W. J. Childs, David R. Cok, and L. S. Goodman, "New line classifications in Ho i based on high-precision hyperfine-structure measurement of low levels," J. Opt. Soc. Am. 73, 151-155 (1983)
Doppler-free laser-fluorescence and laser-rf double-resonance studies have been made of the hyperfine structure (hfs) of four strong, previously unclassified visible lines in Ho i; all are shown to connect with low levels. The hfs of the 4f116s24I11/2,9/2 levels is measured in detail, allowing evaluation of the dipole (a01, a12, a10) and quadrupole (b02, b11, b13) hfs radial integrals. The results are in close agreement with the ab initio values of
Lindgren and Rosen [
Case Stud. Atom. Phys. 4,
93–
292 (
1974)]. The value found for b02 in the 4f116s2 configuration is in reasonable agreement with that of
Wyart and Camus [
Physica 93C,
227–
236 (
1978)], thereby confirming their finding of a substantial dependence of this parameter on the number of 4f electrons in the core.
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Summary of the Ho i Lines Studied in the Present Worka
Lower Level
Upper Level
Wavelength in Air (Å)
Excitation Energy (cm−1)
J, Parity
Excitation Energy (cm−1)
J, Parity
5921.72
0.00
15/2, odd
16882.31
15/2, even
6081.77
0.00
15/2, odd
16438.03
17/2, even
5948.02
5419.70
13/2, odd
22227.36
15/2, even
6002.03
8605.16
11/2, odd
25261.58
11/2, even
5887.55
9147.08
13/2, even
26127.37
13/2, odd
5929.15
10695.75
9/2, odd
27556.90
9/2, even
5922.76
10695.75
9/2, odd
27575.09
7/2, even
5900.00
10695.75
9/2, odd
27640.21
11/2, even
The classifications of the last four lines and the energy levels at 27556, 27575, and 27640 cm−1 are new.
Table 2
Hyperfine Constants Measured for the Levels of Table 1 by Laser Fluorescence Studies of an Ho Atomic Beama
Excitation Energy (cm−1)
Label
J, Parity
Hyperfine Constants
A (MHz)
B (MHz)
8605.16
4f116s2 4I11/2
11/2, odd
1034.6
−1051
9147.08
13/2, even
916.6
2668
10695.75
4f116s2 4I9/2
9/2, odd
1138.1
−491 ± 4
16438.03
17/2, even
819.7
2035 ± 20
16882.31
15/2, even
477.7
−675 ± 20
22227.36
15/2, even
1308.6
−2122 ±20
25261.58
11/2, even
1025.9
934
26127.37
13/2, odd
811.8
50.9
27556.90
9/2, even
1121.1
847
27575.09
7/2, even
582.1
50.9
27640.21
11/2, even
1515.2
−645
The uncertainty in the A values is typically±0.5 MHz, and in the B values it is ±7 MHz except for the four levels for which the uncertainties are indicated explicitly. Column 2 gives the identifications of the two levels investigated in detail in the present work; the configurations for most of the other levels are given in Ref. 9.
Table 3
Zero-Field Hyperfine Intervals in the 4f116s24I11/2,9/2 Levels Measured by Laser-rf Double Resonance
State Label
Excitation Energy (cm − 1)
hfs Interval F–F′
Measured Interval (MHz)
4I11/2
8605.16
9–8
8947.242(4)
8–7
8138.996(3)
7–6
7265.143(3)
6–5
6333.882(3)
5–4
5353.417(3)
4–3
4331.942(3)
3–2
3277.663(3)
4I9/2
10695.75
8–7
8913.249(4)
7–6
7902.066(3)
6–5
6849.720(3)
5–4
5762.070(4)
4–3
4644.995(3)
3–2
3504.366(3)
2–1
2346.064(3)
Table 4
Comparison of Experimental and Theoretical Values of the Relativistic Radial hfs Integrals for the 4f116s2 Configuration of Ho ia
Parameter
Value (Atomic Units)
Experimental
Theoretical Lindgren–Rosen OHFS
〈r−3〉01
9.469
9.870
〈r−3〉12
9.842
10.801
〈r−3〉10
− 0.517
− 0.442
〈r−3〉12/〈r−3〉01
1.039
1.094
〈r−3〉02
9.898
9.898
〈r−3〉11
− 0.575
− 0.595
〈r−3〉13
1.521
1.298
The experimental dipole values follow from the measured quantities a01, a12, and a01 and the known nuclear magnetic dipole moment of 165Ho. For the quadrupole interaction, the theoretical optimized Hartree–Fock–Slater (OHFS) 〈r−2〉02 value of Lindgren and Rosen was assumed correct, and the experimental values of 〈r−3〉11 and 〈r−3〉13 were extracted from the measured quantities b11 and b13. The relative uncertainty in each of the values is the same as for the corresponding axy or bxy given in the text. For the dipole values there is an additional 1% uncertainty (a common scaling factor for the three parameters) that is due to uncertainty in the dipole moment. The corresponding scaling uncertainty in the quadrupole case is unknown.
Tables (4)
Table 1
Summary of the Ho i Lines Studied in the Present Worka
Lower Level
Upper Level
Wavelength in Air (Å)
Excitation Energy (cm−1)
J, Parity
Excitation Energy (cm−1)
J, Parity
5921.72
0.00
15/2, odd
16882.31
15/2, even
6081.77
0.00
15/2, odd
16438.03
17/2, even
5948.02
5419.70
13/2, odd
22227.36
15/2, even
6002.03
8605.16
11/2, odd
25261.58
11/2, even
5887.55
9147.08
13/2, even
26127.37
13/2, odd
5929.15
10695.75
9/2, odd
27556.90
9/2, even
5922.76
10695.75
9/2, odd
27575.09
7/2, even
5900.00
10695.75
9/2, odd
27640.21
11/2, even
The classifications of the last four lines and the energy levels at 27556, 27575, and 27640 cm−1 are new.
Table 2
Hyperfine Constants Measured for the Levels of Table 1 by Laser Fluorescence Studies of an Ho Atomic Beama
Excitation Energy (cm−1)
Label
J, Parity
Hyperfine Constants
A (MHz)
B (MHz)
8605.16
4f116s2 4I11/2
11/2, odd
1034.6
−1051
9147.08
13/2, even
916.6
2668
10695.75
4f116s2 4I9/2
9/2, odd
1138.1
−491 ± 4
16438.03
17/2, even
819.7
2035 ± 20
16882.31
15/2, even
477.7
−675 ± 20
22227.36
15/2, even
1308.6
−2122 ±20
25261.58
11/2, even
1025.9
934
26127.37
13/2, odd
811.8
50.9
27556.90
9/2, even
1121.1
847
27575.09
7/2, even
582.1
50.9
27640.21
11/2, even
1515.2
−645
The uncertainty in the A values is typically±0.5 MHz, and in the B values it is ±7 MHz except for the four levels for which the uncertainties are indicated explicitly. Column 2 gives the identifications of the two levels investigated in detail in the present work; the configurations for most of the other levels are given in Ref. 9.
Table 3
Zero-Field Hyperfine Intervals in the 4f116s24I11/2,9/2 Levels Measured by Laser-rf Double Resonance
State Label
Excitation Energy (cm − 1)
hfs Interval F–F′
Measured Interval (MHz)
4I11/2
8605.16
9–8
8947.242(4)
8–7
8138.996(3)
7–6
7265.143(3)
6–5
6333.882(3)
5–4
5353.417(3)
4–3
4331.942(3)
3–2
3277.663(3)
4I9/2
10695.75
8–7
8913.249(4)
7–6
7902.066(3)
6–5
6849.720(3)
5–4
5762.070(4)
4–3
4644.995(3)
3–2
3504.366(3)
2–1
2346.064(3)
Table 4
Comparison of Experimental and Theoretical Values of the Relativistic Radial hfs Integrals for the 4f116s2 Configuration of Ho ia
Parameter
Value (Atomic Units)
Experimental
Theoretical Lindgren–Rosen OHFS
〈r−3〉01
9.469
9.870
〈r−3〉12
9.842
10.801
〈r−3〉10
− 0.517
− 0.442
〈r−3〉12/〈r−3〉01
1.039
1.094
〈r−3〉02
9.898
9.898
〈r−3〉11
− 0.575
− 0.595
〈r−3〉13
1.521
1.298
The experimental dipole values follow from the measured quantities a01, a12, and a01 and the known nuclear magnetic dipole moment of 165Ho. For the quadrupole interaction, the theoretical optimized Hartree–Fock–Slater (OHFS) 〈r−2〉02 value of Lindgren and Rosen was assumed correct, and the experimental values of 〈r−3〉11 and 〈r−3〉13 were extracted from the measured quantities b11 and b13. The relative uncertainty in each of the values is the same as for the corresponding axy or bxy given in the text. For the dipole values there is an additional 1% uncertainty (a common scaling factor for the three parameters) that is due to uncertainty in the dipole moment. The corresponding scaling uncertainty in the quadrupole case is unknown.