Calculation of the Hyperfine Structure and g<sub>J</sub> Values of the 3d<sup>9</sup>4s4p Configuration of Copper

Donald A. Landman; L. A. Levin; Allen Lurio

doi:10.1364/JOSA.59.000962

Journal of the Optical Society of America
Vol. 59,
Issue 8,
pp. 962-968
(1969)
•https://doi.org/10.1364/JOSA.59.000962

Calculation of the Hyperfine Structure and g_J Values of the 3d⁹4s4p Configuration of Copper

Donald A. Landman, L. A. Levin, and Allen Lurio

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Donald A. Landman, L. A. Levin, and Allen Lurio, "Calculation of the Hyperfine Structure and g_J Values of the 3d⁹4s4p Configuration of Copper," J. Opt. Soc. Am. 59, 962-968 (1969)

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Abstract

Wave functions that take into account departures from LS coupling and configuration interaction are obtained for the 3d⁹4s4p configuration of copper by treating the radial integrals as parameters and adjusting them to fit the experimental energy levels. The relativistic dipole and quadrupole hfs matrix elements between all levels of the same J within the 3d⁹4s4p configuration are derived. The hfs and g_J values of most states of the 3d⁹4s4p configuration are then obtained by evaluating these matrix elements with the derived wave functions. Good agreement between calculated and most experimental hfs and g_J measurements is obtained. The quadrupole moment of ⁶³Cu obtained from the d hole is −0.267b and from the p electron is −0.184b. Sternheimer corrections are not included.

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Equations (14)

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Parameter	Value (cm⁻¹)
A	100 000
B	1000
C	4500
H	85
α	80
F₂	F₂′+130
G₁	G₁′+40
G₃	G₃′+30
G_ds	G_ds′
J	J′
K	K′+1000
ζ_d	ζ_d′
ζ_p	2ζ_p′−ζ_p″

Parameter	Value (cm⁻¹)
A′	51 353±70
A″	32 667±115
F₂′	318±4
G₁′	241±9
G₃′	47±4
G_sp′	8085±61
G_ds′	1104±57
J′	1439±100
K′	3611±78
ζ_d′	833±15
ζ_p′	326±40
ζ_p″	194±60

Configuration	Designation	J	obs.	calc.	O–C
3d¹⁰4p	²P	$\frac{1}{2}$	30535	30539	−4
		$\frac{3}{2}$	30784	30779	5
3d⁹4s4p	⁴P(³P)	$\frac{1}{2}$	40944	40959	−15
		$\frac{3}{2}$	40114	40149	−35
		$\frac{5}{2}$	39019	39092	−73
	⁴D(³P)	$\frac{1}{2}$	44916	44918	−2
		$\frac{3}{2}$	44544	44549	−5
		$\frac{5}{2}$	44406	44420	−14
		$\frac{7}{2}$	43514	43533	−19
	⁴F(³P)	$\frac{3}{2}$	42302	42282	20
		$\frac{5}{2}$	41563	41533	30
		$\frac{7}{2}$	41153	41105	48
		$\frac{9}{2}$	40909	40825	84
	²P(³P)	$\frac{1}{2}$	45821	45853	−32
		$\frac{3}{2}$	45879	45833	46
	²D(³P)	$\frac{3}{2}$	46173	46167	6
		$\frac{5}{2}$	46598	46634	−36
	²F(³P)	$\frac{5}{2}$	43726	43717	9
		$\frac{7}{2}$	44963	44973	−10
	²P(¹P)	$\frac{1}{2}$	58365	58272	93
		$\frac{3}{2}$	56344	56444	−100
	²D(¹P)	$\frac{3}{2}$	58691	58719	−28
		$\frac{5}{2}$	56651	56619	32
	²F(¹P)	$\frac{5}{2}$	58119	58133	−14
		$\frac{7}{2}$	56030	56018	12

Conf.	Desig.	J	⁴P	⁴D	⁴F	²P(³P)	²P(¹P)	²D(³P)	²D(¹P)	²F(³P)	²F(¹P)	d¹⁰p	d⁸s²p
3d¹⁰4p	²P	$\frac{1}{2}$				−0.059	−0.029					0.911	0.001
		$\frac{3}{2}$				0.056	0.034					−0.908	0.002
4s4p	⁴P(³P)	$\frac{1}{2}$	−0.98	−0.01		0.01
		$\frac{3}{2}$	0.96	0.01		−0.02
		$\frac{5}{2}$	−0.99	−0.01
	⁴D(³P)	$\frac{1}{2}$	−0.02	0.63		−0.32	0.01					−0.02
		$\frac{3}{2}$	0.01	−0.66	0.04	0.02		0.26
		$\frac{5}{2}$		−0.46	0.14			0.08		0.31
		$\frac{7}{2}$		0.88						0.12
	⁴F(³P)	$\frac{3}{2}$		0.02	0.95			−0.02
		$\frac{5}{2}$		−0.02	−0.82			0.01		0.15
		$\frac{7}{2}$		−0.02	−0.90					0.08
		$\frac{9}{2}$			1.00
	²P(³P)	$\frac{1}{2}$		0.36		0.59	−0.02					0.03
		$\frac{3}{2}$	0.02	−0.03		0.62	−0.03	−0.26				0.03
	²D(³P)	$\frac{3}{2}$		−0.27		−0.25	0.01	−0.45				−0.01
		$\frac{5}{2}$	−0.01	0.15				0.84
	²F(³P)	$\frac{5}{2}$		0.35	0.04			−0.06		0.54
		$\frac{7}{2}$		−0.10	0.10					0.80
	²P(¹P)	$\frac{1}{2}$				−0.02	−0.90					−0.04	0.04
		$\frac{3}{2}$				−0.03	−0.82		−0.06			−0.05	0.04
	²D(¹P)	$\frac{3}{2}$					−0.06		0.85				0.08
		$\frac{5}{2}$							−0.79		−0.13		0.08
	²F(¹P)	$\frac{5}{2}$							−0.12		0.83		0.05
		$\frac{7}{2}$									−0.96		0.04

(J, J)	B_JJ
⁴F_9/2	b_p′−b_d′
⁴F_7/2	$\frac{1}{75} {(- 41 b^{'} + 12 η b^{'} - 30 b^{″})}_{d} + \frac{2}{3} {b_{p}}^{'}$
⁴D_7/2	$- \frac{1}{75} {(46 b^{'} - 12 η b^{'} + 5 b^{″})}_{d} - \frac{1}{9} {(b^{'} + 8 η b^{'})}_{p}$
z²F_7/2	$- \frac{1}{75} {(23 b^{'} + 24 η b^{'} + 40 b^{″})}_{d} + \frac{1}{9} {(7 b^{'} + 2 η b^{'})}_{p}$
y²F_7/2	$- {b_{d}}^{'} + \frac{1}{3} {(b^{'} + 2 η b^{'})}_{p}$
⁴F_5/2	$- \frac{1}{15750} {(4097 b^{'} - 1824 η b^{'} + 7360 b^{″})}_{d} + \frac{1}{1890} {(667 b^{'} + 224 η b^{'})}_{p}$
⁴D_5/2	$\frac{1}{1575} {(- 541 b^{'} + 237 η b^{'} + \frac{65}{2} b^{″})}_{d} + \frac{1}{378} {(13 b^{'} - 148 η b^{'})}_{p}$
⁴P_5/2	$\frac{1}{125} {(- 63 b^{'} + 21 η b^{'} - \frac{5}{2} b^{″})}_{d} + \frac{1}{10} {(- 3 b^{'} + 4 η b^{'})}_{p}$
z²F_5/2	$\frac{1}{1575} {(- 841 b^{'} - 348 η b^{'} - 230 b^{″})}_{d} + \frac{2}{189} {(7 b^{'} + 74 η b^{'})}_{p}$
y²F_5/2	$- \frac{1}{525} {(23 b^{'} + 84 η b^{'} + 490 b^{″})}_{d} + \frac{2}{7} {(b^{'} + 2 η b^{'})}_{p}$
z²D_5/2	$- \frac{1}{225} {(26 b^{'} + 48 η b^{'} + 55 b^{″})}_{d} - \frac{1}{27} {(5 b^{'} + 22 η b^{'})}_{p}$
y²D_5/2	$\frac{1}{75} {(- 46 b^{'} + 12 η b^{'} - 5 b^{″})}_{d} - \frac{1}{3} {(b^{'} + 2 η b^{'})}_{p}$
⁴F_3/2	$- \frac{2}{1875} {(23 b^{'} + 84 η b^{'} + 490 b^{″})}_{d} + \frac{4}{225} {(- b^{'} + 28 η b^{'})}_{p}$
⁴D_3/2	$- \frac{2}{375} {(28 b^{'} - 21 η b^{'} - 10 b^{″})}_{d} + \frac{4}{45} {(b^{'} - η b^{'})}_{p}$
⁴P_3/2	$- \frac{2}{625} {(14 b^{'} - 63 η b^{'} - 55 b^{'})}_{d} + \frac{2}{225} {(- 23 b^{'} + 14 η b^{'})}_{p}$
z²D_3/2	$- \frac{1}{750} {(154 b^{'} + 42 η b^{'} + 95 b^{″})}_{d} - \frac{1}{90} {(25 b^{'} + 38 η b^{'})}_{p}$
y²D_3/2	$- \frac{1}{250} {(14 b^{'} + 42 η b^{'} + 45 b^{″})}_{d} - \frac{7}{30} {(b^{'} + 2 η b^{'})}_{p}$
z²P_3/2	$- \frac{1}{250} {(14 b^{'} + 42 η b^{'} + 45 b^{″})}_{d} + \frac{1}{90} {(- 17 b^{'} + 26 η b^{'})}_{p}$
y²P_3/2	$- \frac{1}{250} {(126 b^{'} - 42 η b^{'} + 5 b^{″})}_{d} + \frac{1}{30} {(b^{'} + 2 η b^{'})}_{p}$

State	A (exp) MHz	A (calc) MHz	B (exp) MHz	B (calc) MHz	Ref.
⁴F_9/2	1324	1307	138	138	a
⁴F_7/2	1140	1063	⋯	133	b
⁴D_7/2	1545	1525	⋯	160	b
²F_7/2	1920	1789	⋯	109	b
⁴F_5/2	450	497	⋯	115	b
⁴D_5/2	1200	1232	⋯	44	b
⁴P_5/2	2031	2020	79	79	a
z²F_5/2	750	832	⋯	98	b
z²D_5/2	2535	2257	⋯	141	b
⁴F_3/2	⋯	305	⋯	98
⁴D_3/2	small	124	⋯	−3	d
⁴P_3/2	2140	2166	−37.9	−38.7	c
z²D_3/2	⋯	1937	⋯	103
z²P_3/2	⋯	1619	⋯	27
⁴D_1/2	−510	−53			d
⁴P_1/2	2280	2613			d
z²P_1/2	⋯	948

Configuration	State	Q_p	Q_d
d¹⁰p	²P_3/2	−0.304^a
		−0.249^b
d⁹s²	²D_3/2		−0.181^c
d⁹s²	²D_5/2		−0.174^c
d⁹sp	⋯	−0.267^d	−0.184^d

Level	LS coupling	Intermediate coupling	Exp
⁴F_9/2	1.3341	1.3341	1.3340(2)
⁴F_7/2	1.2386	1.2348	1.25
⁴D_7/2	1.4295	1.395	1.45
z²F_7/2	1.1432	1.1813	1.21
⁴F_5/2	1.0286	1.0115	1.01
⁴D_5/2	1.3723	1.1506	1.38
⁴P_5/2	1.6014	1.5991	1.600(2)
z²F_5/2	0.8568	1.0647	0.92
z²D_5/2	1.2005	1.2302	1.20
⁴F_3/2	0.3990	0.4263	0.43
⁴D_3/2	1.2005	1.0722	1.18
⁴P_3/2	1.7350	1.7171	1.714(2)
			(1.75)
z²D_3/2	0.7995	1.0545	1.00
z²P_3/2	1.3341	1.1966	1.28
⁴D_1/2	−0.0023	0.2850	0.10
⁴P_1/2	2.6705	2.6238	2.63
z²P_1/2	0.6659	0.4296	0.48

Abstract

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Tables (9)

Equations (14)

Journal of the Optical Society of America