Hyperfine spectra of KBr and KI

Journal of Molecular Spectroscopy 250 (2008) 114–116

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Hyperfine spectra of KBr and KI James Cederberg *, J. Randolph 1, B. McDonald 2, B. Paulson, C. McEachern Department of Physics, St. Olaf College, 1520 St. Olaf Avenue, Northfield, MN 55057, USA

a r t i c l e

i n f o

Article history: Received 3 April 2008 In revised form 7 May 2008 Available online 27 May 2008

Keywords: Potassium Bromide Potassium Iodide Hyperfine interactions Nuclear electric quadrupole interaction Nuclear electric hexadecapole interaction Potassium iodide electric dipole moment

a b s t r a c t The molecular beam electric resonance technique has been used to conduct a high precision examination of the hyperfine spectra of 39K79Br, 39K81Br and 39K127I. Coupling constants for the nuclear electric quadrupole interactions, the spin–rotation interactions, the tensor and scalar spin–spin interactions, as well as the electric dipole moment of KI, and their dependence on vibrational and rotational state have been determined. A few transitions observed for 41K127I show a small shift in the iodine nuclear electric quadrupole interaction, and the fit improves somewhat with the inclusion of an iodine nuclear electric hexadecapole interaction term. Ó 2008 Elsevier Inc. All rights reserved.

1. Introduction In this paper, we present the results of an examination of the hyperfine spectra of the molecules KBr and KI, continuing our extended investigation [1–10] of alkali halide molecules using an electric resonance molecular beam spectrometer. The experimental details as they relate to the current experiments are described in a document included in Supplementary material. The quantum mechanics of the transition process is described in ref. [11]. The molecules KBr and KI, along with several other alkali halides, were examined by both microwave and molecular beam methods relatively early in the history of these techniques [12– 18]. Our current experiments improve upon these early measurements by 3 orders of magnitude in the precision of the hyperfine interactions for KBr and 5 orders of magnitude for KI. This precision is sufficient to show several additional terms in the dependence of the hyperfine interactions on vibrational and rotational state. This dependence for each interaction parameter is described by the P expansion Xðv; JÞ ¼ i;j X ij ðv þ 1=2Þi ½JðJ þ 1Þj . In addition, we have been able to determine the electric dipole moment of KI to an order of magnitude better precision than Story [17], and have resolved its vibrational dependence.

* Corresponding author. Fax: +1 507 646 3968. E-mail address: [email protected] (J. Cederberg). 1 Present address: Department of Geology and Geophysics, University of Minnesota, Minneapolis, MN, USA. 2 Present address: Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN, USA. 0022-2852/$ - see front matter Ó 2008 Elsevier Inc. All rights reserved. doi:10.1016/j.jms.2008.05.005

For both molecules the largest hyperfine interaction is that due to the electric quadrupole moment of the alkali nucleus, so we use an angular momentum coupling scheme defined by

F1 ¼ J þ IBr;I ;

F ¼ F1 þ IK :

ð1Þ

The fitting of the molecular constants to the observed line frequencies used the singular value decomposition method (SVD), which has the effect of de-correlating the errors. It also shows that there are no undetermined linear combinations of the parameters. 2. Potassium bromide We have measured a total of 210 transitions in KBr, with a precision that ranges between 0.33 and 8.7 Hz, including vibrational states v = 0  4 and rotational states J = 2  9. From these we have fit for the coefficients that describe the dependence of the interactions on v and J, including the two Br isotopes together by using the expected dependence on atomic masses and magnetic moments. In spite of a careful search, no transitions in 41KBr were found. The molecular constants we have found for KBr are listed in Table 1, with their one-sigma uncertainties scaled by the reduced chi value of 1.218. No significant improvement was obtained in the fit by including a term for a magnetic octupole interaction for the bromine nucleus, and no significant shift was found in the value of eQqK00 between the two bromine isotopes. The results shown were consequently obtained by constraining the octupole interaction to zero, and forcing the same value of eQqK00 for both isotopic forms.

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J. Cederberg et al. / Journal of Molecular Spectroscopy 250 (2008) 114–116 Table 1 KBr molecular constants determined from fit (all in kHz) 39 79

i,j

K Br constants

Table 2 KI molecular constants from fit (all except dipole in kHz)

39 81

K Br constants

39 127

i,j

a

K

I constants

41 127

K

I constants

a

Bromine quadrupole (eQqBrij) 0,0 9739.6633 ± 0.0060 1,0 999.4060 ± 0.0093 2,0 8.1211 ± 0.0045 3,0 0.01175 ± 0.00062 0,1 0.25912 ± 0.00044 1,1 0.00228 ± 0.00022

8136.4043 ± 0.0050 831.4785 ± 0.0077 6.7289 ± 0.0037 0.00969 ± 0.00051 0.21470 ± 0.00037 0.00188 ± 0.00018

Iodine quadrupole (eQqIij) 0,0 85471.1377 ± 0.0074 1,0 2860.073 ± 0.011 2,0 22.0895 ± 0.0036 3,0 0.03490 ± 0.00031 0,1 0.66788 ± 0.00013 1,1 0.00640 ± 0.00012

85471.721 ± 0.012 2806.207 ± 0.011 21.2651 ± 0.0035 0.03297 ± 0.00029 0.64295 ± 0.00013 0.00605 ± 0.00011

Potassium quadrupole (eQqKij) 0,0 5032.9569 ± 0.0085 1,0 36.1020 ± 0.0013 2,0 0.1145 ± 0.0057 3,0 0.00045 ± 0.00078 0,1 0.00750 ± 0.00054 1,1 0.00017 ± 0.00022

5032.9569 ± 0.0085 35.954 ± 0.013 0.1136 ± 0.0057 0.00045 ± 0.00077 0.00744 ± 0.00053 0.00017 ± 0.00022

Potassium quadrupole (eQqKij) 0,0 4294.782 ± 0.021 1,0 27.515 ± 0.031 2,0 0.079 ± 0.012 3,0 0.0001 ± 0.0014 0,1 0.00467 ± 0.00091 1,1 0.0008 ± 0.0010

5228.877 ± 0.026 32.869 ± 0.037 0.092 ± 0.014 0.00006 ± 0.00090 0.0055 ± 0.0011 0.0010 ± 0.0012

Bromine spin–rotation (cBrij) 0,0 1.23999 ± 0.00012 1,0 0.00608 ± 0.00012 2,0 0.000004 ± 0.000027 0,1 0.0000005 ± 0.0000019

1.32573 ± 0.00013 0.00647 ± 0.00013 0.000004 ± 0.000028 0.0000005 ± 0.0000020

Potassium spin–rotation (cKij) 0,0 0.10930 ± 0.00022 1,0 0.00059 ± 0.00024 2,0 0.000047 ± 0.000056 0,1 0.0000103 ± 0.0000044

0.10840 ± 0.00022 0.00059 ± 0.00024 0.000046 ± 0.000056 0.0000101 ± 0.0000043

Tensor spin–spin (c3ij) 0,0 0.03749 ± 0.00040 1,0 0.00013 ± 0.00041 2,0 0.000042 ± 0.000096 0,1 0.000006 ± 0.000021 Scalar spin–spin (c4ij) 0,0 0.02189 ± 0.00018 a

Xij denotes the coefficient in the expansion Xðv; JÞ ¼

0.04041 ± 0.00044 0.00014 ± 0.00044 0.00004 ± 0.00010 0.000007 ± 0.000023 0.02359 ± 0.00019 P

i;j X ij ðv

i

j

þ 1=2Þ ½JðJ þ 1Þ .

3. Potassium iodide For 39KI we have 105 transitions with precision 0.5–90 Hz, for v = 0  7 and J = 2  10 that we have used in fitting for the molecular constants shown in Table 2. The reduced chi value for this fit was 1.48, and the uncertainties shown in the table are scaled to take this into account. In addition, we were able to accurately measure 6 transitions for 41KI, which fit nicely to the constants determined for 39KI, transformed by the expected dependence on the reduced mass and nuclear moments, except for two small changes. The value of eQqI00 has to be shifted by 0.587 ± 0.012 kHz beyond the still smaller shift of +.0045 kHz estimated for the mass dependence of that parameter. The ratio of the nuclear electric quadrupole moment of the two potassium isotopes also takes the value Q(41K)/Q(39K) = 1.2174953 ± 0.0000099, compared to the value 1.217699 ± 0.000055 we found for KF [3]. A few other 41KI lines were also observed, confirming this shift, but were in situations where an accurate fit was not feasible. The shift is of the same type that we found earlier for LiI [8], but smaller. The fractional shift in eQqI00 in KI is 6.9  106, compared to 7.239  105 for LiI. In both cases eQqI00 is more negative for the heavier isotope. We are not aware of any explanation for these shifts, but this additional observation may offer a clue. In order to determine the molecular electric dipole moment, we need to know the amplitude of the rf field as well as the dc field. This is a problem because of standing wave effects in the cables leading from the rf amplifier to the plates, as well as in the 2.0 m long plates themselves. There is an rf probe mounted on the plates to tell us what the voltage is at their midpoint, but that is still not sufficient to account for variation of the amplitude over their length. We therefore use the molecules themselves as a probe, by a procedure shown in Fig. 1. The pure hyperfine transitions we observe violate the DJ = ±1 selection rule,

Iodine spin–rotation (cIij) 0,0 0.88954 ± 0.00019 1,0 0.00330 ± 0.00028 2,0 0.000028 ± 0.000058

0.85634 ± 0.00018 0.00311 ± 0.00026 0.000026 ± 0.000053

Potassium spin–rotation (cKij) 0,0 0.10043 ± 0.00049 1,0 0.00136 ± 0.00040 2,0 0.000149 ± 0.000088

0.05306 ± 0.00026 0.00071 ± 0.00021 0.000076 ± 0.000045

Tensor spin–spin (c3ij) 0,0 0.01092 ± 0.00056 1,0 0.00020 ± 0.00036

0.00599 ± 0.00031 0.00011 ± 0.00020

Scalar spin–spin (c4ij) 0,0 0.02409 ± 0.00027 1,0 0.00002 ± 0.00019

0.01322 ± 0.00015 0.00001 ± 0.00011

Iodine hexadecapole (eHhIij) 0,0 0.0102 ± 0.0015

0.0102 ± 0.0015

Electric dipole moment (in debye) (lij) 0,0 11.064 ± 0.014 1,0 0.049 ± 0.023

11.064 ± 0.014 0.048 ± 0.023

a

Xij denotes the coefficient in the expansion Xðv; JÞ ¼

P

i;j X ij ðv

þ 1=2Þi ½JðJ þ 1Þj .

so that both rf and dc fields are necessary to produce them, with the probability of transition determined by the product of the two. The stark splitting, on the other hand, is determined by the sum of the squares of the dc and (rms) rf. We first do a run in which a line, or set of lines, is stark split primarily by a dc field, allowing us to determine an appropriate value for the dc–rf product to be near optimal saturation of the stark components, as shown in the top graph of the figure. Then we would do a run with the same product, but the rf field dominating, as in the lower graph. This allows us to determine the effective average of the square of the rf field over the length of the plates. We can then find an ‘‘RF Factor” as the ratio of the effective field to that produced by the frequency synthesizer. The dc-split run would then be refitted with a correction for the rf contribution to its stark splitting. From this information the dipole moment can be determined. The middle graph in the figure shows how the stark shifts can be minimized by making the dc and rf fields equal in magnitude. The dc and rf values given are the effective voltages across the 1.27 cm gap between the plates. The fit of our data for KI is improved slightly by the inclusion of a parameter with the dependence on angular momentum that corresponds to a nuclear electric hexadecapole interaction. As in the case of our previous investigation of LiI [8], where we found a similar term, we suspect that this is not a true hexadecapole but rather a ‘‘pseudohexadecapole” resulting from the nuclear electric quadrupole perturbing the electron orbitals and these acting back on the same nucleus. Thyssen et al. [19] calculated a value for the true hexadecapole interaction parameter in LiI that is three orders of magnitude smaller than our experimental value for that molecule, whereas a simple estimate of the pseudohexadecapole interaction

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J. Cederberg et al. / Journal of Molecular Spectroscopy 250 (2008) 114–116

5 4

RF = 0.071 V

3

DC = 5.874 V

2 1 0 -1 10 RF = 0.676 V

8

DC = 0.648 V 6 4 2 0 10 RF = 5.876 V 9

DC = 0.070 V

8 7 6 5 17942

17942.2

17942.4

17942.6

17942.8

17943

Frequency (kHz) Fig. 1. Fitted data showing the v = 0, J = 3, F1 = 1/2, F = 2 to F1 = 5/2, F = 3 transition in 39K127I. In the top graph the two stark components are split by the dc field, in the bottom by the rf field. The middle graph shows them merged together by making the dc and rf magnitudes equal.

(as suggested by Pyykkö, [20], and noted in [6]) gives an effect of the same order of magnitude as our observations. The same reasoning should apply in the case of KI. The hexadecapole value listed in the table is based on the same definition we used in [6]. We tried including a nuclear magnetic octupole interaction term in the fit, but found that it did not contribute significantly, or produce a significant change in the fitted value of the hexadecapole term. That term was therefore constrained to be zero in the fit used to generate the parameters in the table. Tables of the observed line frequencies, along with their experimentally estimated uncertainties, predicted frequencies, and residuals, for both KBr and KI, are included in Supplementary material. Appendix A. Supplementary data Supplementary data for this article are available on ScienceDirect (www.sciencedirect.com) and as part of the Ohio State University Molecular Spectroscopy Archives (http://msa.lib.ohiostate.edu/jmsa_hp.htm). Supplementary data associated with this article can be found, in the online version, at doi:10.1016/ j.jms.2008.05.005. References [1] D. Nitz, J. Cederberg, A. Kotz, K. Hetzler, T. Aakre, T. Walhout, J. Mol. Spectrosc. 108 (1984) 6–16.

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