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The hyperfine spectrum of KF
Journal of Molecular Structure, 190 (1988) 143-148 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
THE HYPERFINE
SPECTRUM
143
OF KF*
G. PAQUETTE, A. KOTZ, J. CEDERBERG, D. NITZ, A. KOLAN, D. OLSON, K. GUNDERSON, S. LINDAAS and S. WICK Physics Department, St. Olaf College, Northfield, MN 55057 (U.S.A.) (Received 1 February 1988)
ABSTRACT A molecular beam electric resonance spectrometer was used to observe the hyperfine spectrum of KF, including both K isotopes, vibrational states O-7 and rotational states l-3. The 73 observed transitions were fitted with 14 parameters expressing the vibrational and rotational dependence of each of the molecular hyperfine constants. Experimental uncertainties of the order of 1 Hz were achieved.
Molecular beam resonance techniques have been widely used over the years to examine the hyperfine interactions of simple molecules in various rotational and vibrational states. We present here a systematic experimental study of KF in vibrational states O-7 and rotational states 1-3, including both potassium isotopes. The experimental and analytical techniques used were similar to those of earlier papers on KC1 [ 11 and NaBr [ 2 1. The KF molecule has been studied previously using a similar molecular beam electric resonance technique [3] with uncertainties of a few hundred hertz. The 2 m transition region used in our experiment produces a linewidth of about 200 Hz, and our statistical technique of finding the line center and extrapolating to zero field allows us to achieve an uncertainty in the zero-field line frequency of less than 1 Hz for the stronger transitions. With this precision we were able to resolve several additional terms which express the dependence of the hyperfine constants on both vibrational and rotational state. By comparing the spectrum of 41K1gFwith that of 3gK1gFwe were able to obtain an improved value for the nuclear quadrupole moment ratio of the two potassium isotopes. A total of 73 transitions were measured, 67 for 3gK1gFand 6 for 41K1gF.In order to achieve the best possible precision for these measurements, two techniques developed in connection with the NaBr study [ 21 were used. The first technique is a statistical method, using the reflection symmetry of the spectral *Dedicated to the memory of Professor Walter Gordy.
0022-2860/88/$03.50
0 1988 Elsevier Science Publishers B.V.
144 TABLE 1 Comparison of experimental data with fit v
J
n,
n2
Obs. freq.
Uncert.
Pred. freq.
0.00650 0.05300 0.05506 0.05300 0.05300 0.05200 0.05100 0.05300 0.05300 0.05400 0.01600 0.01200 0.05300 0.05300 0.05300 0.05300 0.00980 0.00550 0.00370 0.00250 0.00250 0.05000 0.00990 0.00770 0.00400 0.00340 0.00250 0.00170 0.00083 0.00060 0.01070 0.00740 0.00600 0.00430 0.00320 0.00210 0.05000 0.00740 0.00510 0.00350 0.00220 0.00170 0.00560 0.00490 0.00340
1987.28371 1559.30361 1578.46634 1553.48403 1572.52180 1591.82029 3479.79952 3522.48149 3565.75004 3484.67841 3527.40691 3570.72199 1598.57724 3486.41952 3529.16996 3572.50699 1892.01474 1915.15253 1938.60433 1962.37607 1986.47368 1961.30872 3118.62870 3156.62870 3195.13658 3234.16248 3273.71656 3313.80898 3354.44989 3395.64944 3214.13021 3253.35688 3293.11173 3333.40490 3374.24656 3415.64686 1981.61107 1880.41012 1903.34949 1926.59691 1950.15829 1974.03956 3233.57282 3273.12134 3313.20820
Resid.
Ratio (resid./uncert.)
0.01829 -0.00861 -0.01034 - 0.00503 -0.00780 -0.01629 0.01348 0.04451 0.03396 0.02059 -0.02281 -0.01369 -0.03124 0.09848 0.07404 0.03101 -0.00384 0.00337 -0.00083 - 0.00097 -0.00128 -0.05872 - 0.00920 0.00150 -0.00098 -0.00178 -0.00166 0.00002 0.00055 -0.00028 0.02599 0.00362 0.00077 - 0.00130 -0.00316 -0.00016 0.02893 0.00638 - 0.00329 - 0.00231 -0.00109 0.00384 0.00178 -0.00164 0.00000
2.81457 -0.16253 -0.18793 - 0.09489 -0.14710 -0.31336 0.26437 0.83987 0.64073 0.38133 - 1.42545 - 1.14100 -0.58946 1.85820 1.39702 0.58514 -0.39187 0.61332 -0.22444 -0.38992 -0.51336 - 1.17432 - 0.92882 0.19450 - 0.24485 -0.52393 -0.66531 0.01170 0.66645 -0.46419 2.42898 0.48894 0.12863 -0.30328 -0.98885 -0.07803 0.57862 0.86167 -0.64559 - 0.65880 -0.49369 2.26113 0.31806 -0.33440 0.00115
Transitions observed for “9K’gF 0113 115 015 215 1 1 5 015 215 115 015 2 15 1 1 5 015 016 216 1 1 6 016 421 321 2213 1213 0213 022 727 627 527 427 327 227 127 027 527 427 327 227 127 027 027 527 427 327 227 127 428 328 228
1 1 2 2 2 3 3 3 4 4 4 2 3 3 3 3 3
3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 5 6 6 6 6 6 4 4 4
1987.30200 1559.29500 1578.45600 1553.47900 1572.51400 1591.80400 3479.81300 3522.52600 3565.78400 3484.69900 3527.38410 3570.70830 1598.54600 3486.51800 3529.24400 3572.53800 1892.01090 1915.15590 1938.60350 1962.37510 1986.47240 1961.25000 3118.61950 3156.63020 3195.13560 3234.16070 3273.71490 3313.80900 3354.45044 3395.64916 3214.15620 3253.36050 3293.11250 3333.40360 3374.24340 3415.64670 1981.64000 1880.41650 1903.34620 1926.59460 1950.15720 1974.04340 3233.57460 3273.11970 3313.20820
145 TABLE 1 (continued)
v
J
n,
n2
Obs. freq.
Uncert.
Pred. freq.
Resid.
Ratio (resid./uncert.)
0.00270 0.00210 0.00660 0.00790 0.05000 0.05500 0.01100 0.00640 0.00450 0.00350 0.00220 0.00170 0.00140 0.01300 0.01800 0.00520 0.01200 0.01900 0.01400 0.01100 0.01100
3353.84355 3395.03754 1913.65742 1937.16666 1961.00175 2905.61832 2938.35842 1865.15250 1887.92979 1911.01517 1934.41457 1958.13393 1982.17915 1941.00062 1964.71123 1988.74177 2013.09814 1878.46145 1901.52271 1924.90393 1948.61103
0.00025 -0.00014 0.00438 -0.00266 -0.00175 -0.01532 0.02968 0.00830 0.00071 0.00153 -0.00167 0.00007 0.00105 - 0.00482 -0.01563 -0.01637 - 0.00504 - 0.00505 -0.00011 0.00247 -0.00383
0.09388 -0.06900 0.66410 -0.33714 -0.03500 -0.27850 2.69849 1.29672 0.15881 0.43747 -0.76134 0.04284 0.75075 - 0.37056 -0.86841 -3.14729 - 0.42035 - 0.26559 -0.00796 0.22444 -0.34808
0.01800 0.01100 0.02500 0.02900 0.01300 0.01500
4155.51053 4135.68047 3539.05482 4105.52531 4085.89372 4036.77644
- 0.00373 0.00553 - 0.03862 - 0.02781 0.01298 - 0.00564
- 0.20731 0.50245 - 1.54482 - 0.95889 0.99871 - 0.37577
Transitions observed for 39K’9F 128 028 228 128 028 037 037 537 437 337 237 1 3 037 337 237 137 037 338 238 138 038
7
4 4 5 5 5 3 4 5 5 5 5 5 5 6 6 6 6 5 5 5 5
3353.84380 3395.03740 1913.66180 1937.16400 1961.00000 2905.60300 2938.38810 1865.16080 1887.93050 1911.01670 1934.41290 1958.13400 1982.18020 1940.99580 1964.69560 1988.72540 2013.09310 1878.45640 1901.52260 1924.90640 1948.60720
Transitions observed for 4’K’9F 027 027 037 127 127 227
4 3 3 4 3 3
4155.50680 4135.68600 3539.01620 4105.49750 4085.90670 4036.77080
lines to locate the centers. The second technique involves the use of several measurements for each transition at different d.c. and r.f. fields, extrapolating to a true zero-field frequency to eliminate the small stark shifts of the actual transitions. The extrapolated zero-field transition frequencies are listed in Table 1. The hyperfine Hamiltonian for the KF molecule in zero external field consists of six terms. H/h=V~~QK+~KIK~J+~FIF~J+~~IK~D~IF+~IIK~IF+~K~~K The first five, just as in refs. l-3, are, respectively, the potassium nuclear quad-
146 TABLE 2 Molecular constants
obtained
from fit
Term Potassium
eQqO, eQq10 eQqzO eQqSO eQqO, eQq,,
Potassium
Fitted constants
for 3gKF
Constants
for *lKF
nuclear quadrupole -7981.013 97.566 -0.6695 0.00395 0.0306 -0.0012
(0.008) (0.006) (0.0021) (0.00024) (0.0010) (0.0005)
-9716.845 117.852 -0.8022 0.00470 0.0367 -0.0014
(0.015) (0.007) (0.0025) (0.00027) (0.0012) (0.0006)
spin-rotation
CKO
CK1
0.2005 -0.0031
(0.0006) (0.0003)
0.1083 -0.0017
(0.0008) (0.0002)
10.8325 -0.1094
(0.0021) (0.0009)
10.659 -0.1068
(0.003) (0.0009)
0.4749 -0.0065
(0.0027) (0.0010)
0.2606 - 0.0035
(0.0015) (0.0005)
0.0578
(0.0013)
0.0317
(0.0007)
Fluorine spin-rotation cFO
cF1
Tensor spin-spin %I %I Scalar spin-spin cd Nuclear moment ratio
Q(“‘K)/Q(3gK)
Reduced X-square of fit “All values except eQq,, computed
1.217699 (0.000055) 1.14
0.95
from 3gKF values.
rupole interaction, the potassium spin-rotation interaction, the fluorine spinrotation interaction, the tensor part of the spin-spin interaction and the scalar spin-spin interaction. The sixth, expressing the nuclear magnetic octupole interaction of the potassium nucleus, is included here for completeness, although it does not differ significantly from zero in the fitting of the data. In our data analysis we found it necessary to expand the parameters related to most of these interactions in terms which depended on their vibrational and rotational state. This can be done on the basis of the Born-Oppenheimer approximation as described in ref. 1. For the nuclear quadrupole interaction six terms were needed
which are complete to third order in the parameter B,/ao,. For the spin-rotation interactions and the tensor spin-spin interaction two terms were needed
147
CF =cFO
+C&+f)
c3 =c30
+c,,(u+f)
No vibrational dependence of c4 was necessary. These 13 parameters were evaluated from the data for the 67 line frequencies of 3gK’gF using a least-squares procedure, with the results listed in Table 2. The reduced X-squared value of this fit was about 1.14, which indicated excellent agreement between the data and the 13 parameter model in relation to the error estimates that were given by the center-finding and extrapolation procedures. Because the natural abundance of 41K is less than 7%, the transitions for this isotope were much weaker than for 3gK. With only a few transitions strong enough to be readily observed, we were unable to fit all 13 parameters independently. Instead, our procedure was to take advantage of the expected isotopic transformations of the different interactions. With the exception of eQq,,, the values for 41KF can be calculated from those for 3gKF using the reduced mass ratio and the nuclear moment ratios, as shown in Table 3. According to the derivations of Schlier [ 41, qoo should be given by q,,=q,+
[(-2
a,+?
a,a2-g
a, yql+ 2
(-5x2+fa,
2)42-Ti
w3+;
q41
(> 2
e
In this expression, the qe term gives rise to a term of eQq,, which is independent of the reduced mass, whereas the remainder is inversely proportional to the reduced mass. These observations were sufficient to allow us to fit the observed transitions of 41KF using only two free parameters, namely eQq,, and the nuTABLE 3 Isotope substitution
relations (whereB=
[B,/w,(4’KF)]/[B,/~,(39KF)]
(where ,u=~(“‘K)/,u(“~K))
andQ=Q(4’K)/Q(39K))
148
clear electric quadrupole moment ratio, Q( 41K) /Q ( 3gK). The results are listed in Table 2. The reduced X-squared values of the 41KF fit is about 0.95, indicating excellent agreement between the model and the data. The new value of the nuclear electric quadrupole moment ratio is a significant improvement over the value of 1.2177 + 0.0006 cited in ref. 3. It appears that both isotopes of KF can be quite satisfactorily treated to the precision of this experiment by the standard Hamiltonian without resorting to a nuclear octupole interaction or any new Born-Oppenheimer violating effects. ACKNOWLEDGEMENT
The authors express their appreciation for support for this work from a Northwest Area Foundation Grant of the Research Corporation and National Science Foundation RUI grants Nos. PHY -8319293 and PHY -8617538.
REFERENCES 1 D. Nitz, J. Cederberg, A. Kotz, K. Hetzler, T. Aakre and T. Walhout, J. Mol. Spectrosc., 108 (1984) 6. 2 J. Cederberg, D. Nitz, A. Kolan, T. Rasmusson, K. Hoffman and S. Tufte, J. Mol. Spectrosc., 122 (1987) 171. 3 R. van Wachem and A. Dymanus, J. Chem. Phys., 46 (1967) 3749. 4 Ch. Schlier, Fortschr. Phys., 9 (1961) 455.
THE HYPERFINE
SPECTRUM
143
OF KF*
G. PAQUETTE, A. KOTZ, J. CEDERBERG, D. NITZ, A. KOLAN, D. OLSON, K. GUNDERSON, S. LINDAAS and S. WICK Physics Department, St. Olaf College, Northfield, MN 55057 (U.S.A.) (Received 1 February 1988)
ABSTRACT A molecular beam electric resonance spectrometer was used to observe the hyperfine spectrum of KF, including both K isotopes, vibrational states O-7 and rotational states l-3. The 73 observed transitions were fitted with 14 parameters expressing the vibrational and rotational dependence of each of the molecular hyperfine constants. Experimental uncertainties of the order of 1 Hz were achieved.
Molecular beam resonance techniques have been widely used over the years to examine the hyperfine interactions of simple molecules in various rotational and vibrational states. We present here a systematic experimental study of KF in vibrational states O-7 and rotational states 1-3, including both potassium isotopes. The experimental and analytical techniques used were similar to those of earlier papers on KC1 [ 11 and NaBr [ 2 1. The KF molecule has been studied previously using a similar molecular beam electric resonance technique [3] with uncertainties of a few hundred hertz. The 2 m transition region used in our experiment produces a linewidth of about 200 Hz, and our statistical technique of finding the line center and extrapolating to zero field allows us to achieve an uncertainty in the zero-field line frequency of less than 1 Hz for the stronger transitions. With this precision we were able to resolve several additional terms which express the dependence of the hyperfine constants on both vibrational and rotational state. By comparing the spectrum of 41K1gFwith that of 3gK1gFwe were able to obtain an improved value for the nuclear quadrupole moment ratio of the two potassium isotopes. A total of 73 transitions were measured, 67 for 3gK1gFand 6 for 41K1gF.In order to achieve the best possible precision for these measurements, two techniques developed in connection with the NaBr study [ 21 were used. The first technique is a statistical method, using the reflection symmetry of the spectral *Dedicated to the memory of Professor Walter Gordy.
0022-2860/88/$03.50
0 1988 Elsevier Science Publishers B.V.
144 TABLE 1 Comparison of experimental data with fit v
J
n,
n2
Obs. freq.
Uncert.
Pred. freq.
0.00650 0.05300 0.05506 0.05300 0.05300 0.05200 0.05100 0.05300 0.05300 0.05400 0.01600 0.01200 0.05300 0.05300 0.05300 0.05300 0.00980 0.00550 0.00370 0.00250 0.00250 0.05000 0.00990 0.00770 0.00400 0.00340 0.00250 0.00170 0.00083 0.00060 0.01070 0.00740 0.00600 0.00430 0.00320 0.00210 0.05000 0.00740 0.00510 0.00350 0.00220 0.00170 0.00560 0.00490 0.00340
1987.28371 1559.30361 1578.46634 1553.48403 1572.52180 1591.82029 3479.79952 3522.48149 3565.75004 3484.67841 3527.40691 3570.72199 1598.57724 3486.41952 3529.16996 3572.50699 1892.01474 1915.15253 1938.60433 1962.37607 1986.47368 1961.30872 3118.62870 3156.62870 3195.13658 3234.16248 3273.71656 3313.80898 3354.44989 3395.64944 3214.13021 3253.35688 3293.11173 3333.40490 3374.24656 3415.64686 1981.61107 1880.41012 1903.34949 1926.59691 1950.15829 1974.03956 3233.57282 3273.12134 3313.20820
Resid.
Ratio (resid./uncert.)
0.01829 -0.00861 -0.01034 - 0.00503 -0.00780 -0.01629 0.01348 0.04451 0.03396 0.02059 -0.02281 -0.01369 -0.03124 0.09848 0.07404 0.03101 -0.00384 0.00337 -0.00083 - 0.00097 -0.00128 -0.05872 - 0.00920 0.00150 -0.00098 -0.00178 -0.00166 0.00002 0.00055 -0.00028 0.02599 0.00362 0.00077 - 0.00130 -0.00316 -0.00016 0.02893 0.00638 - 0.00329 - 0.00231 -0.00109 0.00384 0.00178 -0.00164 0.00000
2.81457 -0.16253 -0.18793 - 0.09489 -0.14710 -0.31336 0.26437 0.83987 0.64073 0.38133 - 1.42545 - 1.14100 -0.58946 1.85820 1.39702 0.58514 -0.39187 0.61332 -0.22444 -0.38992 -0.51336 - 1.17432 - 0.92882 0.19450 - 0.24485 -0.52393 -0.66531 0.01170 0.66645 -0.46419 2.42898 0.48894 0.12863 -0.30328 -0.98885 -0.07803 0.57862 0.86167 -0.64559 - 0.65880 -0.49369 2.26113 0.31806 -0.33440 0.00115
Transitions observed for “9K’gF 0113 115 015 215 1 1 5 015 215 115 015 2 15 1 1 5 015 016 216 1 1 6 016 421 321 2213 1213 0213 022 727 627 527 427 327 227 127 027 527 427 327 227 127 027 027 527 427 327 227 127 428 328 228
1 1 2 2 2 3 3 3 4 4 4 2 3 3 3 3 3
3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 5 6 6 6 6 6 4 4 4
1987.30200 1559.29500 1578.45600 1553.47900 1572.51400 1591.80400 3479.81300 3522.52600 3565.78400 3484.69900 3527.38410 3570.70830 1598.54600 3486.51800 3529.24400 3572.53800 1892.01090 1915.15590 1938.60350 1962.37510 1986.47240 1961.25000 3118.61950 3156.63020 3195.13560 3234.16070 3273.71490 3313.80900 3354.45044 3395.64916 3214.15620 3253.36050 3293.11250 3333.40360 3374.24340 3415.64670 1981.64000 1880.41650 1903.34620 1926.59460 1950.15720 1974.04340 3233.57460 3273.11970 3313.20820
145 TABLE 1 (continued)
v
J
n,
n2
Obs. freq.
Uncert.
Pred. freq.
Resid.
Ratio (resid./uncert.)
0.00270 0.00210 0.00660 0.00790 0.05000 0.05500 0.01100 0.00640 0.00450 0.00350 0.00220 0.00170 0.00140 0.01300 0.01800 0.00520 0.01200 0.01900 0.01400 0.01100 0.01100
3353.84355 3395.03754 1913.65742 1937.16666 1961.00175 2905.61832 2938.35842 1865.15250 1887.92979 1911.01517 1934.41457 1958.13393 1982.17915 1941.00062 1964.71123 1988.74177 2013.09814 1878.46145 1901.52271 1924.90393 1948.61103
0.00025 -0.00014 0.00438 -0.00266 -0.00175 -0.01532 0.02968 0.00830 0.00071 0.00153 -0.00167 0.00007 0.00105 - 0.00482 -0.01563 -0.01637 - 0.00504 - 0.00505 -0.00011 0.00247 -0.00383
0.09388 -0.06900 0.66410 -0.33714 -0.03500 -0.27850 2.69849 1.29672 0.15881 0.43747 -0.76134 0.04284 0.75075 - 0.37056 -0.86841 -3.14729 - 0.42035 - 0.26559 -0.00796 0.22444 -0.34808
0.01800 0.01100 0.02500 0.02900 0.01300 0.01500
4155.51053 4135.68047 3539.05482 4105.52531 4085.89372 4036.77644
- 0.00373 0.00553 - 0.03862 - 0.02781 0.01298 - 0.00564
- 0.20731 0.50245 - 1.54482 - 0.95889 0.99871 - 0.37577
Transitions observed for 39K’9F 128 028 228 128 028 037 037 537 437 337 237 1 3 037 337 237 137 037 338 238 138 038
7
4 4 5 5 5 3 4 5 5 5 5 5 5 6 6 6 6 5 5 5 5
3353.84380 3395.03740 1913.66180 1937.16400 1961.00000 2905.60300 2938.38810 1865.16080 1887.93050 1911.01670 1934.41290 1958.13400 1982.18020 1940.99580 1964.69560 1988.72540 2013.09310 1878.45640 1901.52260 1924.90640 1948.60720
Transitions observed for 4’K’9F 027 027 037 127 127 227
4 3 3 4 3 3
4155.50680 4135.68600 3539.01620 4105.49750 4085.90670 4036.77080
lines to locate the centers. The second technique involves the use of several measurements for each transition at different d.c. and r.f. fields, extrapolating to a true zero-field frequency to eliminate the small stark shifts of the actual transitions. The extrapolated zero-field transition frequencies are listed in Table 1. The hyperfine Hamiltonian for the KF molecule in zero external field consists of six terms. H/h=V~~QK+~KIK~J+~FIF~J+~~IK~D~IF+~IIK~IF+~K~~K The first five, just as in refs. l-3, are, respectively, the potassium nuclear quad-
146 TABLE 2 Molecular constants
obtained
from fit
Term Potassium
eQqO, eQq10 eQqzO eQqSO eQqO, eQq,,
Potassium
Fitted constants
for 3gKF
Constants
for *lKF
nuclear quadrupole -7981.013 97.566 -0.6695 0.00395 0.0306 -0.0012
(0.008) (0.006) (0.0021) (0.00024) (0.0010) (0.0005)
-9716.845 117.852 -0.8022 0.00470 0.0367 -0.0014
(0.015) (0.007) (0.0025) (0.00027) (0.0012) (0.0006)
spin-rotation
CKO
CK1
0.2005 -0.0031
(0.0006) (0.0003)
0.1083 -0.0017
(0.0008) (0.0002)
10.8325 -0.1094
(0.0021) (0.0009)
10.659 -0.1068
(0.003) (0.0009)
0.4749 -0.0065
(0.0027) (0.0010)
0.2606 - 0.0035
(0.0015) (0.0005)
0.0578
(0.0013)
0.0317
(0.0007)
Fluorine spin-rotation cFO
cF1
Tensor spin-spin %I %I Scalar spin-spin cd Nuclear moment ratio
Q(“‘K)/Q(3gK)
Reduced X-square of fit “All values except eQq,, computed
1.217699 (0.000055) 1.14
0.95
from 3gKF values.
rupole interaction, the potassium spin-rotation interaction, the fluorine spinrotation interaction, the tensor part of the spin-spin interaction and the scalar spin-spin interaction. The sixth, expressing the nuclear magnetic octupole interaction of the potassium nucleus, is included here for completeness, although it does not differ significantly from zero in the fitting of the data. In our data analysis we found it necessary to expand the parameters related to most of these interactions in terms which depended on their vibrational and rotational state. This can be done on the basis of the Born-Oppenheimer approximation as described in ref. 1. For the nuclear quadrupole interaction six terms were needed
which are complete to third order in the parameter B,/ao,. For the spin-rotation interactions and the tensor spin-spin interaction two terms were needed
147
CF =cFO
+C&+f)
c3 =c30
+c,,(u+f)
No vibrational dependence of c4 was necessary. These 13 parameters were evaluated from the data for the 67 line frequencies of 3gK’gF using a least-squares procedure, with the results listed in Table 2. The reduced X-squared value of this fit was about 1.14, which indicated excellent agreement between the data and the 13 parameter model in relation to the error estimates that were given by the center-finding and extrapolation procedures. Because the natural abundance of 41K is less than 7%, the transitions for this isotope were much weaker than for 3gK. With only a few transitions strong enough to be readily observed, we were unable to fit all 13 parameters independently. Instead, our procedure was to take advantage of the expected isotopic transformations of the different interactions. With the exception of eQq,,, the values for 41KF can be calculated from those for 3gKF using the reduced mass ratio and the nuclear moment ratios, as shown in Table 3. According to the derivations of Schlier [ 41, qoo should be given by q,,=q,+
[(-2
a,+?
a,a2-g
a, yql+ 2
(-5x2+fa,
2)42-Ti
w3+;
q41
(> 2
e
In this expression, the qe term gives rise to a term of eQq,, which is independent of the reduced mass, whereas the remainder is inversely proportional to the reduced mass. These observations were sufficient to allow us to fit the observed transitions of 41KF using only two free parameters, namely eQq,, and the nuTABLE 3 Isotope substitution
relations (whereB=
[B,/w,(4’KF)]/[B,/~,(39KF)]
(where ,u=~(“‘K)/,u(“~K))
andQ=Q(4’K)/Q(39K))
148
clear electric quadrupole moment ratio, Q( 41K) /Q ( 3gK). The results are listed in Table 2. The reduced X-squared values of the 41KF fit is about 0.95, indicating excellent agreement between the model and the data. The new value of the nuclear electric quadrupole moment ratio is a significant improvement over the value of 1.2177 + 0.0006 cited in ref. 3. It appears that both isotopes of KF can be quite satisfactorily treated to the precision of this experiment by the standard Hamiltonian without resorting to a nuclear octupole interaction or any new Born-Oppenheimer violating effects. ACKNOWLEDGEMENT
The authors express their appreciation for support for this work from a Northwest Area Foundation Grant of the Research Corporation and National Science Foundation RUI grants Nos. PHY -8319293 and PHY -8617538.
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