Radiative lifetimes, absolute transition probabilities, and oscillator strengths in Kr ii

Nissan Spector; Sten Garpman

doi:10.1364/JOSA.67.000155

Journal of the Optical Society of America
Vol. 67,
Issue 2,
pp. 155-161
(1977)
•https://doi.org/10.1364/JOSA.67.000155

Radiative lifetimes, absolute transition probabilities, and oscillator strengths in Kr ii

Nissan Spector and Sten Garpman

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Nissan Spector and Sten Garpman, "Radiative lifetimes, absolute transition probabilities, and oscillator strengths in Kr ii," J. Opt. Soc. Am. 67, 155-161 (1977)

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Abstract

Absolute transition probabilities and oscillator strengths for the 4p ⁴5p-4p ⁴5s transition array are calculated using the effective operator formalism for the radial integrals and intermediate coupling for the angular coefficients. Radiative lifetimes are obtained for the 21 4p ⁴5p levels that agree with recent observations better than previously calculated ones.

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Name	Diag. (cm⁻¹)	Least squares (cm⁻¹)
A	127 200	127 248 ± 139
F₂	1865	1867 ± 16
G₁	1200	1222 ± 79
α	−100	−121 ± 32
ζ₄_p	3850	3772 ± 170
rms error		173 (0.5%)

J	Percentage composition	Obs. design.	Observed level (cm⁻¹)	Calculated level (cm⁻¹)	O–C (cm⁻1)	g_obs	g_calc
$\frac{1}{2}$	97% ⁴P	⁴P	117 603	117 625	−22	2.64	2.63
$1 \frac{1}{2}$	56% ⁴P + 40% ²P	⁴P	115 092	115 098	−6	1.54	1.54
$2 \frac{1}{2}$	97% ⁴P	⁴P	112 828	112 845	−17	1.60	1.59
$\frac{1}{2}$	97% ²P	²P	121 002	121 037	−35	0.70	0.71
$1 \frac{1}{2}$	56% ²P + 42% ⁴P	²P	118 474	118 389	85	1.52	1.49
$1 \frac{1}{2}$	96% ²D	²D′	127 597	127 800	−203	0.80	0.83
$2 \frac{1}{2}$	97% ²D	²D′	127 861	127 663	198	1.20	1.21
$\frac{1}{2}$	97% ²S″	²S″	145 812	145 811	1	2.00	1.99

$J = \frac{1}{2}$	²S″	²P	⁴P
145 812	0.9777	0.1322	0.1634
121 002	−0.1483	0.9847	0.0911
117 603	−0.1439	−0.1133	0.9823
$J = 1 \frac{1}{2}$	²P	⁴P	²D′

118 474	0.7470	0.6524	−0.1279
115 092	−0.6257	0.7550	0.1965
127 597	0.2247	−0.0667	0.9721
$J = 2 \frac{1}{2}$	⁴P	2D′

112 828	−0.9827	−0.1854
127 861	0.1854	−0.9827

Name	Diag. (cm⁻¹)	Least squares (cm⁻¹)
A	147 300	147 300 ± 42
F₂	1917	1917 ± 5
$F_{2}^{'}$	354	354 ± 7
G₀	1580	1580 ± 28
G₂	85	85 ± 8
α	−17	−17 ± 10
ζ₄_p	3907	3907 ± 48
ζ₅_p	501	501 ± 37
rms error		78(0.4%)

J	Percentage composition	Obs. design.	Observed levels (cm⁻¹)	Calculated level (cm⁻¹)	O–C (cm⁻¹)	g_obs	g_calc
$\frac{1}{2}$	60% ⁴P	⁴P	135 781	135 873	−92	1.98	2.01
	32% ²P + 20% ²S + 37% ⁴P	²P	139 101	139 146	−45	1.78	1.69
	96% ⁴D	⁴D	140 161	140 056	105	0.00	0.08
	64% ²S + 30% ²P	²S	142 361	142 493	−131	1.50	1.53
	80% ²P′	²P′	152 239	152 206	33	0.70	1.68
	96% ²P″	²P″	168 261	168 366	−105	1.24	0.67
$1 \frac{1}{2}$	72% ⁴P	⁴P	134 286	134 267	19	1.67	1.66
	32% ²P + 25% ²D + 22% ⁴D	⁴D	138 379	138 319	60	1.26	1.26
	64% ⁴D + 30% ²P	²P	140 135	140 064	71	1.26	1.25
	52% ⁴S + 37% ²D	⁴S	141 721	141 745	−24	1.54	1.50
	36% ²D + 23% ⁴S + 18% ²P	²D	141 994	142 001	−7	1.33	1.34
	86% ²P′	²P′	150 201	150 239	−38	1.33	1.35
	96% ²D′	²D′	152 190	152 133	57	0.80	0.83
	96% ²P″	²P″	168 937	168 833	104	0.90	1.33
$2 \frac{1}{2}$	81% ⁴P	⁴P	133 923	133 922	1	1.58	1.55
	69% ²D	⁴D	136 069	136 057	12	1.23	1.24
	59% ⁴D + 29% ²D	²D	140 117	140 113	4	1.34	1.35
	96% ²F′	²F′	149 171	149 147	24	0.86	0.88
	97% ²D′	²D′	152 314	152 336	−22	1.20	1.20
$3 \frac{1}{2}$	97% ⁴D	⁴D	135 781	135 763	18	1.43	1.42
	97% ²F′	²F′	149 703	149 741	−38	1.14	1.15

Observed level (cm⁻¹)	J	Obs. desig.	²S	⁴S	²P″	²P	²P′	⁴P	²D	²D′	⁴D	²F′
139 101	$\frac{1}{2}$	²P	0.4572		−0.0343	0.5689	−0.3024	0.6103			0.0471
168 261		²P″	0.0823		−0.9710	−0.1369	0.0732	0.0592			−0.1507
142 361		²S	−0.8066		−0.1478	0.5390	−0.1820	0.0081			−0.0626
152 239		²P′	0.0924		0.0101	0.4425	0.8910	−0.0397			0.0002
135 781		⁴P	0.3538		−0.0697	0.4100	−0.2740	−0.7739			−0.1672
140 161		⁴D	−0.0005		−0.1706	0.0564	−0.0331	−0.1531			0.9712
141 994	$1 \frac{1}{2}$	²D		−0.4764	0.1498	0.4328	−0.2206	0.3462	−0.5945	−0.0550	−0.1956
168 937		²P″		−0.0812	−0.9744	0.0231	0.1029	0.0948	−0.1110	−0.0024	−0.1077
138 379		⁴D		0.3265	0.0043	0.5714	−0.0416	0.2801	0.5001	−0.1314	−0.4683
150 201		²P′		0.1873	−0.1124	−0.2399	−0.9301	0.0791	0.0363	0.1443	−0.0350
134 286		⁴P		−0.3015	−0.0511	0.2483	−0.1925	−0.8454	0.0881	−0.1016	−0.2738
141 721		⁴S		0.7247	0.0096	0.1291	0.0670	−0.2523	−0.6087	−0.0279	−0.1362
152 190		²D′		0.0166	−0.0122	−0.1972	−0.0938	0.0535	−0.0234	−0.9721	0.0589
140 135		²P		0.0914	−0.1125	0.5576	−0.1535	−0.0718	0.0626	−0.0525	0.7954
133 923	$2 \frac{1}{2}$	⁴P						0.9032	−0.0053	0.1485	0.4006	0.0396
136 069		⁴D						0.2213	0.8191	0.0458	−0.4843	−0.2085
152 314		²D′						−0.1257	−0.0913	0.9785	−0.0691	−0.1169
140 117		²D						0.3452	−0.5355	−0.0558	−0.7680	0.0339
149 171		²F′						0.0166	−0.1841	−0.1237	0.1020	−0.9696
135 781	$3 \frac{1}{2}$	⁴D									−0.9794	−0.2019
149 703		²F′									0.2019	−0.9794

Name	Diag.	Least squares
A	136 000	135 837 ± 258
F₂	1877	1892 ± 33
$F_{2}^{'}$	760	760 ± 21
G₁	1177	1151 ± 27
G₃	61	61 ± 4
α	240	246 ± 134
ζ₄_p	3950	3887 ± 229
ζ₄_d	183	145 ± 109
		347(0.8%)

J	Percentage composition	Obs. desig.	Observed level (cm⁻¹)	Calculated level (cm⁻¹)	O–C (cm⁻¹)	g_obs	g_calc
$\frac{9}{2}$	96% ⁴F	⁴F	126 001	126 015	−14		1.32
$\frac{7}{2}$	77% ⁴F	⁴F	127 930	127 864	66		1.21
$\frac{5}{2}$	92% ⁴F	⁴F	129 697	129 561	136		1.04
$\frac{3}{2}$	96% ⁴F	⁴F	130 513	130 352	161		0.42
$\frac{7}{2}$	94% ⁴D	⁴D	120 210	120 372	−162		1.42
$\frac{5}{2}$	90% ⁴D	⁴D	120 427	120 519	−92		1.36
$\frac{3}{2}$	90% ⁴D	⁴D	121 000	121 078	−78		1.20
$\frac{1}{2}$	94% ⁴D	⁴D	121 780	121 776	4	0.0
$\frac{5}{2}$	77% ⁴P	²F	132 970	132 873	97		1.48
$\frac{3}{2}$	82% ⁴P	²P	131 375	131 124	251		1.60
$\frac{1}{2}$	88% ⁴P	⁴P	129 515	129 903	−388		2.47
$\frac{7}{2}$	72% ²F	²F	131 632	132 031	−399		1.15
$\frac{5}{2}$	49% ²F	²P	134 567	134 543	24		1.10
$\frac{5}{2}$	35% ²D + 37% ²F	²D	137 098	136 825	273		1.06
$\frac{3}{2}$	42% ²D + 28% ²D′	⁴P	132 965	132 659	306		0.94
$\frac{3}{2}$	42% ²P + 35% ²P′	²D	134 621	134 890	−269		1.30
$\frac{1}{2}$	53% ²P + 37% ²P′	²P	130 893	130 669	224		0.76
$\frac{9}{2}$	96% ²G′			139 662			1.12
$\frac{7}{2}$	90% ²G′			139 542			0.91
$\frac{7}{2}$	95% ²F′			147 277			1.14
$\frac{5}{2}$	86% ²F′			146 220			0.90
$\frac{5}{2}$	49% ²D′ + 36% ²D	²D	149 514	149 801	−287		1.17
$\frac{3}{2}$	61% ²D′ + 36% ²D	²P	151 826	152 539	−713		0.81
$\frac{3}{2}$	52% ²P′ + 42% ²P	²D	150 178	149 595	583		1.30
$\frac{1}{2}$	56% ²P′ + 44% ²P	²P	152 185	151 874	311		0.68
$\frac{1}{2}$	93% ²S	²S	(160 794)	140 644		2.07	2.01
$\frac{5}{2}$	88% ²D″	²D″	161 011	160 932	79	2.47	1.20
$\frac{3}{2}$	85% ²D″	²D″	161 407	161 513	−106		0.82

λ (Å)	Observed intensity	Classification (this work)		Absolute A (×10⁶ s⁻¹)	Observed (×10⁶ s⁻¹)	KT (Ref. 8)	gf value
λ (Å)	Observed intensity	5s	5p	Absolute A (×10⁶ s⁻¹)	Observed (×10⁶ s⁻¹)	KT (Ref. 8)	gf value
6470.89	50	²P_3/2	⁴P_5/2	0.6			0.01
5208.32	500	⁴P_3/2	⁴P_3/2	17.3	33	14.86	0.07
5022.40	200	²P_3/2	²P_3/2	8.2		30.95	0.03
4846.60	700	²P_3/2	²S_1/2	105.3	175		0.19
4832.07	800	⁴P_3/2	⁴P_1/2	112.7	146	106.05	0.20
4825.18	300	²P_1/2	²D_3/2	38.8	50	7.28	0.27
4811.76	300	⁴P_1/2	²P_3/2	16.6	46	41.17	0.11
4765.74	1000	⁴P_3/2	²D_5/2	113.8	121	68.27	0.58
4762.43	300	²P_1/2	⁴S_3/2	76.6	78	105.87	0.52
4739.00	3000	⁴P_5/2	⁴P_5/2	124.4	150	122.90	0.42
4691.28	100	²D_5/2	${{}^{2}F}_{5 / 2}^{'}$	18.7			0.06
4680.41	500	²P_1/2	²P_1/2	109.4	166	115.01	0.36
4658.87	2000	⁴P_5/2	⁴P_3/2	101.2	112	92.73	0.22
4650.17	30	⁴P_1/2	²S_1/2	6.5			0.02
4633.88	800	${{}^{2}D}_{3 / 2}^{'}$	${{}^{2}F}_{5 / 2}^{'}$	117.3	124		0.56
4619.15	1000	²P_3/2	⁴D_5/2	123.9	147	77.08	0.60
4615.28	500	²P_3/2	⁴D_3/2	73.2	87	78.98	0.23
4609.72	20	²P_3/2	⁴D_1/2	5.3		34.71	0.04
4577.20	800	${{}^{2}D}_{5 / 2}^{'}$	${{}^{2}F}_{7 / 2}^{'}$	141.5	154		0.60
4575.00	800	${{}^{2}D}_{5 / 2}^{'}$	${{}^{2}P}_{3 / 2}^{'}$	110.0	112		0.22
4453.21	50	²S_1/2	²P_1/2	153.3			0.45
4436.81	600	⁴P_1/2	⁴D_3/2	60.3		24.04	0.36
4431.67	500	⁴P_1/2	⁴D_1/2	141.9	114	97.63	0.42
4422.70	100	${{}^{2}D}_{3 / 2}^{'}$	${{}^{2}P}_{3 / 2}^{'}$	22.6	117		0.06
4355.47	3000	⁴P_5/2	⁴D_7/2	164.2	100	164.20	0.62
4322.98	150	${{}^{2}S}_{1 / 2}^{″}$	${{}^{2}P}_{3 / 2}^{″}$	166.0	950		0.93
4301.53	40	⁴P_5/2	²D_5/2	1.1		4.59	0.003
4300.49	200	²P_3/2	²D_3/2	40.9	35	0.26	0.11
4292.92	600	⁴P_3/2	²P_3/2	109.7	67	48.93	0.30
4250.58	150	²P_3/2	⁴S_3/2	13.9	51	0.79	0.04
4185.12	50	²P_3/2	²P_1/2	11.4		14.90	0.02
4145.12	250	⁴P_1/2	²D_3/2	35.5	38	69.82	0.18
4109.23	100	${{}^{2}D}_{5 / 2}^{'}$	${{}^{2}D}_{3 / 2}^{'}$	31.6			0.05
4098.72	250	⁴P_1/2	⁴S_3/2	44.5	183	17.27	0.22
4088.33	500	${{}^{2}D}_{5 / 2}^{'}$	${{}^{2}D}_{5 / 2}^{'}$	170.4	84		0.43
4065.11	300	${{}^{2}D}_{3 / 2}^{'}$	${{}^{2}D}_{3 / 2}^{'}$	169.0	63		0.40
4057.01	300	${{}^{2}D}_{3 / 2}^{'}$	${{}^{2}P}_{1 / 2}^{'}$	180.1	78		0.22

Designation this work	Observed level (cm⁻¹)	Observed designation	Lifetimes (in ns)		O–C	MRT (Ref. 11)		KT (Ref. 8)		ES (Ref. 8)		MRB (Ref. 2)
Designation this work	Observed level (cm⁻¹)	Observed designation	Calculated this work	DKB(O)	O–C	C	O–C	C	O–C	C	O–C	O	O–C
²S_1/2	139 101	²P_1/2	8.6	9.11	0.5	11.0	−1.9	8.5	0.6
⁴S_3/2	141 721	⁴S_3/2	5.3	8.31	3.0	6.1	2.2	4.1	4.2	5.4	2.9	7.1	+1.8
²P_1/2	142 361	²S_1/2	7.4	9.41	2.0	8.5	0.9	7.4	2.0
²P_3/2	138 379	⁴D_3/2	6.4	8.42	2.0	7.9	0.5	7.3	1.1	7.2	1.2	7.7	1.3
⁴P_1/2	135 781	⁴P_1/2	8.6	8.89	0.3	9.2	−0.3	8.7	0.2
⁴P_3/2	134 286	⁴P_3/2	8.2	8.83	0.6	8.6	0.2	8.6	0.2			7.8	−0.4
⁴P_5/2	133 923	⁴P_5/2	7.9	8.21	0.3	8.4	−0.2	7.9	0.3	8.5	−0.3	5.2	−2.7
²D_3/2	141 994	²D_3/2	6.6	8.69	2.1	7.1	1.6	7.8	0.9			4.8	−1.8
²D_5/2	136 069	⁴D_5/2	8.2	10.18	2.0	8.8	1.4	9.6	0.6	10.2	0.0	7.2	−1.0
⁴D_1/2	140 161	⁴D_1/2	6.4	8.12	1.7	7.2	0.9	6.3	1.8
⁴D_3/2	140 135	²P_3/2	7.0	8.49	1.5	8.6	−0.1	6.3	2.2	9.4	−0.9
⁴D_5/2	140 117	²D_5/2	6.8	8.22	1.4	9.6	−1.4	5.7	2.5	7.3	0.9	5.9	−0.9
⁴D_7/2	135 781	⁴D_7/2	6.1	7.70	1.6	6.8	0.9	6.1	1.6			8.7	2.6
${{}^{2}P}_{1 / 2}^{'}$	152 239	${{}^{2}P}_{1 / 2}^{'}$	4.4	5.95	1.6	3.9	2.1	3.7	3.3			11.0	6.6
${{}^{2}P}_{3 / 2}^{'}$	150 201	${{}^{2}P}_{3 / 2}^{'}$	5.4	6.28	0.9	7.5	−1.2	5.1	1.2			7.7	2.3
${{}^{2}D}_{3 / 2}^{'}$	152 190	${{}^{2}D}_{3 / 2}^{'}$	4.9	7.69	2.8	4.9	2.8	4.6	3.1
${{}^{2}D}_{5 / 2}^{'}$	152 314	${{}^{2}D}_{5 / 2}^{'}$	5.0	7.80	2.8	5.6	2.2	4.7	3.1			10.0	5.0
${{}^{2}F}_{5 / 2}^{'}$	149 171	${{}^{2}F}_{5 / 2}^{'}$	7.3	8.89	1.6	6.9	2.0	6.7	2.2	10.0	−1.1	7.0	−0.3
${{}^{2}F}_{7 / 2}^{'}$	149 703	${{}^{2}F}_{7 / 2}^{'}$	7.1	8.35	1.3	8.5	−0.1	6.3	2.1	9.7	−1.4	6.5	−0.6
${{}^{2}P}_{1 / 2}^{″}$	168 261	${{}^{2}P}_{1 / 2}^{″}$	6.2
${{}^{2}P}_{3^{'} / 2}^{″}$	168 937	${{}^{2}P}_{3 / 2}^{″}$	5.6									0.9	−4.7

Abstract

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Tables (10)

Equations (10)

Journal of the Optical Society of America