073	−0.006	0.087	0.385	0.564	0.720	−0.030
2073	11/2			0.094	−0.077	−0.052		−0.688	−0.116	0.678	0.176
2569	9/2		0.043	0.086	−0.066	−0.030	−0.274	−0.620	−0.085	0.701	0.162
2782	5/2	0.012	0.021	0.023	−0.054	−0.011	0.031	0.221	0.458	−0.851	0.110
3255	13/2				0.014	0.090			0.830	−0.499	−0.233
3354	3/2	0.005	0.021	0.055	−0.035			0.093	0.323	0.936	0.081
3592	7/2	−0.022	0.026	0.102	−0.050	−0.005	−0.195	−0.692	−0.291	0.619	−0.038
3695	1/2		0.013	0.075					0.166	0.983
4284	17/2										1
4352	5/2	0.040	0.010	−0.093	0.020	0.009	0.119	0.699	0.523	−0.453	−0.088
4997	15/2					−0.445				−0.248	0.860
5004	11/2			−0.095	−0.027	0.071		−0.503	0.757	−0.295	−0.266
5083	3/2	0.041	0.043	−0.073	0.007			0.615	0.720	−0.303	−0.044
5421	9/2		0.078	−0.121	−0.010	0.048	−0.417	−0.325	0.748	−0.296	−0.222
5707	1/2		0.084	−0.043					0.982	−0.164
5883	13/2				0.046	−0.327			0.113	−0.287	0.892
6184	7/2	−0.025	0.085	−0.097	0.013	−0.005	−0.255	−0.514	0.754	−0.284	0.065
6494	5/2	0.043	−0.080	0.072	0.004	−0.012	0.158	0.645	−0.703	0.189	0.121
6497	11/2			−0.086	0.069	−0.261		−0.080	0.167	−0.284	0.897
6579	3/2	0.057	−0.068	0.044	0.000			0.778	−0.605	0.126	0.044
6938	9/2		0.014	−0.054	0.185	−0.207	−0.131	0.008	0.114	−0.241	0.926
7131	7/2	0.001	−0.003	0.020	0.056	−0.163	0.013	0.019	−0.041	0.067	0.981
7534	5/2	−0.003	0.008	−0.025	0.088	−0.101	−0.013	−0.042	0.083	−0.154	0.974
7708	3/2	−0.001	0.003	−0.012	0.085			−0.015	0.032	−0.092	0.991
7725	11/2			0.952	0.244	0.036		0.052	0.162	0.033	0.046
7817	9/2		−0.083	−0.007	0.005	−0.014	0.829	−0.482	0.248	−0.083	0.067
7850	15/2					0.890				−0.021	0.455
8524	13/2				0.914	0.837			0.047	0.115	0.118
8995	9/2		0.344	0.902	0.211	0.032	0.026	0.050	0.134	−0.043	0.011
10 013	13/2				−0.382	0.864			−0.024	−0.046	0.324
10 130	7/2	−0.022	−0.181	−0.270	−0.058	−0.009	0.885	−0.319	0.066	−0.000	0.005
10 285	7/2	0.107	0.271	0.875	0.182	0.031	0.305	−0.064	0.122	−0.056	−0.016
10 413	11/2			−0.231	0.822	0.498		−0.226	0.112	0.115	0.091
11 265	5/2	0.036	0.224	−0.954	0.167	0.017	−0.015	0.022	0.073	−0.064	−0.006
11 420	9/2		0.890	−0.254	−0.316	−0.154	0.113	0.010	−0.070	−0.014	−0.013
11 467	11/2			0.581	−0.494	0.821		0.009	−0.011	−0.066	0.267
11 725	9/2		0.268	−0.283	0.719	0.561	0.035	−0.009	−0.023	0.101	0.072
11 747	5/2	0.029	−0.044	0.024	0.006	0.001	0.978	−0.201	0.043	−0.006	0.000
11 948	3/2	0.016	0.156	0.977	0.114			0.008	0.049	−0.074	−0.006
12 309	7/2	0.498	0.775	−0.263	−0.245	−0.108	0.079	0.002	−0.073	0.000	−0.001
12 362	1/2		0.078	0.993					0.024	−0.081
12 582	9/2		−0.032	0.111	−0.567	0.783	−0.005	0.007	−0.001	−0.070	0.215
12 728	7/2	0.137	0.145	−0.231	0.731	0.601	0.116	−0.008	−0.021	0.091	0.056
13 378	7/2	−0.050	−0.013	0.107	−0.598	0.774	−0.001	0.005	0.000	−0.046	0.164
13 466	5/2	−0.099	−0.325	−0.057	0.728	0.590	−0.017	−0.006	0.025	0.054	0.002
13 645	5/2	0.277	0.858	−0.235	0.150	0.314	0.041	0.008	−0.080	0.032	0.019
13 962	5/2	−0.041	−0.111	0.122	−0.640	0.736	−0.004	0.000	0.013	−0.054	0.128
14 050	7/2	0.847	−0.515	0.081	−0.034	0.007	−0.078	−0.037	0.041	−0.110	0.003
14 162	3/2	−0.024	−0.153	−0.087	0.979			−0.003	0.010	0.049	−0.081
14 388	3/2	0.170	0.957	−0.166	0.138			0.011	−0.086	0.022	0.012
14 829	1/2		0.993	−0.075					0.087	0.007
15 619	5/2	0.952	−0.293	0.031	−0.002	0.001	−0.055	−0.059	0.027	−0.004	0.000
16 582	3/2	0.983	−0.169	0.011	−0.001			−0.074	0.017	−0.001	0.000

⁸G_13/2	⁸G_15/2	⁸G_11/2
ΔW₇⁸=161.5 mK	ΔW₈⁹=164.8 mK	ΔW₆⁷=156.8 mK
ΔW₆⁷=119.2 mK	ΔW₇⁸=121.3 mK	ΔW₅⁶=109.5 mK
ΔW₅⁶=86.0 mK	ΔW₆⁷=86.0 mK	ΔW₄⁵=73.7 mK

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Equations (8)

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