Advanced Relativistic Energy Approach in Spectroscopy …
21
Table 4 Measured and calculated AS energies (cm −1 ): theoretical data by Van Leeuwen et al. and
this approach (see text)
j sd
K
J
Exp. energy
[22]
This approach
3/2
5/2
2, 3
42509.9
42511.2
42509.8
3/2
7/2
3, 4
42480.1
42480.3
42480.2
3/2
9/2
4, 5
42470.8
42469.5
42470.6
3/2
11/2
5, 6
–
42500.4
42499.7
5/2
3/2
1, 2
43323.4
43322.5
43323.4
5/2
5/2
2, 3
43302.8
43302.5
43302.6
5/2
7/2
3, 4
43282.1
43283.5
43282.2
5/2
9/2
4, 5
43271.02
43271.8
43270.9
5/2
11/2
5, 6
43275.6
43274.8
43275.5
5/2
13/2
6, 7
–
43306.4
43307.0
Table 5 Experimental energy values (cm −1 ) for the 4fnf (n = 15) AS (averaged over the fine
structure) measured experimentally, as well as calculated on the basis of our theory and the
multichannel quantum defect method (MCQD) with empirical fitting (de Graaff et al.) [28] (see
text)
AC
J
Exp.
MCQD
REA
4f 5/2 15f 7/2
6
89758.4 ± 0.5
89759.1
89758.8
4f 7/2 15f 5/2
6
89993.6 ± 0.5
89992.4
89993.6
4f 7/2 15f 7/2
6
89926.6 ± 5.0
89937.1
89926.8
4f 5/2 15f 7/2
5
89726.3 ± 1.0
89718.7
89726.9
4f 5/2 15f 5/2
5
89749.2 ± 0.5
89748.6
89749.7
4f 7/2 15f 7/2
5
89951.0 ± 0.5
89952.9
89951.6
4f 7/2 15f 5/2
5
–
89943.6
89942.3
4f 5/2 15f 5/2
4
89705.6 ± 0.5
89706.8
89705.4
4f 5/2 15f 7/2
4
–
89720.0
89718.5
4f 7/2 15f 5/2
4
89937.8 ± 2.0
89937.2
89937.6
4f 7/2 15f 7/2
4
89951.0 ± 2.0
89951.8
89951.5
4f 5/2 15f 5/2
3
–
89725.9
89728.5
4f 5/2 15f 7/2
3
89741.5 ± 2.0
89738.0
89740.9
4f 7/2 15f 7/2
3
89969.3 ± 2.0
89972.0
89969.8
4f 7/2 15f 5/2
3
–
89955.9
89953.4
4f 5/2 15f 7/2
2
89766.5 ± 5.0
89774.7
89767.8
21
Table 4 Measured and calculated AS energies (cm −1 ): theoretical data by Van Leeuwen et al. and
this approach (see text)
j sd
K
J
Exp. energy
[22]
This approach
3/2
5/2
2, 3
42509.9
42511.2
42509.8
3/2
7/2
3, 4
42480.1
42480.3
42480.2
3/2
9/2
4, 5
42470.8
42469.5
42470.6
3/2
11/2
5, 6
–
42500.4
42499.7
5/2
3/2
1, 2
43323.4
43322.5
43323.4
5/2
5/2
2, 3
43302.8
43302.5
43302.6
5/2
7/2
3, 4
43282.1
43283.5
43282.2
5/2
9/2
4, 5
43271.02
43271.8
43270.9
5/2
11/2
5, 6
43275.6
43274.8
43275.5
5/2
13/2
6, 7
–
43306.4
43307.0
Table 5 Experimental energy values (cm −1 ) for the 4fnf (n = 15) AS (averaged over the fine
structure) measured experimentally, as well as calculated on the basis of our theory and the
multichannel quantum defect method (MCQD) with empirical fitting (de Graaff et al.) [28] (see
text)
AC
J
Exp.
MCQD
REA
4f 5/2 15f 7/2
6
89758.4 ± 0.5
89759.1
89758.8
4f 7/2 15f 5/2
6
89993.6 ± 0.5
89992.4
89993.6
4f 7/2 15f 7/2
6
89926.6 ± 5.0
89937.1
89926.8
4f 5/2 15f 7/2
5
89726.3 ± 1.0
89718.7
89726.9
4f 5/2 15f 5/2
5
89749.2 ± 0.5
89748.6
89749.7
4f 7/2 15f 7/2
5
89951.0 ± 0.5
89952.9
89951.6
4f 7/2 15f 5/2
5
–
89943.6
89942.3
4f 5/2 15f 5/2
4
89705.6 ± 0.5
89706.8
89705.4
4f 5/2 15f 7/2
4
–
89720.0
89718.5
4f 7/2 15f 5/2
4
89937.8 ± 2.0
89937.2
89937.6
4f 7/2 15f 7/2
4
89951.0 ± 2.0
89951.8
89951.5
4f 5/2 15f 5/2
3
–
89725.9
89728.5
4f 5/2 15f 7/2
3
89741.5 ± 2.0
89738.0
89740.9
4f 7/2 15f 7/2
3
89969.3 ± 2.0
89972.0
89969.8
4f 7/2 15f 5/2
3
–
89955.9
89953.4
4f 5/2 15f 7/2
2
89766.5 ± 5.0
89774.7
89767.8