Kenneth L. Andrew, Robert D. Cowan, and Athos Giacchetti, "Zeeman Effect and Configuration Interaction in Germanium*," J. Opt. Soc. Am. 57, 715-727 (1967)
The Zeeman effect of Ge i and Ge ii is investigated both experimentally and theoretically. In many configurations, intermediate-coupling wavefunctions derived by energy-level fitting show large departures from all of the pure-basis couplings LS, LK, jK, and jj, and the computed g values depart correspondingly from the pure-coupling values. Provided important configuration-interaction effects are taken into account, the calculated g values are found to agree well with observation. Strong wavefunction mixing in the configurations Ge i 4p4f and Ge ii 4f is produced by the magnetic field (24025 G); the theoretically calculated effects agree well with observation.
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Most levels of Ge i are designated in jK notation, in line with Table I.
Intermediate-coupling values in the single-configuration approximation, except configuration interaction included in the cases 4s4p3−4p4d−4p6s, 4p6d−4p4f, and 4s4p2−4d.
Uncertainties are those in the last decimal place for g, determined as described in the text. I = incomplete pattern, but giving both g values; Δ = incomplete pattern yielding only Δg; U = g value obtained from unresolved pseudo-triplet plus known g for other level.
Results to five decimals from Childs and Goodman (Ref. 8), other values from van den Bosch and Klinkenberg (Ref. 9).
Strong configuration-interaction effects to be expected, but not taken into account.
See Sec. IV.
Table III
Least-squares fit and theoretical parameter values for Ge ii (parameter values in cm−1).
Values of Eav are relative to the center of gravity of Ge ii 4s24p, which is 1178 cm−1 above 4s24p.
Standard deviation of the fit of the eleven levels of the three configurations sp2−4d−5s.
Standard deviation of the fit of the twelve levels of the three configurations sp2−4d−5d.
Table IV
Theoretical and observed g factors for Ge i.
Conf.
Level
J
g
LS
LK
jK
jj
In term.
Obs.
4p2
557 cm−1
1
1.500
⋯
⋯
1.500
1.500
1.502 ±1
1 409
2
1.500
⋯
⋯
1.333
1.493
1.498 ±4
7 125
2
1.000
⋯
⋯
1.167
1.007
1.007 ±2
4p5s
37 702
1
1.500
1.333
1.333
1.333
1.434
1.435 ±1
40 021
1
1.000
1.167
1.167
1.167
1.066
1.068 ±1
39 118
2
1.500
1.500
1.500
1.500
1.500
1.500 ±2
4p5p
45 986
1
1.000
0.500
0.611
0.667
0.788
⋯
46 765
1
0.500
1.333
1.566
1.500
0.973
0.980 ±8
48 088
1
1.500
1.167
1.056
1.333
1.371
1.362 ±8
49 076
1
2.000
2.000
1.778
1.500
1.868
1.862 ±4
46 834
2
1.167
1.100
1.167
1.167
1.181
1.182 ±7
48 726
2
1.500
1.500
1.433
1.167
1.421
1.427 ±5
49 650
2
1.000
1.067
1.067
1.333
1.065
1.062 ±8
48 104
3
1.333
1.333
1.333
1.333
1.333
1.332 ±6
Table V
Parameter values (cm−1) for least-squares fits in Ge i, 4s24p4d−4s2 4p6s−4s4p3.
As shown by the values of the configuration-interaction parameters R, case A is for no interaction among the three configurations, case B includes only the 4p4d−4p6s interaction, case C only the 4s4p3−4s24p4d interaction, and cases D and E include all three interactions. In case E, the parameter ζ(4d) is held fixed at about its theoretical value.
Relative to Eav(4p2) = 0, or 4p2 3P0 = −4047.62 cm−1.
Parameters held fixed at values estimated partly from theory and partly from the resulting values of rms error σ (or standard deviation s).
Usual least-squares fit.
Modified least-squares fit (described in Sec. VII).
Usual least-squares fit with 4f−6p (Rt = 5, Rs = 3) and 4f−7p (Rt = 4, Rs = 3) interactions.
Modified least-squares fit, with interactions as in C.
Relative to Eav(4p2) = 0, or 4p2 3P0 = −4047.62 cm−1.
Tables (7)
Table I
Coupling type in Ge i and Ge ii (from single-configuration least-squares energy fits).
Config.
Error of fit
Average purity (percent)
LS
LK
jK
jj
Ge i
4p5s
0.05%
87
94
94
94
4p6s
4.3
74
99
99
99
4p7s
2.3
72
100
100
100
4s4p3
0.27
89
⋯
⋯
⋯
4p2
0.25
99
⋯
⋯
65
4p5p
0.45
73
72
77
73
4p6p
0.55
65
71
86
87
4p4d
3.3
71
62
73
74
4p5d
8.5
61
70
88
84
4p6d
4.3
56
61
85
90
4p4f
0.19
49
69
99
94
4p5f
0.14
51
70
99
95
4p6f
0.02
52
71
99
95
Ge ii
4s4p2
11.1
100
⋯
⋯
⋯
Table II
Theoretical and experimental g factors for germanium.
Most levels of Ge i are designated in jK notation, in line with Table I.
Intermediate-coupling values in the single-configuration approximation, except configuration interaction included in the cases 4s4p3−4p4d−4p6s, 4p6d−4p4f, and 4s4p2−4d.
Uncertainties are those in the last decimal place for g, determined as described in the text. I = incomplete pattern, but giving both g values; Δ = incomplete pattern yielding only Δg; U = g value obtained from unresolved pseudo-triplet plus known g for other level.
Results to five decimals from Childs and Goodman (Ref. 8), other values from van den Bosch and Klinkenberg (Ref. 9).
Strong configuration-interaction effects to be expected, but not taken into account.
See Sec. IV.
Table III
Least-squares fit and theoretical parameter values for Ge ii (parameter values in cm−1).
Values of Eav are relative to the center of gravity of Ge ii 4s24p, which is 1178 cm−1 above 4s24p.
Standard deviation of the fit of the eleven levels of the three configurations sp2−4d−5s.
Standard deviation of the fit of the twelve levels of the three configurations sp2−4d−5d.
Table IV
Theoretical and observed g factors for Ge i.
Conf.
Level
J
g
LS
LK
jK
jj
In term.
Obs.
4p2
557 cm−1
1
1.500
⋯
⋯
1.500
1.500
1.502 ±1
1 409
2
1.500
⋯
⋯
1.333
1.493
1.498 ±4
7 125
2
1.000
⋯
⋯
1.167
1.007
1.007 ±2
4p5s
37 702
1
1.500
1.333
1.333
1.333
1.434
1.435 ±1
40 021
1
1.000
1.167
1.167
1.167
1.066
1.068 ±1
39 118
2
1.500
1.500
1.500
1.500
1.500
1.500 ±2
4p5p
45 986
1
1.000
0.500
0.611
0.667
0.788
⋯
46 765
1
0.500
1.333
1.566
1.500
0.973
0.980 ±8
48 088
1
1.500
1.167
1.056
1.333
1.371
1.362 ±8
49 076
1
2.000
2.000
1.778
1.500
1.868
1.862 ±4
46 834
2
1.167
1.100
1.167
1.167
1.181
1.182 ±7
48 726
2
1.500
1.500
1.433
1.167
1.421
1.427 ±5
49 650
2
1.000
1.067
1.067
1.333
1.065
1.062 ±8
48 104
3
1.333
1.333
1.333
1.333
1.333
1.332 ±6
Table V
Parameter values (cm−1) for least-squares fits in Ge i, 4s24p4d−4s2 4p6s−4s4p3.
As shown by the values of the configuration-interaction parameters R, case A is for no interaction among the three configurations, case B includes only the 4p4d−4p6s interaction, case C only the 4s4p3−4s24p4d interaction, and cases D and E include all three interactions. In case E, the parameter ζ(4d) is held fixed at about its theoretical value.
Relative to Eav(4p2) = 0, or 4p2 3P0 = −4047.62 cm−1.
Parameters held fixed at values estimated partly from theory and partly from the resulting values of rms error σ (or standard deviation s).
Usual least-squares fit.
Modified least-squares fit (described in Sec. VII).
Usual least-squares fit with 4f−6p (Rt = 5, Rs = 3) and 4f−7p (Rt = 4, Rs = 3) interactions.
Modified least-squares fit, with interactions as in C.
Relative to Eav(4p2) = 0, or 4p2 3P0 = −4047.62 cm−1.