W. J. Childs, H. Crosswhite, L. S. Goodman, and V. Pfeufer, "Hyperfine structure of 4fN 6S2 configurations in 159Tb, 161,163Dy, and 169Tm," J. Opt. Soc. Am. B 1, 22-29 (1984)
The atomic-beam, laser-rf, double-resonance method has been used to measure the hyperfine structure in excited levels of the 4fN 6s2 configurations of the neutral rare earths 159Tb, 161,163Dy, and 169Tm. On combining the new information with earlier results for the lower levels, it is possible to extract many of the hyperfine radial integrals 〈〈r−3〉xy). The present results, together with work published during the last year on 165Ho and 167Er, now make it possible to plot the values of the integrals completely across the 4f shell. The ab initio calculations of Lindgren and Roien reproduce the magnetic-dipole hfs integrals well but appear to overestimate the electric-quadrupole integrals 〈r−3〉11 and 〈r−3〉13.
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Excitation energies and J values are given for the upper and lower states of each transition. A Doppler-free laser scan through the line 5985.99 Å is shown in Fig. 1.
Lines not listed in Ref. 13.
Lines used in double-resonance measurements.
Excitation energies and J values are given for the upper and lower states of each transition.
Not listed in Ref. 13.
Line used for double-resonance rf measurement on 2F5/2169Tm level at 8771.243 cm−1.
Table 3
Hyperfine Splittings Measured by Double Resonance in 159Tb and 169Tm
Atom
State
F ↔ F′
Observed Frequency (MHz)
159Tb
6H11/2
7 ↔ 6
5719.214(2)
6 ↔ 5
4215.612(2)
5 ↔ 4
3028.955(2)
169Tm
2F7/2
4 ↔ 3
1496.550(1)
2F5/2
3 ↔ 2
2113.946(1)
Table 4
Hfs Constants Measured for Dy I Levels by Laser Fluorescencea
State
hfs Const ants (MHz)
Excitation Energy (cm−1)
J, Parity
A (161Dy)
B (161Dy)
A (163Dy)
B (163Dy)
7 050.61
6, even
−139.5
959
195.3
1014
9 211.58
5, even
−162.1
891
226.7
946
10 925.25
4, even
−205.5
964
286.9
1016
22 061.29
7, odd
−129.7
345
181.6
364
23 687.87
6, odd
−144.5
1972
202.4
2081
24 634.07b
5, odd
−104.6
−225
146.5
−248
25 825.83
6, odd
−232.5
354
325.5
384
25 912.63
5, odd
−200.2
1580
280.2
1673
27 643.57b
3, odd
−191.4
1295
269.4
1382
27 685.87b
5, odd
−267.6
727
373.7
766
27 751.46b
4, odd
−216.4
968
302.9
1022
The uncertainties are ±0.4 MHz in the A values and ±6 MHz in the B values except for the levels labeled b, for which they are ±1 MHz for the A values and ±10 MHz for the B values.
Table 5
Dipole hfs Constants Measured for Excited Levels in 169Tm by Laser Fluorescencea
The present values (fourth column) are in close agreement with earlier measurements (final column).
Ref. 20.
Ref. 21.
Table 6
Hfs Constants Determined for Levels in 161,163Dy, 159Tb, and 169Tm by Atomic-Beam, Laser-rf Double Resonancea
Atom
State
Excitation Energy (cm−1)
hfs Constant
Effective Value (MHz)
Corrected Value (MHz)
161Dy
5I6
7050.61
A
−139.6345
−139.6345
B
960.891
960.889
5I5
9211.58
A
−161.9708
−161.9709
B
894.023
894.027
5I4
10925.25
A
−205.3400
−205.3399
B
961.154
961.156
163Dy
5I6
7050.61
A
195.5240
195.5235
B
1014.843
1014.829
5I5
9211.58
A
226.8008
226.8001
B
944.235
944.217
5I4
10925.25
A
287.5280
287.5272
B
1015.109
1015.114
159Tb
6H11/2
4670.455
A
729.012(1)
728.998(3)
B
968.188(10)
967.997(40)
169Tm
2F5/2
8771.243
A
−704.649(1)
−704.649(1)
The effective values given in the fifth column are those needed to reproduce the observed hfs splittings with the simple first-order theory. The values in the final column have been corrected for the effects of hyperfine interactions with other atomic states. These corrections are significant only in the case of 159Tb. The uncertainties are 0.001 MHz in the A values and 0.010 MHz in the B values, except where indicated.
Table 7
Spin–Orbit Interaction Strength (ζ4f) Required for a Best Fit to Various Observables in 161Dy ia
Atom
Interaction
ζ(cm−1)
ζ/ζ0
161Dy
Fine-structure energies
1777.77
1.000
Zeeman effect
1786.66
1.005
Magnetic–dipole hfs
1763.55
0.992
Electric-quadrupole hfs
1768.88
0.995
The value found for a best fit to the 5I excitiation energies is denoted by ζ. That the four values ζ4f agree to within less than 1% is evidence of the quality of the present eigenvectors for the 4f10 6s2 5I ground term of Dy i.
Table 8
Values of the Radial hfs Integrals axy, bxy, and 〈r−3〉xy Determined from rf Measurements of hfs Splittings in 161Dya
Parameter
Value in 161Dy
a01
−158.0(2) MHz
a12
−181(4) MHz
a10
6.0(3) MHz
b02
4335(3) MHz
b11
−203(4) MHz
b13
509(16) MHz
〈r−3〉01
8.64(8) a.u.
〈r−3〉12
9.88(22) a.u.
〈r−3〉10
−0.33(2) a.u.
〈r−3〉11/〈−3〉02
−0.047(1) a.u.
〈−3〉13/〈r−3〉02
0.117(4) a.u.
These values are compared with those for neighboring 4f-shell atoms and with the ab initio calculations (the curves labeled OHFS) of Lindgren and Rośen3 in Fig. 5.
Table 9
Isotopic Ratios of hfs Constants in the 4f10 6s2 5I Ground Term of Dy ia
State
A (163Dy)/A (161Dy)
B (163Dy)/B (161Dy)
5I8
−1.400 26(3)
1.056 15(6)
5I7
−1.400 26(3)
1.056 14(9)
5I6
−1.400 252(3)
1.056 136(4)
5I5
−1.400 252(3)
1.056 139(4)
5I4
−1.400 250(3)
1.056 139(4)
The results for the 5I8,7 states are from old atomic-beam magnetic-resonance results28; those for 5I6,5,4 are new. The absence of any state dependence is clear.
Table 10
Values Found for the hfs Radial Integrals in the 4f9 6s2 Configuration of 159Tba
Excitation energies and J values are given for the upper and lower states of each transition. A Doppler-free laser scan through the line 5985.99 Å is shown in Fig. 1.
Lines not listed in Ref. 13.
Lines used in double-resonance measurements.
Excitation energies and J values are given for the upper and lower states of each transition.
Not listed in Ref. 13.
Line used for double-resonance rf measurement on 2F5/2169Tm level at 8771.243 cm−1.
Table 3
Hyperfine Splittings Measured by Double Resonance in 159Tb and 169Tm
Atom
State
F ↔ F′
Observed Frequency (MHz)
159Tb
6H11/2
7 ↔ 6
5719.214(2)
6 ↔ 5
4215.612(2)
5 ↔ 4
3028.955(2)
169Tm
2F7/2
4 ↔ 3
1496.550(1)
2F5/2
3 ↔ 2
2113.946(1)
Table 4
Hfs Constants Measured for Dy I Levels by Laser Fluorescencea
State
hfs Const ants (MHz)
Excitation Energy (cm−1)
J, Parity
A (161Dy)
B (161Dy)
A (163Dy)
B (163Dy)
7 050.61
6, even
−139.5
959
195.3
1014
9 211.58
5, even
−162.1
891
226.7
946
10 925.25
4, even
−205.5
964
286.9
1016
22 061.29
7, odd
−129.7
345
181.6
364
23 687.87
6, odd
−144.5
1972
202.4
2081
24 634.07b
5, odd
−104.6
−225
146.5
−248
25 825.83
6, odd
−232.5
354
325.5
384
25 912.63
5, odd
−200.2
1580
280.2
1673
27 643.57b
3, odd
−191.4
1295
269.4
1382
27 685.87b
5, odd
−267.6
727
373.7
766
27 751.46b
4, odd
−216.4
968
302.9
1022
The uncertainties are ±0.4 MHz in the A values and ±6 MHz in the B values except for the levels labeled b, for which they are ±1 MHz for the A values and ±10 MHz for the B values.
Table 5
Dipole hfs Constants Measured for Excited Levels in 169Tm by Laser Fluorescencea
The present values (fourth column) are in close agreement with earlier measurements (final column).
Ref. 20.
Ref. 21.
Table 6
Hfs Constants Determined for Levels in 161,163Dy, 159Tb, and 169Tm by Atomic-Beam, Laser-rf Double Resonancea
Atom
State
Excitation Energy (cm−1)
hfs Constant
Effective Value (MHz)
Corrected Value (MHz)
161Dy
5I6
7050.61
A
−139.6345
−139.6345
B
960.891
960.889
5I5
9211.58
A
−161.9708
−161.9709
B
894.023
894.027
5I4
10925.25
A
−205.3400
−205.3399
B
961.154
961.156
163Dy
5I6
7050.61
A
195.5240
195.5235
B
1014.843
1014.829
5I5
9211.58
A
226.8008
226.8001
B
944.235
944.217
5I4
10925.25
A
287.5280
287.5272
B
1015.109
1015.114
159Tb
6H11/2
4670.455
A
729.012(1)
728.998(3)
B
968.188(10)
967.997(40)
169Tm
2F5/2
8771.243
A
−704.649(1)
−704.649(1)
The effective values given in the fifth column are those needed to reproduce the observed hfs splittings with the simple first-order theory. The values in the final column have been corrected for the effects of hyperfine interactions with other atomic states. These corrections are significant only in the case of 159Tb. The uncertainties are 0.001 MHz in the A values and 0.010 MHz in the B values, except where indicated.
Table 7
Spin–Orbit Interaction Strength (ζ4f) Required for a Best Fit to Various Observables in 161Dy ia
Atom
Interaction
ζ(cm−1)
ζ/ζ0
161Dy
Fine-structure energies
1777.77
1.000
Zeeman effect
1786.66
1.005
Magnetic–dipole hfs
1763.55
0.992
Electric-quadrupole hfs
1768.88
0.995
The value found for a best fit to the 5I excitiation energies is denoted by ζ. That the four values ζ4f agree to within less than 1% is evidence of the quality of the present eigenvectors for the 4f10 6s2 5I ground term of Dy i.
Table 8
Values of the Radial hfs Integrals axy, bxy, and 〈r−3〉xy Determined from rf Measurements of hfs Splittings in 161Dya
Parameter
Value in 161Dy
a01
−158.0(2) MHz
a12
−181(4) MHz
a10
6.0(3) MHz
b02
4335(3) MHz
b11
−203(4) MHz
b13
509(16) MHz
〈r−3〉01
8.64(8) a.u.
〈r−3〉12
9.88(22) a.u.
〈r−3〉10
−0.33(2) a.u.
〈r−3〉11/〈−3〉02
−0.047(1) a.u.
〈−3〉13/〈r−3〉02
0.117(4) a.u.
These values are compared with those for neighboring 4f-shell atoms and with the ab initio calculations (the curves labeled OHFS) of Lindgren and Rośen3 in Fig. 5.
Table 9
Isotopic Ratios of hfs Constants in the 4f10 6s2 5I Ground Term of Dy ia
State
A (163Dy)/A (161Dy)
B (163Dy)/B (161Dy)
5I8
−1.400 26(3)
1.056 15(6)
5I7
−1.400 26(3)
1.056 14(9)
5I6
−1.400 252(3)
1.056 136(4)
5I5
−1.400 252(3)
1.056 139(4)
5I4
−1.400 250(3)
1.056 139(4)
The results for the 5I8,7 states are from old atomic-beam magnetic-resonance results28; those for 5I6,5,4 are new. The absence of any state dependence is clear.
Table 10
Values Found for the hfs Radial Integrals in the 4f9 6s2 Configuration of 159Tba
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