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Low-field zeeman effect of OH in the 2Π32 , J = 72, 92, 112, 132, and152 states
JOURNAL
OF
MOLECULAR
Low-Field
SPECTROSCOPY
83, 332-338 (1980)
Zeeman Effect of OH in the 2l&,2, J = 7/2, 9/2, 1 l/2, 13/2, and 15/2 States K. V. L. N. SASTRY ANDJ.
VANDERLINDE
Department of Physics, university of New Brunswick, Fredericton. New Brunswick, E3B 5,43, Canada The Zeeman effect of OH in the X *&, .I = 112, 912, 1112, 1312, and 1512 levels, in magnetic fields up to 12 G was investigated using a square-wave Zeeman modulation microwave spectrometer. The molecular g factors obtained are compared with those calculated from a theory by Radford [Phys. Rev. 122, 114-130(1961)]. The X 2II3,2, J = 712, F = 3 -+ 4, and F = 4 -+ 3 transitions were directly measured for the first time. INTRODUCTION
The microwave spectrum of the OH radical has been investigated by many workers over several decades (2). Radford (I, 3) studied the ESR spectrum of OH in the 2II3,2 state, J = 312, 5/2, and 712 levels and in the *I& state, J = 3/2 and 5/2 levels. Johnson and Lin (4) studied the low-field Zeeman effect in the *IIs,*, J = 9/2 level. More recently Brown et al. (5) investigated the ESR spectrum in the *l&,2, J = 9/2 and 11/2 levels at 26 and 35 GHz, respectively. The present work describes a systematic study of the low-field Zeeman effect of the OH radical in the *IIs,*, J = 712, 912, 11/2, 13/2, and 15/2 states. EXPERIMENTAL
DETAILS
The microwave spectrum of OH was observed using a 5-kHz square-wave Zeeman modulation spectrometer. The absorption cell consists of a 120-cm-long, 7-cm-diameter Pyrex tube. A solenoid is wound on the tube in four sections using #20 copper wire. The four coils are connected in parallel to reduce the inductance of the solenoid. The solenoid is driven by a Zeeman modulator operating at a frequency of 5 kHz. The circuit diagram of the modulator is shown in Fig. 1. It consists of a driver and an output stage capable of driving the solenoid with a maximum zero-based square-wave current of 8 A at 5 kHz. Because the shape of the square wave deteriorated seriously above 3.6 A a maximum square-wave. current of 3.6 A was used yielding a 12.162-G magnetic field. The field obtained at each current was measured using the known g values for the J = 7/2 lines. The absorption cell was enclosed in a micrometer-metal casing to reduce the earth’s magnetic field. The residual magnetic field inside the cell is less than 0.002 G. The klystrons used (Varian X-12 and OK1 24VlO,3OVlO, 35V10,45V12, 5OV10, 70Vll) were indirectly phase-locked, as described in Ref. (6), to the high-stability clock of an HP counter (5360A), whose frequency was checked 0022-2852/80/100332-07$02.00/O Copyright
0 1980 by Academic
All rights of reproduction
Press, Inc.
in any form reserved.
332
LOW-FIELD
ZEEMAN EFFECT OF OH TO + IBV
t
FINAL
STAGE
RET O/P
ZEEMAN
MODULATOR
m/vi!%
STAGE
5KHz
IN%% DRIVER STAGE
ZEEMAN FIG. 1. Circuit diagram of the Zeeman modulator.
against the WWV time standard: klystron frequencies thus obtained are accurate to better than one part in 107. OH radicals were produced by reacting ozone with atomic hydrogen. The total pressure inside the absorption cell is maintained at about 15 mTorr. The full linewidth at half-maximum at this pressure is found to be about 200 kHz. The SIN ratio of OH lines at an effective time constant of 2 set is of the order of 1000/l. With this resolution and sensitivity we were able to measure the frequency
334
SASTRY AND VANDERLINDE
b J = 15/2 F=
6-6
B=
7.276
G
I 70.057.0
I
70,861.O
e--MHz
FIG. 2. (a) OH, z&,2, J = 712, F = 4-4 zero-field line. Modulation 5.368 G. Effective time constant 2 sec. (b) Spectrum of OH, 2113,2,J = 15/2, F = 8-8 line, B = 7.276 G. Effective time constant is 2 sec.
of the unsplit main line to an accuracy of 5 kHz and the Zeeman components to an accuracy of 10 kHz or better. Figures 2a and b show typical signals obtained by this spectrometer. THEORY AND RESULTS
The J = 712 Level
The microwave absorption spectrum of OH is due to transitions between the members of a A doublet having different Kronig symmetry. Each member of
LOW-FIELD
FIG. 3. Spectrum
this doublet
ZEEMAN
EFFECT
of OH, Z&,2. J = 7/2. Vertical
is further
335
OF OH
bars represent
the calculated
spectrum.
split by hyperhne effects. For J = 7/2 we observe the as well as the much weaker F = 3 -+ 4
F = 4 + 4 and F = 3 + 3 transitions. and F = 4 + 3 transitions.
In the present experiment the applied magnetic field is perpendicular to the microwave E field; hence transitions having AmF = +-1 are observed. Since the g factors of the + and - levels are very close, normally one expects only two Zeeman components corresponding to Am F = ? 1 transitions near each AF = 0 main line. However, the two hyperhne levels, F = 3,4, of the same symmetry are nearly degenerate. Consequently, the magnetic field will partially decouple I and J, mixing the levels having the same mF value. We observed nonlinear Zeeman effects for this transition. The theoretical spectrum was generated as shown in Fig. 3, using the g factors obtained by Radford (1) and using the Zeeman Hamiltonian Xz = -/L.,J.B
- /.L,I.B.
The basis functions used are IJ,Z,F,mF) IJ,Z,F’,mF)
= r-y1I./, Z, mF + l/2, ml = -l/2)
+ p, (J, I, mF - l/2, m, = +1/2),
= a,IJ,Z,
+ &lJ,
mF + l/2, ml = -l/2)
I, mF -
l/2, m, = +1/2),
where
t
’
2J+l
I
(J + 1/2) + mF
1’2
( ap =
(J + 112) + mF
(J + 1/2) - m,? 1’2
a, = -
2J+l
I
’
P* = (
2J+l
I’* 1
(J + 1/2) - mF P2
=
(
2J+l
’ 1’2
i
’
F and F’ correspond to the J + l/2 and J - l/2 levels of the same symmetry. In this case F = 4 and F’ = 3. On this basis
r
EF + m(J
X=
F’, m
F, m - s
-(Fz~~2)1’2B(pl
+ f!-)B
- p,)
-(
F2iFm’
EFt + mB(J
)“‘B(P,
- g
- PI)
+ $-)
The secular equation is solved for each mF level to obtain 16 energy levels of each
TABLE Molecular
Parameters
of the OH 2II3,2, J = 712 Level
Used for Calibration REF.
VALUE
PARAMETER
UO
I
F = 49
13433.956 +
.005
This work
F = 3-3
13434.643 f
.005
This work
F = 4-4
13441.438 f
.005
This work
F = 3-4
13442.129 f
.005
This work
9+
0.32454 f 0.00004
RAOFORO
9-
0.32668 f 0.00004
RAOFORO
91 = -3.042 Y 10-3
Kronig symmetry. Applying the selection rules AmF = + 1, AF = 0, k 1, 56 Zeeman components are obtained at a particular magnetic field. Of these 56 Zeeman components about 20 well-resolved Zeeman lobes are used for the field calibration. A typical observed Zeeman spectrum, along with the calculated spectrum, is shown in Fig. 3. The accuracy of the calibrated field is about 0.1%. The constants used in this calculation are given in Table I. The J = 912, 1112, 1312, and 1512 Levels For these levels the hypetline splittings are sufficiently large so that the Zeeman components merge into AmF = kl lob es, where the individual Zeeman components are not resolved. Only the AF = 0 transitions were studied for each of these levels. The spectra were obtained at five different field values ranging from 5.633 to 12.162 G. The observed Zeeman splittings for these transitions are given in Table II. At each field setting an average of at least three different traces with an effective time constant of 2 set were used to obtain data. g, factors were obtained using the frequency spacing between AmF = + 1 and AmF = - 1 Zeeman components. In this way any nonlinearity due to the quadratic term in the Zeeman spectrum is eliminated. Assuming strong coupling of Z and J, the observed g, is
TABLE Observed
FIELD pJSS)
Zeeman
J-912 F=4_4 =_1giq AM=+1 '&I
Splittings
II
for the 2113,2, F + F J = 912, 11/2, 1312, and 1512 Lines
of OH
Av(MHz) F=5-5
1A&+
F=5-5
5=11/Z
F=& A&-l
5.1312 F-6-6 F=7-7 AM=+1 A#-, A&+1 A#-, ---~
J=15/2 F.&Z3 F=7-7 hM=+l M=-1 nM=+, *M=-l ----
5.363 -2.096
2.016 -1.658
1.696 -1.657
1.640 -1.392
1.403 -1.329
1.367 -1.175
1.192 -1.144
1.141 -1.000
0.995
7.276 -2.801
2.710 -2.232
2.276 -2.222
2.174 -1.854
1.880 -1.786
1.830 -1.568
1.585 -1.524
1.539 -1.351
1.339
8.407 -3.234
3.127 -2.537
2.670 -2.575
2.512 -2.132
2.157 -2.050
2.108 -1.813
1.832 -1.755
1.775 -1.547
1.545
9.955 -3.836
3.682 -3.002
3.154 -3.068
2.946 -2.510
2.546 -2.447
2.517 -2.131
2.151 -2.069
2.106 -1.839
1.809
12.162 -5.067
4.430 -3.629
3.933 -3.728
3.556 -3.071
3.115 -2.990
3.061 -2.613
2.615 -2.500
2.586 -2.212
2.222
336
LOW-FIELD
ZEEMAN
337
EFFECT OF OH
TABLE III Experimental
Results. Calculated and Observed Molecular g Factors b9J)5
OH LEVEL
(6QJ)N
1/w6QJ);+ (&lJ;l
gJ Cdl.
gJ Obs.
2, 312 3 = 9/z
0.24493
0.00020
-0.00054
0.00137
0.2460
0.2465 + 0.0008
J = 11/Z
0.1975
0.00018
-0.00055
0.00141
0.1983
0.1996 : 0.0006
J = 13/z
0.16534
0.00015
-0.00055
0.00743
0.1664
0.1665 t 0.0005
J = 15/z
0.14239
0.00014
-0.00056
0.00145
L
0.1434
0.1409 t 0.0004
related to g, by g, = (1 ? l/(25 + l))gJ. The value of was first calculated by least-squares fitting the data for each pair of lines to Au = g,,p,,B. This procedure accords more importance to the higher-field results than to those at low field in determining As considerable broadening occurs at higher fields, it was felt that it is more realistic to compute the simple average of g, = Av/~,B. The standard deviation of the mean was estimated as the square root of the ratio of the sample variance to the number of data points. g, factors as well as the calculated average of g: and g; are given in Table III. The g factors are calculated using the equations given by Radford (1) and the constants given by Beaudet and Poynter (2). gJ
gJ.
DISCUSSION
The observed g factors shown in Table III agree fairly well with the calculated factors. The errors indicated in the observed g factors correspond to one standard deviation. The accuracy of the observed g factors is slightly better than 0.5%. Although this accuracy is an order of magnitude worse than that which could be obtained by ESR spectra at high fields, it is possible to improve the accuracy of these measurements considerably by working in dc magnetic fields of about 100 G and using the square-wave magnetic field to modulate the lines. Presently, we are planning to use this method. The frequencies of the J = 7/2 transition given in Table I do not agree with those obtained by Destombes and Marliere (7) within the experimental errors. We believe our measurements to be accurate to the error limits quoted. We have, to our knowledge, measured the F = 3 + 4 and F = 4 - 3 transitions directly for the first time. The combination differences show our results to be internally consistent. Interestingly our measured frequencies are closer to the calculated frequencies of Beaudet and Poynter (2). Ter Meulen er al. (8) measured the frequencies of the J = 712, F = 4 + 4, and F = 3 + 3 transitions accurately using a molecular beam maser. Though the 4 - 4 transition frequency we measured is consistent with their result, the 3 + 3 transition differs significantly. We can find no plausible reason for this discrepancy.
SASTRY
338
AND VANDERLINDE
ACKNOWLEDGMENTS We are grateful to the National Science and Engineering Research Council of Canada for financial support. We wish to thank Mr. A. Makosinski for his help in building the Zeeman modulator and
Mr. D. Homibrook RECEIVED:
for fabricating microwave components.
September
21, 1979 REFERENCES
I. H. E. RADFORD, Phys. Rev. 122, 114-130 (1961). 2. R. A. BEAUDET AND R. L. POYNTER, J. Phys. Chem. Ref. Data 7, 311-362 (1978). 3. H. E. RADFORD, Phys. Rev. 126, 1035-1045 (1962). 4. D. R. JOHNSONAND C. C. LIN, J. Mol. Spectrosc. 23, 201-209 (1967). 5. J. M. BROWN, M. KAISE, C. M. L. KERR, AND D. J. MILTON, Mol. Phys. 36, 553-582 (1978). 6. J. A. COXON, K. V. L. N. SASTRY, J. A. AUSTIN, AND D. H. LEVY, Canad. J. Phys. 56,
619-634 (1979). 7. J. L. DESTOMBESAND C. MARLIERE, Chem. Phys. Lett. 34, 532-536 (1975). 8. J. J. TER MEULEN, W. L. MEERTS, G. W. M. VAN MIERLO, AND A. DYMANUS, Phys. Rev. Lett. 36, 1031-1034
(1976).
OF
MOLECULAR
Low-Field
SPECTROSCOPY
83, 332-338 (1980)
Zeeman Effect of OH in the 2l&,2, J = 7/2, 9/2, 1 l/2, 13/2, and 15/2 States K. V. L. N. SASTRY ANDJ.
VANDERLINDE
Department of Physics, university of New Brunswick, Fredericton. New Brunswick, E3B 5,43, Canada The Zeeman effect of OH in the X *&, .I = 112, 912, 1112, 1312, and 1512 levels, in magnetic fields up to 12 G was investigated using a square-wave Zeeman modulation microwave spectrometer. The molecular g factors obtained are compared with those calculated from a theory by Radford [Phys. Rev. 122, 114-130(1961)]. The X 2II3,2, J = 712, F = 3 -+ 4, and F = 4 -+ 3 transitions were directly measured for the first time. INTRODUCTION
The microwave spectrum of the OH radical has been investigated by many workers over several decades (2). Radford (I, 3) studied the ESR spectrum of OH in the 2II3,2 state, J = 312, 5/2, and 712 levels and in the *I& state, J = 3/2 and 5/2 levels. Johnson and Lin (4) studied the low-field Zeeman effect in the *IIs,*, J = 9/2 level. More recently Brown et al. (5) investigated the ESR spectrum in the *l&,2, J = 9/2 and 11/2 levels at 26 and 35 GHz, respectively. The present work describes a systematic study of the low-field Zeeman effect of the OH radical in the *IIs,*, J = 712, 912, 11/2, 13/2, and 15/2 states. EXPERIMENTAL
DETAILS
The microwave spectrum of OH was observed using a 5-kHz square-wave Zeeman modulation spectrometer. The absorption cell consists of a 120-cm-long, 7-cm-diameter Pyrex tube. A solenoid is wound on the tube in four sections using #20 copper wire. The four coils are connected in parallel to reduce the inductance of the solenoid. The solenoid is driven by a Zeeman modulator operating at a frequency of 5 kHz. The circuit diagram of the modulator is shown in Fig. 1. It consists of a driver and an output stage capable of driving the solenoid with a maximum zero-based square-wave current of 8 A at 5 kHz. Because the shape of the square wave deteriorated seriously above 3.6 A a maximum square-wave. current of 3.6 A was used yielding a 12.162-G magnetic field. The field obtained at each current was measured using the known g values for the J = 7/2 lines. The absorption cell was enclosed in a micrometer-metal casing to reduce the earth’s magnetic field. The residual magnetic field inside the cell is less than 0.002 G. The klystrons used (Varian X-12 and OK1 24VlO,3OVlO, 35V10,45V12, 5OV10, 70Vll) were indirectly phase-locked, as described in Ref. (6), to the high-stability clock of an HP counter (5360A), whose frequency was checked 0022-2852/80/100332-07$02.00/O Copyright
0 1980 by Academic
All rights of reproduction
Press, Inc.
in any form reserved.
332
LOW-FIELD
ZEEMAN EFFECT OF OH TO + IBV
t
FINAL
STAGE
RET O/P
ZEEMAN
MODULATOR
m/vi!%
STAGE
5KHz
IN%% DRIVER STAGE
ZEEMAN FIG. 1. Circuit diagram of the Zeeman modulator.
against the WWV time standard: klystron frequencies thus obtained are accurate to better than one part in 107. OH radicals were produced by reacting ozone with atomic hydrogen. The total pressure inside the absorption cell is maintained at about 15 mTorr. The full linewidth at half-maximum at this pressure is found to be about 200 kHz. The SIN ratio of OH lines at an effective time constant of 2 set is of the order of 1000/l. With this resolution and sensitivity we were able to measure the frequency
334
SASTRY AND VANDERLINDE
b J = 15/2 F=
6-6
B=
7.276
G
I 70.057.0
I
70,861.O
e--MHz
FIG. 2. (a) OH, z&,2, J = 712, F = 4-4 zero-field line. Modulation 5.368 G. Effective time constant 2 sec. (b) Spectrum of OH, 2113,2,J = 15/2, F = 8-8 line, B = 7.276 G. Effective time constant is 2 sec.
of the unsplit main line to an accuracy of 5 kHz and the Zeeman components to an accuracy of 10 kHz or better. Figures 2a and b show typical signals obtained by this spectrometer. THEORY AND RESULTS
The J = 712 Level
The microwave absorption spectrum of OH is due to transitions between the members of a A doublet having different Kronig symmetry. Each member of
LOW-FIELD
FIG. 3. Spectrum
this doublet
ZEEMAN
EFFECT
of OH, Z&,2. J = 7/2. Vertical
is further
335
OF OH
bars represent
the calculated
spectrum.
split by hyperhne effects. For J = 7/2 we observe the as well as the much weaker F = 3 -+ 4
F = 4 + 4 and F = 3 + 3 transitions. and F = 4 + 3 transitions.
In the present experiment the applied magnetic field is perpendicular to the microwave E field; hence transitions having AmF = +-1 are observed. Since the g factors of the + and - levels are very close, normally one expects only two Zeeman components corresponding to Am F = ? 1 transitions near each AF = 0 main line. However, the two hyperhne levels, F = 3,4, of the same symmetry are nearly degenerate. Consequently, the magnetic field will partially decouple I and J, mixing the levels having the same mF value. We observed nonlinear Zeeman effects for this transition. The theoretical spectrum was generated as shown in Fig. 3, using the g factors obtained by Radford (1) and using the Zeeman Hamiltonian Xz = -/L.,J.B
- /.L,I.B.
The basis functions used are IJ,Z,F,mF) IJ,Z,F’,mF)
= r-y1I./, Z, mF + l/2, ml = -l/2)
+ p, (J, I, mF - l/2, m, = +1/2),
= a,IJ,Z,
+ &lJ,
mF + l/2, ml = -l/2)
I, mF -
l/2, m, = +1/2),
where
t
’
2J+l
I
(J + 1/2) + mF
1’2
( ap =
(J + 112) + mF
(J + 1/2) - m,? 1’2
a, = -
2J+l
I
’
P* = (
2J+l
I’* 1
(J + 1/2) - mF P2
=
(
2J+l
’ 1’2
i
’
F and F’ correspond to the J + l/2 and J - l/2 levels of the same symmetry. In this case F = 4 and F’ = 3. On this basis
r
EF + m(J
X=
F’, m
F, m - s
-(Fz~~2)1’2B(pl
+ f!-)B
- p,)
-(
F2iFm’
EFt + mB(J
)“‘B(P,
- g
- PI)
+ $-)
The secular equation is solved for each mF level to obtain 16 energy levels of each
TABLE Molecular
Parameters
of the OH 2II3,2, J = 712 Level
Used for Calibration REF.
VALUE
PARAMETER
UO
I
F = 49
13433.956 +
.005
This work
F = 3-3
13434.643 f
.005
This work
F = 4-4
13441.438 f
.005
This work
F = 3-4
13442.129 f
.005
This work
9+
0.32454 f 0.00004
RAOFORO
9-
0.32668 f 0.00004
RAOFORO
91 = -3.042 Y 10-3
Kronig symmetry. Applying the selection rules AmF = + 1, AF = 0, k 1, 56 Zeeman components are obtained at a particular magnetic field. Of these 56 Zeeman components about 20 well-resolved Zeeman lobes are used for the field calibration. A typical observed Zeeman spectrum, along with the calculated spectrum, is shown in Fig. 3. The accuracy of the calibrated field is about 0.1%. The constants used in this calculation are given in Table I. The J = 912, 1112, 1312, and 1512 Levels For these levels the hypetline splittings are sufficiently large so that the Zeeman components merge into AmF = kl lob es, where the individual Zeeman components are not resolved. Only the AF = 0 transitions were studied for each of these levels. The spectra were obtained at five different field values ranging from 5.633 to 12.162 G. The observed Zeeman splittings for these transitions are given in Table II. At each field setting an average of at least three different traces with an effective time constant of 2 set were used to obtain data. g, factors were obtained using the frequency spacing between AmF = + 1 and AmF = - 1 Zeeman components. In this way any nonlinearity due to the quadratic term in the Zeeman spectrum is eliminated. Assuming strong coupling of Z and J, the observed g, is
TABLE Observed
FIELD pJSS)
Zeeman
J-912 F=4_4 =_1giq AM=+1 '&I
Splittings
II
for the 2113,2, F + F J = 912, 11/2, 1312, and 1512 Lines
of OH
Av(MHz) F=5-5
1A&+
F=5-5
5=11/Z
F=& A&-l
5.1312 F-6-6 F=7-7 AM=+1 A#-, A&+1 A#-, ---~
J=15/2 F.&Z3 F=7-7 hM=+l M=-1 nM=+, *M=-l ----
5.363 -2.096
2.016 -1.658
1.696 -1.657
1.640 -1.392
1.403 -1.329
1.367 -1.175
1.192 -1.144
1.141 -1.000
0.995
7.276 -2.801
2.710 -2.232
2.276 -2.222
2.174 -1.854
1.880 -1.786
1.830 -1.568
1.585 -1.524
1.539 -1.351
1.339
8.407 -3.234
3.127 -2.537
2.670 -2.575
2.512 -2.132
2.157 -2.050
2.108 -1.813
1.832 -1.755
1.775 -1.547
1.545
9.955 -3.836
3.682 -3.002
3.154 -3.068
2.946 -2.510
2.546 -2.447
2.517 -2.131
2.151 -2.069
2.106 -1.839
1.809
12.162 -5.067
4.430 -3.629
3.933 -3.728
3.556 -3.071
3.115 -2.990
3.061 -2.613
2.615 -2.500
2.586 -2.212
2.222
336
LOW-FIELD
ZEEMAN
337
EFFECT OF OH
TABLE III Experimental
Results. Calculated and Observed Molecular g Factors b9J)5
OH LEVEL
(6QJ)N
1/w6QJ);+ (&lJ;l
gJ Cdl.
gJ Obs.
2, 312 3 = 9/z
0.24493
0.00020
-0.00054
0.00137
0.2460
0.2465 + 0.0008
J = 11/Z
0.1975
0.00018
-0.00055
0.00141
0.1983
0.1996 : 0.0006
J = 13/z
0.16534
0.00015
-0.00055
0.00743
0.1664
0.1665 t 0.0005
J = 15/z
0.14239
0.00014
-0.00056
0.00145
L
0.1434
0.1409 t 0.0004
related to g, by g, = (1 ? l/(25 + l))gJ. The value of was first calculated by least-squares fitting the data for each pair of lines to Au = g,,p,,B. This procedure accords more importance to the higher-field results than to those at low field in determining As considerable broadening occurs at higher fields, it was felt that it is more realistic to compute the simple average of g, = Av/~,B. The standard deviation of the mean was estimated as the square root of the ratio of the sample variance to the number of data points. g, factors as well as the calculated average of g: and g; are given in Table III. The g factors are calculated using the equations given by Radford (1) and the constants given by Beaudet and Poynter (2). gJ
gJ.
DISCUSSION
The observed g factors shown in Table III agree fairly well with the calculated factors. The errors indicated in the observed g factors correspond to one standard deviation. The accuracy of the observed g factors is slightly better than 0.5%. Although this accuracy is an order of magnitude worse than that which could be obtained by ESR spectra at high fields, it is possible to improve the accuracy of these measurements considerably by working in dc magnetic fields of about 100 G and using the square-wave magnetic field to modulate the lines. Presently, we are planning to use this method. The frequencies of the J = 7/2 transition given in Table I do not agree with those obtained by Destombes and Marliere (7) within the experimental errors. We believe our measurements to be accurate to the error limits quoted. We have, to our knowledge, measured the F = 3 + 4 and F = 4 - 3 transitions directly for the first time. The combination differences show our results to be internally consistent. Interestingly our measured frequencies are closer to the calculated frequencies of Beaudet and Poynter (2). Ter Meulen er al. (8) measured the frequencies of the J = 712, F = 4 + 4, and F = 3 + 3 transitions accurately using a molecular beam maser. Though the 4 - 4 transition frequency we measured is consistent with their result, the 3 + 3 transition differs significantly. We can find no plausible reason for this discrepancy.
SASTRY
338
AND VANDERLINDE
ACKNOWLEDGMENTS We are grateful to the National Science and Engineering Research Council of Canada for financial support. We wish to thank Mr. A. Makosinski for his help in building the Zeeman modulator and
Mr. D. Homibrook RECEIVED:
for fabricating microwave components.
September
21, 1979 REFERENCES
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