Effective Interactions between d Electrons in the Second Spectra of the Iron Group*

Y. Shadmi; J. Oreg; J. Stein

doi:10.1364/JOSA.58.000909

Journal of the Optical Society of America
Vol. 58,
Issue 7,
pp. 909-914
(1968)
•https://doi.org/10.1364/JOSA.58.000909

Effective Interactions between d Electrons in the Second Spectra of the Iron Group

Y. Shadmi, J. Oreg, and J. Stein

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Y. Shadmi, J. Oreg, and J. Stein, "Effective Interactions between d Electrons in the Second Spectra of the Iron Group*," J. Opt. Soc. Am. 58, 909-914 (1968)

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Abstract

650 levels belonging to the configurations (3d + 4s)ⁿ of all second spectra of the iron group were calculated, and 472 observed levels were fitted to them. In addition to the usually used approximation, a complete set of two-body and three-body effective-interaction parameters between 3d electrons was also introduced. Using only two-body effective interactions, we obtained a mean error of ±192 cm⁻¹; while the addition of three-body effective interactions reduced the mean error to ±87 cm⁻¹.

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Equations (18)

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	Diag. 1	L.S. 1a	L.S. 1b	L.S. 1c	L.S. 2a	L.S. 2b	L.S. 2c	L.S. 3a
D′₀	8094	8118±23	8116±24	8115±24	8117±23	8109±19	8112±18	8112±18
D″₀	36002	36073±32	36071±32	36068±32	36043±33	36055±28	36054±26	36056±26
D′₁	3944	3939±7	3938±7	3938±8	3942±7	3943±7	3943±6	3943±7
D″₁	5856	5864±12	5868±12	5867±12	5841±12	5838±10	5836±9	5836±9
D′₂	−112	−113±3	−114±3	−114±3	−111±3	−112±2	−112±2	−112±2
D″₂	−112	−118±4	−119±4	−119±4	−115±4	−112±2	−112±2	−112±2
B₀	759	777±3	775±2	774±2	776±2	777±2	775±2	774±2
B′₀	863	870±1	870±1	871±1	873±1	873±1	874±1	873±1
B₁	55	65±1	64±1	63±1	64±1	64±1	63±1	63±1
B′₁	54	56±1	56±1	56±1	57±1	57±1	57±1	57±1
C₀	3084	2911±20	2941±15	2946±13	2914±15	2918±14	2948±15	2960±11
C′₀	3427	3389±10	3389±10	3382±9	3382±10	3380±10	3379±9	3376±8
C₁	367	327±9	343±5	342±5	328±7	333±5	339±5	340±4
C′₁	333	325±6	332±4	329±4	316±6	316±4	319±4	318±4
G₀	1590	1583±4	1583±4	1583±4	1581±4	1582±4	1580±4	1581±4
G₁	0	3±3	3±3	3±3	4±3	⋯	⋯	⋯
H₀	96	93±2	94±2	94±2	93±2	93±2	93±2	93±2
H₁	−24	−24±1	−24±1	−24±1	−25±1	−24±1	−24±1	−24±1
α₀	33	34±3	31±1	32±1	42±2	41±2	37±2	36±2
α′₀	33	31±1	31±1	32±1	31±1	31±1	31±1	32±1
α₁	7	4±1	3±1	4±0.5	7±1	5.5±0.5	5.2±0.4	5.1±0.4
α′₁	7	4±1	3±1	4±0.5	5±1	5.5±0.5	5.2±0.4	5.1±0.4
β₀	−538	−346±35	−409±24	−423±19	−340±30	−349±28	−394±27	−418±17
β′₀	−538	−443±23	−435±21	−423±19	−436±21	−434±21	−429±20	−418±17
β₁	0	51±18	⋯	⋯	48±17	34±10	28±9	26±6
β′₁	0	14±14	⋯	⋯	34±13	34±10	28±9	26±6
T₀	−3.6	−2.2±0.3	−2.6±0.2	−2.4±0.2	−1.6±0.2	−1.7±0.2	−2.1±0.2	−2.2±0.2
T′₀	−3.6	−4.2±0.1	−4.1±0.1	−4.1±0.1	−4.2±0.1	−4.1±0.1	−4.2±0.1	−4.1±0.1
T₁	0	−0.1±0.1	−0.2±0.1	⋯	0.1±0.1	⋯	⋯	⋯
T′₁	0	−0.1±0.1	−0.2±0.1	⋯	0.1±0.1	⋯	⋯	⋯
Tx₀	0	−6.2±0.5	−5.8±0.5	−5.5±0.4	−4.6±0.3	−4.7±0.3	−4.6±0.3	−4.4±0.3
Tx′₀	0	−2.0±0.3	−2.0±0.3	−2.1±0.2	−2.2±0.3	−2.2±0.2	−2.3±0.2	−2.3±0.2
Tx₁	0	−1.1±0.2	−0.9±0.2	−0.7±0.2	−0.6±0.2	−0.7±0.1	−0.7±0.1	−0.7±0.1
Tx′₁	0	−0.4±0.2	−0.5±0.1	−0.3±0.1	−0.7±0.1	−0.7±0.1	−0.7±0.1	−0.7±0.1
ζ₀	369	356±14	357±14	358±14	360±13	359±13	358±12	359±12
ζ′₀	393	391±10	391±10	391±11	393±11	393±11	393±9	392±10
ζ₁	86	87±5	87±5	87±5	88±5	87±5	87±5	87±5
ζ′₁	97	95±3	94±3	95±3	96±3	95±3	96±3	96±3
ζ₂ = ζ′₂	7	8±1	8±1	8±1	8±1	8±1	8±1	8±1

Δ	⋯	±90.1	±91.3	±92.0	±93.2	±93.0	±87.5	±87.0

	AEL			Ref. 5		Ref. 12		Present work
Obs. level	Conf.	Term	J	Assignment	J	Assignment	J	Assignment	J
54444.19	d³s²	e²G	$\frac{7}{2}$	discarded	⋯	d⁴s ⁴F	$\frac{7}{2}$	discarded	⋯
54678.95	d³s²	e²G	$\frac{9}{2}$	discarded	⋯	d⁴s ⁴F	$\frac{9}{2}$	discarded	⋯
55023.30	d³s²	c⁴P	$\frac{5}{2}$	d⁴s ⁴P	$\frac{5}{2}$	d⁴s ⁴F	$\frac{5}{2}$	d⁴s ⁴F	$\frac{5}{2}$
55081.7?	d³s²	c⁴P	$\frac{3}{2}$	d⁴s ⁴P	$\frac{3}{2}$	d⁴s ⁴F	$\frac{3}{2}$	d⁴s ⁴P	$\frac{3}{2}$
59130.51	d³s²	b²P	$\frac{3}{2}$	d⁴s ²P	$\frac{3}{2}$	d⁴s ²P	$\frac{3}{2}$	d⁴s ⁴P	$\frac{3}{2}$
59527.05	d³s²	e²D	$\frac{3}{2}$	discarded	⋯	discarded	⋯	d⁴s ²P	$\frac{1}{2}$
59570.23	d³s²	e²D	$\frac{5}{2}$	discarded	⋯	d⁴s ²F	$\frac{5}{2}$	d⁴s ²F	$\frac{7}{2}$

No.	Effective interaction parameters included in the calculation	Total number of free parameters	Mean error (cm⁻¹)
1	α	36	±230
2	α,β	37	±192
3	α,T	37	±227
4	α,β,T	39	±117
5	α,β,T,Tx	42	±87
6	α,β,Tx	40	±170

Effective interaction parameters included in the calculation	Mean error for the obs. levels of 3dⁿ (cm⁻¹)	Mean error for the obs. levels of 3dⁿ⁻¹4s (cm⁻¹)
α	±223	±235
α,β	±165	±193
α,β,T	±126	±75
α,β,T,Tx	±92	±60

Number of obs. levels	152	280

	Diag. 1	L.S. 1a	L.S. 1b	L.S. 1c	L.S. 2a	L.S. 2b	L.S. 2c	L.S. 3a
D′₀	8094	8118±23	8116±24	8115±24	8117±23	8109±19	8112±18	8112±18
D″₀	36002	36073±32	36071±32	36068±32	36043±33	36055±28	36054±26	36056±26
D′₁	3944	3939±7	3938±7	3938±8	3942±7	3943±7	3943±6	3943±7
D″₁	5856	5864±12	5868±12	5867±12	5841±12	5838±10	5836±9	5836±9
D′₂	−112	−113±3	−114±3	−114±3	−111±3	−112±2	−112±2	−112±2
D″₂	−112	−118±4	−119±4	−119±4	−115±4	−112±2	−112±2	−112±2
B₀	759	777±3	775±2	774±2	776±2	777±2	775±2	774±2
B′₀	863	870±1	870±1	871±1	873±1	873±1	874±1	873±1
B₁	55	65±1	64±1	63±1	64±1	64±1	63±1	63±1
B′₁	54	56±1	56±1	56±1	57±1	57±1	57±1	57±1
C₀	3084	2911±20	2941±15	2946±13	2914±15	2918±14	2948±15	2960±11
C′₀	3427	3389±10	3389±10	3382±9	3382±10	3380±10	3379±9	3376±8
C₁	367	327±9	343±5	342±5	328±7	333±5	339±5	340±4
C′₁	333	325±6	332±4	329±4	316±6	316±4	319±4	318±4
G₀	1590	1583±4	1583±4	1583±4	1581±4	1582±4	1580±4	1581±4
G₁	0	3±3	3±3	3±3	4±3	⋯	⋯	⋯
H₀	96	93±2	94±2	94±2	93±2	93±2	93±2	93±2
H₁	−24	−24±1	−24±1	−24±1	−25±1	−24±1	−24±1	−24±1
α₀	33	34±3	31±1	32±1	42±2	41±2	37±2	36±2
α′₀	33	31±1	31±1	32±1	31±1	31±1	31±1	32±1
α₁	7	4±1	3±1	4±0.5	7±1	5.5±0.5	5.2±0.4	5.1±0.4
α′₁	7	4±1	3±1	4±0.5	5±1	5.5±0.5	5.2±0.4	5.1±0.4
β₀	−538	−346±35	−409±24	−423±19	−340±30	−349±28	−394±27	−418±17
β′₀	−538	−443±23	−435±21	−423±19	−436±21	−434±21	−429±20	−418±17
β₁	0	51±18	⋯	⋯	48±17	34±10	28±9	26±6
β′₁	0	14±14	⋯	⋯	34±13	34±10	28±9	26±6
T₀	−3.6	−2.2±0.3	−2.6±0.2	−2.4±0.2	−1.6±0.2	−1.7±0.2	−2.1±0.2	−2.2±0.2
T′₀	−3.6	−4.2±0.1	−4.1±0.1	−4.1±0.1	−4.2±0.1	−4.1±0.1	−4.2±0.1	−4.1±0.1
T₁	0	−0.1±0.1	−0.2±0.1	⋯	0.1±0.1	⋯	⋯	⋯
T′₁	0	−0.1±0.1	−0.2±0.1	⋯	0.1±0.1	⋯	⋯	⋯
Tx₀	0	−6.2±0.5	−5.8±0.5	−5.5±0.4	−4.6±0.3	−4.7±0.3	−4.6±0.3	−4.4±0.3
Tx′₀	0	−2.0±0.3	−2.0±0.3	−2.1±0.2	−2.2±0.3	−2.2±0.2	−2.3±0.2	−2.3±0.2
Tx₁	0	−1.1±0.2	−0.9±0.2	−0.7±0.2	−0.6±0.2	−0.7±0.1	−0.7±0.1	−0.7±0.1
Tx′₁	0	−0.4±0.2	−0.5±0.1	−0.3±0.1	−0.7±0.1	−0.7±0.1	−0.7±0.1	−0.7±0.1
ζ₀	369	356±14	357±14	358±14	360±13	359±13	358±12	359±12
ζ′₀	393	391±10	391±10	391±11	393±11	393±11	393±9	392±10
ζ₁	86	87±5	87±5	87±5	88±5	87±5	87±5	87±5
ζ′₁	97	95±3	94±3	95±3	96±3	95±3	96±3	96±3
ζ₂ = ζ′₂	7	8±1	8±1	8±1	8±1	8±1	8±1	8±1

Δ	⋯	±90.1	±91.3	±92.0	±93.2	±93.0	±87.5	±87.0

Abstract

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Tables (4)

Equations (18)

Journal of the Optical Society of America