F. R. Petersen, J. S. Wells, A. G. Maki, and K. J. Siemsen, "Heterodyne frequency measurements of 13CO2
laser hot band transitions," Appl. Opt. 20, 3635-3640 (1981)
The frequencies of twenty-eight lines in the P-branch of the
0111–[1110, 0310]I band of
13C16O2, observed in laser emission, and
three lines in the R-branch, observed in absorption with a
diode laser, have been carefully measured with stabilized CO2 lasers.
A significant improvement in the ro-vibrational constants has been obtained from
a least squares fit to these data. The laser lines stabilized by saturated
absorption techniques provide convenient, accurate (uncertainty <0.1 MHz)
frequency references near 11.7 μm.
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For laser lines P(9) and
P(31)–P(39), the
13CO2 frequency was set to the peak of the
gain curve. Other laser line frequencies in the
P-branch were set to the minimum in the saturation dip.
Lines in the R-branch were observed in absorption with
a TDL which was set to the absorption maximum. All reference lasers were
stabilized to standing wave saturation resonances in CO2.
Number in parentheses is the estimated uncertainty in the measured
frequency. For lines P(10)–P(30), it
is the 1-σ estimated uncertainty in the synthesized
frequency and the of the measured frequency combined in
quadrature. For lines in the R-branch, the uncertainty
is estimated from the width of the beat note and the Doppler width and
SNR of the absorption line.
Frequencies were calculated with the ro-vibrational constants from the
fit without the H terms.
Table II
Ro-vibrational constants for the 0111–[1110,
0310]I Band of
13C16O2
Uncertainty in the last digits (one estimated standard error) is given in
parentheses. c = 299 792 458 m/sec.14
Fitting H′ alone gives a better approximation to the
value of H′–H″ rather than to
H′ alone.
Table III
Varlance-Covarlance Matrix (in units of MHz2) for the Constants
Given in Table II (Without the H
Terms)
ν0
B′
D′
q′
μ′
B″
D″
q″
μ″
ν0
6.19634 ×
10−2
3.81243 ×
10−3
1.23631 ×
10−6
7.58418 ×
10−4
3.21301 ×
10−7
3.62650 ×
10−3
1.07378 ×
10−6
6.83929 ×
10−4
2.52226 ×
10−7
B′
2.49503 ×
10−4
6.31490 ×
10−8
3.00904 ×
10−5
3.66665 ×
10−8
2.35627 ×
10−4
5.31320 ×
10−8
2.82634 ×
10−5
3.21583 ×
10−8
D′
6.99841 ×
10−11
3.19308 ×
10−8
−4.30197 ×
10−11
6.29620 ×
10−8
6.39580 ×
10−11
2.62703 ×
10−8
−4.15322 ×
10−11
q′
6.88183 ×
10−5
−4.73735 ×
10−8
3.05629 ×
10−5
2.96891 ×
10−8
5.81902 ×
10−5
−4.83105 ×
10−8
μ′
1.82935 ×
10−10
3.15223 ×
10−8
−4.09967 ×
10−11
−3.36912 ×
10−8
1.71443 ×
10−10
B″
2.22769 ×
10−4
5.33249 ×
10−8
2.84439 ×
10−5
2.73754 ×
10−8
D″
5.85956 ×
10−11
2.43775 ×
10−8
−3.95425 ×
10−11
q″
4.94904 ×
10−5
−3.49741 ×
10−8
n″
1.60978 ×
10−10
Table IV
Frequencies and Wave Numbers for the 0111–[1110,
0310]I Band of 13CO2
Calculated with the Ro-vibrational Constants from Table II (without the H
terms)
For laser lines P(9) and
P(31)–P(39), the
13CO2 frequency was set to the peak of the
gain curve. Other laser line frequencies in the
P-branch were set to the minimum in the saturation dip.
Lines in the R-branch were observed in absorption with
a TDL which was set to the absorption maximum. All reference lasers were
stabilized to standing wave saturation resonances in CO2.
Number in parentheses is the estimated uncertainty in the measured
frequency. For lines P(10)–P(30), it
is the 1-σ estimated uncertainty in the synthesized
frequency and the of the measured frequency combined in
quadrature. For lines in the R-branch, the uncertainty
is estimated from the width of the beat note and the Doppler width and
SNR of the absorption line.
Frequencies were calculated with the ro-vibrational constants from the
fit without the H terms.
Table II
Ro-vibrational constants for the 0111–[1110,
0310]I Band of
13C16O2
Uncertainty in the last digits (one estimated standard error) is given in
parentheses. c = 299 792 458 m/sec.14
Fitting H′ alone gives a better approximation to the
value of H′–H″ rather than to
H′ alone.
Table III
Varlance-Covarlance Matrix (in units of MHz2) for the Constants
Given in Table II (Without the H
Terms)
ν0
B′
D′
q′
μ′
B″
D″
q″
μ″
ν0
6.19634 ×
10−2
3.81243 ×
10−3
1.23631 ×
10−6
7.58418 ×
10−4
3.21301 ×
10−7
3.62650 ×
10−3
1.07378 ×
10−6
6.83929 ×
10−4
2.52226 ×
10−7
B′
2.49503 ×
10−4
6.31490 ×
10−8
3.00904 ×
10−5
3.66665 ×
10−8
2.35627 ×
10−4
5.31320 ×
10−8
2.82634 ×
10−5
3.21583 ×
10−8
D′
6.99841 ×
10−11
3.19308 ×
10−8
−4.30197 ×
10−11
6.29620 ×
10−8
6.39580 ×
10−11
2.62703 ×
10−8
−4.15322 ×
10−11
q′
6.88183 ×
10−5
−4.73735 ×
10−8
3.05629 ×
10−5
2.96891 ×
10−8
5.81902 ×
10−5
−4.83105 ×
10−8
μ′
1.82935 ×
10−10
3.15223 ×
10−8
−4.09967 ×
10−11
−3.36912 ×
10−8
1.71443 ×
10−10
B″
2.22769 ×
10−4
5.33249 ×
10−8
2.84439 ×
10−5
2.73754 ×
10−8
D″
5.85956 ×
10−11
2.43775 ×
10−8
−3.95425 ×
10−11
q″
4.94904 ×
10−5
−3.49741 ×
10−8
n″
1.60978 ×
10−10
Table IV
Frequencies and Wave Numbers for the 0111–[1110,
0310]I Band of 13CO2
Calculated with the Ro-vibrational Constants from Table II (without the H
terms)
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