The energy level structure, relative line strengths, and Landé g factors of two-electron configurations are discussed for four important types of pure coupling: LS, LK(Ls), jK(jl), and jj. Transitions from one type of coupling to another are discussed in detail, the configuration pf being used as an example. The appropriateness of LS- and jj-coupling notation in two-electron spectra is quite limited for atoms of medium atomic weight, where nearly all excited configurations show a strong tendency toward pair (LK to jK) coupling. For other atoms, pair coupling occurs mainly for high values of orbital angular momentum of the excited electron: the coupling may then be near LK for small values of the principal quantum number of this electron, approaching pure jK as this quantum number increases. Either LK or jK notation can serve unambiguously to identify levels throughout the range of intermediate pair couplings, but neither will correctly designate the nature of the quantum states in all cases because of exchanges of the L (and of the j) compositions of certain states which occur as the coupling conditions change from pure LK to pure jK. Examples are discussed from the spectra of N, P, Ge, and the rare gases.
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Transformation matrices for pf, p5f, or f13p. (Matrices for the LS–jK, LK–jj, and LS–jj transformations are readily obtainable by multiplication of those given here.)
LS–LK
LK–jK
jK–jj
Table II
Coefficient matrices for pf. (Coefficients are for F2, G2, G4, ζp, ζf, in that order.)
LS Coupling
LK Coupling
jK Coupling
jj Coupling
Table III
Coefficient matrices for p5f. Coefficients for F2, ζp, and ζf are, respectively, −1, −1, and +1 times those for pf. The only nonzero coefficients for G2 and G4 are as shown below.
LS coupling
jK coupling
LK coupling
jj coupling
Table IV
Calculated compositions of the 4p4f states of Ge i.
With −αL(L + 1) correction; α = 14.3.
From Ge ii 4s24p, limζ4p = 1178.24 cm−1.
Table VI
Relative line strengths for pf–pg (or p5f–p5g) transitions in LK coupling.
pg
G
F
H
pf
[11/2]
F
25515
⋯
1620
81
⋯
⋯
(27216)
945
33075
81
2187
⋯
⋯
(36288)
(59535)
(3969)
D
⋯
⋯
18144
⋯
⋯
⋯
(18144)
⋯
⋯
1296
25920
⋯
⋯
(27216)
(45360)
G
1715
49
27
1
34496
⋯
(36288)
49
2156
⋯
35
784
42336
(45360)
(3969)
(63)
(77616)
(28224)
(35280)
(21168)
(28224)
(35280)
(42336)
Table VII
Relative line strengths for pf–pg (or p5f–p5g) transitions in jK coupling.
pg
pf
[11/2]
27216
⋯
⋯
⋯
⋯
⋯
(27216)
1008
35280
⋯
⋯
⋯
⋯
(36288)
(63504)
⋯
⋯
18144
⋯
⋯
⋯
(18144)
⋯
⋯
2916
24300
⋯
⋯
(27216)
⋯
⋯
108
3840
32340
⋯
(36288)
⋯
⋯
⋯
84
2940
42336
(45360)
(127008)
(28224)
(35280)
(21168)
(28224)
(35280)
(42336)
Table VIII
J = 1 g matrices for pp′ or p5p′ in the representations LS, LK, jK, jj.
Table IX
Landé g factors, least-square parameters, and coupling type in p5p′.
Level
gkk
Ne i
A i
Kr i
2p53p
2p54p
3p54p
3p55p
4p55p
4p56p
SLJ
j1K
j2
LS
LK
jK
jj
obs
calc
obs
calc
obs
calc
obs
calc
obs
calc
obs
calc
3D1
0.500
0.500
0.611
0.667
0.999
1.129
0.685
0.700
0.819
0.888
0.61
0.644
0.647
0.645
0.648
0.648
1P1
1.000
1.167
1.056
1.333
0.669
0.540
0.974
0.965
0.838
0.775
1.01
1.007
1.004
1.005
1.034
1.031
3P1
1.500
1.333
1.556
1.500
1.340
1.336
1.397
1.406
1.380
1.361
1.45
1.458
1.452
1.457
1.401
1.494
3S1
2.000
2.000
1.778
1.500
1.984
1.995
1.929
1.929
1.985
1.976
1.90
1.891
1.898
1.893
1.834
1.827
1D2
1.000
1.067
1.067
1.167
1.137
1.134
1.112
1.117
1.112
1.116
1.09
1.109
1.099
1.108
1.107
1.125
3D2
1.167
1.100
1.167
1.167
1.301
1.459
1.184
1.189
1.260
1.276
1.18
1.179
1.181
1.182
1.158
1.169
3P2
1.500
1.500
1.433
1.333
1.229
1.074
1.360
1.360
1.305
1.275
1.42
1.379
1.388
1.377
1.403
1.373
3D3
1.333
1.333
1.333
1.333
1.329
1.333
1.328
1.333
1.338
1.333
⋯
1.333
1.336
1.333
1.333
1.333
F2
170± 5
45± 3
181± 8
47±1
175± 5
44±2
Parameter
G0
778±18
238± 5
699±11
217±4
652±15
202±5
value
G2
29±13
14± 4
39± 8
13±2
40± 9
14±3
(cm−1)
ζp
333±87
517±10
909±27
947±6
3539±21
3556±8
ζp′
13±60
1±12
28±29
16±7
159±25
58±9
Fit
s (cm−1)
77
19
43
12
47
17
s/w (%)
1.6
1.1
0.9
0.6
0.6
0.3
LS
85
65
64
60
60
61
Average purity
LK
93
79
74
75
74
74
(%)
jK
63
91
83
96
96
96
jj
55
80
73
85
86
89
Tables (9)
Table I
Transformation matrices for pf, p5f, or f13p. (Matrices for the LS–jK, LK–jj, and LS–jj transformations are readily obtainable by multiplication of those given here.)
LS–LK
LK–jK
jK–jj
Table II
Coefficient matrices for pf. (Coefficients are for F2, G2, G4, ζp, ζf, in that order.)
LS Coupling
LK Coupling
jK Coupling
jj Coupling
Table III
Coefficient matrices for p5f. Coefficients for F2, ζp, and ζf are, respectively, −1, −1, and +1 times those for pf. The only nonzero coefficients for G2 and G4 are as shown below.
LS coupling
jK coupling
LK coupling
jj coupling
Table IV
Calculated compositions of the 4p4f states of Ge i.