4f<sup>13</sup>5d<sup>2</sup> Configuration of Singly Ionized Ytterbium (Yb ii)†

Nissan Spector

doi:10.1364/JOSA.58.000837

Journal of the Optical Society of America
Vol. 58,
Issue 6,
pp. 837-842
(1968)
•https://doi.org/10.1364/JOSA.58.000837

4f¹³5d² Configuration of Singly Ionized Ytterbium (Yb ii)

Nissan Spector

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Nissan Spector, "4f¹³5d² Configuration of Singly Ionized Ytterbium (Yb ii)†," J. Opt. Soc. Am. 58, 837-842 (1968)

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Abstract

Sixty high odd levels of Yb ii are interpreted as 4f¹³5d² levels. A least-squares fit with 10 parameters results in a rms error of 239 cm⁻¹ (1.1% of the total width). Good agreement is also obtained between calculated and observed g factors. Designations in J_IL_II coupling are given.

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Parameter	Value used in last diagonalization (cm⁻¹)	Value obtained by least-squares fit (cm⁻¹)
A	55 500	55 636 ± 74
B	370	376 ± 9
C	1460	1431 ± 65
F₂	160	159 ± 4
F₄	11	11 ± 1
G₁	144	143 ± 4
G₃	21	22 ± 3
G₅	3.3	3.0 ± 0.6
ζ_f	2910	2897 ± 27
ζ_d	830	813 ± 34
rms error in cm⁻¹		239
rms error in % configuration width		1.1%

Designation	J	Comp.	Observed level (cm⁻¹)	Calc. level (cm⁻¹)	Obs.–Calc. (cm⁻¹)	g (obs.)	g (calc.)
$^{3} F [2 \frac{1}{2}]$	$3 \frac{1}{2}$	30%	47 759	47 877	− 118	1.08	1.17
	$2 \frac{1}{2}$	50%	45 013	45 259	− 246	1.281	1.30
	$1 \frac{1}{2}$	30%	50 833	50 965	− 132	0.956	0.97
$^{3} F [3 \frac{1}{2}]$	$4 \frac{1}{2}$	68%	46 355	46 444	− 89	1.29	1.29
	$3 \frac{1}{2}$	42%	45 273	45 399	− 126	1.18	1.24
	$2 \frac{1}{2}$	18%	51 249	51 201	48	1.034	1.07
$^{3} F [1 \frac{1}{2}]$	$0 \frac{1}{2}$	56%	46 902	47 282	− 380	1.30	1.38
	$1 \frac{1}{2}$	49%	45 737	45 590	147	1.333	1.47
	$2 \frac{1}{2}$	43%	48 273	48 161	112	1.14	1.21
$^{3} F [6 \frac{1}{2}]$	$5 \frac{1}{2}$	81%	46 548	46 606	− 58	0.97	0.97
	$6 \frac{1}{2}$	86%	47 680	47 592	88	1.12	1.12
	$7 \frac{1}{2}$	96%	48 923	48 660	263	1.14?	1.20
$^{3} F [5 \frac{1}{2}]$	$4 \frac{1}{2}$	56%	47 663	47 669	− 6	0.98	1.02
	$5 \frac{1}{2}$	51%	48 504	48 512	− 8	1.10	1.14
	$6 \frac{1}{2}$	83%	49 727	49 650	77	1.20	1.20
$^{3} F [0 \frac{1}{2}]$	$0 \frac{1}{2}$	63%	49 419	49 833	− 414	1.41	1.37
	$1 \frac{1}{2}$	53%	48 025	48 168	− 143	1.38	1.36
$^{3} F [4 \frac{1}{2}]$	$3 \frac{1}{2}$	44%	49 008	49 124	− 116	1.03	1.01
	$4 \frac{1}{2}$	49%	49 916	50 030	− 114	1.090	1.05
	$5 \frac{1}{2}$	56%	50 468	50 315	153	1.213	1.19
$^{1} G [0 \frac{1}{2}]$	$0 \frac{1}{2}$	66%	52 068	52 170	− 102	0.54	0.53
$^{1} G [7 \frac{1}{2}]$	$7 \frac{1}{2}$	96%	53 323	53 174	149	1.04	1.07
$^{1} G [2 \frac{1}{2}]$	$2 \frac{1}{2}$	37%	53 716	53 696	20	1.183	1.14
$^{1} G [3 \frac{1}{2}]$	$3 \frac{1}{2}$	72%	57 103	57 322	− 219	1.10	1.07
$^{1} G [6 \frac{1}{2}]$	$6 \frac{1}{2}$	83%	57 562	57 688	− 126	1.05?	1.05
$^{1} G [4 \frac{1}{2}]$	$4 \frac{1}{2}$	74%	58 484	58 843	− 359	1.02	1.05
$^{1} G [5 \frac{1}{2}]$	$5 \frac{1}{2}$	82%	59 753	60 023	− 270	1.13	1.08
$^{3} P [3 \frac{1}{2}]$	$4 \frac{1}{2}$	42%	52 881	52 285	596	1.26	1.21
	$3 \frac{1}{2}$	71%	52 922	52 875	47	1.15	1.19
	$2 \frac{1}{2}$	38%	53 121	53 112	9	0.944	0.96
$^{3} P [4 \frac{1}{2}]$	$3 \frac{1}{2}$	53%	55 462	55 638	− 176	0.878	0.88
	$4 \frac{1}{2}$	71%	56 088	56 154	− 66	1.11	1.11
	$5 \frac{1}{2}$	71%	56 621	56 555	65	1.12	1.22
$^{3} P [2 \frac{1}{2}]$	$3 \frac{1}{2}$	70%	56 500	56 581	− 81	1.352	1.36
	$2 \frac{1}{2}$	52%	57 799	57 672	127	1.151	1.16
	$1 \frac{1}{2}$	70%	58 162	58 299	− 137	0.94	0.91
$^{1} D [3 \frac{1}{2}]$	$3 \frac{1}{2}$	37%	53 645	53 020	625	1.18	1.23
$^{1} D [5 \frac{1}{2}]$	$5 \frac{1}{2}$	79%	54 193	53 691	502	1.11	1.11
$^{1} D [4 \frac{1}{2}]$	$4 \frac{1}{2}$	43%	54 640	53 623	( 1018)	1.13	1.18
$^{1} D [1 \frac{1}{2}]$	$1 \frac{1}{2}$	78%	55 221	54 949	272	1.11	1.12
$^{1} D [2 \frac{1}{2}]$	$2 \frac{1}{2}$	45%	56 057	55 901	156	1.12	1.11
$^{1} S [3 \frac{1}{2}]$	$3 \frac{1}{2}$	38%		69 039			1.13
$^{3} F^{'} [5 \frac{1}{2}]$	$4 \frac{1}{2}$	95%	56 480	56 369	111	0.76	0.76
	$5 \frac{1}{2}$	95%	58 051	57 999	52	0.95	0.97
	$6 \frac{1}{2}$	90%	59 632?	59 859	(− 227)		1.09
$^{3} F^{'} [2 \frac{1}{2}]$	$1 \frac{1}{2}$	45%	56 840	56 794	46	0.90	0.93
	$2 \frac{1}{2}$	12%	59 439	59 369	70	0.994	1.04
	$3 \frac{1}{2}$	61%	62 046	64 463	(−2417)	1.14	1.12
$^{3} F^{'} [0 \frac{1}{2}]$	$0 \frac{1}{2}$	90%	56 977	57 164	− 187	2.19	2.17
	$1 \frac{1}{2}$	35%	60 910	60 686	224	1.00	1.08
$^{3} F^{'} [4 \frac{1}{2}]$	$3 \frac{1}{2}$	48%	57 534	57 619	− 85	0.87	0.86
	$4 \frac{1}{2}$	45%	59 046	59 307	(− 260)	1.08	1.07
	$5 \frac{1}{2}$	90%	61 442	61 630	− 188		1.13
$^{3} F^{'} [3 \frac{1}{2}]$	$2 \frac{1}{2}$	57%	58 661	58 407	253	0.86	0.84
	$3 \frac{1}{2}$	57%	59 625	59 440	185		0.90
	$4 \frac{1}{2}$	49%	60 649	60 577	( 72)	1.10	1.11
$^{3} F^{'} [1 \frac{1}{2}]$	$0 \frac{1}{2}$	64%	58 672	58 663	9	0.538	0.54
	$1 \frac{1}{2}$	70%	59 777	59 511	266	1.63	1.60
	$2 \frac{1}{2}$	31%	62 164	62 031	133		1.06
$^{3} P^{'} [2 \frac{1}{2}]$	$1 \frac{1}{2}$	65%	63 028	62 754	274	0.51	0.57
	$2 \frac{1}{2}$	44%	63 417	63 321	96	1.01	1.02
	$3 \frac{1}{2}$	61%	64 169	64 463	(− 294)		1.12
$^{3} P^{'} [3 \frac{1}{2}]$	$2 \frac{1}{2} ?$	44%	65 594	64 462	( 1132)	1.19?	0.91
	$3 \frac{1}{2}$	81%	66 796	66 585	211		0.87
	$4 \frac{1}{2}$	72%		67 708			1.12
$^{3} P^{'} [1 \frac{1}{2}]$	$2 \frac{1}{2}$	66%	67 934	68 089	(− 155)	1.17	1.18
	$1 \frac{1}{2}$	88%	67 790?	67 685	( 105)		1.07
	$0 \frac{1}{2}$	72%		67 871			0.20
$^{1} G^{'} [6 \frac{1}{2}]$	$6 \frac{1}{2}$	92%		64 091			0.97
$^{1} G^{'} [1 \frac{1}{2}]$	$1 \frac{1}{2}$	81%	64 192	64 616	− 424	1.193	1.11
$^{1} G^{'} [2 \frac{1}{2}]$	$2 \frac{1}{2}$	70%	65 739	65 718	21	0.879	0.70
$^{1} G^{'} [3 \frac{1}{2}]$	$3 \frac{1}{2}$	58%		68 306			0.99
$^{1} G^{'} [5 \frac{1}{2}]$	$5 \frac{1}{2}$	98%		68 960			0.96
$^{1} G^{'} [4 \frac{1}{2}]$	$4 \frac{1}{2}$	94%		70 053			0.95
$^{1} D^{'} [4 \frac{1}{2}]$	$4 \frac{1}{2}$	81%	64 365	63 732	( 633)		0.96
$^{1} D^{'} [3 \frac{1}{2}]$	$3 \frac{1}{2}$	52%	64 971	63 819	( 1162)		1.06
$^{1} D^{'} [0 \frac{1}{2}]$	$0 \frac{1}{2}$	70%	65 142	65 046	( 93)		0.47
$^{1} D^{'} [2 \frac{1}{2}]$	$2 \frac{1}{2}$	56%	66 206	66 292	− 86		1.06
$^{1} D^{'} [1 \frac{1}{2}]$	$1 \frac{1}{2}$	79%	66 189	65 610	(579)	0.91	0.86
$^{1} S^{'} [2 \frac{1}{2}]$	$2 \frac{1}{2}$	66%		78 605			0.86

Parameter	Value used in last diagonalization (cm⁻¹)	Value obtained by least-squares fit (cm⁻¹)
A	55 500	55 636 ± 74
B	370	376 ± 9
C	1460	1431 ± 65
F₂	160	159 ± 4
F₄	11	11 ± 1
G₁	144	143 ± 4
G₃	21	22 ± 3
G₅	3.3	3.0 ± 0.6
ζ_f	2910	2897 ± 27
ζ_d	830	813 ± 34
rms error in cm⁻¹		239
rms error in % configuration width		1.1%

Designation	J	Comp.	Observed level (cm⁻¹)	Calc. level (cm⁻¹)	Obs.–Calc. (cm⁻¹)	g (obs.)	g (calc.)
$^{3} F [2 \frac{1}{2}]$	$3 \frac{1}{2}$	30%	47 759	47 877	− 118	1.08	1.17
	$2 \frac{1}{2}$	50%	45 013	45 259	− 246	1.281	1.30
	$1 \frac{1}{2}$	30%	50 833	50 965	− 132	0.956	0.97
$^{3} F [3 \frac{1}{2}]$	$4 \frac{1}{2}$	68%	46 355	46 444	− 89	1.29	1.29
	$3 \frac{1}{2}$	42%	45 273	45 399	− 126	1.18	1.24
	$2 \frac{1}{2}$	18%	51 249	51 201	48	1.034	1.07
$^{3} F [1 \frac{1}{2}]$	$0 \frac{1}{2}$	56%	46 902	47 282	− 380	1.30	1.38
	$1 \frac{1}{2}$	49%	45 737	45 590	147	1.333	1.47
	$2 \frac{1}{2}$	43%	48 273	48 161	112	1.14	1.21
$^{3} F [6 \frac{1}{2}]$	$5 \frac{1}{2}$	81%	46 548	46 606	− 58	0.97	0.97
	$6 \frac{1}{2}$	86%	47 680	47 592	88	1.12	1.12
	$7 \frac{1}{2}$	96%	48 923	48 660	263	1.14?	1.20
$^{3} F [5 \frac{1}{2}]$	$4 \frac{1}{2}$	56%	47 663	47 669	− 6	0.98	1.02
	$5 \frac{1}{2}$	51%	48 504	48 512	− 8	1.10	1.14
	$6 \frac{1}{2}$	83%	49 727	49 650	77	1.20	1.20
$^{3} F [0 \frac{1}{2}]$	$0 \frac{1}{2}$	63%	49 419	49 833	− 414	1.41	1.37
	$1 \frac{1}{2}$	53%	48 025	48 168	− 143	1.38	1.36
$^{3} F [4 \frac{1}{2}]$	$3 \frac{1}{2}$	44%	49 008	49 124	− 116	1.03	1.01
	$4 \frac{1}{2}$	49%	49 916	50 030	− 114	1.090	1.05
	$5 \frac{1}{2}$	56%	50 468	50 315	153	1.213	1.19
$^{1} G [0 \frac{1}{2}]$	$0 \frac{1}{2}$	66%	52 068	52 170	− 102	0.54	0.53
$^{1} G [7 \frac{1}{2}]$	$7 \frac{1}{2}$	96%	53 323	53 174	149	1.04	1.07
$^{1} G [2 \frac{1}{2}]$	$2 \frac{1}{2}$	37%	53 716	53 696	20	1.183	1.14
$^{1} G [3 \frac{1}{2}]$	$3 \frac{1}{2}$	72%	57 103	57 322	− 219	1.10	1.07
$^{1} G [6 \frac{1}{2}]$	$6 \frac{1}{2}$	83%	57 562	57 688	− 126	1.05?	1.05
$^{1} G [4 \frac{1}{2}]$	$4 \frac{1}{2}$	74%	58 484	58 843	− 359	1.02	1.05
$^{1} G [5 \frac{1}{2}]$	$5 \frac{1}{2}$	82%	59 753	60 023	− 270	1.13	1.08
$^{3} P [3 \frac{1}{2}]$	$4 \frac{1}{2}$	42%	52 881	52 285	596	1.26	1.21
	$3 \frac{1}{2}$	71%	52 922	52 875	47	1.15	1.19
	$2 \frac{1}{2}$	38%	53 121	53 112	9	0.944	0.96
$^{3} P [4 \frac{1}{2}]$	$3 \frac{1}{2}$	53%	55 462	55 638	− 176	0.878	0.88
	$4 \frac{1}{2}$	71%	56 088	56 154	− 66	1.11	1.11
	$5 \frac{1}{2}$	71%	56 621	56 555	65	1.12	1.22
$^{3} P [2 \frac{1}{2}]$	$3 \frac{1}{2}$	70%	56 500	56 581	− 81	1.352	1.36
	$2 \frac{1}{2}$	52%	57 799	57 672	127	1.151	1.16
	$1 \frac{1}{2}$	70%	58 162	58 299	− 137	0.94	0.91
$^{1} D [3 \frac{1}{2}]$	$3 \frac{1}{2}$	37%	53 645	53 020	625	1.18	1.23
$^{1} D [5 \frac{1}{2}]$	$5 \frac{1}{2}$	79%	54 193	53 691	502	1.11	1.11
$^{1} D [4 \frac{1}{2}]$	$4 \frac{1}{2}$	43%	54 640	53 623	( 1018)	1.13	1.18
$^{1} D [1 \frac{1}{2}]$	$1 \frac{1}{2}$	78%	55 221	54 949	272	1.11	1.12
$^{1} D [2 \frac{1}{2}]$	$2 \frac{1}{2}$	45%	56 057	55 901	156	1.12	1.11
$^{1} S [3 \frac{1}{2}]$	$3 \frac{1}{2}$	38%		69 039			1.13
$^{3} F^{'} [5 \frac{1}{2}]$	$4 \frac{1}{2}$	95%	56 480	56 369	111	0.76	0.76
	$5 \frac{1}{2}$	95%	58 051	57 999	52	0.95	0.97
	$6 \frac{1}{2}$	90%	59 632?	59 859	(− 227)		1.09
$^{3} F^{'} [2 \frac{1}{2}]$	$1 \frac{1}{2}$	45%	56 840	56 794	46	0.90	0.93
	$2 \frac{1}{2}$	12%	59 439	59 369	70	0.994	1.04
	$3 \frac{1}{2}$	61%	62 046	64 463	(−2417)	1.14	1.12
$^{3} F^{'} [0 \frac{1}{2}]$	$0 \frac{1}{2}$	90%	56 977	57 164	− 187	2.19	2.17
	$1 \frac{1}{2}$	35%	60 910	60 686	224	1.00	1.08
$^{3} F^{'} [4 \frac{1}{2}]$	$3 \frac{1}{2}$	48%	57 534	57 619	− 85	0.87	0.86
	$4 \frac{1}{2}$	45%	59 046	59 307	(− 260)	1.08	1.07
	$5 \frac{1}{2}$	90%	61 442	61 630	− 188		1.13
$^{3} F^{'} [3 \frac{1}{2}]$	$2 \frac{1}{2}$	57%	58 661	58 407	253	0.86	0.84
	$3 \frac{1}{2}$	57%	59 625	59 440	185		0.90
	$4 \frac{1}{2}$	49%	60 649	60 577	( 72)	1.10	1.11
$^{3} F^{'} [1 \frac{1}{2}]$	$0 \frac{1}{2}$	64%	58 672	58 663	9	0.538	0.54
	$1 \frac{1}{2}$	70%	59 777	59 511	266	1.63	1.60
	$2 \frac{1}{2}$	31%	62 164	62 031	133		1.06
$^{3} P^{'} [2 \frac{1}{2}]$	$1 \frac{1}{2}$	65%	63 028	62 754	274	0.51	0.57
	$2 \frac{1}{2}$	44%	63 417	63 321	96	1.01	1.02
	$3 \frac{1}{2}$	61%	64 169	64 463	(− 294)		1.12
$^{3} P^{'} [3 \frac{1}{2}]$	$2 \frac{1}{2} ?$	44%	65 594	64 462	( 1132)	1.19?	0.91
	$3 \frac{1}{2}$	81%	66 796	66 585	211		0.87
	$4 \frac{1}{2}$	72%		67 708			1.12
$^{3} P^{'} [1 \frac{1}{2}]$	$2 \frac{1}{2}$	66%	67 934	68 089	(− 155)	1.17	1.18
	$1 \frac{1}{2}$	88%	67 790?	67 685	( 105)		1.07
	$0 \frac{1}{2}$	72%		67 871			0.20
$^{1} G^{'} [6 \frac{1}{2}]$	$6 \frac{1}{2}$	92%		64 091			0.97
$^{1} G^{'} [1 \frac{1}{2}]$	$1 \frac{1}{2}$	81%	64 192	64 616	− 424	1.193	1.11
$^{1} G^{'} [2 \frac{1}{2}]$	$2 \frac{1}{2}$	70%	65 739	65 718	21	0.879	0.70
$^{1} G^{'} [3 \frac{1}{2}]$	$3 \frac{1}{2}$	58%		68 306			0.99
$^{1} G^{'} [5 \frac{1}{2}]$	$5 \frac{1}{2}$	98%		68 960			0.96
$^{1} G^{'} [4 \frac{1}{2}]$	$4 \frac{1}{2}$	94%		70 053			0.95
$^{1} D^{'} [4 \frac{1}{2}]$	$4 \frac{1}{2}$	81%	64 365	63 732	( 633)		0.96
$^{1} D^{'} [3 \frac{1}{2}]$	$3 \frac{1}{2}$	52%	64 971	63 819	( 1162)		1.06
$^{1} D^{'} [0 \frac{1}{2}]$	$0 \frac{1}{2}$	70%	65 142	65 046	( 93)		0.47
$^{1} D^{'} [2 \frac{1}{2}]$	$2 \frac{1}{2}$	56%	66 206	66 292	− 86		1.06
$^{1} D^{'} [1 \frac{1}{2}]$	$1 \frac{1}{2}$	79%	66 189	65 610	(579)	0.91	0.86
$^{1} S^{'} [2 \frac{1}{2}]$	$2 \frac{1}{2}$	66%		78 605			0.86

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Journal of the Optical Society of America