C. Bauche-Arnoult, J. Sinzelle, and A. Bachelier, "Extensive theoretical analysis of the f6d and f8d configurations. Application to 4f85d6s2 in Tb i," J. Opt. Soc. Am. 68, 368-374 (1978)
For configurations with large numbers of levels, such as the fNd configurations of the lanthanides, the theoretical calculations are often restricted to the levels built on a few terms of fN. As part of an effort toward getting better intermediate-coupling eigenfunctions we have considered the whole f6d (and f8d) configuration, which involves 2492 levels for J = 1/2 to 17/2. The matrices of the coefficients for the usual electrostatic and spin-orbit parameters have been computed, as well as for some second-order parameters. A method has been devised to check these matrices in the computer. The study of the energy levels of the 4f85d6s2 configuration of Tb i is presented. For the 45 known levels the mean deviation obtained is 41 cm−1. The intermediate-coupling eigenfunctions are used for the analysis of the hyperfine structure.
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Different LS terms of f8d. The number under the term designation indicates the number of terms of this kind occurring in the configuration. The terms between brackets appear only for
and have not been considered.
2S
2p
2D
2F
2G
2H
2I
2K
2L
2M
(2N)
(2O)
(2Q)
(2R)
(2T)
11
31
50
59
65
63
57
47
37
25
17
10
5
2
1
4S
4P
4D
4F
4G
4H
4I
4K
4L
4M
4N
(4O)
(4Q)
(4R)
8
26
37
47
48
47
40
33
23
16
9
5
2
1
6S
6P
6D
6F
6G
6H
6I
6K
6L
6M
6N
3
7
11
12
13
11
9
6
4
2
1
8P
8D
8F
8G
8H
1
1
1
1
1
TABLE II
Orders of the different J matrices up to
.
J
Order
130
246
329
371
377
347
295
231
166
TABLE III
Values of the parameters used for the verification of the matrices.
Eav = −378
F2(fd) = −6
F4(fd) = −1
G5(fd)= −1
= −7
α = 7
X3(fd) = −6
Y4(fd) = 126
ζf = 0
ζd = 0
TABLE IV
Values of the parameters obtained for the configuration 4f85d6s2 of terbium i (in cm−1).
Eav
1.1212 ± 105
E1
6047 ± 164
E2
30
E3
610
F2(fd)
149.2 ± 1.1
F4(fd)
17.16 ± 0.34
G1(fd)
166.5 ± 3.2
G3(fd)
21.73 ± 0.84
G5(fd)
3.45 ± 0.23
ζf
1.695.2 ± 12.4
ζd
742.1 ± 15.4
17.5
α
7.64 ± 1.38
X3(fd)
37
Y2(fd)
−39.53 ± 3.95
Y4(fd)
−336.05
No. of experimental levels
45
〈ΔE〉av
41
τΔEav〉/(Emax − Emin)
3.2 × 10−3
TABLE V
Properties of the low levels of 4f85d6s2.
J
Experimental energy
Calculated energy
Squares of the amplitudesa of the three main LS components
Values given in Table IX of Ref. 1 have been divided by
for
and
and by
for
and
because of the difference in the definition of the Hamiltonian.
Tables (7)
TABLE I
Different LS terms of f8d. The number under the term designation indicates the number of terms of this kind occurring in the configuration. The terms between brackets appear only for
and have not been considered.
2S
2p
2D
2F
2G
2H
2I
2K
2L
2M
(2N)
(2O)
(2Q)
(2R)
(2T)
11
31
50
59
65
63
57
47
37
25
17
10
5
2
1
4S
4P
4D
4F
4G
4H
4I
4K
4L
4M
4N
(4O)
(4Q)
(4R)
8
26
37
47
48
47
40
33
23
16
9
5
2
1
6S
6P
6D
6F
6G
6H
6I
6K
6L
6M
6N
3
7
11
12
13
11
9
6
4
2
1
8P
8D
8F
8G
8H
1
1
1
1
1
TABLE II
Orders of the different J matrices up to
.
J
Order
130
246
329
371
377
347
295
231
166
TABLE III
Values of the parameters used for the verification of the matrices.
Eav = −378
F2(fd) = −6
F4(fd) = −1
G5(fd)= −1
= −7
α = 7
X3(fd) = −6
Y4(fd) = 126
ζf = 0
ζd = 0
TABLE IV
Values of the parameters obtained for the configuration 4f85d6s2 of terbium i (in cm−1).
Eav
1.1212 ± 105
E1
6047 ± 164
E2
30
E3
610
F2(fd)
149.2 ± 1.1
F4(fd)
17.16 ± 0.34
G1(fd)
166.5 ± 3.2
G3(fd)
21.73 ± 0.84
G5(fd)
3.45 ± 0.23
ζf
1.695.2 ± 12.4
ζd
742.1 ± 15.4
17.5
α
7.64 ± 1.38
X3(fd)
37
Y2(fd)
−39.53 ± 3.95
Y4(fd)
−336.05
No. of experimental levels
45
〈ΔE〉av
41
τΔEav〉/(Emax − Emin)
3.2 × 10−3
TABLE V
Properties of the low levels of 4f85d6s2.
J
Experimental energy
Calculated energy
Squares of the amplitudesa of the three main LS components