Multi-configuration Hartree-Fock wave functions have been obtained for many atoms of the Mg sequence for 3p2 1D, 3s 3d1,3D, 3p 3d1,3F, and 3s 4f1,3F states. Theoretical ionization energies are reported. Oscillator strengths for allowed D -F transitions are presented and compared with experiment, when available. Agreement is better for the 3s 3d3D -3p 3d3F sequence than for 3s 3d3D -3s 4f3F. Smoother trends are observed when f values for the 1Dlowest-1Flowest transition, for example, are plotted than for the 3s 3d1D -3s 4f1F transition.
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Approximations for some 1,3D and 1,3F states of the Mg Sequence.
Term
Configurations in the expansion
(i) Nonrelativistic
1D
3s 3d, 3p2,
, 3p24f, 4s 4d, 4p2,
,
, 3d3 5g
3D
3s 3d, 3p 4p, 3d2 4d2, 3p2 4f, 4s 4d, 3d3 5g
1F, 3F
3s 4f, 3p 3d, 3d2 4f2, 3p2 5g, 4p 4d
(ii) Intermediate coupling with relativistic corrections
1,3D
3s 3d (1,3D), 3p2 (1D, 3P),
(3F, 1D, 3P)
1,3F
3s 4f (1,3F), 3p 4d (1,3F, 1,3D, 3P)
TABLE II
Nonrelativistic ionization energies for 1,3D and 1,3F states of the Mg Sequence in atomic units.
Z
3p2 1D
3s 3d3D
3s 3d1D
3p 3d3F
3p 3d1F
3s 4f3F
3s 4f1F
12
0.062 67
0.071 17
0.031 93
0.031 92
13
0.304 71
0.255 46
0.188 89
0.050 66
0.129 96
0.129 60
14
0.675 08
0.575 74
0.469 18
0.327 93
0.275 94
0.298 22
15
1.169 8
1.020 8
0.880 69
0.698 62
0.567 46
0.505 27
0.453 47
16
1.783 9
1.587 7
1.418 9
1.195 7
0.991 55
0.793 91
0.759 13
17
2.514 8
2.274 1
2.079 8
1.812 0
1.556 8
1.144 3
1.112 6
18
3.360 0
3.078 1
2.860 5
2.545 5
2.247 3
1.558 5
1.525 1
20
5.395 4
5.033 5
4.773 4
4.358 9
3.985 9
2.575 1
2.535 6
26
14.203
13.629
13.255
12.527
11.961
7.137 9
7.069 6
30
22.312
21.607
21.161
20.219
19.534
11.434
11.347
36
36.926
36.374
19.756
19.642
42
56.257
55.600
30.332
30.189
50
89.586
88.263
87.468
85.451
84.194
47.935
47.756
74
226.98
225.77
124.75
124.47
TABLE III
Comparison of theoretical and observed ionization energies in atomic units. In each case the theoretical value is quoted above the observed and followed by the difference, IEobs − IEth.
Theoretical ionization energies corrected for correlation with the core.
Mg I 3s 3d1D
Al II 3p2 1D
Al II 3p 3d3F
th
0.069 61
0.303 55
0.048 19
obs
0.069 56
0.302 46
0.048 96
diff
−0.000 05
−0.001 09
0.000 77
TABLE V
Comparison of nonrelativistic and intermediate coupling ionization energies with relativistic corrections for some highly ionized atoms. (The nonrelativistic values are given in parentheses).
State
Zn xix
Mo xxxi
Sn xxxix
W lxii
3s 3d3D
(21.607)
(56.257)
(88.26)
(226.98)
J = 3
21.602
56.312
88.43
228.24
2
21.623
56.440
88.82
230.93
1
21.636
56.519
88.92
231.31
3s 3d1D
(21.161)
(55.600)
(87.47)
(225.77)
J = 2
21.128
55.619
87.47
227.72
3p2 1D
(22.312)
(89.59)
J = 2
22.318
57.546
90.16
233.09
3s 4f3F
(11.434)
(30.332)
(47.93)
(124.75)
J = 4
11.416
30.325
47.95
125.02
3
11.418
30.348
48.01
125.48
2
11.420
30.364
48.04
125.38
3s 4f1F
(11.347)
(30.189)
(47.76)
(124.47)
J = 3
11.322
30.179
47.78
124.87
TABLE VI
Nonrelativistic f values for some 1D − 1F and 3D − 3F transitions in the Mg sequence.
Z
λ(Å)
fl
fυ
α(Å)
fl
fυ
(i) 3s 3d1D − 3s 4f1F
(ii) 3s 3d3D − 3s 4f3F
12
11 607.
0.472
0.472
14 819.
0.780
0.786
13
7 685.
0.624
0.624
3 630.
0.617
0.646
14
2 665.
0.232
0.230
1 520.
1.007
0.946
15
1 066.5
1.436
1.423
883.9
0.916
0.905
16
690.6
1.141
1.135
574.0
0.867
0.872
17
471.1
0.939
0.932
403.3
0.860
0.865
18
341.2
0.842
0.834
299.8
0.850
0.866
20
203.6
0.756
0.749
185.3
0.855
0.872
26
73.67
0.694
0.704
70.19
0.898
0.888
30
46.42
0.685
0.675
44.79
0.921
0.912
36
27.23
0.681
0.675
26.54
0.938
0.929
42
17.93
0.679
0.673
17.58
0.950
0.942
50
11.47
0.677
0.673
11.30
0.961
0.954
74
4.50
0.675
0.672
4.46
0.980
0.975
(iii) 3p2 1D − 3s 4f1F
(iv) 3s 3d3D − 3p 3d3F
13
2602.
0.352
0.352
2224.
0.298
0.239
14
1209.
0.465
0.486
1838.
0.002
0.001
15
636.1
0.047
0.051
1414.
0.152
0.115
16
444.6
0.016
0.015
1162.
0.195
0.168
17
324.9
0.065
0.063
986.1
0.205
0.186
18
248.2
0.100
0.097
855.5
0.204
0.191
20
159.3
0.142
0.139
675.5
0.192
0.186
26
63.87
0.195
0.181
413.3
0.151
0.151
30
41.55
0.228
0.227
328.3
0.130
0.131
50
10.89
0.286
0.284
162.0
0.076
0.077
(v) 3s 3d1D − 3p 3d1F
(vi) 3p2 1D − 3p 3d1F
15
1455.
0.021
0.022
756.5
0.727
0.744
16
1066.
0.339
0.344
575.0
0.698
0.725
17
871.1
0.481
0.487
475.6
0.594
0.625
18
743.0
0.515
0.521
409.1
0.512
0.544
20
578.6
0.406
0.502
323.3
0.398
0.429
26
352.0
0.378
0.385
203.2
0.232
0.257
30
280.0
0.321
0.327
164.0
0.179
0.200
50
139.2
0.180
0.185
84.5
0.082
0.094
TABLE VII
A comparison of nonrelativistic (NR) and intermediate coupling relativistic (R) data for several D − F transitions. (Nonrelativistic wavelengths for multiplets are given in parentheses).
Transition J − J′
Zn xix
Mo xxxi
Sn xxxix
W lxiii
λ(Å)
fR
fNR
λR(Å)
λ(Å)
fNR
λ(Å)
f
fNR
λ(Å)
fR
fNR
3s 3d3D − 3s 4f3F
(44.79)
(17.58)
(11.30)
(4.46)
3 − 4
44.73
0.859
0.845
17.53
0.888
0.872
11.25
0.898
0.883
4.41
0.917
0.900
−3
44.74
0.074
0.073
17.55
0.077
0.075
11.27
0.076
0.076
4.43
0.065
0.078
−2
44.75
0.002
0.002
17.56
0.002
0.002
11.28
0.002
0.002
4.43
0.000
0.002
2 − 3
44.65
0.832
0.819
17.46
0.839
0.844
11.16
0.757
0.854
4.32
0.865
0.871
−2
44.66
0.104
0.102
17.47
0.106
0.106
11.17
0.087
0.107
4.32
0.012
0.109
1 − 2
44.60
0.936
0.921
17.42
0.977
0.950
11.15
0.993
0.961
4.30
0370
0.980
3s 3d1D − 3s 4f1F
(46.42)
(17.93)
(11.47)
(4.50)
2 − 3
46.46
0.709
0.685
17.91
0.646
0.679
11.48
0.464
0.677
4.43
0.868
0.675
3p2 1D − 3s 4f1F
(41.55)
(10.89)
2 − 3
41.43
0.147
0.228
16.54
0.167
10.75
0.153
0.286
4.21
0.133
TABLE VIII
A comparison of the present f values with other theoretical and experimental values.
Approximations for some 1,3D and 1,3F states of the Mg Sequence.
Term
Configurations in the expansion
(i) Nonrelativistic
1D
3s 3d, 3p2,
, 3p24f, 4s 4d, 4p2,
,
, 3d3 5g
3D
3s 3d, 3p 4p, 3d2 4d2, 3p2 4f, 4s 4d, 3d3 5g
1F, 3F
3s 4f, 3p 3d, 3d2 4f2, 3p2 5g, 4p 4d
(ii) Intermediate coupling with relativistic corrections
1,3D
3s 3d (1,3D), 3p2 (1D, 3P),
(3F, 1D, 3P)
1,3F
3s 4f (1,3F), 3p 4d (1,3F, 1,3D, 3P)
TABLE II
Nonrelativistic ionization energies for 1,3D and 1,3F states of the Mg Sequence in atomic units.
Z
3p2 1D
3s 3d3D
3s 3d1D
3p 3d3F
3p 3d1F
3s 4f3F
3s 4f1F
12
0.062 67
0.071 17
0.031 93
0.031 92
13
0.304 71
0.255 46
0.188 89
0.050 66
0.129 96
0.129 60
14
0.675 08
0.575 74
0.469 18
0.327 93
0.275 94
0.298 22
15
1.169 8
1.020 8
0.880 69
0.698 62
0.567 46
0.505 27
0.453 47
16
1.783 9
1.587 7
1.418 9
1.195 7
0.991 55
0.793 91
0.759 13
17
2.514 8
2.274 1
2.079 8
1.812 0
1.556 8
1.144 3
1.112 6
18
3.360 0
3.078 1
2.860 5
2.545 5
2.247 3
1.558 5
1.525 1
20
5.395 4
5.033 5
4.773 4
4.358 9
3.985 9
2.575 1
2.535 6
26
14.203
13.629
13.255
12.527
11.961
7.137 9
7.069 6
30
22.312
21.607
21.161
20.219
19.534
11.434
11.347
36
36.926
36.374
19.756
19.642
42
56.257
55.600
30.332
30.189
50
89.586
88.263
87.468
85.451
84.194
47.935
47.756
74
226.98
225.77
124.75
124.47
TABLE III
Comparison of theoretical and observed ionization energies in atomic units. In each case the theoretical value is quoted above the observed and followed by the difference, IEobs − IEth.
Theoretical ionization energies corrected for correlation with the core.
Mg I 3s 3d1D
Al II 3p2 1D
Al II 3p 3d3F
th
0.069 61
0.303 55
0.048 19
obs
0.069 56
0.302 46
0.048 96
diff
−0.000 05
−0.001 09
0.000 77
TABLE V
Comparison of nonrelativistic and intermediate coupling ionization energies with relativistic corrections for some highly ionized atoms. (The nonrelativistic values are given in parentheses).
State
Zn xix
Mo xxxi
Sn xxxix
W lxii
3s 3d3D
(21.607)
(56.257)
(88.26)
(226.98)
J = 3
21.602
56.312
88.43
228.24
2
21.623
56.440
88.82
230.93
1
21.636
56.519
88.92
231.31
3s 3d1D
(21.161)
(55.600)
(87.47)
(225.77)
J = 2
21.128
55.619
87.47
227.72
3p2 1D
(22.312)
(89.59)
J = 2
22.318
57.546
90.16
233.09
3s 4f3F
(11.434)
(30.332)
(47.93)
(124.75)
J = 4
11.416
30.325
47.95
125.02
3
11.418
30.348
48.01
125.48
2
11.420
30.364
48.04
125.38
3s 4f1F
(11.347)
(30.189)
(47.76)
(124.47)
J = 3
11.322
30.179
47.78
124.87
TABLE VI
Nonrelativistic f values for some 1D − 1F and 3D − 3F transitions in the Mg sequence.
Z
λ(Å)
fl
fυ
α(Å)
fl
fυ
(i) 3s 3d1D − 3s 4f1F
(ii) 3s 3d3D − 3s 4f3F
12
11 607.
0.472
0.472
14 819.
0.780
0.786
13
7 685.
0.624
0.624
3 630.
0.617
0.646
14
2 665.
0.232
0.230
1 520.
1.007
0.946
15
1 066.5
1.436
1.423
883.9
0.916
0.905
16
690.6
1.141
1.135
574.0
0.867
0.872
17
471.1
0.939
0.932
403.3
0.860
0.865
18
341.2
0.842
0.834
299.8
0.850
0.866
20
203.6
0.756
0.749
185.3
0.855
0.872
26
73.67
0.694
0.704
70.19
0.898
0.888
30
46.42
0.685
0.675
44.79
0.921
0.912
36
27.23
0.681
0.675
26.54
0.938
0.929
42
17.93
0.679
0.673
17.58
0.950
0.942
50
11.47
0.677
0.673
11.30
0.961
0.954
74
4.50
0.675
0.672
4.46
0.980
0.975
(iii) 3p2 1D − 3s 4f1F
(iv) 3s 3d3D − 3p 3d3F
13
2602.
0.352
0.352
2224.
0.298
0.239
14
1209.
0.465
0.486
1838.
0.002
0.001
15
636.1
0.047
0.051
1414.
0.152
0.115
16
444.6
0.016
0.015
1162.
0.195
0.168
17
324.9
0.065
0.063
986.1
0.205
0.186
18
248.2
0.100
0.097
855.5
0.204
0.191
20
159.3
0.142
0.139
675.5
0.192
0.186
26
63.87
0.195
0.181
413.3
0.151
0.151
30
41.55
0.228
0.227
328.3
0.130
0.131
50
10.89
0.286
0.284
162.0
0.076
0.077
(v) 3s 3d1D − 3p 3d1F
(vi) 3p2 1D − 3p 3d1F
15
1455.
0.021
0.022
756.5
0.727
0.744
16
1066.
0.339
0.344
575.0
0.698
0.725
17
871.1
0.481
0.487
475.6
0.594
0.625
18
743.0
0.515
0.521
409.1
0.512
0.544
20
578.6
0.406
0.502
323.3
0.398
0.429
26
352.0
0.378
0.385
203.2
0.232
0.257
30
280.0
0.321
0.327
164.0
0.179
0.200
50
139.2
0.180
0.185
84.5
0.082
0.094
TABLE VII
A comparison of nonrelativistic (NR) and intermediate coupling relativistic (R) data for several D − F transitions. (Nonrelativistic wavelengths for multiplets are given in parentheses).
Transition J − J′
Zn xix
Mo xxxi
Sn xxxix
W lxiii
λ(Å)
fR
fNR
λR(Å)
λ(Å)
fNR
λ(Å)
f
fNR
λ(Å)
fR
fNR
3s 3d3D − 3s 4f3F
(44.79)
(17.58)
(11.30)
(4.46)
3 − 4
44.73
0.859
0.845
17.53
0.888
0.872
11.25
0.898
0.883
4.41
0.917
0.900
−3
44.74
0.074
0.073
17.55
0.077
0.075
11.27
0.076
0.076
4.43
0.065
0.078
−2
44.75
0.002
0.002
17.56
0.002
0.002
11.28
0.002
0.002
4.43
0.000
0.002
2 − 3
44.65
0.832
0.819
17.46
0.839
0.844
11.16
0.757
0.854
4.32
0.865
0.871
−2
44.66
0.104
0.102
17.47
0.106
0.106
11.17
0.087
0.107
4.32
0.012
0.109
1 − 2
44.60
0.936
0.921
17.42
0.977
0.950
11.15
0.993
0.961
4.30
0370
0.980
3s 3d1D − 3s 4f1F
(46.42)
(17.93)
(11.47)
(4.50)
2 − 3
46.46
0.709
0.685
17.91
0.646
0.679
11.48
0.464
0.677
4.43
0.868
0.675
3p2 1D − 3s 4f1F
(41.55)
(10.89)
2 − 3
41.43
0.147
0.228
16.54
0.167
10.75
0.153
0.286
4.21
0.133
TABLE VIII
A comparison of the present f values with other theoretical and experimental values.