Two frequency-doubled diode-pumped Nd:YAG lasers are used to study the hyperfine spectrum of 127I2 near 532 nm by heterodyne spectroscopy. Eight rovibrational transitions between the lowest vibrational level in the ground (X) state to vibrational levels 32–36 in the B state are observed. The measured frequency splittings are used to determine the difference in the hyperfine constants for these transitions. The standard deviation of the theoretical fit to the measured spectra is better than 10 kHz. The root Allan variance of the beat frequency between the I2-locked lasers follows a
dependence for measurements times τ > 0.002 s and reaches a minimum value of 2.5 × 10−13 (two-sample beat frequency of 70 Hz) at τ = 32 s. A method for accurately determining the absolute frequency of the iodine lines near 532 nm is proposed.
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Beat frequency between the a1 line of each rovibrational transition and the a1 line of R(56)32–0.
Calculated using expressions (2a) and (2b) and the measurements of the a1 spacings.
Difference between calculated absolute frequencies (see third column in Table 1).
The measured a1–a21 beat frequency of P(119)35–0 is 949.286 MHz.
Table 3
Measured and Calculated Hyperfine Components of P(53)32–0a
Fitting parameters are ΔeQq = 1908.4757 ± 0.08 MHz, ΔC = 86.047 ± 0.15 kHz, Δa = −10.27 ± 4.4 kHz, and Δd = −44.4 ± 3.7 kHz, and the standard deviation of the fit is 6.51 kHz. Reference line is a1.
Unresolved from the b4 line of P(103)34–0, hence not used in the fitting process.
Table 4
Measured and Calculated Hyperfine Components of R(56)32–0a
Fitting parameters are ΔeQq = 1908.4057 ± 0.01 MHz, ΔC = 86.34 ± 0.23 kHz, Δa = −10.60 ± 5.4 kHz, and Δd = −44.95 ± 4.5 kHz, and the standard deviation of the fit is 6.92 kHz. Reference line is a1.
Unresolved lines.
The a11 and a12 lines are only 4.7 MHz apart, whereas the modulation frequency is 4 MHz. This is probably causing the large deviation between measurement and theory.
Table 5
Measured and Calculated Hyperfine Components of P(83)33–0a
Fitting parameters are ΔeQq = 1906.9447 ± 0.077 MHz, ΔC = 94.483 ± 0.56 kHz, Δa = −10.14 ± 4.2 kHz, and Δd = −48.65 ± 4.5 kHz, and the standard deviation of the fit is 4.50 kHz. Reference line is a2. a1 and a4 were measured but not used in the fitting process, since they lie close to the a10 and a15 lines of R(134)36–0, see Tables 2 and 6, which shifted the measured frequencies for these two lines.
Table 6
Measured and Calculated Hyperfine Components of R(134)36–0a
Measured (MHz)
Calculated (MHz)
Calc − Meas (MHz)
F − J
I
a1
0
0
0
0
2
a2
212.275
−4
4
a3
269.647
269.649
0.002
−1
2
a4
300.075
300.089
0.013
1
2
a5
356.780
356.783
0.002
4
4
a6
369.626
369.625
−0.001
−3
4
a7
391.664
391.674
0.009
−2
4
a8
462.596
462.588
−0.008
2
4
a9
484.314
484.318
0.004
3
4
a10
569.776
0
4
a11
674.726
−2
2
a12
691.949
691.948
−0.001
−1
4
a13
732.420
732.403
−0.017
1
4
a14
750.452
750.458
0.006
2
2
a15
855.214
0
0
Fitting parameters are ΔeQq = 1902.2662 ± 0.15 MHz, ΔC = 128.694 ± 1.6 kHz, Δa = −15.14 ± 8.8 kHz, and Δd = −64.7 ± 7 kHz, and the standard deviation of the fit is 9.81 kHz. Reference line is a1.
Table 7
Measured and Calculated Hyperfine Components of R(106)34–0a
Measured (MHz)
Calculated (MHz)
Calc − Meas (MHz)
F − J
I
a1
0
0
0
0
2
a2
236.870
236.870
0.0002
−4
4
a3
276.953
276.938
−0.015
−1
2
a4
293.871
293.857
−0.014
1
2
a5
333.343
333.349
0.006
4
4
a6
387.631
387.634
0.003
−3
4
a7
404.629
404.631
0.002
−2
4
a8
451.167
451.169
0.002
2
4
a9
467.977
467.979
0.002
3
4
a10
570.790
570.790
0.0002
0
4
a11
687.525
687.532
0.007
−2
2
a12
698.652
698.654
0.002
−1
4
a13
728.254
728.251
−0.003
1
4
a14
740.179
470.176
−0.002
2
2
a15
856.663
856.664
0.001
0
0
Fitting parameters are ΔeQq = 1905.2577 ± 0.125 MHz, ΔC = 104.829 ± 0.18 kHz, Δa = −9.87 ± 5.7 kHz, and Δd = −53.67 ± 5.4 kHz, and the standard deviation of the fit is 7.13 kHz. Reference line is a1.
Table 8
Measured and Calculated Hyperfine Components of R(86)33–0a
Measured (MHz)
Calculated (MHz)
Calc − Meas (MHz)
F − J
I
a1
0
0
0
0
2
a2
248.204
248.204
0.0006
−4
4
a3
280.800
280.799
−0.001
−1
2
a4
290.505
290.501
−0.004
1
2
a5
322.528
322.527
−0.001
4
4
a6
395.382
395.384
0.002
−3
4
a7
410.695
410.692
−0.003
−2
4
a8
445.755
445.757
0.001
2
4
a9
460.968
460.972
0.004
3
4
a10
571.257
571.256
−0.001
0
4
a11
693.196
693.197
0.0004
−2
2
a12
701.367
701.369
0.002
−1
4
a13
726.702
726.702
0.001
1
4
a14
735.789
735.789
−0.001
2
2
a15
857.376
857.375
−0.001
0
0
Fitting parameters are ΔeQq = 1906.8107 ± 0.044 MHz, ΔC = 95.043 ± 0.05 kHz, Δa = −10.09 ± 1.4 kHz, and Δd = −48.54 ± 0.7 kHz, and the standard deviation of the fit is 2.25 kHz. Reference line is a1.
Table 9
Standard Deviation of the Fit (σ) and Hyperfine Constants Difference
Line
σ (kHz)
ΔeQq (MHz)
ΔC (kHz)
Δa (kHz)
Δd (kHz)
P(53)32–0
6.51
1908.4757 ± 0.08
86.047 ± 0.15
−10.27 ± 4.4
−44.4 + 3.7
R(56)32–0
6.92
1908.4057 ± 0.01
86.34 ± 0.23
−10.60 ± 5.4
−44.95 + 4.5
P(83)33–0
4.50
1906.9447 ± 0.077
94.483 ± 0.56
−10.14 ± 4.2
−48.65 + 4.5
R(86)33–0
2.25
1906.8107 ± 0.044
95.043 ± 0.05
−10.09 ± 1.4
−48.54 + 0.7
P(106)34–0
7.13
1905.2577 ± 0.125
104.829 ± 0.18
−9.87 ± 5.7
−53.67 + 5.4
R(134)32–0
9.81
1902.2662 ± 0.15
128.694 ± 1.6
−15.14 ± 8.6
−64.7 ± 7
Tables (9)
Table 1
127I2 Absorption Lines within the Tuning Range of the Frequency-Doubled Nd:YAG Laser
Beat frequency between the a1 line of each rovibrational transition and the a1 line of R(56)32–0.
Calculated using expressions (2a) and (2b) and the measurements of the a1 spacings.
Difference between calculated absolute frequencies (see third column in Table 1).
The measured a1–a21 beat frequency of P(119)35–0 is 949.286 MHz.
Table 3
Measured and Calculated Hyperfine Components of P(53)32–0a
Fitting parameters are ΔeQq = 1908.4757 ± 0.08 MHz, ΔC = 86.047 ± 0.15 kHz, Δa = −10.27 ± 4.4 kHz, and Δd = −44.4 ± 3.7 kHz, and the standard deviation of the fit is 6.51 kHz. Reference line is a1.
Unresolved from the b4 line of P(103)34–0, hence not used in the fitting process.
Table 4
Measured and Calculated Hyperfine Components of R(56)32–0a
Fitting parameters are ΔeQq = 1908.4057 ± 0.01 MHz, ΔC = 86.34 ± 0.23 kHz, Δa = −10.60 ± 5.4 kHz, and Δd = −44.95 ± 4.5 kHz, and the standard deviation of the fit is 6.92 kHz. Reference line is a1.
Unresolved lines.
The a11 and a12 lines are only 4.7 MHz apart, whereas the modulation frequency is 4 MHz. This is probably causing the large deviation between measurement and theory.
Table 5
Measured and Calculated Hyperfine Components of P(83)33–0a
Fitting parameters are ΔeQq = 1906.9447 ± 0.077 MHz, ΔC = 94.483 ± 0.56 kHz, Δa = −10.14 ± 4.2 kHz, and Δd = −48.65 ± 4.5 kHz, and the standard deviation of the fit is 4.50 kHz. Reference line is a2. a1 and a4 were measured but not used in the fitting process, since they lie close to the a10 and a15 lines of R(134)36–0, see Tables 2 and 6, which shifted the measured frequencies for these two lines.
Table 6
Measured and Calculated Hyperfine Components of R(134)36–0a
Measured (MHz)
Calculated (MHz)
Calc − Meas (MHz)
F − J
I
a1
0
0
0
0
2
a2
212.275
−4
4
a3
269.647
269.649
0.002
−1
2
a4
300.075
300.089
0.013
1
2
a5
356.780
356.783
0.002
4
4
a6
369.626
369.625
−0.001
−3
4
a7
391.664
391.674
0.009
−2
4
a8
462.596
462.588
−0.008
2
4
a9
484.314
484.318
0.004
3
4
a10
569.776
0
4
a11
674.726
−2
2
a12
691.949
691.948
−0.001
−1
4
a13
732.420
732.403
−0.017
1
4
a14
750.452
750.458
0.006
2
2
a15
855.214
0
0
Fitting parameters are ΔeQq = 1902.2662 ± 0.15 MHz, ΔC = 128.694 ± 1.6 kHz, Δa = −15.14 ± 8.8 kHz, and Δd = −64.7 ± 7 kHz, and the standard deviation of the fit is 9.81 kHz. Reference line is a1.
Table 7
Measured and Calculated Hyperfine Components of R(106)34–0a
Measured (MHz)
Calculated (MHz)
Calc − Meas (MHz)
F − J
I
a1
0
0
0
0
2
a2
236.870
236.870
0.0002
−4
4
a3
276.953
276.938
−0.015
−1
2
a4
293.871
293.857
−0.014
1
2
a5
333.343
333.349
0.006
4
4
a6
387.631
387.634
0.003
−3
4
a7
404.629
404.631
0.002
−2
4
a8
451.167
451.169
0.002
2
4
a9
467.977
467.979
0.002
3
4
a10
570.790
570.790
0.0002
0
4
a11
687.525
687.532
0.007
−2
2
a12
698.652
698.654
0.002
−1
4
a13
728.254
728.251
−0.003
1
4
a14
740.179
470.176
−0.002
2
2
a15
856.663
856.664
0.001
0
0
Fitting parameters are ΔeQq = 1905.2577 ± 0.125 MHz, ΔC = 104.829 ± 0.18 kHz, Δa = −9.87 ± 5.7 kHz, and Δd = −53.67 ± 5.4 kHz, and the standard deviation of the fit is 7.13 kHz. Reference line is a1.
Table 8
Measured and Calculated Hyperfine Components of R(86)33–0a
Measured (MHz)
Calculated (MHz)
Calc − Meas (MHz)
F − J
I
a1
0
0
0
0
2
a2
248.204
248.204
0.0006
−4
4
a3
280.800
280.799
−0.001
−1
2
a4
290.505
290.501
−0.004
1
2
a5
322.528
322.527
−0.001
4
4
a6
395.382
395.384
0.002
−3
4
a7
410.695
410.692
−0.003
−2
4
a8
445.755
445.757
0.001
2
4
a9
460.968
460.972
0.004
3
4
a10
571.257
571.256
−0.001
0
4
a11
693.196
693.197
0.0004
−2
2
a12
701.367
701.369
0.002
−1
4
a13
726.702
726.702
0.001
1
4
a14
735.789
735.789
−0.001
2
2
a15
857.376
857.375
−0.001
0
0
Fitting parameters are ΔeQq = 1906.8107 ± 0.044 MHz, ΔC = 95.043 ± 0.05 kHz, Δa = −10.09 ± 1.4 kHz, and Δd = −48.54 ± 0.7 kHz, and the standard deviation of the fit is 2.25 kHz. Reference line is a1.
Table 9
Standard Deviation of the Fit (σ) and Hyperfine Constants Difference