Spectrum of Doubly Ionized Gadolinium*

Wm. R. Callahan

doi:10.1364/JOSA.53.000695

Journal of the Optical Society of America
Vol. 53,
Issue 6,
pp. 695-700
(1963)
•https://doi.org/10.1364/JOSA.53.000695

Spectrum of Doubly Ionized Gadolinium

Wm. R. Callahan

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Wm. R. Callahan, "Spectrum of Doubly Ionized Gadolinium*," J. Opt. Soc. Am. 53, 695-700 (1963)

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Abstract

The spectrum of doubly ionized gadolinium was photographed and measured over the region 1900–12 000 Å. The following transitions involving 18 levels and 42 lines were classified: 4f⁷(⁸S_7/2)6s–6p and 4f⁷(⁸S_7/2)5d–6p. The Coulombic and spin–orbit matrix elements of the f⁷(⁸S_7/2)l states were evaluated and the energy levels calculated. Close agreement was obtained between the calculated and experimental values. These calculations indicate that the 4f⁷(⁸S_7/2)6p states are close to J₁j coupling while those of 4f⁷(⁸S_7/2)5d are close to LS coupling.

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Wavelength	I₃^a	I₄^a	Wavenumber	Lower	Upper
(⁸S_7/2)6s–6p
3176.662	4000	1000	31 470.480	(a6s_1/2)₃	(a6p_1/2)₃
3118.041	2500	800	32 062.120	(a6s_1/2)₃	(a6p_1/2)₄
2955.534	9500	4000	33 824.950	(a6s_1/2)₄	(a6p_1/2)₃
2904.726	9000	2000	34 416.570	(a6s_1/2)₄	(a6p_1/2)₄
2717.357	6000	3000	36 789.570	(a6s_1/2)₃	(a6p_3/2)₄
2679.449	3000	1500	37 310.020	(a6s_1/2)₃	(a6p_3/2)₃
2655.599	2500	1200	37 645.080	(a6s_1/2)₃	(a6p_3/2)₂
2628.108	4000	2000	38 038.840	(a6s_1/2)₄	(a6p_3/2)₅
2553.904	4000	1000	39 144.000	(a6s_1/2)₄	(a6p_3/2)₄
2520.389	1300	600	39 664.480	(a6s_1/2)₄	(a6p_1/2)₃
(⁸S_7/2)5d–6p
3049.241	300	20	32 785.510	a⁷D₂	(a6p_1/2)₃
3028.936	600	150	33 005.280	a⁷D₃	(a6p_1/2)₃
3001.918	800	250	33 302.330	a⁷D₄	(a6p_1/2)₃
2975.594	400	50	33 596.930	a⁷D₃	(a6p_1/2)₄
2949.512	1000	600	33 894.010	a⁷D₄	(a6p_3/2)₄
2918.398	1800	900	34 255.350	a⁷D₅	(a6p_3/2)₄
2664.722	100		37 516.210	a⁷D₄	(a6p_3/2)₅
2639.299	400	50	37 877.560	a⁷D₅	(a6p_3/2)₅
2608.530	600	150	38 324.320	a⁷D₃	(a6p_3/2)₄
2588.467	1800	800	38 621.350	a⁷D₄	(a6p_3/2)₄
2588.221	1800	800	38 625.020	a⁷D₂	(a6p_3/2)₃
2576.068	1500	600	38 807.230	a⁷D₁	(a6p_3/2)₂
2573.573	1500	700	38 844.850	a⁷D₃	(a6p_3/2)₃
2565.959	1200	600	38 960.110	a⁷D₂	(a6p_3/2)₂
2564.469	2000	1000	38 982.740	a⁷D₅	(a6p_3/2)₄
2554.045	3000	1000	39 141.830	a⁷D₄	(a6p_3/2)₃
2551.560	1200	600	39 179.960	a⁷D₃	(a6p_3/2)₂
2363.261	4000	1000	42 301.480	a⁹D₅	(a6p_1/2)₄
2361.913	2000	800	42 325.620	a⁹D₄	(a6p_1/2)₃
2338.973	3000	800	42 740.710	a⁹D₃	(a6p_1/2)₃
2329.347	3000	250	42 917.320	a⁹D₄	(a6p_1/2)₄
2323.783	3000	300	43 020.070	a⁹D₂	(a6p_1/2)₃
2307.031	1800	150	43 332.430	a⁹D₃	(a6p_1/2)₄
2223.943	3000	200	44 951.200	a⁹D₆	(a6p_3/2)₅
2176.844	1500	1000	45 923.680	a⁹D₅	(a6p_3/2)₅
2148.034	800	100	46 539.550	a⁹D₄	(a6p_3/2)₅
2125.683	500	100	47 028.840	a⁹D₅	(a6p_3/2)₄
2098.204	500	100	47 644.680	a⁹D₄	(a6p_3/2)₄
2080.080	500	20	48 059.770	a⁹D₃	(a6p_3/2)₄
2057.792	250	1	48 580.240	a⁹D₃	(a6p_3/2)₃
2046.029	250	1	48 859.520	a⁹D₂	(a6p_3/2)₃
2043.698	5		48 915.220	a⁹D₃	(a6p_3/2)₂

Gd iii 4f⁷(⁸S_7/2)6p
Energy levels				Eigenvector
Level	Calculated	Observed	Diff.	Eigenvector
(a6p_3/2)₂	49 221	49 194.7	−26		p_3/2
(a6p_3/2)₃	48 857	48 859.6	3	0.989	p_3/2	+0.148 p_1/2
(a6p_3/2)₄	48 284	48 339.1	55	0.977	p_3/2	+0.213 p_1/2
(a6p_3/2)₅	47 253	47 234.0	−19		p_3/2
(a6p_1/2)₄	43 615	43 611.8	−3	0.213	p_3/2	−0.977 p_1/2
(a6p_1/2)₃	43 043	43 020.1	−23	0.148	p_3/2	−0.989 p_1/2
Gd iii 4f⁷(⁸S_7/2)5d
Energy levels				Eigenvector
Level	Calculated	Observed	Diff.	Eigenvector
⁷D₁	10 548	10 387.4	−161		⁷D₁
⁷D₂	10 346	10 234.5	−112	0.997	⁷D₂	+0.076 ⁹D₂
⁷D₃	10 034	10 014.7	−19	0.992	⁷D₃	+0.124 ⁹D₃
⁷D₄	9 566	9 717.7	152	0.989	⁷D₄	+0.151 ⁹D₄
⁷D₅	8 915	9 356.4	441	0.986	⁷D₅	+0.168 ⁹D₅
⁹D₆	2 443	2 282.7	−160		⁹D₆
⁹D₅	1451	1 310.2	−141	0.168	⁷D₅	−0.986 ⁹D₅
⁹D₄	800	694.4	−106	0.151	⁷D₄	−0.989 ⁹D₄
⁹D₃	332	279.4	−53	0.124	⁷D₃	−0.992 ⁹D₃
⁹D₂	20	0	−20	0.076	⁷D₂	−0.997 ⁹D₂

Wavelength	I₃^a	I₄^a	Wavenumber	Lower	Upper
(⁸S_7/2)6s–6p
3176.662	4000	1000	31 470.480	(a6s_1/2)₃	(a6p_1/2)₃
3118.041	2500	800	32 062.120	(a6s_1/2)₃	(a6p_1/2)₄
2955.534	9500	4000	33 824.950	(a6s_1/2)₄	(a6p_1/2)₃
2904.726	9000	2000	34 416.570	(a6s_1/2)₄	(a6p_1/2)₄
2717.357	6000	3000	36 789.570	(a6s_1/2)₃	(a6p_3/2)₄
2679.449	3000	1500	37 310.020	(a6s_1/2)₃	(a6p_3/2)₃
2655.599	2500	1200	37 645.080	(a6s_1/2)₃	(a6p_3/2)₂
2628.108	4000	2000	38 038.840	(a6s_1/2)₄	(a6p_3/2)₅
2553.904	4000	1000	39 144.000	(a6s_1/2)₄	(a6p_3/2)₄
2520.389	1300	600	39 664.480	(a6s_1/2)₄	(a6p_1/2)₃
(⁸S_7/2)5d–6p
3049.241	300	20	32 785.510	a⁷D₂	(a6p_1/2)₃
3028.936	600	150	33 005.280	a⁷D₃	(a6p_1/2)₃
3001.918	800	250	33 302.330	a⁷D₄	(a6p_1/2)₃
2975.594	400	50	33 596.930	a⁷D₃	(a6p_1/2)₄
2949.512	1000	600	33 894.010	a⁷D₄	(a6p_3/2)₄
2918.398	1800	900	34 255.350	a⁷D₅	(a6p_3/2)₄
2664.722	100		37 516.210	a⁷D₄	(a6p_3/2)₅
2639.299	400	50	37 877.560	a⁷D₅	(a6p_3/2)₅
2608.530	600	150	38 324.320	a⁷D₃	(a6p_3/2)₄
2588.467	1800	800	38 621.350	a⁷D₄	(a6p_3/2)₄
2588.221	1800	800	38 625.020	a⁷D₂	(a6p_3/2)₃
2576.068	1500	600	38 807.230	a⁷D₁	(a6p_3/2)₂
2573.573	1500	700	38 844.850	a⁷D₃	(a6p_3/2)₃
2565.959	1200	600	38 960.110	a⁷D₂	(a6p_3/2)₂
2564.469	2000	1000	38 982.740	a⁷D₅	(a6p_3/2)₄
2554.045	3000	1000	39 141.830	a⁷D₄	(a6p_3/2)₃
2551.560	1200	600	39 179.960	a⁷D₃	(a6p_3/2)₂
2363.261	4000	1000	42 301.480	a⁹D₅	(a6p_1/2)₄
2361.913	2000	800	42 325.620	a⁹D₄	(a6p_1/2)₃
2338.973	3000	800	42 740.710	a⁹D₃	(a6p_1/2)₃
2329.347	3000	250	42 917.320	a⁹D₄	(a6p_1/2)₄
2323.783	3000	300	43 020.070	a⁹D₂	(a6p_1/2)₃
2307.031	1800	150	43 332.430	a⁹D₃	(a6p_1/2)₄
2223.943	3000	200	44 951.200	a⁹D₆	(a6p_3/2)₅
2176.844	1500	1000	45 923.680	a⁹D₅	(a6p_3/2)₅
2148.034	800	100	46 539.550	a⁹D₄	(a6p_3/2)₅
2125.683	500	100	47 028.840	a⁹D₅	(a6p_3/2)₄
2098.204	500	100	47 644.680	a⁹D₄	(a6p_3/2)₄
2080.080	500	20	48 059.770	a⁹D₃	(a6p_3/2)₄
2057.792	250	1	48 580.240	a⁹D₃	(a6p_3/2)₃
2046.029	250	1	48 859.520	a⁹D₂	(a6p_3/2)₃
2043.698	5		48 915.220	a⁹D₃	(a6p_3/2)₂

Gd iii 4f⁷(⁸S_7/2)6p
Energy levels				Eigenvector
Level	Calculated	Observed	Diff.	Eigenvector
(a6p_3/2)₂	49 221	49 194.7	−26		p_3/2
(a6p_3/2)₃	48 857	48 859.6	3	0.989	p_3/2	+0.148 p_1/2
(a6p_3/2)₄	48 284	48 339.1	55	0.977	p_3/2	+0.213 p_1/2
(a6p_3/2)₅	47 253	47 234.0	−19		p_3/2
(a6p_1/2)₄	43 615	43 611.8	−3	0.213	p_3/2	−0.977 p_1/2
(a6p_1/2)₃	43 043	43 020.1	−23	0.148	p_3/2	−0.989 p_1/2
Gd iii 4f⁷(⁸S_7/2)5d
Energy levels				Eigenvector
Level	Calculated	Observed	Diff.	Eigenvector
⁷D₁	10 548	10 387.4	−161		⁷D₁
⁷D₂	10 346	10 234.5	−112	0.997	⁷D₂	+0.076 ⁹D₂
⁷D₃	10 034	10 014.7	−19	0.992	⁷D₃	+0.124 ⁹D₃
⁷D₄	9 566	9 717.7	152	0.989	⁷D₄	+0.151 ⁹D₄
⁷D₅	8 915	9 356.4	441	0.986	⁷D₅	+0.168 ⁹D₅
⁹D₆	2 443	2 282.7	−160		⁹D₆
⁹D₅	1451	1 310.2	−141	0.168	⁷D₅	−0.986 ⁹D₅
⁹D₄	800	694.4	−106	0.151	⁷D₄	−0.989 ⁹D₄
⁹D₃	332	279.4	−53	0.124	⁷D₃	−0.992 ⁹D₃
⁹D₂	20	0	−20	0.076	⁷D₂	−0.997 ⁹D₂

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Equations (6)

Journal of the Optical Society of America