S. H. Koozekanani and G. L. Trusty, "Lifetime and Transition Probabilities of np4(n+1)p States of Ne ii, Ar ii, and Kr ii*," J. Opt. Soc. Am. 59, 1281-1284 (1969)
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Radial integrals for ionized Ne, Ar, and Kr as found by fitting and calculated by computer using Hartree–Fock wave-functions.6 The experimental value of F2(pcore−pcore) was found from the relation 6F2(pcore−pcore) = (1D) − (3P). For Ne, the iteratively found ζ′p−ex converges to a negative number, even when the starting conditions are changed. However, the effect of ζ′p−ex on the wavefunction is negligible even if the sign is reversed.
Ne
Ar
Kr
Calculate cm−1
Fitting cm−1
Calculate cm−1
Fitting cm−1
Calculate cm−1
Fitting cm−1
F2(pcore−pex)
422
433
424
365
415
397
G0(pcore−pex)
4166
2452
2614
1752
2176
1802
G2(pcore−pex)
160
167
122.5
86
111
171
ζpcore
1104
790
1198
1075
2593
2929
ζp−ex2
63
−33
107
187
251
570
[3P]
⋯
252 853
⋯
159 918
⋯
140 669
[1D]
⋯
278 205
⋯
173 491
⋯
152 937
F2(pcore−pcore)
4757
4225
2827
2262
2488
2044
Table II
Experimental and theoretical energy levels of Ne ii taken from Moore,a tables of atomic energy levels and this calculation. The mixing coefficients aij are those given in Eq. (1).
Ne ii states
Eexp cm−1
Etheor cm−1
4D
4P
4S
2D
2P
2S
2P′
2D′
2F′
4D7/2
249 110.8
248 652.5
0.99976
0.21956
2F7/2′
274 411.3
274 228.2
0.21956
−0.99976
4P5/2
246 194.8
246 314.4
0.10198
0.99415
0.03104
0.01720
0.00042
4D5/2
249 448.0
249 217.8
0.98594
−0.09696
−0.13543
0.00271
0.01307
2D5/2
251 013.3
251 158.4
−0.13166
0.04497
−0.98950
−0.03385
0.01966
2F5/2′
274 366.9
274 229.0
0.01038
0.00010
−0.02106
−0.00511
−0.99971
2D5/2′
277 346.1
277 407.1
−0.00883
−0.01525
−0.03379
0.99926
−0.00449
4P3/2
247 417.4
246 617.2
0.09174
0.99253
0.06423
0.00625
−0.04273
0.02033
0.00773
4D3/2
249 697.7
249 553.3
−0.99010
0.09102
0.01201
0.09658
0.04061
−0.00908
−0.00448
2D3/2
251 524.7
251 713.3
0.10309
−0.00654
0.01349
0.97118
0.20859
−0.04265
0.02494
2P3/2
254 167.0
253 922.7
0.02353
0.05218
−0.11802
−0.21197
0.94040
−0.23011
−0.02373
4S3/2
252 956.0
253 072.9
−0.00743
0.05933
−0.99058
0.04020
−0.11599
0.00933
0.00375
2P3/2′
276 278.6
276 396.3
−0.00025
−0.00729
−0.01897
−0.00409
0.23087
0.96654
−0.10978
2D3/2′
277 327.6
277 411.8
0.00721
0.00697
0.00196
0.02967
−0.04370
−0.10217
−0.99331
4P1/2
246 599.9
246 861.7
0.05282
0.99729
−0.02210
−0.04454
−0.01249
4D1/2
249 841.8
249 749.7
0.99720
−0.05422
−0.04947
−0.00301
0.01401
2P1/2
254 294.0
254 197.1
0.04669
0.00333
0.89586
−0.37847
−0.22804
2S1/2
252 800.8
252 885.9
0.02493
0.04932
0.36197
0.92444
−0.10641
2P1/2′
276 514.1
276 598.9
0.00137
0.00587
−0.25193
−0.01308
−0.96764
C. E. Moore, Atomic Energy Levels, Natl. Bur. Std. (U.S.) Circ., (U. S. Gov’t. Printing Office, Washington, D. C., 1949).
Table III
Experimental and theoretical energy levels of Ar ii taken from Minnhagen7 and from this calculation. The mixing coefficients of aij are those given in Eq. (1).
Ar ii states
Eexp cm−1
Etheor cm−1
4D
4P
4S
2D
2P
2S
2P′
2D′
2F′
4D7/2
157 233.93
157 176.6
0.99839
0.05680
2F7/2′
170 530.31
170 582.7
0.05680
−0.99839
4P5/2
155 043.07
155 128.2
0.18291
0.98206
0.02312
0.03949
0.00299
4D5/2
157 673.32
157 556.9
0.86726
−0.15036
−0.47202
−0.00525
0.04919
2D5/2
158 730.21
158 710.3
−0.46181
0.10820
−0.87867
−0.04014
0.03689
2F5/2′
170 400.94
170 364.6
−0.02553
0.00160
0.05688
−0.03043
0.99759
2D5/2′
173 393.38
173 432.7
0.02203
0.03525
0.03701
−0.99794
−0.03204
4P3/2
155 351.03
155 383.5
0.16724
0.96996
0.11854
−0.91561
−0.11366
0.05959
0.02102
4D3/2
158 167.71
158 007.6
0.91426
−0.18070
−0.04193
−0.31306
−0.17205
0.04422
0.01261
2D3/2
159 393.31
159 244.3
0.36791
0.00919
0.00421
0.80472
0.44766
−0.12847
0.00763
2P3/2
160 239.35
160 354.7
0.01598
0.09361
0.06872
−0.50253
0.81016
−0.27314
−0.05244
4S3/2
161 048.64
161 012.7
0.01607
−0.13135
0.98834
0.01899
−0.03572
0.06355
0.00052
2P3/2′
172 213.80
172 213.8
−0.00095
0.01493
0.05133
0.02018
−0.30918
−0.94747
0.05873
2D3/2′
173 347.83
173 349.9
0.01702
0.01413
0.00192
0.02951
−0.06202
−0.04059
−0.99657
4P1/2
155 708.02
155 781.9
0.09789
0.99105
−0.06195
−0.05442
0.03795
4D1/2
158 428.03
158 331.0
−0.98840
0.10630
0.09918
0.01678
−0.04050
2P1/2
159 706.46
159 869.7
−0.11005
−0.07824
−0.80018
−0.49034
0.31788
2S1/2
161 089.31
161 306.5
−0.03676
0.01627
−0.46980
0.86912
0.14933
2P1/2′
172 816.21
172 726.4
−0.00350
−0.01162
0.35401
0.03085
0.93465
Table IV
Experimental and theoretical energy levels of Kr ii taken from Moore,a tables of atomic energy levels and this calculation. The mixing coefficients aij are those given in Eq. (1).
Eexp cm−1
Etheor cm−1
4D
4P
4S
2D
2P
2S
2P′
2D′
2F′
4D7/2
135 783.18
136 046.4
0.98818
0.15329
2F7/2′
149 704.55
149 720.5
0.15329
−0.98818
4P5/2
133 925.65
133 855.3
0.35157
0.92956
−0.00191
0.10898
0.02069
4D5/2
136 071.00
136 913.7
0.69899
−0.26376
−0.64380
−0.04663
0.15873
2D5/2
140 118.99
139 794.1
−0.61630
0.24015
−0.73946
−0.08975
0.08744
2F5/2′
149 173.42
149 096.5
−0.06087
0.00875
0.17647
−0.05814
0.98066
2D5/2′
154 316.20
152 377.9
0.06542
0.09275
0.08704
−0.98717
−0.07092
4P3/2
134 288.44
134 032.7
0.29227
0.86841
0.24557
−0.06918
−0.25507
0.15819
0.07257
4D3/2
138 381.35
138 171.7
0.70387
−0.33387
−0.23513
−0.42128
−0.39352
0.05687
−0.04741
2D3/2
141 995.68
142 424.3
0.15404
−0.21173
0.13765
0.80116
−0.43082
0.25429
0.14271
2P3/2
140 137.15
140 117.4
0.62449
0.04557
0.03686
0.32338
0.67428
−0.21368
−0.04111
4S3/2
141 722.72
141 508.3
0.05458
−0.29324
0.91550
−0.23728
0.06388
0.10487
−0.03901
2P3/2′
150 203.48
150 519.5
−0.00713
0.02327
0.16055
0.07215
−0.32003
−0.91809
0.15208
2D3/2′
152 191.86
152 172.6
0.04903
0.03093
0.01389
0.09900
−0.18255
−0.08685
−0.97251
4P1/2
135 783.03
135 638.4
0.20533
0.92476
−0.20833
−0.19012
0.15203
4D1/2
140 163.25
139 549.3
−0.85103
0.01265
−0.28601
−0.40360
0.17577
2P1/2
139 103.36
139 042.2
−0.47019
0.37937
0.56136
0.46584
−0.32072
2S1/2
142 363.55
142 592.5
−0.11170
0.000795
−0.59032
0.76087
0.24507
2P1/2′
152 240.97
152 094.4
−0.00571
−0.02610
0.45955
0.07095
0.88491
C. E. Moore, Atomic Energy Levels, Natl. Bur. Std. (U. S.) Circ, (U. S. Gov’t. Printing Office, Washington, D. C., 1949).
Table V
Transition probabilities between 3p–3s levels of Ne ii, 4p–4s levels of Ar ii, and 5p–5s levels of Kr ii, each with ap4 [3P] core. A in sec−1. In this table for the purposes of comparison we have reproduced the results of Statz et al.3 and Garstang4 for the case of Ar ii and the experimental intensities I.
Lifetimes of some of the 3p states of Ne ii, 4p states of Ar ii, and 5p states of Kr ii (in nsec).
Ne ii
Ar ii
Kr ii
4D7/2
5.0579
6.8457
6.0841
4D5/2
5.1276
7.7325
9.5710
2D5/2
6.9104
8.5926
5.7454
4P5/2
6.9598
8.9995
7.8594
4D3/2
5.1102
7.3537
7.2848
2D3/2
6.8593
8.6801
7.8240
4P3/2
6.9615
9.4748
8.6004
2P3/2
5.3463
9.0649
6.2623
4S3/2
3.6508
4.6504
4.1172
4D1/2
5.0853
6.9650
6.3331
4P1/2
6.9967
9.5673
8.7047
2S1/2
5.8307
7.8869
7.3880
2P1/2
5.5149
9.2892
8.5162
2F7/2′
6.1745
8.0360
6.3348
2F5/2′
6.2084
7.9657
6.7005
2D5/2′
4.5647
5.5537
4.6621
2D3/2′
4.5505
5.4526
4.5695
2P3/2′
4.1451
5.3876
5.0771
2P1/2′
3.9419
4.7836
3.7494
Tables (6)
Table I
Radial integrals for ionized Ne, Ar, and Kr as found by fitting and calculated by computer using Hartree–Fock wave-functions.6 The experimental value of F2(pcore−pcore) was found from the relation 6F2(pcore−pcore) = (1D) − (3P). For Ne, the iteratively found ζ′p−ex converges to a negative number, even when the starting conditions are changed. However, the effect of ζ′p−ex on the wavefunction is negligible even if the sign is reversed.
Ne
Ar
Kr
Calculate cm−1
Fitting cm−1
Calculate cm−1
Fitting cm−1
Calculate cm−1
Fitting cm−1
F2(pcore−pex)
422
433
424
365
415
397
G0(pcore−pex)
4166
2452
2614
1752
2176
1802
G2(pcore−pex)
160
167
122.5
86
111
171
ζpcore
1104
790
1198
1075
2593
2929
ζp−ex2
63
−33
107
187
251
570
[3P]
⋯
252 853
⋯
159 918
⋯
140 669
[1D]
⋯
278 205
⋯
173 491
⋯
152 937
F2(pcore−pcore)
4757
4225
2827
2262
2488
2044
Table II
Experimental and theoretical energy levels of Ne ii taken from Moore,a tables of atomic energy levels and this calculation. The mixing coefficients aij are those given in Eq. (1).
Ne ii states
Eexp cm−1
Etheor cm−1
4D
4P
4S
2D
2P
2S
2P′
2D′
2F′
4D7/2
249 110.8
248 652.5
0.99976
0.21956
2F7/2′
274 411.3
274 228.2
0.21956
−0.99976
4P5/2
246 194.8
246 314.4
0.10198
0.99415
0.03104
0.01720
0.00042
4D5/2
249 448.0
249 217.8
0.98594
−0.09696
−0.13543
0.00271
0.01307
2D5/2
251 013.3
251 158.4
−0.13166
0.04497
−0.98950
−0.03385
0.01966
2F5/2′
274 366.9
274 229.0
0.01038
0.00010
−0.02106
−0.00511
−0.99971
2D5/2′
277 346.1
277 407.1
−0.00883
−0.01525
−0.03379
0.99926
−0.00449
4P3/2
247 417.4
246 617.2
0.09174
0.99253
0.06423
0.00625
−0.04273
0.02033
0.00773
4D3/2
249 697.7
249 553.3
−0.99010
0.09102
0.01201
0.09658
0.04061
−0.00908
−0.00448
2D3/2
251 524.7
251 713.3
0.10309
−0.00654
0.01349
0.97118
0.20859
−0.04265
0.02494
2P3/2
254 167.0
253 922.7
0.02353
0.05218
−0.11802
−0.21197
0.94040
−0.23011
−0.02373
4S3/2
252 956.0
253 072.9
−0.00743
0.05933
−0.99058
0.04020
−0.11599
0.00933
0.00375
2P3/2′
276 278.6
276 396.3
−0.00025
−0.00729
−0.01897
−0.00409
0.23087
0.96654
−0.10978
2D3/2′
277 327.6
277 411.8
0.00721
0.00697
0.00196
0.02967
−0.04370
−0.10217
−0.99331
4P1/2
246 599.9
246 861.7
0.05282
0.99729
−0.02210
−0.04454
−0.01249
4D1/2
249 841.8
249 749.7
0.99720
−0.05422
−0.04947
−0.00301
0.01401
2P1/2
254 294.0
254 197.1
0.04669
0.00333
0.89586
−0.37847
−0.22804
2S1/2
252 800.8
252 885.9
0.02493
0.04932
0.36197
0.92444
−0.10641
2P1/2′
276 514.1
276 598.9
0.00137
0.00587
−0.25193
−0.01308
−0.96764
C. E. Moore, Atomic Energy Levels, Natl. Bur. Std. (U.S.) Circ., (U. S. Gov’t. Printing Office, Washington, D. C., 1949).
Table III
Experimental and theoretical energy levels of Ar ii taken from Minnhagen7 and from this calculation. The mixing coefficients of aij are those given in Eq. (1).
Ar ii states
Eexp cm−1
Etheor cm−1
4D
4P
4S
2D
2P
2S
2P′
2D′
2F′
4D7/2
157 233.93
157 176.6
0.99839
0.05680
2F7/2′
170 530.31
170 582.7
0.05680
−0.99839
4P5/2
155 043.07
155 128.2
0.18291
0.98206
0.02312
0.03949
0.00299
4D5/2
157 673.32
157 556.9
0.86726
−0.15036
−0.47202
−0.00525
0.04919
2D5/2
158 730.21
158 710.3
−0.46181
0.10820
−0.87867
−0.04014
0.03689
2F5/2′
170 400.94
170 364.6
−0.02553
0.00160
0.05688
−0.03043
0.99759
2D5/2′
173 393.38
173 432.7
0.02203
0.03525
0.03701
−0.99794
−0.03204
4P3/2
155 351.03
155 383.5
0.16724
0.96996
0.11854
−0.91561
−0.11366
0.05959
0.02102
4D3/2
158 167.71
158 007.6
0.91426
−0.18070
−0.04193
−0.31306
−0.17205
0.04422
0.01261
2D3/2
159 393.31
159 244.3
0.36791
0.00919
0.00421
0.80472
0.44766
−0.12847
0.00763
2P3/2
160 239.35
160 354.7
0.01598
0.09361
0.06872
−0.50253
0.81016
−0.27314
−0.05244
4S3/2
161 048.64
161 012.7
0.01607
−0.13135
0.98834
0.01899
−0.03572
0.06355
0.00052
2P3/2′
172 213.80
172 213.8
−0.00095
0.01493
0.05133
0.02018
−0.30918
−0.94747
0.05873
2D3/2′
173 347.83
173 349.9
0.01702
0.01413
0.00192
0.02951
−0.06202
−0.04059
−0.99657
4P1/2
155 708.02
155 781.9
0.09789
0.99105
−0.06195
−0.05442
0.03795
4D1/2
158 428.03
158 331.0
−0.98840
0.10630
0.09918
0.01678
−0.04050
2P1/2
159 706.46
159 869.7
−0.11005
−0.07824
−0.80018
−0.49034
0.31788
2S1/2
161 089.31
161 306.5
−0.03676
0.01627
−0.46980
0.86912
0.14933
2P1/2′
172 816.21
172 726.4
−0.00350
−0.01162
0.35401
0.03085
0.93465
Table IV
Experimental and theoretical energy levels of Kr ii taken from Moore,a tables of atomic energy levels and this calculation. The mixing coefficients aij are those given in Eq. (1).
Eexp cm−1
Etheor cm−1
4D
4P
4S
2D
2P
2S
2P′
2D′
2F′
4D7/2
135 783.18
136 046.4
0.98818
0.15329
2F7/2′
149 704.55
149 720.5
0.15329
−0.98818
4P5/2
133 925.65
133 855.3
0.35157
0.92956
−0.00191
0.10898
0.02069
4D5/2
136 071.00
136 913.7
0.69899
−0.26376
−0.64380
−0.04663
0.15873
2D5/2
140 118.99
139 794.1
−0.61630
0.24015
−0.73946
−0.08975
0.08744
2F5/2′
149 173.42
149 096.5
−0.06087
0.00875
0.17647
−0.05814
0.98066
2D5/2′
154 316.20
152 377.9
0.06542
0.09275
0.08704
−0.98717
−0.07092
4P3/2
134 288.44
134 032.7
0.29227
0.86841
0.24557
−0.06918
−0.25507
0.15819
0.07257
4D3/2
138 381.35
138 171.7
0.70387
−0.33387
−0.23513
−0.42128
−0.39352
0.05687
−0.04741
2D3/2
141 995.68
142 424.3
0.15404
−0.21173
0.13765
0.80116
−0.43082
0.25429
0.14271
2P3/2
140 137.15
140 117.4
0.62449
0.04557
0.03686
0.32338
0.67428
−0.21368
−0.04111
4S3/2
141 722.72
141 508.3
0.05458
−0.29324
0.91550
−0.23728
0.06388
0.10487
−0.03901
2P3/2′
150 203.48
150 519.5
−0.00713
0.02327
0.16055
0.07215
−0.32003
−0.91809
0.15208
2D3/2′
152 191.86
152 172.6
0.04903
0.03093
0.01389
0.09900
−0.18255
−0.08685
−0.97251
4P1/2
135 783.03
135 638.4
0.20533
0.92476
−0.20833
−0.19012
0.15203
4D1/2
140 163.25
139 549.3
−0.85103
0.01265
−0.28601
−0.40360
0.17577
2P1/2
139 103.36
139 042.2
−0.47019
0.37937
0.56136
0.46584
−0.32072
2S1/2
142 363.55
142 592.5
−0.11170
0.000795
−0.59032
0.76087
0.24507
2P1/2′
152 240.97
152 094.4
−0.00571
−0.02610
0.45955
0.07095
0.88491
C. E. Moore, Atomic Energy Levels, Natl. Bur. Std. (U. S.) Circ, (U. S. Gov’t. Printing Office, Washington, D. C., 1949).
Table V
Transition probabilities between 3p–3s levels of Ne ii, 4p–4s levels of Ar ii, and 5p–5s levels of Kr ii, each with ap4 [3P] core. A in sec−1. In this table for the purposes of comparison we have reproduced the results of Statz et al.3 and Garstang4 for the case of Ar ii and the experimental intensities I.