Relative Line Strengths of the Forbidden 2s22p2P–2s2p2 4P Transitions in the B i Isoelectronic Sequence

J. E. Hansen

doi:10.1364/JOSA.59.000722

Journal of the Optical Society of America
Vol. 59,
Issue 6,
pp. 722-726
(1969)
•https://doi.org/10.1364/JOSA.59.000722

Relative Line Strengths of the Forbidden 2s²2p ²P–2s2p^{2 4}P Transitions in the B i Isoelectronic Sequence

J. E. Hansen

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J. E. Hansen, "Relative Line Strengths of the Forbidden 2s²2p²P–2s2p^{2 4}P Transitions in the B i Isoelectronic Sequence," J. Opt. Soc. Am. 59, 722-726 (1969)

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Abstract

The relative transition probabilities in the forbidden multiplet 2s²2p ²P–2s2p^{2 4}P have been computed for the C ii, N iii, O iv, F v, Na vii, Mg viii, Al ix, Si x, and P xi ions.

The diagonalization of the 2s2p² energy matrix does not give energies which agree with the observed values unless the electrostatic interaction with the 2s²3d configuration is included in the calculations. The influence of the 2s2p²–2s²3d interaction on the transition probabilities turns out to be small. The calculated intensities have been compared with the observations for O iv. The agreement is reasonable.

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Obs. energy levels^a		Calculation A^b		Garstang’s calculation^c		Calculation B^d
Obs. energy levels^a		Levels	Residuals	Levels	Residuals	Levels	Residuals
$2 s 2 p^{2} {{}^{4}P}_{\frac{1}{2}}$	162 060	161 608	452	162 060	0	162 040	20
${{}^{4}P}_{\frac{3}{2}}$	164 500	163 736	764	164 450	50	164 433	67
${{}^{4}P}_{\frac{5}{2}}$	168 090	167 082	1008	168 180	−90	168 169	−79
${{}^{2}D}_{\frac{3}{2}}$	287 830	290 587	−2757	287 750	80	287 770	60
${{}^{2}D}_{\frac{5}{2}}$	287 830	290 711	−2881	287 910	−80	287 926	−96
${{}^{2}S}_{\frac{1}{2}}$	367 650	365 264	2386	367 590	60	367 616	34
${{}^{2}P}_{\frac{1}{2}}$	389 740	389 513	227	389 890	−150	389 866	−126
${{}^{2}P}_{\frac{3}{2}}$	394 000	393 199	801	393 900	100	393 880	120
$2 s^{2} 3 d {{}^{2}D}_{\frac{3}{2}}$	1 979 260					(1 979 260)
${{}^{2}D}_{\frac{5}{2}}$	1 979 730					(1 979 730)

Obs. energy levels^a		Calculation A^b		Calculation B^c
Obs. energy levels^a		Levels	Residuals	Levels	Residuals
$2 s 2 p^{2} {{}^{4}P}_{\frac{1}{2}}$	71 439.9	70 841.1	598.8	71 442.0	−2.1
${{}^{4}P}_{\frac{3}{2}}$	71 570.3	70 920.1	650.2	71 561.4	8.9
${{}^{4}P}_{\frac{5}{2}}$	71 755.7	71 051.2	704.5	71 759.0	−3.3
${{}^{2}D}_{\frac{3}{2}}$	126 950.4	129 382.5	−2432.1	126 942.6	7.8
${{}^{2}D}_{\frac{5}{2}}$	126 936.4	129 382.9	−2446.5	126 943.7	−7.3
${{}^{2}S}_{\frac{1}{2}}$	164 366.5	162 412.1	1954.4	164 372.2	−5.7
${{}^{2}P}_{\frac{1}{2}}$	180 480.8	180 038.7	442.1	180 483.8	−3.0
${{}^{2}P}_{\frac{3}{2}}$	180 724.1	180 195.4	528.7	180 719.4	4.7
$2 s^{2} 3 d {{}^{2}D}_{\frac{3}{2}}$	419 533.5			(419 533.5)
${{}^{2}D}_{\frac{5}{2}}$	419 550.2			(419 550.2)

Parameter	ION
Parameter	C ii	N iii	O iv	F v	Na vii	Mg viii	Al ix	Si x	P xi
F₀	98 416	131 113	163 107	195 006	259 249	291 961	325 176	359 072	393 539
F₂	2060	2943	3 760	4547	6134	6893	7660	8447	9267
G₁	22 537	29 556	36 333	42 920	56 125	62 523	68 927	75 430	81 880
ζ_p	41	109	237.5	465	1342	2137	3153	4556	6441
R¹	−39 047	−65 107	−88 222	−111 916	−156 002	−182 567	−208 173	−231 939	−238 128
E	142 544	263 769	415 953	598 755	1 056 840	1 331 924	1 638 092	1 975 292	2 344 136
Δ	9	10	8	15	35	37	63	118	213

		$2 s 2 p^{2} {{}^{2}D}_{\frac{5}{2}}$ ^b	$2 s^{2} 3 d {{}^{2}D}_{\frac{5}{2}}$	$2 s 2 p^{2} {{}^{4}P}_{\frac{5}{2}}$
C ii	$2 s 2 p^{2} {{}^{2}D}_{\frac{5}{2}}$ ^a	0.97848	−0.20634	0.00089
	$2 s^{2} 3 d {{}^{2}D}_{\frac{5}{2}}$	0.20634	0.97848	0.00006
	$2 s 2 p^{2} {{}^{4}P}_{\frac{5}{2}}$	−0.00088	0.00013	0.99999

Na vii	$2 s 2 p^{2} {{}^{2}D}_{\frac{5}{2}}$	0.99771	−0.06675	0.01070
	$2 s^{2} 3 d {{}^{2}D}_{\frac{5}{2}}$	0.06675	0.99777	0.00007
	$2 s 2 p^{2} {{}^{4}P}_{\frac{5}{2}}$	−0.01068	0.00065	0.99994

P xi	$2 s 2 p^{2} {{}^{2}D}_{\frac{5}{2}}$	0.99848	−0.04283	0.03480
	$2 s^{2} 3 d {{}^{2}D}_{\frac{5}{2}}$	0.04285	0.99908	0.00009
	$2 s 2 p^{2} {{}^{4}P}_{\frac{5}{2}}$	−0.03477	0.00140	0.99939

Transition		Garstang^a Unit 2×10⁻⁶	Kastner^b Unit 2×10⁻⁶	Calculation A Arbitrary units	Calculation B Arbitrary units
⁴P J	²P J	Garstang^a Unit 2×10⁻⁶	Kastner^b Unit 2×10⁻⁶	Calculation A Arbitrary units	Calculation B Arbitrary units
$\frac{1}{2}$	$\frac{1}{2}$	14.5	12	13.9	15.2
$\frac{1}{2}$	$\frac{3}{2}$	7	6	6.9	7.4
$\frac{3}{2}$	$\frac{1}{2}$	1	20.5	1	1
$\frac{3}{2}$	$\frac{3}{2}$	15	1	13.5	14.7
$\frac{5}{2}$	$\frac{3}{2}$	65	135	57.4	61.0

Transition		Observations		Theory Relative gf value
⁴P J	²P J	Bromander^a	Burton et al.^b	Theory Relative gf value
$\frac{1}{2}$	$\frac{1}{2}$	5	20	14.7
$\frac{1}{2}$	$\frac{3}{2}$	5	20	8.8
$\frac{3}{2}$	$\frac{1}{2}$	3 blend	⋯	1.
$\frac{3}{2}$	$\frac{3}{2}$	4	40	14.9
$\frac{5}{2}$	$\frac{3}{2}$	7	60	56.3

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Journal of the Optical Society of America